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Re: Abstract mathematical development versus particle physics analysis

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  • brhalluk@hotmail.com
    Hi again, ... **So in terms of foundations and the generation of necessary truths (the business of mathematics) it really doesn t matter whether you call a
    Message 1 of 28 , Dec 31, 2011
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      Hi again,



      --- In Fabric-of-Reality@yahoogroups.com, Kermit Rose <kermit@...> wrote:
      >
      > > 7a. Re: Abstract mathematical development versus particle physics analys
      > > Posted by:"brhalluk@..." brhalluk@... brhallway
      > > Date: Sat Dec 31, 2011 4:46 am ((PST))
      > >
      > > Hi Kermit!
      > :)
      > Hello Brett.
      > >
      > > --- InFabric-of-Reality@yahoogroups.com, Kermit Rose<kermit@> wrote:
      > >> >
      > >> > I see an analogy here:
      > >> >
      > >> > In one development of a given abstract math theory, a given statement might be a theorem. In another development of the same abstract math theory, that same statement might be an axiom.
      > > This is true. But, I don't see the analogy with what you say below. An axiom is not actually true - but rather a statement assumed true in order to allow theorems to be deduced which are only as true as the axioms were to begin with.


      **So in terms of "foundations" and the generation of necessary truths (the business of mathematics) it really doesn't matter whether you call a theorem an axiom or vice versa - in terms of what you end up doing with those lines in a proof. **

      >>What is usually done with a system - logical or mathematical - you start with axioms that are 'self evident'. It's hard to imagine things that are 'logically prior' to Euclid's axioms for example. You have to start somewhere of course. Ultimately though, if your axioms are false, then so will your proofs be and your theorems. There's always a chance that during this process mistakes are made - a reason why mathematics cannot give you certain truth anymore than any other subject can...as explained in FoR.
      >
      > In a pre Calculus class I was asked to prove:
      > For all real numbers, a,b and c.
      > a < b if and only if a+c < b+c.
      >
      > I pondered this for a long time. What could possibly be more elementary than what I was asked to prove.
      >
      > Finally, I realized something that appeared to be more elementary.
      >
      > The sum of two negative numbers is a negative number. I used this to prove what I was asked to prove.
      >
      > Later I wondered why I used that axiom, that the sum of two negative numbers is a negative number,
      >
      > instead of the more "fundamental" rule that the sum of two positive numbers is a positive number".
      >
      > Later still, I realized that the "axiom",
      >
      > For all real numbers, a,b and c.
      > a < b if and only if a+c < b+c.
      >
      > Could be used to prove as theorems, both "The sum of two negative numbers is a negative number" and "The sum of two positive numbers is a positive number".
      >
      > There is no objective way to decide which determinants of a mathematical theory must be the defining axioms.

      Right. Perfect. Exactly. :) A good example of precisely the point I was making in the bit I've emphasised above.

      >
      > >> >
      > >> > What is the foundation of particle physics? We have tried various particle interactions to determine which particles are, in reality, the most fundamental.
      > > And until the LHC shows what electrons and photons and quarks are "made of" then we proceed as if they are fundamental. No explanation is improved by presuming - without evidence - that they are composite.
      >
      > Even if we show that electrons cannot be composed of other particles in the sense that we say that protons are composed of quarks, how do we explain the nature of the electron?
      >
      > We have advanced wave particle duality ideas to explain electron nature.

      This is counter to the MWI where there's no such thing as the mysterious "wave-particle duality" required. Particles are particles. End of story. The way they are distributed across the multiverse is governed by wave equations. But these do not represent the wave-like nature of single particles but rather how many particles are distributed. David Deutsch himself explains this better:

      http://groups.yahoo.com/group/Fabric-of-Reality/message/7552
      This is very succinct:
      http://groups.yahoo.com/group/Fabric-of-Reality/message/8375


      >
      > It would not surprise me if particle physicists eventually find that theory is necessarily circular.
      >
      > Currently we think observations are the foundation of physics.

      Well, I'm not too sure about that. I don't know that BoI or FoR is making the point that observations are the foundations of physics - or anything. Explanations are key. The role of observations is to decide between rival explanations. One needs to know what to look for first...you don't start with raw observations (which aren't possible anyways).

      >We are, in analogy, at the level of ancient Greek thinking. The ancient Greeks thought plane geometry was true in the same sense that we today think that Physics is true.

      This is quite wide of the mark. Aristotelean physics was "at the level of ancient Greek thinking". Since then we have made objective *progress*. Read BoI. Plane geometry is *true*. It's perfectly true within its own domain - It just doesn't work for curved space.

      I'm not too clear what you are trying to get at. You seem to be suggesting a type of weak relativism. Physics is about finding ever better explanations of physical reality: not ultimate truth. This doesn't make current theories less reliable (than Greek ones, say) - it makes them more so. This all makes me wonder: have you read FoR and/or BoI? I apologise for asking if you have! It (BoI in particular) does address this sort of thing in detail though.


      >
      > Today, we think of truth in mathematics as being different than truth in nphysics.
      >
      > We think of truth in mathematics as being limited to the relationships among mathematical ideas.


      Yes - relationships between ideas works. So mathematics is about something called "necessary truth" while science is about "contingent truths". We can talk about that distinction, if you like. Also, I get the sense you might be after certainty in both domains. Certainty isn't possible. BoI talks about that but here's a brief post on another topic from way back in 2002 where I talk about certainty.

      http://groups.yahoo.com/group/Fabric-of-Reality/message/5198

      >
      > I suggest that we have this same limitation in physics.
      >
      > Absolute truth in physics in unknowable to us. The best we can do is develop mathematical truths that mirror the truth of physics.

      You're right about absolute truth (i.e: certainty) in physics. I don't know about that final sentence of yours. I have numerous objections to it:

      1. It's not the best we can do. Surely explaining the world as well as possible is? This often (always?) involves the precision that comes with expressing things mathematically. But not only so.

      2. I'm not sure what mirroring means here.

      3. It's again not clear what the intention of the word "truth" is here. Are you after the unobtainable absolute you just divested yourself of in the prior sentence?

      >
      > >> >
      > >> > Looking at the analogy of building an abstract math theory, I suggest that there is no such thing as the most fundamental particles.
      > > But after all this - you might be right. It's a conjecture that seems to mesh well with BoI. I'd tend to agree with you. It's probably 'infinite in both directions'. No biggest thing - no smallest thing. But until we have evidence of what our fundamental particles are made of - there's no point taking the notion seriously. As that (the particles that make up photons for example) are not a problem yet.
      > >
      >
      > :)
      >
      > Time will tell.

      Well of course (now prepare for me to launch into a few paragraphs on those 3 words! Heh!). We can't act upon information we don't have. How can we make use of the theory that what we believe are fundamental particles are, in fact, not? We can't use that theory because - it's not an explanation (in particular it doesn't explain what the particles are made of). Your "Time will tell." statement is worthy of analysis because it can be appended to any bit of knowledge whatsoever. "The universe is 13.7 billion years old"
      Time will tell.
      Rocks lack consciousness.
      Time will tell.
      Time is finite in the future.
      Time will tell.
      Such a statement amounts to an implicit embrace of a weak relativism, to my mind. It says "Oh you act as though that is correct. But you can never know you are correct."

      Time actually *won't* tell. What *if* electrons *are* fundamental? What is a reasonable amount of *time* one would need to wait to *tell* that we were right? Or can you simply *always* say "Time will tell." at any epoch on any question or claim? If so, is the statement meaningless?

      Sorry if that was badgering! It's not meant to be :)

      :)

      >
      > Kermit
      >
      Brett.
    • Kermit Rose
      ... Ahh.... This suggests another picture to me. I imagine a particle to be spread out over four space dimensions. The density of the particle at each
      Message 2 of 28 , Jan 1, 2012
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        > ________________________________________________________________________
        > 4b. Re: Abstract mathematical development versus particle physics analys
        > Posted by:"brhalluk@..." brhalluk@... brhallway
        > Date: Sun Jan 1, 2012 2:26 am ((PST))
        >
        >
        >
        > --- InFabric-of-Reality@yahoogroups.com, Kermit Rose<kermit@...> wrote:
        >> >
        >>> > > 7a. Re: Abstract mathematical development versus particle physics analys
        >>> > > Posted by:"brhalluk@..." brhalluk@... brhallway
        >>> > > Date: Sat Dec 31, 2011 4:46 am ((PST))
        >>> > >
        >>> > > Hi Kermit!
        >> > :)
        >> > Hello Brett.
        >>> > >
        >>> > > ---InFabric-of-Reality@yahoogroups.com, Kermit Rose<kermit@> wrote:
        >>> >
        >>> > Even if we show that electrons cannot be composed of other particles in the sense that we say that protons are composed of quarks, how do we explain the nature of the electron?
        >>> >
        >>> > We have advanced wave particle duality ideas to explain electron nature.
        > Brett said: This is counter to the MWI where there's no such thing as the mysterious "wave-particle duality" required. Particles are particles. End of story. The way they are distributed across the multiverse is governed by wave equations. But these do not represent the wave-like nature of single particles but rather how many particles are distributed. David Deutsch himself explains this better:
        >
        > http://groups.yahoo.com/group/Fabric-of-Reality/message/7552
        > This is very succinct:
        > http://groups.yahoo.com/group/Fabric-of-Reality/message/8375
        >

        Ahh.... This suggests another picture to me. I imagine a particle to be spread out over four space dimensions. The density of the particle at each point in the four dimensional space is specified by the wave equation. Three of the space dimensions corresponds to our perceived three dimensional space. The fourth space dimension is perpendicular to any one world of the multi-verse. Travel along that direction for any distance takes you to a different world of the multiverse.


        > Brett said:
        > This all makes me wonder: have you read FoR and/or BoI? I apologise
        > for asking if you have! It (BoI in particular) does address this sort
        > of thing in detail though.

        In fact I do not have access to FOR or BOI. My only source to either is what I've been able to gleam from this email group. Everything I've posted has been my own ideas sparked by discussions that I've seen here.


        > Brett says: Yes - relationships between ideas works. So mathematics
        > is about something called "necessary truth" while science is about
        > "contingent truths". We can talk about that distinction, if you like.
        > Also, I get the sense you might be after certainty in both domains.
        > Certainty isn't possible. BoI talks about that but here's a brief post
        > on another topic from way back in 2002 where I talk about certainty.
        > http://groups.yahoo.com/group/Fabric-of-Reality/message/5198

        You have effectively argued me away from my hypothesis that analysis of mathematics and physics needed to be considered equivalent.

        I was not searching for certainty in either domain.

        I like your distinction between "necessary" and "contingent".

        How will you apply these to both math and physics?

        You at first focused on "necessary truths" of mathematics and "contingent truths" of science.

        I presume you were thinking of all the theorems of mathematics being necessary truths because they were contingent on known axioms which were either presumed or stipulated true.

        But in science, we don't know the axioms that imply all scientific knowledge. Therefore, scientific knowledge is different than mathematical knowledge because we don't know the foundation axioms.


        >> > Kermit said:
        >> > :)
        >> >
        >> > Time will tell.
        >>
        > Brett said: Well of course (now prepare for me to launch into a few paragraphs on those 3 words! Heh!). We can't act upon information we don't have. How can we make use of the theory that what we believe are fundamental particles are, in fact, not? We can't use that theory because - it's not an explanation (in particular it doesn't explain what the particles are made of). Your "Time will tell." statement is worthy of analysis because it can be appended to any bit of knowledge whatsoever. "The universe is 13.7 billion years old"
        > Time will tell.
        > Rocks lack consciousness.
        > Time will tell.
        > Time is finite in the future.
        > Time will tell.
        > Such a statement amounts to an implicit embrace of a weak relativism, to my mind. It says "Oh you act as though that is correct. But you can never know you are correct."
        >
        > Time actually*won't* tell. What*if* electrons*are* fundamental? What is a reasonable amount of*time* one would need to wait to*tell* that we were right? Or can you simply*always* say "Time will tell." at any epoch on any question or claim? If so, is the statement meaningless?
        >
        > Sorry if that was badgering! It's not meant to be:)
        >
        > :)

        :) I did not perceive badgering. I perceived that you gave a thoughtful response.

        Probably I do embrace a weak relativism. More explanation of what is meant by "weak relativism" may either confirm or disconfirm.
      • brhalluk@hotmail.com
        It depends on what you mean by truth. You seem to be suggesting here that for something to be true it needs to exist in the physical world. I don t agree. Of
        Message 3 of 28 , Jan 2, 2012
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          It depends on what you mean by truth. You seem to be suggesting here that for something to be true it needs to exist in the physical world. I don't agree. Of course abstract objects by their very definition have some other existence: but we can still speak about the truth and falsity of them or conclusions drawn using them.

          I mean to say (using a tired old example) Peano's axioms for arithmetic (or whatever axioms one wants to use to generate arithmetic) allow us to say things like:
          1+1=2
          It seems to me you would want to be able to say "that's true" while something like 1+1=3 is false. It's not a mere matter of it being "consistent with the axioms" and it is also true *independent* of the fact it can be conveniently used for objects in the physical world.

          But is that "true" or, using your words, is it the case that "The (Peano Axioms) have *nothing whatsoever* to do with *truth*. They just serve to *define* the system we wish to study."

          Meaning that all such conclusions are neither true or false either and so it becomes meaningless to say that "1+1=2" ?

          I ask a couple more questions below...



          --- In Fabric-of-Reality@yahoogroups.com, "gich7" <gich7@...> wrote:
          >
          >
          > ----- Original Message -----
          > From: <brhalluk@...>
          > To: <Fabric-of-Reality@yahoogroups.com>
          > Sent: Sunday, January 01, 2012 12:41 AM
          > Subject: Re: Abstract mathematical development versus particle physics analysis
          >
          > Hi again,
          >
          > --- In Fabric-of-Reality@yahoogroups.com, Kermit Rose <kermit@> wrote:
          > >
          > > > 7a. Re: Abstract mathematical development versus particle physics analys
          > > > Posted by:"brhalluk@" brhalluk@ brhallway
          > > > Date: Sat Dec 31, 2011 4:46 am ((PST))
          > > >
          > > > Hi Kermit!
          > > :)
          > > Hello Brett.
          > > >
          > > > --- InFabric-of-Reality@yahoogroups.com, Kermit Rose<kermit@> wrote:
          > > >> >
          > > >> > I see an analogy here:
          > > >> >
          > > >> > In one development of a given abstract math theory, a given statement
          > > >> > might be a theorem. In another development of the same abstract math
          > > >> > theory, that same statement might be an axiom.
          > > > This is true. But, I don't see the analogy with what you say below. An axiom
          > > > is not actually true - but rather a statement assumed true in order to allow
          > > > theorems to be deduced which are only as true as the axioms were to begin
          > > > with.
          >
          > I haven't been following this discussion, but as a mathematician let me comment
          > as follows:
          >
          > In Pure Mathematics, when studying a *particular* mathematical system:
          >
          > (1) An AXIOM is something that we state as a *given*, . . . something that
          > *defines* the mathematical system we are studying.
          >
          > For example, The vast subject of Group Theory begins from just four axioms:
          > (i) CLOSURE of the group operation,
          > (ii) ASSOCIATIVITY of the group operation,
          > (iii) the *existence* of an IDENTITY element for *all* elements of the group,
          > (iv) the *existence* of an INVERSE element for *all* elements of the group.
          >
          > The Group Axioms have *nothing whatsoever* to do with *truth*. They just serve
          > to *define* the system we wish to study.

          Do you believe that this applies only to the axioms for Group Theory or does it apply to all mathematical systems of whatever complexity? Down to Peano's Axioms as I suggest above?

          >
          > (2) A THEOREM is something that can be *proved* to be a consequence of (OR to
          > follow from) the axioms.
          >
          > (a) Theorem 1 is something we can *prove* to be a consequence of (OR to follow
          > from) the axioms alone.
          > (b) Theorem 2 is something we can *prove* to be a consequence of (OR to follow
          > from) the axioms together with, if required, Theorem 1.
          > (c) Theorem 3 is something we can *prove* to be a consequence of (OR to follow
          > from) the axioms together with, if required, Theorems 1 and 2.
          > (d) . . .
          > (e) . . .
          >
          > And so it goes on and the mathematical system develops.

          Are there other axioms one could choose to generate Group Theory? If so, can any of *your* chosen axioms be generated as a theory by a different choice of axioms?

          >
          > But note carefully, pure mathematics does *not* have to have anything to do with
          > 'the real world'. Pure mathematical systems can exist for their own sake, they
          > *do not* have to have any connection with science. Much the same is true of
          > abstract art and fictional literature. Indeed, some would argue that pure
          > mathematics is much more an art than a science. The entities of a mathematical
          > system: domain of operations, definitions, axioms, theorems, proofs, etc. are
          > *all* products of the mathematician's intellect and are studied 'for their own
          > sake'. If it should turn out that they do have useful applications in 'the real
          > world', then fine, but many, systems of mathematics have been invented and
          > studied to great depth by pure mathematicians for millennia and none have what
          > we might call real-world applications.


          Yes that's fine. There's a long history of pure mathematicians suggesting this (I think in particular of G.H Hardy's "A Mathematician's Apology" where this great pure mathematician spoke the same way you do. Of course many of Hardy's ideas are being used in the "real world" now when he believed they were basically creations like abstract art is. So were those things he discovered (created?) true before they were applied to the real world or only once they were? I think the theorems of pure mathematics are true. Necessarily so. I think consistency is about truth, isn't it? I compare discovered and created there because if you "discover" something then you find it to be true or false, don't you? You're not *merely* creating fiction, are you?

          BTW, Hardy's book is long out of copyright and you can get it here: http://www.math.ualberta.ca/~mss/misc/A%20Mathematician's%20Apology.pdf

          >
          > For example, the web site on Number theory [ http://www.numbertheory.org/ ],
          > contains much information about just one of the enormous number of 'areas of
          > pure mathematics' that are (presently) studied 'for their own sake'. The home
          > page has over four hundred links, each of which is, often, a vast area in it's
          > own right.
          >
          > Mathematicians investigate the problems that interest them, *just because* the
          > problems interest them! If the investigations turn out to be useful in the real
          > world then fine, but this is *not* the objective of the activity.

          Granted. Some questions remain: Do you include the theorems of pure mathematics as part of the "real" world? How many "worlds" are there? Are 'fictional worlds' like 'abstract worlds' or something different?

          Happy New Year!

          Brett.



          >
          > [ snip ]
          >
          > Happy New Year!
          > Gich
          >
        • brhalluk@hotmail.com
          ... I don t think that s science. I think this is your own conjecture. You say you haven t read FoR or BoI as you don t have access. Okay. Well here is The
          Message 4 of 28 , Jan 2, 2012
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            --- In Fabric-of-Reality@yahoogroups.com, Kermit Rose <kermit@...> wrote:
            >
            > > ________________________________________________________________________
            > > 4b. Re: Abstract mathematical development versus particle physics analys
            > > Posted by:"brhalluk@..." brhalluk@... brhallway
            > > Date: Sun Jan 1, 2012 2:26 am ((PST))
            > >
            > >
            > >
            > > --- InFabric-of-Reality@yahoogroups.com, Kermit Rose<kermit@> wrote:
            > >> >
            > >>> > > 7a. Re: Abstract mathematical development versus particle physics analys
            > >>> > > Posted by:"brhalluk@" brhalluk@ brhallway
            > >>> > > Date: Sat Dec 31, 2011 4:46 am ((PST))
            > >>> > >
            > >>> > > Hi Kermit!
            > >> > :)
            > >> > Hello Brett.
            > >>> > >
            > >>> > > ---InFabric-of-Reality@yahoogroups.com, Kermit Rose<kermit@> wrote:
            > >>> >
            > >>> > Even if we show that electrons cannot be composed of other particles in the sense that we say that protons are composed of quarks, how do we explain the nature of the electron?
            > >>> >
            > >>> > We have advanced wave particle duality ideas to explain electron nature.
            > > Brett said: This is counter to the MWI where there's no such thing as the mysterious "wave-particle duality" required. Particles are particles. End of story. The way they are distributed across the multiverse is governed by wave equations. But these do not represent the wave-like nature of single particles but rather how many particles are distributed. David Deutsch himself explains this better:
            > >
            > > http://groups.yahoo.com/group/Fabric-of-Reality/message/7552
            > > This is very succinct:
            > > http://groups.yahoo.com/group/Fabric-of-Reality/message/8375
            > >
            >
            > Ahh.... This suggests another picture to me. I imagine a particle to be spread out over four space dimensions. The density of the particle at each point in the four dimensional space is specified by the wave equation. Three of the space dimensions corresponds to our perceived three dimensional space. The fourth space dimension is perpendicular to any one world of the multi-verse. Travel along that direction for any distance takes you to a different world of the multiverse.

            I don't think that's science. I think this is your own conjecture. You say you haven't read FoR or BoI as you don't have access. Okay. Well here is "The Structure of the Multiverse" by David Deutsch from back in 2002, published in Proceedings of the Royal Society - you can get it here
            http://rspa.royalsocietypublishing.org/content/458/2028/2911.full.pdf or here:

            http://arxiv.org/pdf/quant-ph/0104033

            It's hard going - which is why FoR is your better option to get into how the Multiverse is structured. Postulated "spread out" particles and other spatial dimensions are misconceptions that would be rectified by reading these things. David Deutsch takes quite a few pages of text to explain the structure of the multiverse. I can't really do it justice in a few paragraphs here. :)


            >
            >
            > > Brett said:
            > > This all makes me wonder: have you read FoR and/or BoI? I apologise
            > > for asking if you have! It (BoI in particular) does address this sort
            > > of thing in detail though.
            >
            > In fact I do not have access to FOR or BOI. My only source to either is what I've been able to gleam from this email group. Everything I've posted has been my own ideas sparked by discussions that I've seen here.

            You've shown a lot of interest and insight. If you send me your details, I will send you a copy of both books. My email address is brhalluk@...

            >
            >
            > > Brett says: Yes - relationships between ideas works. So mathematics
            > > is about something called "necessary truth" while science is about
            > > "contingent truths". We can talk about that distinction, if you like.
            > > Also, I get the sense you might be after certainty in both domains.
            > > Certainty isn't possible. BoI talks about that but here's a brief post
            > > on another topic from way back in 2002 where I talk about certainty.
            > > http://groups.yahoo.com/group/Fabric-of-Reality/message/5198
            >
            > You have effectively argued me away from my hypothesis that analysis of mathematics and physics needed to be considered equivalent.
            >
            > I was not searching for certainty in either domain.
            >
            > I like your distinction between "necessary" and "contingent".
            >
            > How will you apply these to both math and physics?
            >
            > You at first focused on "necessary truths" of mathematics and "contingent truths" of science.
            >
            > I presume you were thinking of all the theorems of mathematics being necessary truths because they were contingent on known axioms which were either presumed or stipulated true.
            >
            > But in science, we don't know the axioms that imply all scientific knowledge. Therefore, scientific knowledge is different than mathematical knowledge because we don't know the foundation axioms.


            There are many ways of "getting into" the necessary versus contingent truth distinction. Leibnitz wrote a large amount about this. If you Google his name and those key terms you will find a wealth of stuff. A quick definition:

            Necessary Truth is that which is true by definition (roughly speaking) - analytical truths. "All bachelors are men" "Triangles have three sides" and "1+1=2" and everything in mathematics. David Lewis wrote a book called "On the plurality of worlds" and made the point that necessary truths are true in *all possible worlds*. It's *not possible* for a necessary truth to be false as that would imply a strict contradiction.

            Contingent truths are things that *could have been* otherwise. "Earth is the third planet from the Sun", "World War 2 ended in 1945" and every truth in science.

            Here's the key where maths is concerned though - and I think is a brilliant distillation of how to think about truth in mathematics and its relationship to physics: "Necessary truth is merely the subject matter of mathematics, not the reward we get for doing mathematics. The objective of mathematics is not, and cannot be, mathematical certainty. It is not even mathematical truth, certain or otherwise. It is, and must be, mathematical explanation."
            -David Deutsch, FoR, p 253.

            Now this arises due to the amazing consequence of mathematics as a system of proving things being a computational process. And computational processes like proofs are physical processes and our understanding of physical processes is due to...physics! So our confidence in our proofs of mathematics can only ever scale with our confidence in our understanding of the laws of physics. I find that amazing.

            >
            >
            > >> > Kermit said:
            > >> > :)
            > >> >
            > >> > Time will tell.
            > >>
            > > Brett said: Well of course (now prepare for me to launch into a few paragraphs on those 3 words! Heh!). We can't act upon information we don't have. How can we make use of the theory that what we believe are fundamental particles are, in fact, not? We can't use that theory because - it's not an explanation (in particular it doesn't explain what the particles are made of). Your "Time will tell." statement is worthy of analysis because it can be appended to any bit of knowledge whatsoever. "The universe is 13.7 billion years old"
            > > Time will tell.
            > > Rocks lack consciousness.
            > > Time will tell.
            > > Time is finite in the future.
            > > Time will tell.
            > > Such a statement amounts to an implicit embrace of a weak relativism, to my mind. It says "Oh you act as though that is correct. But you can never know you are correct."
            > >
            > > Time actually*won't* tell. What*if* electrons*are* fundamental? What is a reasonable amount of*time* one would need to wait to*tell* that we were right? Or can you simply*always* say "Time will tell." at any epoch on any question or claim? If so, is the statement meaningless?
            > >
            > > Sorry if that was badgering! It's not meant to be:)
            > >
            > > :)
            >
            > :) I did not perceive badgering. I perceived that you gave a thoughtful response.
            >
            > Probably I do embrace a weak relativism. More explanation of what is meant by "weak relativism" may either confirm or disconfirm.

            I *really* want to send you BoI and FoR to divest you of this. I'm wrong to have suggested that there is a weak version of relativism. There's just relativism. And it's false.

            Brett.

            >
          • Bruno Marchal
            ... It depends on your hypotheses, notably in the cognitive science. If you assume computationalism, which is the doctrine according to which the brain
            Message 5 of 28 , Jan 3, 2012
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              On 01 Jan 2012, at 15:34, gich7 wrote:

              >
              > ----- Original Message -----
              > From: <brhalluk@...>
              > To: <Fabric-of-Reality@yahoogroups.com>
              > Sent: Sunday, January 01, 2012 12:41 AM
              > Subject: Re: Abstract mathematical development versus particle
              > physics analysis
              >
              > Hi again,
              >
              > --- In Fabric-of-Reality@yahoogroups.com, Kermit Rose <kermit@...>
              > wrote:
              > >
              > > > 7a. Re: Abstract mathematical development versus particle
              > physics analys
              > > > Posted by:"brhalluk@..." brhalluk@... brhallway
              > > > Date: Sat Dec 31, 2011 4:46 am ((PST))
              > > >
              > > > Hi Kermit!
              > > :)
              > > Hello Brett.
              > > >
              > > > --- InFabric-of-Reality@yahoogroups.com, Kermit Rose<kermit@>
              > wrote:
              > > >> >
              > > >> > I see an analogy here:
              > > >> >
              > > >> > In one development of a given abstract math theory, a given
              > statement
              > > >> > might be a theorem. In another development of the same
              > abstract math
              > > >> > theory, that same statement might be an axiom.
              > > > This is true. But, I don't see the analogy with what you say
              > below. An axiom
              > > > is not actually true - but rather a statement assumed true in
              > order to allow
              > > > theorems to be deduced which are only as true as the axioms were
              > to begin
              > > > with.
              >
              > I haven't been following this discussion, but as a mathematician let
              > me comment
              > as follows:
              >
              > In Pure Mathematics, when studying a *particular* mathematical system:
              >
              > (1) An AXIOM is something that we state as a *given*, . . .
              > something that
              > *defines* the mathematical system we are studying.
              >
              > For example, The vast subject of Group Theory begins from just four
              > axioms:
              > (i) CLOSURE of the group operation,
              > (ii) ASSOCIATIVITY of the group operation,
              > (iii) the *existence* of an IDENTITY element for *all* elements of
              > the group,
              > (iv) the *existence* of an INVERSE element for *all* elements of the
              > group.
              >
              > The Group Axioms have *nothing whatsoever* to do with *truth*. They
              > just serve
              > to *define* the system we wish to study.
              >
              > (2) A THEOREM is something that can be *proved* to be a consequence
              > of (OR to
              > follow from) the axioms.
              >
              > (a) Theorem 1 is something we can *prove* to be a consequence of (OR
              > to follow
              > from) the axioms alone.
              > (b) Theorem 2 is something we can *prove* to be a consequence of (OR
              > to follow
              > from) the axioms together with, if required, Theorem 1.
              > (c) Theorem 3 is something we can *prove* to be a consequence of (OR
              > to follow
              > from) the axioms together with, if required, Theorems 1 and 2.
              > (d) . . .
              > (e) . . .
              >
              > And so it goes on and the mathematical system develops.
              >
              > But note carefully, pure mathematics does *not* have to have
              > anything to do with
              > 'the real world'.
              >
              It depends on your hypotheses, notably in the cognitive science. If
              you assume computationalism, which is the doctrine according to which
              the brain functions like a digital computer, then the appearance of a
              "real world" has to be explained entirely by "pure arithmetic".
              Physicalness arises from number's dream, which are explained by
              computations + self-reference. In fact, if we are digitalisable
              machine, physics is independent of the initial ontology, provided it
              is rich enough to define the notion of Turing universality (so instead
              of numbers+addition+multiplication, you can take any first order
              logical specification of a any programming language). If we are
              machine, we are already in infinities of "universal matrices" whose
              existences are theorems of elementary number theory. This makes also
              computationalism testable: just compare the physics inferred from
              observation and the intrinsic physics of universal numbers/machines.

              Bruno





              > Pure mathematical systems can exist for their own sake, they
              > *do not* have to have any connection with science. Much the same is
              > true of
              > abstract art and fictional literature. Indeed, some would argue that
              > pure
              > mathematics is much more an art than a science. The entities of a
              > mathematical
              > system: domain of operations, definitions, axioms, theorems, proofs,
              > etc. are
              > *all* products of the mathematician's intellect and are studied 'for
              > their own
              > sake'. If it should turn out that they do have useful applications
              > in 'the real
              > world', then fine, but many, systems of mathematics have been
              > invented and
              > studied to great depth by pure mathematicians for millennia and none
              > have what
              > we might call real-world applications.
              >
              > For example, the web site on Number theory [ http://www.numbertheory.org/
              > ],
              > contains much information about just one of the enormous number of
              > 'areas of
              > pure mathematics' that are (presently) studied 'for their own sake'.
              > The home
              > page has over four hundred links, each of which is, often, a vast
              > area in it's
              > own right.
              >
              > Mathematicians investigate the problems that interest them, *just
              > because* the
              > problems interest them! If the investigations turn out to be useful
              > in the real
              > world then fine, but this is *not* the objective of the activity.
              >
              > [ snip ]
              >
              > Happy New Year!
              > Gich
              >
              >

              http://iridia.ulb.ac.be/~marchal/





              [Non-text portions of this message have been removed]
            • hibbsa
              ... analys ... physics analys ... particles in the sense that we say that protons are composed of quarks, how do we explain the nature of the electron? ...
              Message 6 of 28 , Jan 3, 2012
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                --- In Fabric-of-Reality@yahoogroups.com, brhalluk@... wrote:
                >
                >
                >
                > --- In Fabric-of-Reality@yahoogroups.com, Kermit Rose kermit@ wrote:
                > >
                > > >
                ________________________________________________________________________
                > > > 4b. Re: Abstract mathematical development versus particle physics
                analys
                > > > Posted by:"brhalluk@" brhalluk@ brhallway
                > > > Date: Sun Jan 1, 2012 2:26 am ((PST))
                > > >
                > > >
                > > >
                > > > --- InFabric-of-Reality@yahoogroups.com, Kermit Rose<kermit@>
                wrote:
                > > >> >
                > > >>> > > 7a. Re: Abstract mathematical development versus particle
                physics analys
                > > >>> > > Posted by:"brhalluk@" brhalluk@ brhallway
                > > >>> > > Date: Sat Dec 31, 2011 4:46 am ((PST))
                > > >>> > >
                > > >>> > > Hi Kermit!
                > > >> > :)
                > > >> > Hello Brett.
                > > >>> > >
                > > >>> > > ---InFabric-of-Reality@yahoogroups.com, Kermit Rose<kermit@>
                wrote:
                > > >>> >
                > > >>> > Even if we show that electrons cannot be composed of other
                particles in the sense that we say that protons are composed of quarks,
                how do we explain the nature of the electron?
                > > >>> >
                > > >>> > We have advanced wave particle duality ideas to explain
                electron nature.
                > > > Brett said: This is counter to the MWI where there's no such thing
                as the mysterious "wave-particle duality" required. Particles are
                particles. End of story. The way they are distributed across the
                multiverse is governed by wave equations. But these do not represent the
                wave-like nature of single particles but rather how many particles are
                distributed. David Deutsch himself explains this better:
                > > >
                > > > http://groups.yahoo.com/group/Fabric-of-Reality/message/7552
                > > > This is very succinct:
                > > > http://groups.yahoo.com/group/Fabric-of-Reality/message/8375
                > > >
                > >
                > > Ahh.... This suggests another picture to me. I imagine a particle to
                be spread out over four space dimensions. The density of the particle at
                each point in the four dimensional space is specified by the wave
                equation. Three of the space dimensions corresponds to our perceived
                three dimensional space. The fourth space dimension is perpendicular to
                any one world of the multi-verse. Travel along that direction for any
                distance takes you to a different world of the multiverse.
                >
                > I don't think that's science. I think this is your own conjecture. You
                say you haven't read FoR or BoI as you don't have access. Okay. Well
                here is "The Structure of the Multiverse" by David Deutsch from back in
                2002, published in Proceedings of the Royal Society - you can get it
                here
                > http://rspa.royalsocietypublishing.org/content/458/2028/2911.full.pdf
                or here:
                >
                > http://arxiv.org/pdf/quant-ph/0104033
                <http://arxiv.org/pdf/quant-ph/0104033>



                After I went to that paper, I suddenly wondered how many times
                multiverse papers get cited...as an indication of the status of MWI in
                the science community. I noticed that ordered by citation Deutsch's
                multiverse papers were at the low end. Does this reflect the current
                non-acceptance of MWI...is it generally the case that multiverse QM
                papers don't tend to get referenced very much?

                Or...is it just that MWI insights/logic are not yet very productive in
                terms of research. What I mean is...do they create new or any questions
                that scientists have any ability to answer?






                [Non-text portions of this message have been removed]
              • Bruno Marchal
                ... It shows that, contrary to what you said, pure mathematics might have everything to do with the real world . Indeed, if we postulate computationalism, the
                Message 7 of 28 , Jan 4, 2012
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                  On 03 Jan 2012, at 20:15, gich7 wrote:

                  >
                  > ----- Original Message -----
                  > From: "Bruno Marchal" <marchal@...>
                  > To: <Fabric-of-Reality@yahoogroups.com>
                  > Sent: Tuesday, January 03, 2012 10:21 AM
                  > Subject: Re: Abstract mathematical development versus particle
                  > physics analysis
                  >
                  > On 01 Jan 2012, at 15:34, gich7 wrote:
                  >
                  > >
                  > > ----- Original Message -----
                  > > From: <brhalluk@...>
                  > > To: <Fabric-of-Reality@yahoogroups.com>
                  > > Sent: Sunday, January 01, 2012 12:41 AM
                  > > Subject: Re: Abstract mathematical development versus particle
                  > > physics analysis
                  > >
                  > > Hi again,
                  > >
                  > > --- In Fabric-of-Reality@yahoogroups.com, Kermit Rose <kermit@...>
                  > > wrote:
                  > > >
                  > > > > 7a. Re: Abstract mathematical development versus particle
                  > > physics analys
                  > > > > Posted by:"brhalluk@..." brhalluk@... brhallway
                  > > > > Date: Sat Dec 31, 2011 4:46 am ((PST))
                  > > > >
                  > > > > Hi Kermit!
                  > > > :)
                  > > > Hello Brett.
                  > > > >
                  > > > > --- InFabric-of-Reality@yahoogroups.com, Kermit Rose<kermit@>
                  > > wrote:
                  > > > >> >
                  > > > >> > I see an analogy here:
                  > > > >> >
                  > > > >> > In one development of a given abstract math theory, a given
                  > > statement
                  > > > >> > might be a theorem. In another development of the same
                  > > abstract math
                  > > > >> > theory, that same statement might be an axiom.
                  > > > > This is true. But, I don't see the analogy with what you say
                  > > below. An axiom
                  > > > > is not actually true - but rather a statement assumed true in
                  > > order to allow
                  > > > > theorems to be deduced which are only as true as the axioms were
                  > > to begin
                  > > > > with.
                  > >
                  > > I haven't been following this discussion, but as a mathematician let
                  > > me comment
                  > > as follows:
                  > >
                  > > In Pure Mathematics, when studying a *particular* mathematical
                  > system:
                  > >
                  > > (1) An AXIOM is something that we state as a *given*, . . .
                  > > something that
                  > > *defines* the mathematical system we are studying.
                  > >
                  > > For example, The vast subject of Group Theory begins from just four
                  > > axioms:
                  > > (i) CLOSURE of the group operation,
                  > > (ii) ASSOCIATIVITY of the group operation,
                  > > (iii) the *existence* of an IDENTITY element for *all* elements of
                  > > the group,
                  > > (iv) the *existence* of an INVERSE element for *all* elements of the
                  > > group.
                  > >
                  > > The Group Axioms have *nothing whatsoever* to do with *truth*. They
                  > > just serve
                  > > to *define* the system we wish to study.
                  > >
                  > > (2) A THEOREM is something that can be *proved* to be a consequence
                  > > of (OR to
                  > > follow from) the axioms.
                  > >
                  > > (a) Theorem 1 is something we can *prove* to be a consequence of (OR
                  > > to follow
                  > > from) the axioms alone.
                  > > (b) Theorem 2 is something we can *prove* to be a consequence of (OR
                  > > to follow
                  > > from) the axioms together with, if required, Theorem 1.
                  > > (c) Theorem 3 is something we can *prove* to be a consequence of (OR
                  > > to follow
                  > > from) the axioms together with, if required, Theorems 1 and 2.
                  > > (d) . . .
                  > > (e) . . .
                  > >
                  > > And so it goes on and the mathematical system develops.
                  > >
                  > > But note carefully, pure mathematics does *not* have to have
                  > > anything to do with
                  > > 'the real world'.
                  > >
                  > It depends on your hypotheses, notably in the cognitive science. If
                  > you assume computationalism, which is the doctrine according to which
                  > the brain functions like a digital computer, then the appearance of a
                  > "real world" has to be explained entirely by "pure arithmetic".
                  >
                  > But this has *nothing whatsoever* to do with *pure mathematics*
                  > which was the
                  > subject of my posting.
                  >
                  >

                  It shows that, contrary to what you said, pure mathematics might have
                  everything to do with the 'real world'. Indeed, if we postulate
                  computationalism, the 'real world" happens to be an aspect of *pure
                  mathematics*. Consciousness becomes a fixed point of a purely
                  mathematical transformation, and physics becomes the border of
                  mathematics as seen from inside. The idea that there is something real
                  apart from mathematics is an assumption (more or less taken for
                  granted since Aristotle, the Platonists were divided on this).
                  My point is that "reality" might be purely mathematical (even purely
                  arithmetical). I call that position "mathematicalism" to oppose it to
                  physicalism". Comp is better seen as "theologicalism", because it
                  concerns consciousness and survival which still needs to be invoke at
                  some meta-level to make comp comprehensible at the epistemological
                  level. The ontology becomes pure number theory though.

                  Bruno



                  http://iridia.ulb.ac.be/~marchal/






                  [Non-text portions of this message have been removed]
                • Bruno Marchal
                  ... You are right. It does not have to have anything to do with the real world. For example, the mechanist hypothesis in cognitive science might be true. But
                  Message 8 of 28 , Jan 5, 2012
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                    On 05 Jan 2012, at 10:31, gich7 wrote:

                    > ----- Original Message -----
                    > From: "Bruno Marchal" <marchal@...>
                    > To: <Fabric-of-Reality@yahoogroups.com>
                    > Sent: Wednesday, January 04, 2012 10:11 AM
                    > Subject: Re: Abstract mathematical development versus particle
                    > physics analysis
                    >
                    > >
                    > > On 03 Jan 2012, at 20:15, gich7 wrote:
                    > >
                    >
                    > [ snip ]
                    >
                    > >> > I haven't been following this discussion, but as a
                    > mathematician let
                    > >> > me comment
                    > >> > as follows:
                    > >> >
                    > >> > In Pure Mathematics, when studying a *particular* mathematical
                    > >> system:
                    > >> >
                    > >> > (1) An AXIOM is something that we state as a *given*, . . .
                    > >> > something that
                    > >> > *defines* the mathematical system we are studying.
                    > >> >
                    > >> > For example, The vast subject of Group Theory begins from just
                    > four
                    > >> > axioms:
                    > >> > (i) CLOSURE of the group operation,
                    > >> > (ii) ASSOCIATIVITY of the group operation,
                    > >> > (iii) the *existence* of an IDENTITY element for the group,
                    >
                    > Note: error corrected.
                    >
                    > >> > (iv) the *existence* of an INVERSE element for *all* elements
                    > of the
                    > >> > group.
                    > >> >
                    > >> > The Group Axioms have *nothing whatsoever* to do with *truth*.
                    > They
                    > >> > just serve
                    > >> > to *define* the system we wish to study.
                    > >> >
                    > >> > (2) A THEOREM is something that can be *proved* to be a
                    > consequence
                    > >> > of (OR to
                    > >> > follow from) the axioms.
                    > >> >
                    > >> > (a) Theorem 1 is something we can *prove* to be a consequence
                    > of (OR
                    > >> > to follow
                    > >> > from) the axioms alone.
                    > >> > (b) Theorem 2 is something we can *prove* to be a consequence
                    > of (OR
                    > >> > to follow
                    > >> > from) the axioms together with, if required, Theorem 1.
                    > >> > (c) Theorem 3 is something we can *prove* to be a consequence
                    > of (OR
                    > >> > to follow
                    > >> > from) the axioms together with, if required, Theorems 1 and 2.
                    > >> > (d) . . .
                    > >> > (e) . . .
                    > >> >
                    > >> > And so it goes on and the mathematical system develops.
                    > >> >
                    > >> > But note carefully, pure mathematics does *not* have to have
                    > >> > anything to do with
                    > >> > 'the real world'.
                    > >> >
                    > >> It depends on your hypotheses, notably in the cognitive science. If
                    > >> you assume computationalism, which is the doctrine according to
                    > which
                    > >> the brain functions like a digital computer, then the appearance
                    > of a
                    > >> "real world" has to be explained entirely by "pure arithmetic".
                    > >>
                    > >> But this has *nothing whatsoever* to do with *pure mathematics*
                    > >> which was the
                    > >> subject of my posting.
                    > >>
                    > >>
                    > >
                    > > It shows that, contrary to what you said, pure mathematics might
                    > have
                    > > everything to do with the 'real world'.
                    >
                    > You seem to be misquoting (or misunderstanding) me. I wrote,
                    >
                    > ". . . pure mathematics does *not* have to have anything to do with
                    > 'the real
                    > world'.
                    >
                    You are right. It does not have to have anything to do with the real
                    world. For example, the mechanist hypothesis in cognitive science
                    might be true.
                    But my point is that IF the mechanist hypothesis in the cognitive
                    science is correct, then pure mathematics has to have something to do
                    with reality. Indeed, in that case 100% of physics, and 99,9% of
                    theology becomes branch of pure mathematics. Even the feeding amoeba
                    is doing pure mathematics, without knowing that of course, like Mister
                    Jourdain is doing prose.




                    >
                    > In other words, investigations in pure mathematics do not *have* to
                    > have
                    > anything to do with 'the real world'.
                    >
                    You are right. I agree with you on that point. But IF mechanism is
                    true, it has to have everything to do with the real world. Even the
                    most abstract non computationalist theory mathematical theory has to
                    do with arithmetic, in that case, under the form of the following
                    question "why should a number ever imagine such a theory"?



                    >
                    > As an example, consider a particular (easily stated) 'unsolved
                    > problem' of
                    > number theory: the GOLDBACH CONJECTURE. In its modern form, it
                    > states that every
                    > even number larger than two can be expressed as a sum of two prime
                    > numbers.
                    > Examples: 6 = 3 + 3, 8 = 3 + 5, 10 = 3 + 7, etc. The conjecture was
                    > first stated
                    > in 1742 and mathematicians have been trying to *prove* its truth
                    > ever since, so
                    > far, without success. And the mathematicians trying to discover a
                    > proof have *no
                    > interest whatsoever* in whether their work may or may not have 'real
                    > world'
                    > applications.
                    >
                    Some are even proud that their theories have no applications. Some
                    even destroy or discourage the applications of some theory. When I
                    studied mathematics, at the university, after two years we were asked
                    to choose between the pure and applied option of the curriculum. I was
                    naive and told them that I was interested in pure mathematics for
                    their application to computer science and biology. I think that I am
                    still paying the price for what they took as a blasphem of some sort!




                    > Mathematicians investigate the problems that interest them, *just
                    > because* the problems interest them!
                    >
                    Yes. Like a rocket scientist who does not want his rocket to be
                    lunched. Analytical philosopher have the same problem. They love so
                    much their theories that they forget to apply it to real problem in
                    philosophy.




                    > If the investigations turn out to be useful
                    > in the real world then fine, but this is *not* the objective of the
                    > activity.
                    >
                    Sure.



                    >
                    > > Indeed, if we postulate
                    > > computationalism, the 'real world" happens to be an aspect of *pure
                    > > mathematics*.
                    >
                    > [ snip ]
                    >
                    > But this "postulating of computationalism" has *nothing whatsoever*
                    > to do with
                    > *pure mathematics* which was the subject of my original posting.
                    >
                    But it has something to do with your statement that pure mathematics
                    does not have to have applications. With mechanism, there is a sense
                    to say that the biological and physical phenomena are only tools for
                    doing pure mathematics, that is surviving and studying the reality
                    which appears to be almost completely mathematical. Note that
                    mechanism explains easily in this way the unreasonable effectiveness
                    of mathematics. Indeed reality is *purely* mathematical. Of course
                    manypure mathematicians dislike such an idea.




                    > There are no
                    > *postulations* of the sort you have in mind in pure mathematics.
                    >
                    Correct.




                    > You are
                    > studying (or inventing) a new system but this system is *not* pure
                    > mathematics,
                    > nor does it have anything to do with pure mathematics.
                    >
                    Not correct. The postulation makes disappear the frontier between
                    applied and pure mathematics.
                    And once you postulate, perhaps at some meta-level, the mechanist
                    hypothesis, then the theory of everything, at least one of them among
                    an infinity of equivalent presentation, is just number theory. Physics
                    is reduced to the study of emergent interfering numbers' dreams. To be
                    short.




                    > When a mathematician
                    > investigates some system in pure mathematics, possible applications
                    > in the 'real
                    > world' are of no concern to him.
                    >
                    Sure.



                    >
                    > Pure mathematics consists of *precise* DEFINITIONS concerning the
                    > particular
                    > system we want to study followed by an *investigation* of the
                    > resulting system.
                    > But note carefully, *postulations* to do not play *any* part in this
                    > process.
                    >
                    I disagree. When you do group theory you assume axioms. Those are
                    scientific postulations. We believe in them because we have examples,
                    but to make those example existent, we need other postulations (like
                    classes, sets, self-consistency, etc.). The situation is not different
                    from theoretical physics, which you can seen indeed as pure mathematics.




                    >
                    > Consider GROUP THEORY. To describe a group we have to *define* a
                    > DOMAIN of
                    > interest and a *closed* OPERATOR that *combines* [or "pairs", or
                    > "joins
                    > together"] the entities contained in the domain. The operator is
                    > sometimes
                    > called a "pairing operator".
                    >
                    > EXAMPLE
                    >
                    > DOMAIN OF INTEREST, K = { a, b, c, d }
                    > Note that the individual elements a, b, c, d, do *not* have any
                    > *properties* nor
                    > is their individual *nature* of any significance.
                    >
                    You have to assume they exist.



                    > The *symbols*, a, b, c, d are just *labels* and have *no*
                    > significance as
                    > individuals. You can choose whatever four labels you like, . . . it
                    > makes *no*
                    > difference whatsoever to the mathematical system. Any other set of
                    > labels will
                    > do just as well, e.g.:
                    > (1) apple, bird, rock, air;
                    > (2) Fred, fish, music, Mary;
                    > (3) 9, 7, 4, 6;
                    > etc.
                    >
                    You assume that your interlocutor can distinguish those labels, and
                    that all this makes sense. You assume (unconsciously) some part of
                    logic, so that you can reason and proof theorems. Logicians like to
                    make theories making explicit all assumptions.



                    >
                    > GROUP OPERATOR, $
                    > I've chosen $ as the symbol for the GROUP OPERATOR but *any other
                    > symbol* will
                    > do just as well, e.g.: +, *, o, etc. It does not matter although
                    > obviously,
                    > since this is mathematics and therefore almost all about numbers,
                    > some symbols
                    > read more easily than others. But to emphasize the point, the
                    > *particular*
                    > symbol we choose *does not matter* as far as the mathematical
                    > investigation is
                    > concerned.
                    >
                    Of course, ... in the formal deductive theory. But group theorists are
                    interested mostly in particular groups, like Lie groups, or like the
                    Galois groups (permutation of roots of some equations, etc.). In that
                    case, they will interpret the group laws "$" by some object in some
                    other structure (category, set, lattice, etc.).
                    In fact you can *apply* the theory of *group* to another branch of
                    "pure" mathematics. And vice versa.



                    >
                    > The way $ combines the elements of K is *defined* by the following
                    > table.
                    > ---------------------
                    > a $ a = a, a $ b = b, a $ c = c, a $ d = d
                    > b $ a = b, b $ b = a, b $ c = d, b $ d = c
                    > c $ a = c, c $ b = d, c $ c = a, c $ d = b
                    > d $ a = d, d $ b = c, d $ c = b, d $ d = a
                    > ---------------------
                    >
                    > Having *defined* his system the mathematician now embarks on a
                    > mathematical
                    > *investigation*: theorems and lemmas, leading to new definitions,
                    > leading to new
                    > theorems and lemmas, etc.
                    >
                    This is not different than any theoreticians. They build theories and
                    then investigate the consequences of that theory, sometime interested
                    in, or not, applications. I do pure theoretical computer science. It
                    is a branch of pure mathematics too. There is even a part of it which
                    provably cannot have applications, by being provably non constructive.

                    Sometimes, "pure " and "applied" get interchanged. For example, as a
                    number theorist amateur, I consider that the bosonic string theory is
                    a purely mathematical tools fro proving theorem in pure number theory.
                    You can use mathematical bosonic strings to prove hard theorems in
                    number theory by Lagranges and Jacobi. (That all positive integers can
                    be written as the sum of four squared integers, that all even numbers
                    have 24 times the sum of their odd divisors, such four squares
                    representations, etc.)

                    -- Bruno Marchal



                    >
                    > For those interested in pursuing this further a useful introduction
                    > to the Klein
                    > four-group and other group-concepts will be found at.
                    > http://en.wikipedia.org/wiki/Klein_four-group
                    >
                    > Gich
                    >
                    >

                    http://iridia.ulb.ac.be/~marchal/





                    [Non-text portions of this message have been removed]
                  • Bruno Marchal
                    ... [I meant might be false] ... I totally agree with you on this. That makes my point: N exists. It is part of reality. And if you have study my work you know
                    Message 9 of 28 , Jan 6, 2012
                    • 0 Attachment
                      On 06 Jan 2012, at 11:50, gich7 wrote:
                      > marchal wrote:
                      > > You are right. It does not have to have anything to do with the real
                      > > world. For example, the mechanist hypothesis in cognitive science
                      > > might be true.
                      >
                      [I meant might be false]

                      > > But my point is that IF the mechanist hypothesis in the cognitive
                      > > science is correct, then pure mathematics has to have something to
                      > do
                      > > with reality.
                      >
                      > I don't know why this follows.
                      > Consider the positive integers, N = {1, 2, 3, . . . }.
                      > It seems to me that N exists *outside* of human reality. If there
                      > had never been
                      > a planet Earth, if the human race had never existed, N would still
                      > exist.
                      >
                      I totally agree with you on this. That makes my point: N exists. It is
                      part of reality. And if you have study my work you know that IF we are
                      machine THEN it logically follows that the physical laws are theorems
                      of arithmetic. I don't pretend this is obvious.




                      > --------------------------
                      > [Roger Scruton, Modern Philosophy -- An Introduction and Survey ]
                      > . . . Numbers especially are the source of much philosophy, as we
                      > have already
                      > seen in discussing Russell. They are 'objects' in Frege's sense:
                      > that is, we
                      > give them names, and strive to discover the truth about them. Yet it
                      > is absurd
                      > to say that they exist in space and time: as though there were some
                      > place where
                      > the number nine could at last be encountered. . . .
                      >
                      Totally OK with this.



                      > . . . numbers cannot be known through the senses, but only through
                      > thought.
                      > Moreover, they do not act on anything, so as to produce results.
                      > They are
                      > 'powerless' in the natural world, and leave no trace there. . . . In
                      > which case,
                      > how do the numbers affect our thought, and why do we say that, by
                      > thinking, we
                      > gain *knowledge* of them? Many empiricists therefore try to construe
                      > numbers and
                      > other abstract objects as 'creations of the mind', with no
                      > independent reality.
                      >
                      They confuse numbers with the human conception of numbers. But with
                      mechanism we know exactly how numbers manage to develop belief in an
                      apparent physical reality. I am explaining this right now on this
                      list, albeit slowly, notably to Elliot Temple, who seems to have
                      agreed with the 6th first step of the Universal Dovetailer Argument
                      which proves this in 8 steps. For more you can study this:
                      http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html




                      > --------------------------
                      >
                      > > Indeed, in that case 100% of physics, and 99,9% of
                      > > theology becomes branch of pure mathematics. Even the feeding amoeba
                      > > is doing pure mathematics, without knowing that of course, like
                      > Mister
                      > > Jourdain is doing prose.
                      > >
                      > >
                      > >
                      > >
                      > >>
                      > >> In other words, investigations in pure mathematics do not *have* to
                      > >> have
                      > >> anything to do with 'the real world'.
                      > >>
                      > > You are right. I agree with you on that point. But IF mechanism is
                      > > true, it has to have everything to do with the real world. Even the
                      > > most abstract non computationalist theory mathematical theory has to
                      > > do with arithmetic, in that case, under the form of the following
                      > > question "why should a number ever imagine such a theory"?
                      > >
                      >
                      > The question sounds nonsensical to me.
                      >
                      The reason is that if we assume digital mechanism, thought process are
                      computation, in the mathematical sense of Post, Turing and Church. In
                      particular if a mathematician invents some finitely describable
                      theory, we know that the statement "some machine invent that theory"
                      will be a theorem of arithmetic. This leads to a reduction of the mind-
                      body problem to a pure body problem in pure arithmetic. this leads to
                      a reversal between Plato and Aristotle, also. It makes physics a
                      branch of computer science, which is itself a branch of number theory.






                      > --------------------------
                      > [Roger Scruton, Modern Philosophy -- An Introduction and Survey ]
                      > . . . There is another worry about necessary existence. Are we sure
                      > that one and
                      > only one thing can possess this feature? What about numbers, for
                      > instance? If
                      > the number two exists, it is hard to conceive how it could exist
                      > contingently.
                      >
                      I agree with this, although I do not assume it to be true in the
                      reasoning mentioned above.




                      > Is there a possible world in which there is no number two (but all
                      > the other
                      > numbers), or no numbers at all? The supposition hardly makes sense.
                      > But the
                      > number two purchases its necessary existence at the expense of its
                      > causal power.
                      >
                      Well, there are certainly theories without natural numbers. We cannot
                      derive the existence of the numbers without assuming them. That is
                      known as "the failure of logicism". Bertrand Russell and Alfred
                      Whitehead were wrong on this. But this does not make the natural
                      numbers contingent. Once you assume succession, addition and
                      multiplication, they behave well in all the possible interpretations.
                      To be short.





                      > >>
                      > >> But this "postulating of computationalism" has *nothing whatsoever*
                      > >> to do with
                      > >> *pure mathematics* which was the subject of my original posting.
                      > >>
                      > > But it has something to do with your statement that pure mathematics
                      > > does not have to have applications. With mechanism, there is a sense
                      > > to say that the biological and physical phenomena are only tools for
                      > > doing pure mathematics, that is surviving and studying the reality
                      > > which appears to be almost completely mathematical. Note that
                      > > mechanism explains easily in this way the unreasonable effectiveness
                      > > of mathematics. Indeed reality is *purely* mathematical.
                      >
                      > I don't understand any of this.
                      > You need to describe how this works.
                      >
                      It is the result of 30 years of hard work. Look at the SANE04 paper
                      referred above. The result is counter-intuitive, and goes against the
                      Aristotelian theology, or metaphysics, used by christian and atheists
                      since the closure of Plato academy. I have shown that there is a many-
                      world interpretation of arithmetic, and that numbers (relatively to
                      each others) find it, in some sense. A bit like Everett explained how
                      QM can be used to derive the collapse appearance. It is a strong
                      generalization of Everett, and also a correction of Penrose use of the
                      incompleteness theorem. It is also a constructive critics of FOR.




                      > As a beginning, you need to explain *how* the assumption of
                      > mechanism *leads to*
                      > the existence of the natural numbers.
                      >
                      As I said above, you cannot prove the existence of the natural
                      numbers. You have to assume them, or assume something equivalent. The
                      assumption of arithmetic is part of the assumption of mechanism.
                      mechanism assume Church thesis, and this makes no sense without
                      assuming the numbers. Most scientific theories assumes the numbers.




                      >
                      >
                      >
                      > I think all human knowledge in theoretical physics stems from number
                      > theory.
                      > Mathematics rules!
                      >
                      As I knew from your post, we are very close on this.



                      > But I don't think we need a postulation of the sort you're
                      > promoting to reach this conclusion.
                      >
                      The conclusion is technical and constructive: it makes mechanism
                      testable because it explains how to derive the laws of physics from
                      number theory. The conception of reality becomes completely different
                      than the current materialism of naturalism suppose. In fact it
                      provides an arithmetical interpretation of the whole work of the
                      neoplatonist Plotinus. To simplify: the physical reality is an
                      illusion, a sharable dreams among infinities of digital machines
                      (relative numbers).


                      > >> Pure mathematics consists of *precise* DEFINITIONS concerning the
                      > >> particular
                      > >> system we want to study followed by an *investigation* of the
                      > >> resulting system.
                      > >> But note carefully, *postulations* to do not play *any* part in
                      > this
                      > >> process.
                      > >>
                      > > I disagree. When you do group theory you assume axioms. Those are
                      > > scientific postulations.
                      > > We believe in them because we have examples,
                      > > but to make those example existent, we need other postulations (like
                      > > classes, sets, self-consistency, etc.). The situation is not
                      > different
                      > > from theoretical physics, which you can seen indeed as pure
                      > mathematics.
                      > >
                      >
                      > This seems wrong to me.
                      > Pure mathematics is not the same as theoretical physics.
                      >
                      You are right. But the result is that IF we are machine THEN
                      theoretical physics is a very special branch of pure mathematics. It
                      concerns stable persistent sharable dreams by universal numbers (code
                      or description of universal machine in Post-Church-Turing sense).



                      > The *axioms* in pure mathematical systems are simply *definitions*
                      > -- products
                      > of the mathematician's intellect.
                      >
                      The theory explains where such "mathematician's intellect" comes from.



                      >
                      > When investigating a new idea, the pure mathematician can make
                      > anything he likes
                      > to be an axiom -- he does *not* have to "believe in the axioms" --
                      > belief has no
                      > role to play. His procedure goes something like this: "starting off
                      > with this
                      > system of axioms (that I've just thought of), can I develop any
                      > results
                      > (theorems) that look interesting? Can the system develop into
                      > something
                      > significant or does it begin and end with the axioms?"
                      >
                      I can agree. It is not entirely true. The axioms have to be
                      interesting. It is also a bit different between algebraist, who have
                      no particular structure in mind (they can study all groups with
                      interest in particular group) and number theorist (say) who study a
                      "reality" (natural numbers) that we know today as not being completely
                      amenable to a particular axiomatic. The number theoretical truth is
                      beyond any formalization we can make of it.




                      >
                      > The pure mathematician deals with questions like, "if such-and-such
                      > is true
                      > (which, initially, would be one of his axioms) does it then follow
                      > that
                      > so-and-so is true. If he can *prove* this result then he's
                      > established a new
                      > theorem -- he's developed his system. But the *existence* of such-
                      > and-such or,
                      > indeed, whether it makes any sense (in the real-world) is of no
                      > concern to him.
                      >
                      That's not entirely true. They want examples and instantiation of
                      their axioms. they postulate numbers and sets to have them. Most
                      mathematicians works in naive set theory. They assume a lot. Sometimes
                      they use strong axioms. To believe that all vectorial (linear) space
                      have a base, you need the axiom of choice for example.



                      >
                      > Now I know, of course, that group theory underlies almost all of
                      > theoretical
                      > physics but it seems to me that this fact is confusing your
                      > thinking. Pure
                      > mathematics is *not* the same as applied mathematics but you seem to
                      > be mixing
                      > the two.
                      >
                      I am saying that IF we are digitalizable machine, THEN the ontological
                      primitive reality are given by the natural numbers and their additive
                      and multiplicative structure. Physics becomes an internal emergent (in
                      the numbers mind) structure. Physics is no more the fundamental
                      science, but arithmetic is.




                      >
                      > >
                      > >
                      > >
                      > >>
                      > >> Consider GROUP THEORY. To describe a group we have to *define* a
                      > >> DOMAIN of
                      > >> interest and a *closed* OPERATOR that *combines* [or "pairs", or
                      > >> "joins
                      > >> together"] the entities contained in the domain. The operator is
                      > >> sometimes
                      > >> called a "pairing operator".
                      > >>
                      > >> EXAMPLE
                      > >>
                      > >> DOMAIN OF INTEREST, K = { a, b, c, d }
                      > >> Note that the individual elements a, b, c, d, do *not* have any
                      > >> *properties* nor
                      > >> is their individual *nature* of any significance.
                      > >>
                      > > You have to assume they exist.
                      >
                      > This is wrong. Assumptions concerning the existence (in nature) of
                      > the elements
                      > is not required. Their 'existence' need only be in the
                      > mathematicians mind. Pure
                      > mathematics is a purely mental activity -- an activity that goes on
                      > *outside* of
                      > the natural world.
                      >
                      When I believe that I am a machine, I stop to believe in the natural
                      world. I certainly do not assume the existence of the natural world.
                      Only in numbers dreams (computation seen from inside, as it can be
                      defined in number theory using G�del arithmetization of
                      metamathematics). I do not pretend this is obvious, but this has been
                      verified many times by courageous peer reviewers. I am open that some
                      flaws still exist, but no one seems able to find them. (Some atheists
                      scientist imagine there is one, but refuse to show it, so ...).





                      >
                      > >
                      > >
                      > >
                      > >> The *symbols*, a, b, c, d are just *labels* and have *no*
                      > >> significance as
                      > >> individuals. You can choose whatever four labels you like, . . . it
                      > >> makes *no*
                      > >> difference whatsoever to the mathematical system. Any other set of
                      > >> labels will
                      > >> do just as well, e.g.:
                      > >> (1) apple, bird, rock, air;
                      > >> (2) Fred, fish, music, Mary;
                      > >> (3) 9, 7, 4, 6;
                      > >> etc.
                      > >>
                      > > You assume that your interlocutor can distinguish those labels, and
                      > > that all this makes sense. You assume (unconsciously) some part of
                      > > logic, so that you can reason and proof theorems. Logicians like to
                      > > make theories making explicit all assumptions.
                      > >
                      >
                      > No. I'm not assuming anything of the sort. I don't need an
                      > interlocutor to do
                      > pure mathematics.
                      >
                      In practice you do assume, at the meta-level some interlocutor, even
                      if it is only yourself. You assume implicitly your own consistency or
                      the consistency of arithmetic or of some part of set theory. By
                      definition you assume some axioms to be satisfied by some structure.

                      Bruno

                      >
                      > >
                      > >
                      > >>
                      > >> GROUP OPERATOR, $
                      > >> I've chosen $ as the symbol for the GROUP OPERATOR but *any other
                      > >> symbol* will
                      > >> do just as well, e.g.: +, *, o, etc. It does not matter although
                      > >> obviously,
                      > >> since this is mathematics and therefore almost all about numbers,
                      > >> some symbols
                      > >> read more easily than others. But to emphasize the point, the
                      > >> *particular*
                      > >> symbol we choose *does not matter* as far as the mathematical
                      > >> investigation is
                      > >> concerned.
                      > >>
                      > > Of course, ... in the formal deductive theory. But group theorists
                      > are
                      > > interested mostly in particular groups, like Lie groups, or like the
                      > > Galois groups (permutation of roots of some equations, etc.). In
                      > that
                      > > case, they will interpret the group laws "$" by some object in some
                      > > other structure (category, set, lattice, etc.).
                      > > In fact you can *apply* the theory of *group* to another branch of
                      > > "pure" mathematics. And vice versa.
                      > >
                      > >
                      > >
                      > >>
                      > >> The way $ combines the elements of K is *defined* by the following
                      > >> table.
                      > >> ---------------------
                      > >> a $ a = a, a $ b = b, a $ c = c, a $ d = d
                      > >> b $ a = b, b $ b = a, b $ c = d, b $ d = c
                      > >> c $ a = c, c $ b = d, c $ c = a, c $ d = b
                      > >> d $ a = d, d $ b = c, d $ c = b, d $ d = a
                      > >> ---------------------
                      > >>
                      > >> Having *defined* his system the mathematician now embarks on a
                      > >> mathematical
                      > >> *investigation*: theorems and lemmas, leading to new definitions,
                      > >> leading to new
                      > >> theorems and lemmas, etc.
                      > >>
                      > > This is not different than any theoreticians. They build theories
                      > and
                      > > then investigate the consequences of that theory, sometime
                      > interested
                      > > in, or not, applications. I do pure theoretical computer science. It
                      > > is a branch of pure mathematics too. There is even a part of it
                      > which
                      > > provably cannot have applications, by being provably non
                      > constructive.
                      > >
                      > > Sometimes, "pure " and "applied" get interchanged. For example, as a
                      > > number theorist amateur, I consider that the bosonic string theory
                      > is
                      > > a purely mathematical tools fro proving theorem in pure number
                      > theory.
                      > > You can use mathematical bosonic strings to prove hard theorems in
                      > > number theory by Lagranges and Jacobi. (That all positive integers
                      > can
                      > > be written as the sum of four squared integers, that all even
                      > numbers
                      > > have 24 times the sum of their odd divisors, such four squares
                      > > representations, etc.)
                      > >
                      > > -- Bruno Marchal
                      > >
                      > >
                      > >
                      > >>
                      > >> For those interested in pursuing this further a useful introduction
                      > >> to the Klein
                      > >> four-group and other group-concepts will be found at.
                      > >> http://en.wikipedia.org/wiki/Klein_four-group
                      > >>
                      > >> Gich
                      > >>
                      > >>
                      >
                      > Gich
                      >
                      >

                      http://iridia.ulb.ac.be/~marchal/





                      [Non-text portions of this message have been removed]
                    • brhalluk@hotmail.com
                      ... Hi Bruno et al, I may have some of my terminology wrong here: so please correct me if that s the case. Assuming that it is possible to program a person
                      Message 10 of 28 , Jan 6, 2012
                      • 0 Attachment
                        > I totally agree with you on this. That makes my point: N exists. It is
                        > part of reality. And if you have study my work you know that IF we are
                        > machine THEN it logically follows that the physical laws are theorems
                        > of arithmetic. I don't pretend this is obvious.

                        > They confuse numbers with the human conception of numbers. But with
                        > mechanism we know exactly how numbers manage to develop belief in an
                        > apparent physical reality. I am explaining this right now on this
                        > list, albeit slowly, notably to Elliot Temple, who seems to have
                        > agreed with the 6th first step of the Universal Dovetailer Argument
                        > which proves this in 8 steps. For more you can study this:
                        > http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
                        >

                        > The reason is that if we assume digital mechanism, thought process are
                        > computation, in the mathematical sense of Post, Turing and Church. In
                        > particular if a mathematician invents some finitely describable
                        > theory, we know that the statement "some machine invent that theory"
                        > will be a theorem of arithmetic. This leads to a reduction of the mind-
                        > body problem to a pure body problem in pure arithmetic. this leads to
                        > a reversal between Plato and Aristotle, also. It makes physics a
                        > branch of computer science, which is itself a branch of number theory.
                        >
                        >
                        > >
                        > The conclusion is technical and constructive: it makes mechanism
                        > testable because it explains how to derive the laws of physics from
                        > number theory. The conception of reality becomes completely different
                        > than the current materialism of naturalism suppose. In fact it
                        > provides an arithmetical interpretation of the whole work of the
                        > neoplatonist Plotinus. To simplify: the physical reality is an
                        > illusion, a sharable dreams among infinities of digital machines
                        > (relative numbers).




                        Hi Bruno et al,

                        I may have some of my terminology wrong here: so please correct me if that's the case.

                        Assuming that it is possible to program a person (and therefore consciousness just arises at some emergent level) then in the future we'll presumably be able to create virtual worlds that contain people.

                        Two somewhat unrelated questions:

                        Firstly, would this mean that the discoveries simulated people make is inherently bounded? Is it possible - given that they are simulated people - that they would be able to discover our world - the one in which the computer on which they are being simulated - is running? I think DD makes the point in FoR that simulated people *would* eventually discover they are simulated and that there was an external reality. Indeed according to BoI this *must* be the case if they are universal explainers.

                        Secondly - and this is probably mainly for Bruno - it is obvious to us who have written the program describing the virtual world and its people - that what they (they virtual people) are discovering is not `real' matter when they do explain their world using terms like "matter". There is no matter in the virtual world. We know this from our privileged position - but they cannot as they are trapped in the simulation. We can see the difference between the stuff in our world (which is real) and the stuff in their world (which is just virtual matter - a consequence of the knowledge we have instantiated in the program).

                        For example in our world two electrons repel each other because there really exist electrons that really do exert a repulsive force upon one another (by exchanging real photons, or whatever). This is realism.

                        In the virtual world the virtual people explain their observations about the repulsion of `electrons' in the same way. At least for a while, realism works. But *we* know, looking on from the outside, that they are mistaken for there are no actual electrons or forces or photons at all. In fact it is just bits of information - numbers actually - doing this or that entirely abstractly. So we can see that their realism is false - everything they take to be physical is actually abstract. The only physical thing is the hardware on which the computer runs and they cannot discover this. Their correct philosophy *should be* mechanism as you describe. Namely - they are *obviously* machines who have *invented* the real world (from our perspective). From our perspective, the ultimate explanation of their world is some instantiation of arithmetic (a program running on a computer).

                        Is this correct?

                        Bruno, would you say that *if* your hypothesis is true *then* our world is precisely as the virtual world I have described above only there's no programmer and there's no inherent limitation to what can be discovered?

                        In other words under digital mechanism, our world is a virtual world, only there's no programmer?

                        Thanks,

                        Brett.
                      • Peter D
                        ... Not part of mine. I ve never seen the set of positive integers.
                        Message 11 of 28 , Jan 7, 2012
                        • 0 Attachment
                          --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal <marchal@...> wrote:
                          >
                          >

                          > I totally agree with you on this. That makes my point: N exists. It is
                          > part of reality.

                          Not part of mine. I've never seen the set of positive integers.
                        • Bruno Marchal
                          ... OK. I don t think we can program person, but we might be unable to enslave universal machine a long time enough, and virtual person might develop in
                          Message 12 of 28 , Jan 7, 2012
                          • 0 Attachment
                            On 07 Jan 2012, at 08:21, brhalluk@... wrote:

                            > > I totally agree with you on this. That makes my point: N exists.
                            > It is
                            > > part of reality. And if you have study my work you know that IF we
                            > are
                            > > machine THEN it logically follows that the physical laws are
                            > theorems
                            > > of arithmetic. I don't pretend this is obvious.
                            >
                            > > They confuse numbers with the human conception of numbers. But with
                            > > mechanism we know exactly how numbers manage to develop belief in an
                            > > apparent physical reality. I am explaining this right now on this
                            > > list, albeit slowly, notably to Elliot Temple, who seems to have
                            > > agreed with the 6th first step of the Universal Dovetailer Argument
                            > > which proves this in 8 steps. For more you can study this:
                            > > http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
                            > >
                            >
                            > > The reason is that if we assume digital mechanism, thought process
                            > are
                            > > computation, in the mathematical sense of Post, Turing and Church.
                            > In
                            > > particular if a mathematician invents some finitely describable
                            > > theory, we know that the statement "some machine invent that theory"
                            > > will be a theorem of arithmetic. This leads to a reduction of the
                            > mind-
                            > > body problem to a pure body problem in pure arithmetic. this leads
                            > to
                            > > a reversal between Plato and Aristotle, also. It makes physics a
                            > > branch of computer science, which is itself a branch of number
                            > theory.
                            > >
                            > >
                            > > >
                            > > The conclusion is technical and constructive: it makes mechanism
                            > > testable because it explains how to derive the laws of physics from
                            > > number theory. The conception of reality becomes completely
                            > different
                            > > than the current materialism of naturalism suppose. In fact it
                            > > provides an arithmetical interpretation of the whole work of the
                            > > neoplatonist Plotinus. To simplify: the physical reality is an
                            > > illusion, a sharable dreams among infinities of digital machines
                            > > (relative numbers).
                            >
                            > Hi Bruno et al,
                            >
                            > I may have some of my terminology wrong here: so please correct me
                            > if that's the case.
                            >
                            > Assuming that it is possible to program a person (and therefore
                            > consciousness just arises at some emergent level) then in the future
                            > we'll presumably be able to create virtual worlds that contain people.
                            >
                            OK. I don't think we can program person, but we might be unable to
                            enslave universal machine a long time enough, and virtual person might
                            develop in virtual realities, yes.




                            >
                            > Two somewhat unrelated questions:
                            >
                            > Firstly, would this mean that the discoveries simulated people make
                            > is inherently bounded?
                            >
                            Not necessarily. But you will have to provide memories regularly to
                            maintain the simulation. If they decide to search for the Higs boson,
                            and build a LAC, you might add some terrabits, and more, on the "hard
                            disk".





                            > Is it possible - given that they are simulated people - that they
                            > would be able to discover our world - the one in which the computer
                            > on which they are being simulated - is running?
                            >
                            This is delicate to answer. Those person, as seen by you, will
                            discover soon or later that they are in a simulation, unless you
                            observe them, and trick them deliberately, which will ask for a more
                            and more complex work. But from their own first person perspective,
                            such a tricked simulation will get a lower and lower measure, so that,
                            assuming their are immortal, they will end up, from their own point of
                            view "in reality", statistically. Your own universe where you trick
                            them will become like an harry Potter universe from their statistical
                            point of view (and your tricky job will be an exploding job: at some
                            point you will have to simulate the whole multiverse!).





                            > I think DD makes the point in FoR that simulated people *would*
                            > eventually discover they are simulated and that there was an
                            > external reality. Indeed according to BoI this *must* be the case if
                            > they are universal explainers.
                            >
                            Except the existence of an external global physical reality is an open
                            problem, with comp. And also, it might be that the quantum phenomenon
                            is already an evidence that we belong to infinities of simulations.
                            But our physics should emerge from this. That should be clear already
                            with UDA-step-7.




                            >
                            > Secondly - and this is probably mainly for Bruno - it is obvious to
                            > us who have written the program describing the virtual world and its
                            > people - that what they (they virtual people) are discovering is not
                            > `real' matter when they do explain their world using terms like
                            > "matter".
                            >
                            This will happen if you stop to trick them purposefully.




                            > There is no matter in the virtual world. We know this from our
                            > privileged position - but they cannot as they are trapped in the
                            > simulation. We can see the difference between the stuff in our world
                            > (which is real) and the stuff in their world (which is just virtual
                            > matter - a consequence of the knowledge we have instantiated in the
                            > program).
                            >
                            We don't know if our stuff is real. If comp is correct, it real with
                            respect to observation, but it is not primitive. The simulated people
                            can make UDA themselves, extract the laws of physics from comp, and
                            compare their observation with that physics, and extract information
                            about they "layers" of simulation.



                            >
                            > For example in our world two electrons repel each other because
                            > there really exist electrons that really do exert a repulsive force
                            > upon one another (by exchanging real photons, or whatever). This is
                            > realism.
                            >
                            It is physical realism, and some amount of it is consistent with comp,
                            but basically physics comes from pure number theoretical relations (or
                            based on some other universal frame: I use numbers because they are
                            more well known).


                            >
                            > In the virtual world the virtual people explain their observations
                            > about the repulsion of `electrons' in the same way. At least for a
                            > while, realism works. But *we* know, looking on from the outside,
                            > that they are mistaken for there are no actual electrons or forces
                            > or photons at all. In fact it is just bits of information - numbers
                            > actually - doing this or that entirely abstractly. So we can see
                            > that their realism is false - everything they take to be physical is
                            > actually abstract. The only physical thing is the hardware on which
                            > the computer runs and they cannot discover this. Their correct
                            > philosophy *should be* mechanism as you describe.
                            >
                            Yes. But they can extract the physics from that, and then compare with
                            the observations.



                            > Namely - they are *obviously* machines who have *invented* the real
                            > world (from our perspective).
                            >
                            But they have a different perspective, and "belongs" to infinities of
                            computations like us. The trick to confuse them will have a quickly
                            growing price.




                            > From our perspective, the ultimate explanation of their world is
                            > some instantiation of arithmetic (a program running on a computer).
                            >
                            > Is this correct?
                            >
                            Not if you install democracy and free-thinking. Either you don't trick
                            them enough, and they will discover "our worlds", or you trick them
                            well enough, and from their perspective they will be in a world as
                            real as yours, statistically. Note that I use the first person
                            indeterminacy all the time!




                            >
                            > Bruno, would you say that *if* your hypothesis is true *then* our
                            > world is precisely as the virtual world I have described above only
                            > there's no programmer and there's no inherent limitation to what can
                            > be discovered?
                            >
                            Not really. The physical worlds is not emulable, normally. Its 'shape"
                            comes from the fact that below our substitution level, we are in
                            infinities of computations at once.



                            >
                            > In other words under digital mechanism, our world is a virtual
                            > world, only there's no programmer?
                            >

                            It is more complex. Our world is a sum on infinities of simulations.
                            It is an open problem to decide if that sum is emulable or not. Its
                            geography is typically not emulable in the detail, like we cannot
                            emulate classically some quantum processes (without duplicating the
                            parallel observers).

                            Many get this wrong, but a priori, if WE are machines, the rest is
                            not. Neither matter nor consciousness. If you study the UDA, this
                            should not be too difficult to understand. I think. It means we have
                            to extend Everett phenomenology to arithmetic and derive the wave
                            itself from machine's self-reference. Advantage: we can use
                            incompleteness-like phenomena to justify the quanta/qualia difference.

                            -- Bruno Marchal

                            >

                            http://iridia.ulb.ac.be/~marchal/





                            [Non-text portions of this message have been removed]
                          • Bruno Marchal
                            ... The correct physical laws/theories are anything relating correctly the observation I can do. More deeply, it is related of what is persistent and
                            Message 13 of 28 , Jan 7, 2012
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                              On 07 Jan 2012, at 18:05, gich7 wrote:

                              >
                              > ----- Original Message -----
                              > From: "Bruno Marchal" <marchal@...>
                              > To: <Fabric-of-Reality@yahoogroups.com>
                              > Sent: Friday, January 06, 2012 2:22 PM
                              > Subject: Re: Abstract mathematical development versus particle
                              > physics analysis
                              >
                              > On 06 Jan 2012, at 11:50, gich7 wrote:
                              > > marchal wrote:
                              > > > You are right. It does not have to have anything to do with the
                              > real
                              > > > world. For example, the mechanist hypothesis in cognitive science
                              > > > might be true.
                              > >
                              > [I meant might be false]
                              >
                              > > > But my point is that IF the mechanist hypothesis in the cognitive
                              > > > science is correct, then pure mathematics has to have something to
                              > > do
                              > > > with reality.
                              > >
                              > > I don't know why this follows.
                              > > Consider the positive integers, N = {1, 2, 3, . . . }.
                              > > It seems to me that N exists *outside* of human reality. If there
                              > > had never been
                              > > a planet Earth, if the human race had never existed, N would still
                              > > exist.
                              > >
                              > I totally agree with you on this. That makes my point: N exists. It is
                              > part of reality. And if you have study my work you know that IF we are
                              > machine THEN it logically follows that the physical laws are theorems
                              > of arithmetic. I don't pretend this is obvious.
                              >
                              > GICH: OK. Let's take this as given.
                              > I think we may be getting close to my major difficulty with your
                              > thesis. What do
                              > you mean by "the physical laws"? Let's remind ourselves of the
                              > origins of our
                              > discussion.
                              > ---------------------------
                              > GICH (before): . . . But note carefully, pure mathematics does *not*
                              > have to
                              > have anything to do with 'the real world'.
                              > BRUNO (before); It depends on your hypotheses, notably in the
                              > cognitive science.
                              > If you assume computationalism . . .
                              > ---------------------------
                              >
                              > GICH (now): To repeat, what do you mean by "the physical laws"?
                              > Quantum theory?
                              > General relativity?
                              > String theory?
                              >

                              The "correct" physical laws/theories are anything relating "correctly"
                              the observation I can do. More deeply, it is related of what is
                              persistent and invariant in those observations.



                              >
                              > I wouldn't call any of these "laws", rather just "theories". They
                              > are *only*
                              > mathematical models and none of them provide any insights whatsoever
                              > into the
                              > *actual* "reality" that *must* underlie the world in which we live.
                              > Ask any
                              > scientist a question like: what is an electron (?) and you'll have
                              > to wait a
                              > long time for an answer. A question like what is a quark (?), or
                              > what is a gluon
                              > (?) will produce even more confusion. Scientists know nothing about
                              > gravity,
                              > they know nothing about how the universe began, they know nothing
                              > about the
                              > fundamental nature of black holes, etc., etc., . . . they know
                              > nothing about
                              > 'reality'.
                              >
                              I kind of agree, but they have interesting "beliefs" (theories,
                              refutable statements). But physicists might not have chosen the right
                              metaphysics or theology. There too, we can propose theories, and the
                              comp theory suggests that the law of physics is in the head of any
                              "universal machine". So we can look at them, and compare with nature
                              to test the comp hypothesis.




                              >
                              > [Penrose, "The Road to reality -- A complete guide to the physical
                              > universe"] "
                              > . . . Yet, for gravitation, things were completely different ..
                              > Gravity seems to
                              > have a very special status, different from that of any other field.
                              > Rather than
                              > sharing in the thermalization that, in the early universe, applies
                              > to all other
                              > fields, gravity remained aloof, its degrees of freedom lying in
                              > wait, so that
                              > the Second Law of Thermodynamics would come into play as these
                              > degrees of
                              > freedom begin to become taken up. Not only does this give us a
                              > second law, but
                              > it gives us one in the particular form that we observe in Nature.
                              >
                              > Gravity just seems to have been different! But *why* was it
                              > different? We enter
                              > more speculative areas when we attempt answers to this kind of
                              > question.
                              > Physicists have made many attempts to come to terms with this puzzle
                              > and related
                              > ones, concerning the origin of the universe. In my opinion, none of
                              > these
                              > attempts comes at all close to dealing with the puzzle addressed in
                              > the
                              > preceding paragraph."
                              >
                              Penrose, at least, has intuited that consciousness might have some
                              role. Alas, he defended a non-comp theory of consciousness, where the
                              comp theory fits much better with both Gödel's theorem, QM, cognitive
                              science, etc.
                              Penrose remains physicalist. And, this, I argue, can't be defended in
                              the comp frame.




                              >
                              > GICH: This is why people like Susskind and Hawking ban the word
                              > 'reality' from
                              > scientific discussion and why Penrose entitled his 1094-page magnum
                              > opus, "The
                              > Road to reality . . .", but failed to come to any conclusions
                              > concerning what
                              > this "reality" might be.
                              >
                              Because, like many, they stick to an aristotelian conception of reality.
                              It is very common (to say the least).



                              > He ended his book with the following paragraph:
                              >
                              > [Penrose] "The space-time singularities lying at the cores of black
                              > holes are
                              > among the known (or presumed) objects in the universe about which
                              > the most
                              > profound mysteries remain -- and which our present-day theories are
                              > powerless to
                              > describe. . . . there are other deeply mysterious issues about which
                              > we have
                              > little comprehension. . . ."
                              >

                              Yeah. I think that science is deeply sleepy since we close Plato
                              academy in Athena. The most interesting questions and concepts (life,
                              soul, death, etc.) are still offered to the authoritative-argument,
                              pseudo-religious, people. Now comp does not solve all mysteries, and
                              on the contrary it measure their degrees on non solvability, their
                              densities, and the shape of our intrinsic ignorance. The machine's
                              'theology' is negative: about the big unnameable it says only that it
                              is not this, nor that, nor this, etc.

                              - Bruno Marchal


                              http://iridia.ulb.ac.be/~marchal/





                              [Non-text portions of this message have been removed]
                            • brhalluk@hotmail.com
                              ... Have you seen gravity?
                              Message 14 of 28 , Jan 7, 2012
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                                --- In Fabric-of-Reality@yahoogroups.com, "Peter D" <peterdjones@...> wrote:
                                >
                                >
                                >
                                > --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal <marchal@> wrote:
                                > >
                                > >
                                >
                                > > I totally agree with you on this. That makes my point: N exists. It is
                                > > part of reality.
                                >
                                > Not part of mine. I've never seen the set of positive integers.
                                >

                                Have you seen gravity?
                              • brhalluk@hotmail.com
                                Hi Bruno, thanks for your response... ... So your thinking is that whatever the laws are that give rise to people (or is it consciousness generally) these are
                                Message 15 of 28 , Jan 7, 2012
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                                  Hi Bruno, thanks for your response...

                                  --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal <marchal@...> wrote:
                                  >
                                  >
                                  > On 07 Jan 2012, at 08:21, brhalluk@... wrote:
                                  >
                                  > > > I totally agree with you on this. That makes my point: N exists.
                                  > > It is
                                  > > > part of reality. And if you have study my work you know that IF we
                                  > > are
                                  > > > machine THEN it logically follows that the physical laws are
                                  > > theorems
                                  > > > of arithmetic. I don't pretend this is obvious.
                                  > >
                                  > > > They confuse numbers with the human conception of numbers. But with
                                  > > > mechanism we know exactly how numbers manage to develop belief in an
                                  > > > apparent physical reality. I am explaining this right now on this
                                  > > > list, albeit slowly, notably to Elliot Temple, who seems to have
                                  > > > agreed with the 6th first step of the Universal Dovetailer Argument
                                  > > > which proves this in 8 steps. For more you can study this:
                                  > > > http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
                                  > > >
                                  > >
                                  > > > The reason is that if we assume digital mechanism, thought process
                                  > > are
                                  > > > computation, in the mathematical sense of Post, Turing and Church.
                                  > > In
                                  > > > particular if a mathematician invents some finitely describable
                                  > > > theory, we know that the statement "some machine invent that theory"
                                  > > > will be a theorem of arithmetic. This leads to a reduction of the
                                  > > mind-
                                  > > > body problem to a pure body problem in pure arithmetic. this leads
                                  > > to
                                  > > > a reversal between Plato and Aristotle, also. It makes physics a
                                  > > > branch of computer science, which is itself a branch of number
                                  > > theory.
                                  > > >
                                  > > >
                                  > > > >
                                  > > > The conclusion is technical and constructive: it makes mechanism
                                  > > > testable because it explains how to derive the laws of physics from
                                  > > > number theory. The conception of reality becomes completely
                                  > > different
                                  > > > than the current materialism of naturalism suppose. In fact it
                                  > > > provides an arithmetical interpretation of the whole work of the
                                  > > > neoplatonist Plotinus. To simplify: the physical reality is an
                                  > > > illusion, a sharable dreams among infinities of digital machines
                                  > > > (relative numbers).
                                  > >
                                  > > Hi Bruno et al,
                                  > >
                                  > > I may have some of my terminology wrong here: so please correct me
                                  > > if that's the case.
                                  > >
                                  > > Assuming that it is possible to program a person (and therefore
                                  > > consciousness just arises at some emergent level) then in the future
                                  > > we'll presumably be able to create virtual worlds that contain people.
                                  > >
                                  > OK. I don't think we can program person, but we might be unable to
                                  > enslave universal machine a long time enough, and virtual person might
                                  > develop in virtual realities, yes.

                                  So your thinking is that whatever the laws are that give rise to people (or is it consciousness generally) these are inexplicable? Why is that?

                                  >
                                  >
                                  >
                                  >
                                  > >
                                  > > Two somewhat unrelated questions:
                                  > >
                                  > > Firstly, would this mean that the discoveries simulated people make
                                  > > is inherently bounded?
                                  > >
                                  > Not necessarily. But you will have to provide memories regularly to
                                  > maintain the simulation. If they decide to search for the Higs boson,
                                  > and build a LAC, you might add some terrabits, and more, on the "hard
                                  > disk".
                                  >
                                  >
                                  >
                                  >
                                  >
                                  > > Is it possible - given that they are simulated people - that they
                                  > > would be able to discover our world - the one in which the computer
                                  > > on which they are being simulated - is running?
                                  > >
                                  > This is delicate to answer. Those person, as seen by you, will
                                  > discover soon or later that they are in a simulation, unless you
                                  > observe them, and trick them deliberately, which will ask for a more
                                  > and more complex work. But from their own first person perspective,
                                  > such a tricked simulation will get a lower and lower measure, so that,
                                  > assuming their are immortal, they will end up, from their own point of
                                  > view "in reality", statistically. Your own universe where you trick
                                  > them will become like an harry Potter universe from their statistical
                                  > point of view (and your tricky job will be an exploding job: at some
                                  > point you will have to simulate the whole multiverse!).

                                  Yes, I understand. You are answering "yes". If you are not observing them and upgrading the memory of the hardware eventually they will discover they are in a simulation.

                                  As a side point, does this make ideas like "The Matrix" testable? FoR does mention the failings of solipsism, but as you say above if such a metaphysical idea leads to consequence that any simulation would have to be a simulation of the entire multiverse eventually in order to keep the wool pulled over our eyes, then there's no sense in which one universe is more real than another, is there? Both embody the same laws and relationships.

                                  Of course - what *if* the simulated people begin making discoveries *faster* than are made in the real world? What if the simulated world is more conducive to enlightenments than our world? You wouldn't be able to keep up with anticipating what they would do next and eventually they'd demonstrate the finiteness of their world faster than you could trick them into believing it was reality.


                                  >
                                  >
                                  >
                                  >
                                  >
                                  > > I think DD makes the point in FoR that simulated people *would*
                                  > > eventually discover they are simulated and that there was an
                                  > > external reality. Indeed according to BoI this *must* be the case if
                                  > > they are universal explainers.
                                  > >
                                  > Except the existence of an external global physical reality is an open
                                  > problem, with comp. And also, it might be that the quantum phenomenon
                                  > is already an evidence that we belong to infinities of simulations.
                                  > But our physics should emerge from this. That should be clear already
                                  > with UDA-step-7.
                                  >
                                  >
                                  >
                                  >
                                  > >
                                  > > Secondly - and this is probably mainly for Bruno - it is obvious to
                                  > > us who have written the program describing the virtual world and its
                                  > > people - that what they (they virtual people) are discovering is not
                                  > > `real' matter when they do explain their world using terms like
                                  > > "matter".
                                  > >
                                  > This will happen if you stop to trick them purposefully.

                                  Yes, agreed. And I tend to this this ability to continue tricking them is probably not possible. Tricking someone amounts to predicting their behaviour perfectly. That can't go on indefinitely as it assumes your own omniscience, doesn't it?

                                  >
                                  >
                                  >
                                  >
                                  > > There is no matter in the virtual world. We know this from our
                                  > > privileged position - but they cannot as they are trapped in the
                                  > > simulation. We can see the difference between the stuff in our world
                                  > > (which is real) and the stuff in their world (which is just virtual
                                  > > matter - a consequence of the knowledge we have instantiated in the
                                  > > program).
                                  > >
                                  > We don't know if our stuff is real. If comp is correct, it real with
                                  > respect to observation, but it is not primitive. The simulated people
                                  > can make UDA themselves, extract the laws of physics from comp, and
                                  > compare their observation with that physics, and extract information
                                  > about they "layers" of simulation.

                                  Yes, fair enough. I don't like 'real' though - I'm not sure why we use that word. Physical or abstract, both are 'real' aren't they? In the sense described by Deutsch: they figure in our best explanations of reality. That aside, what words then could we use to distinguish between electrons in our world and electrons in a simulated world? If ours are real and ultimately abstract, so too are the simulated ones. But we *know* there's a difference, isn't there?

                                  >
                                  >
                                  >
                                  > >
                                  > > For example in our world two electrons repel each other because
                                  > > there really exist electrons that really do exert a repulsive force
                                  > > upon one another (by exchanging real photons, or whatever). This is
                                  > > realism.
                                  > >
                                  > It is physical realism, and some amount of it is consistent with comp,
                                  > but basically physics comes from pure number theoretical relations (or
                                  > based on some other universal frame: I use numbers because they are
                                  > more well known).

                                  Is it? Doesn't realism allow for the existence of abstractions? In fact, doesn't it demand it? I'm not saying that *only* the physical exists - this would be called 'physical realism' wouldn't it? In fact I'd probably call it something else. Physical realism in this sense wouldn't be David Deutsch's position from what I gather in FoR and BoI, it's not mine either. Both the abstract and the physical are real - I call such a point of view 'realism'.

                                  >
                                  >
                                  > >
                                  > > In the virtual world the virtual people explain their observations
                                  > > about the repulsion of `electrons' in the same way. At least for a
                                  > > while, realism works. But *we* know, looking on from the outside,
                                  > > that they are mistaken for there are no actual electrons or forces
                                  > > or photons at all. In fact it is just bits of information - numbers
                                  > > actually - doing this or that entirely abstractly. So we can see
                                  > > that their realism is false - everything they take to be physical is
                                  > > actually abstract. The only physical thing is the hardware on which
                                  > > the computer runs and they cannot discover this. Their correct
                                  > > philosophy *should be* mechanism as you describe.
                                  > >
                                  > Yes. But they can extract the physics from that, and then compare with
                                  > the observations.

                                  I think I understand.
                                  >
                                  >
                                  >
                                  > > Namely - they are *obviously* machines who have *invented* the real
                                  > > world (from our perspective).
                                  > >
                                  > But they have a different perspective, and "belongs" to infinities of
                                  > computations like us. The trick to confuse them will have a quickly
                                  > growing price.

                                  Agreed! And ultimately a price that is impossible to pay.

                                  >
                                  >
                                  >
                                  >
                                  > > From our perspective, the ultimate explanation of their world is
                                  > > some instantiation of arithmetic (a program running on a computer).
                                  > >
                                  > > Is this correct?
                                  > >
                                  > Not if you install democracy and free-thinking. Either you don't trick
                                  > them enough, and they will discover "our worlds", or you trick them
                                  > well enough, and from their perspective they will be in a world as
                                  > real as yours, statistically. Note that I use the first person
                                  > indeterminacy all the time!

                                  Yes, agreed. I think I now have a better appreciation of your position. I have read your original paper (many years ago) and the SANE talk (recently), but much has escaped me. This clears up a lot.

                                  >
                                  >
                                  >
                                  >
                                  > >
                                  > > Bruno, would you say that *if* your hypothesis is true *then* our
                                  > > world is precisely as the virtual world I have described above only
                                  > > there's no programmer and there's no inherent limitation to what can
                                  > > be discovered?
                                  > >
                                  > Not really. The physical worlds is not emulable, normally. Its 'shape"
                                  > comes from the fact that below our substitution level, we are in
                                  > infinities of computations at once.

                                  I get that. David Deutsch uses the word "fungible" - you do not. Is there a reason? I know that ultimately the multiverse interpretation - and your own - are different at the level of metaphysical reality but much remains the same (identical, even?). There are many fungible copies of me in the multiverse which *I* am. In your model, these infinities of computations are the object to which *I* refers - while they are identical in all respects then aren't they fungible in the multiverse sense?

                                  >
                                  >
                                  >
                                  > >
                                  > > In other words under digital mechanism, our world is a virtual
                                  > > world, only there's no programmer?
                                  > >
                                  >
                                  > It is more complex. Our world is a sum on infinities of simulations.
                                  > It is an open problem to decide if that sum is emulable or not. Its
                                  > geography is typically not emulable in the detail, like we cannot
                                  > emulate classically some quantum processes (without duplicating the
                                  > parallel observers).
                                  >
                                  > Many get this wrong, but a priori, if WE are machines, the rest is
                                  > not. Neither matter nor consciousness. If you study the UDA, this
                                  > should not be too difficult to understand. I think.

                                  !!
                                  I think it might be!

                                  > It means we have
                                  > to extend Everett phenomenology to arithmetic and derive the wave
                                  > itself from machine's self-reference. Advantage: we can use
                                  > incompleteness-like phenomena to justify the quanta/qualia difference.

                                  Thanks again,

                                  Brett.


                                  >
                                  > -- Bruno Marchal
                                  >
                                  > >
                                  >
                                  > http://iridia.ulb.ac.be/~marchal/
                                  >
                                  >
                                  >
                                  >
                                  >
                                  > [Non-text portions of this message have been removed]
                                  >
                                • Peter D
                                  ... I ve felt it.
                                  Message 16 of 28 , Jan 7, 2012
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                                    --- In Fabric-of-Reality@yahoogroups.com, brhalluk@... wrote:
                                    >
                                    >
                                    >
                                    > --- In Fabric-of-Reality@yahoogroups.com, "Peter D" <peterdjones@> wrote:
                                    > >
                                    > >
                                    > >
                                    > > --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal <marchal@> wrote:
                                    > > >
                                    > > >
                                    > >
                                    > > > I totally agree with you on this. That makes my point: N exists. It is
                                    > > > part of reality.
                                    > >
                                    > > Not part of mine. I've never seen the set of positive integers.
                                    > >
                                    >
                                    > Have you seen gravity?
                                    >
                                    I've felt it.
                                  • Bruno Marchal
                                    ... With comp physics is, to be short, reduced to an weighting on paths between computational states (relative numbers). The ultimately correct physics can
                                    Message 17 of 28 , Jan 8, 2012
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                                      On 08 Jan 2012, at 09:26, gich7 wrote:

                                      > ----- Original Message -----
                                      > From: "Bruno Marchal" <marchal@...>
                                      > To: <Fabric-of-Reality@yahoogroups.com>
                                      > Sent: Sunday, January 08, 2012 12:06 AM
                                      > Subject: Re: Abstract mathematical development versus particle
                                      > physics analysis
                                      >
                                      > BRUNO:
                                      >
                                      > >> The "correct" physical laws/theories are anything relating
                                      > "correctly"
                                      > >> the observation I can do.
                                      >
                                      > GICH:
                                      >
                                      > > Such theories don't exist!
                                      >

                                      With comp physics is, to be short, reduced to an weighting on paths
                                      between computational states (relative numbers).
                                      The ultimately correct physics can indeed be proved to not exist with
                                      respect to some relation with *your* (plural, singular) substitution
                                      level.





                                      >
                                      > As an example, take general relativity. It produces tremendous
                                      > agreement with
                                      > most of our observations concerning the universe but it breaks down
                                      > in the
                                      > regions of black-holes. And quantum theory is full of theoretical
                                      > (mathematical)
                                      > holes. Etc.
                                      >
                                      > And my original statement still hold, "pure mathematics does *not*
                                      > have to have
                                      > anything to do with 'the real world'."
                                      >

                                      For a rational computationalist "pure mathematics" is the real world.
                                      Pure arithmetic is enough.

                                      Physics and analysis are reduced to number's tool to understand
                                      themselves.

                                      Assuming comp (and assuming there is no flaw in the argument, if you
                                      want).

                                      The world "real" is tricky. For a computationalist (grasping UDA) what
                                      is real and concrete are the numbers, and their laws. The concreteness
                                      of of our physical neighborhood is experienced as real, but is a
                                      construct of the mind (again relative number, with comp).

                                      I do not assume a physical reality. I assume only a tiny (compared to
                                      set theory) part of the arithmetical reality (and the intuitive truth
                                      at the meta-level, like all mathematicians and physicists). Like you,
                                      I see below. (And I think Peter too perhaps).




                                      >
                                      > **************************
                                      > Note Peter's comment elsewhere in this thread.
                                      >
                                      > BRUNO (to Gich):
                                      >
                                      > >> I totally agree with you on this. That makes my point: N
                                      > >> exists. It is part of reality.
                                      >
                                      > Peter D:
                                      >
                                      > > Not part of mine. I've never seen the set of positive integers.
                                      > **************************
                                      >
                                      > I agree with Peter.
                                      > It seems to me that N exists *outside* of human reality.
                                      >

                                      Not sure. Peter might say that N does not exist *anywhere*, but in the
                                      mind of the humans. It is a playword, for comp, because comp assumes
                                      only (besides "yes doctor") the elementary classical arithmetic. We
                                      apply the excluded middle principle for arithmetic and programs. It is
                                      basically based on the famous sharable part of classical and
                                      intuitionist mathematics.




                                      > If there had never been
                                      > a planet Earth, if the human race had never existed, N would still
                                      > exist.
                                      >
                                      I can't agree more with you.




                                      >
                                      > -----------------------
                                      > [ Roger Scruton, Modern Philosophy -- An Introduction and Survey ]
                                      > . . . Numbers especially are the source of much philosophy, as we
                                      > have already
                                      > seen in discussing Russell. They are 'objects' in Frege's sense:
                                      > that is, we
                                      > give them names, and strive to discover the truth about them. Yet it
                                      > is absurd
                                      > to say that they exist in space and time: as though there were some
                                      > place where
                                      > the number nine could at last be encountered. . . .
                                      > . . . numbers cannot be known through the senses, but only through
                                      > thought.
                                      >
                                      >
                                      I agree with all this.



                                      > Moreover, they do not act on anything, so as to produce results.
                                      > They are 'powerless' in the natural world, and leave no trace
                                      > there. . . .
                                      >

                                      I don't assume a natural world. I assume only natural numbers. N.

                                      "natural worlds" are deep, persistent number games exploiting the many
                                      ways universal numbers, notably, get acquainted with themselves,
                                      taking into account consciousness, first person, supervene on
                                      infinities of them.

                                      I don't pretend this to be true, but I do pretend this follows from
                                      the mechanist assumption in the "cognitive science/theology".

                                      I think this gives also a more economical theory of everything.
                                      Elementary arithmetic.

                                      It contains universal dreamers, and there are arithmetical (albeit
                                      intensional, relative) reasons why multi-user dreams appears in deep
                                      (in Bennett sense) and thus *long*, computations, making necessary
                                      sharable first person plural realities (the physical worlds).

                                      And thanks to Gödel 1931, we can separate what the machine can prove
                                      from what she can hope and search. It is a big quasi living quasi
                                      explosive (the logicians say "productive") gap. Universal machines
                                      have rich 'theologies' (the science of machine's truth).

                                      Universal numbers, by themselves, only per the laws of addition and
                                      multiplication, develop many-worlds interpretations of the number
                                      reality. With comp, if the SWE is correct, it should be an invariant
                                      among all first person universal (number) view.

                                      Bruno

                                      >

                                      http://iridia.ulb.ac.be/~marchal/





                                      [Non-text portions of this message have been removed]
                                    • Bruno Marchal
                                      ... No. The laws here are explicable, but they are not really effective. To get person you have to program help yourself , and wait a long time. Or to copy PA
                                      Message 18 of 28 , Jan 8, 2012
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                                        On 08 Jan 2012, at 01:40, brhalluk@... wrote:

                                        >
                                        > > >
                                        > > > Assuming that it is possible to program a person (and therefore
                                        > > > consciousness just arises at some emergent level) then in the
                                        > future
                                        > > > we'll presumably be able to create virtual worlds that contain
                                        > people.
                                        > > >
                                        > > OK. I don't think we can program person, but we might be unable to
                                        > > enslave universal machine a long time enough, and virtual person
                                        > might
                                        > > develop in virtual realities, yes.
                                        >
                                        > So your thinking is that whatever the laws are that give rise to
                                        > people (or is it consciousness generally) these are inexplicable?
                                        > Why is that?
                                        >

                                        No. The laws here are explicable, but they are not really effective.
                                        To get person you have to program "help yourself", and wait a long
                                        time. Or to copy PA + set of beliefs, and, wait for a long time. Or a
                                        swarm of such machines, and wait for a long time.
                                        It is something we can generate only by letting place to a big freedom
                                        on a big exploration space. Consciousness might play a role of self-
                                        acceleration.




                                        >
                                        > >
                                        > >
                                        > >
                                        > >
                                        > > >
                                        > > > Two somewhat unrelated questions:
                                        > > >
                                        > > > Firstly, would this mean that the discoveries simulated people
                                        > make
                                        > > > is inherently bounded?
                                        > > >
                                        > > Not necessarily. But you will have to provide memories regularly to
                                        > > maintain the simulation. If they decide to search for the Higs
                                        > boson,
                                        > > and build a LAC, you might add some terrabits, and more, on the
                                        > "hard
                                        > > disk".
                                        > >
                                        > >
                                        > >
                                        > >
                                        > >
                                        > > > Is it possible - given that they are simulated people - that they
                                        > > > would be able to discover our world - the one in which the
                                        > computer
                                        > > > on which they are being simulated - is running?
                                        > > >
                                        > > This is delicate to answer. Those person, as seen by you, will
                                        > > discover soon or later that they are in a simulation, unless you
                                        > > observe them, and trick them deliberately, which will ask for a more
                                        > > and more complex work. But from their own first person perspective,
                                        > > such a tricked simulation will get a lower and lower measure, so
                                        > that,
                                        > > assuming their are immortal, they will end up, from their own
                                        > point of
                                        > > view "in reality", statistically. Your own universe where you trick
                                        > > them will become like an harry Potter universe from their
                                        > statistical
                                        > > point of view (and your tricky job will be an exploding job: at some
                                        > > point you will have to simulate the whole multiverse!).
                                        >
                                        > Yes, I understand. You are answering "yes". If you are not observing
                                        > them and upgrading the memory of the hardware eventually they will
                                        > discover they are in a simulation.
                                        >
                                        > As a side point, does this make ideas like "The Matrix" testable?
                                        > FoR does mention the failings of solipsism, but as you say above if
                                        > such a metaphysical idea leads to consequence that any simulation
                                        > would have to be a simulation of the entire multiverse eventually in
                                        > order to keep the wool pulled over our eyes, then there's no sense
                                        > in which one universe is more real than another, is there? Both
                                        > embody the same laws and relationships.
                                        >
                                        Is QM testable? yes. Comp shows "the matrix" is testable, and that QM
                                        might be the reflect of the digital seen by itself.



                                        >
                                        > Of course - what *if* the simulated people begin making discoveries
                                        > *faster* than are made in the real world? What if the simulated
                                        > world is more conducive to enlightenments than our world? You
                                        > wouldn't be able to keep up with anticipating what they would do
                                        > next and eventually they'd demonstrate the finiteness of their world
                                        > faster than you could trick them into believing it was reality.
                                        >
                                        They will know that they are virtually elsewhere, but they might still
                                        ask you to make it possible to share your reality with you.



                                        >
                                        > >
                                        > >
                                        > >
                                        > >
                                        > >
                                        > > > I think DD makes the point in FoR that simulated people *would*
                                        > > > eventually discover they are simulated and that there was an
                                        > > > external reality. Indeed according to BoI this *must* be the
                                        > case if
                                        > > > they are universal explainers.
                                        > > >
                                        > > Except the existence of an external global physical reality is an
                                        > open
                                        > > problem, with comp. And also, it might be that the quantum
                                        > phenomenon
                                        > > is already an evidence that we belong to infinities of simulations.
                                        > > But our physics should emerge from this. That should be clear
                                        > already
                                        > > with UDA-step-7.
                                        > >
                                        > >
                                        > >
                                        > >
                                        > > >
                                        > > > Secondly - and this is probably mainly for Bruno - it is obvious
                                        > to
                                        > > > us who have written the program describing the virtual world and
                                        > its
                                        > > > people - that what they (they virtual people) are discovering is
                                        > not
                                        > > > `real' matter when they do explain their world using terms like
                                        > > > "matter".
                                        > > >
                                        > > This will happen if you stop to trick them purposefully.
                                        >
                                        > Yes, agreed. And I tend to this this ability to continue tricking
                                        > them is probably not possible. Tricking someone amounts to
                                        > predicting their behaviour perfectly. That can't go on indefinitely
                                        > as it assumes your own omniscience, doesn't it?
                                        >
                                        Yes it is the error of all dictator sand prohibitionist doctrines.





                                        >
                                        > >
                                        > >
                                        > >
                                        > >
                                        > > > There is no matter in the virtual world. We know this from our
                                        > > > privileged position - but they cannot as they are trapped in the
                                        > > > simulation. We can see the difference between the stuff in our
                                        > world
                                        > > > (which is real) and the stuff in their world (which is just
                                        > virtual
                                        > > > matter - a consequence of the knowledge we have instantiated in
                                        > the
                                        > > > program).
                                        > > >
                                        > > We don't know if our stuff is real. If comp is correct, it real with
                                        > > respect to observation, but it is not primitive. The simulated
                                        > people
                                        > > can make UDA themselves, extract the laws of physics from comp, and
                                        > > compare their observation with that physics, and extract information
                                        > > about they "layers" of simulation.
                                        >
                                        > Yes, fair enough. I don't like 'real' though - I'm not sure why we
                                        > use that word. Physical or abstract, both are 'real' aren't they?
                                        >
                                        Hmm... Physical can be opposed to non physical. Non physical can be
                                        concrete, like a pain could be an example (assuming comp). And
                                        physical can be an abstract, or concrete, arithmetical situation.

                                        It is not so much a question of reality than a question of what we
                                        take as real and primitive. With comp we have to take elementary
                                        arithmetic seriously, and derived the physical laws as sort of "well
                                        founded collective number's hallucination".




                                        > In the sense described by Deutsch: they figure in our best
                                        > explanations of reality. That aside, what words then could we use to
                                        > distinguish between electrons in our world and electrons in a
                                        > simulated world? If ours are real and ultimately abstract, so too
                                        > are the simulated ones. But we *know* there's a difference, isn't
                                        > there?
                                        >

                                        Yes. The 'real one', when you look close to them, you get the trace of
                                        the many dreams. The emulated one, you get stable pixellisation only.
                                        If you want the real one have a deep number theoretical origin, when
                                        the emulated one are truncated at some level.




                                        >
                                        > >
                                        > >
                                        > >
                                        > > >
                                        > > > For example in our world two electrons repel each other because
                                        > > > there really exist electrons that really do exert a repulsive
                                        > force
                                        > > > upon one another (by exchanging real photons, or whatever). This
                                        > is
                                        > > > realism.
                                        > > >
                                        > > It is physical realism, and some amount of it is consistent with
                                        > comp,
                                        > > but basically physics comes from pure number theoretical relations
                                        > (or
                                        > > based on some other universal frame: I use numbers because they are
                                        > > more well known).
                                        >
                                        > Is it? Doesn't realism allow for the existence of abstractions?
                                        >
                                        Physical realism? Primitive physical realism (physicalism/weak
                                        materialism) is inconsistent with mechanism (UDA).



                                        > In fact, doesn't it demand it? I'm not saying that *only* the
                                        > physical exists -
                                        >

                                        With comp any physical reality is embarrasing. It is like an invisible
                                        horse. We can't use it to singularize consciousness in arithmetic.




                                        > this would be called 'physical realism' wouldn't it?
                                        >

                                        Would be more physical reductionism. I take physical realism as "a
                                        physical reality exist" or "physical reality exist ontologically".
                                        With comp I think that "physical reality exist ontologically" is non
                                        sensical. But comp can still have "a physical reality exist". But that
                                        physical reality is machine phenomenological. Physics become a branch
                                        of computer/infomation/theology science, itself branch of number theory.



                                        > In fact I'd probably call it something else. Physical realism in
                                        > this sense wouldn't be David Deutsch's position from what I gather
                                        > in FoR and BoI, it's not mine either. Both the abstract and the
                                        > physical are real - I call such a point of view 'realism'.
                                        >

                                        Both are real, but which one is the more fundamental?

                                        I think it is more easy to explain the illusion of matter to something
                                        conscious than to explain the illusion of consciousness to something
                                        material.



                                        >
                                        > >
                                        > >
                                        > > >
                                        > > > In the virtual world the virtual people explain their observations
                                        > > > about the repulsion of `electrons' in the same way. At least for a
                                        > > > while, realism works. But *we* know, looking on from the outside,
                                        > > > that they are mistaken for there are no actual electrons or forces
                                        > > > or photons at all. In fact it is just bits of information -
                                        > numbers
                                        > > > actually - doing this or that entirely abstractly. So we can see
                                        > > > that their realism is false - everything they take to be
                                        > physical is
                                        > > > actually abstract. The only physical thing is the hardware on
                                        > which
                                        > > > the computer runs and they cannot discover this. Their correct
                                        > > > philosophy *should be* mechanism as you describe.
                                        > > >
                                        > > Yes. But they can extract the physics from that, and then compare
                                        > with
                                        > > the observations.
                                        >
                                        > I think I understand.
                                        >

                                        OK.


                                        > >
                                        > >
                                        > >
                                        > > > Namely - they are *obviously* machines who have *invented* the
                                        > real
                                        > > > world (from our perspective).
                                        > > >
                                        > > But they have a different perspective, and "belongs" to infinities
                                        > of
                                        > > computations like us. The trick to confuse them will have a quickly
                                        > > growing price.
                                        >
                                        > Agreed! And ultimately a price that is impossible to pay.
                                        >

                                        Yes.



                                        >
                                        > >
                                        > >
                                        > >
                                        > >
                                        > > > From our perspective, the ultimate explanation of their world is
                                        > > > some instantiation of arithmetic (a program running on a
                                        > computer).
                                        > > >
                                        > > > Is this correct?
                                        > > >
                                        > > Not if you install democracy and free-thinking. Either you don't
                                        > trick
                                        > > them enough, and they will discover "our worlds", or you trick them
                                        > > well enough, and from their perspective they will be in a world as
                                        > > real as yours, statistically. Note that I use the first person
                                        > > indeterminacy all the time!
                                        >
                                        > Yes, agreed. I think I now have a better appreciation of your
                                        > position. I have read your original paper (many years ago) and the
                                        > SANE talk (recently), but much has escaped me. This clears up a lot.
                                        >
                                        Nice.



                                        >
                                        > >
                                        > >
                                        > >
                                        > >
                                        > > >
                                        > > > Bruno, would you say that *if* your hypothesis is true *then* our
                                        > > > world is precisely as the virtual world I have described above
                                        > only
                                        > > > there's no programmer and there's no inherent limitation to what
                                        > can
                                        > > > be discovered?
                                        > > >
                                        > > Not really. The physical worlds is not emulable, normally. Its
                                        > 'shape"
                                        > > comes from the fact that below our substitution level, we are in
                                        > > infinities of computations at once.
                                        >
                                        > I get that. David Deutsch uses the word "fungible" - you do not. Is
                                        > there a reason?
                                        >
                                        Since Deutsch coin the terms, I have use it. I use often the idea that
                                        Y = II, that is a bifurcation (Y) doubles the weight on the past. It
                                        creates fundigible pasts. But the term is hard to define formally, so
                                        I am cautious. The identity relations differ for each points of view.




                                        > I know that ultimately the multiverse interpretation - and your own
                                        > - are different at the level of metaphysical reality but much
                                        > remains the same (identical, even?).
                                        >
                                        I think they should be identical. QM is quite solid, and smells number
                                        theory a lot. And then the comp-physics extracted from self-reference
                                        smells also already the quantum, and it would be nice that QM survives
                                        comp. But with the current knowledge it is an open problem.
                                        The metaphysical nuances are not negligible. I think we might differ
                                        on immortality and other theological point. Not sure if David is aware
                                        that comp makes it *obligatory* to derive QM (or its "correction"),
                                        from universal machine self-reference/number theory.




                                        > There are many fungible copies of me in the multiverse which *I* am.
                                        > In your model, these infinities of computations are the object to
                                        > which *I* refers - while they are identical in all respects then
                                        > aren't they fungible in the multiverse sense?
                                        >
                                        I would say so. OK.




                                        >
                                        > >
                                        > >
                                        > >
                                        > > >
                                        > > > In other words under digital mechanism, our world is a virtual
                                        > > > world, only there's no programmer?
                                        > > >
                                        > >
                                        > > It is more complex. Our world is a sum on infinities of simulations.
                                        > > It is an open problem to decide if that sum is emulable or not. Its
                                        > > geography is typically not emulable in the detail, like we cannot
                                        > > emulate classically some quantum processes (without duplicating the
                                        > > parallel observers).
                                        > >
                                        > > Many get this wrong, but a priori, if WE are machines, the rest is
                                        > > not. Neither matter nor consciousness. If you study the UDA, this
                                        > > should not be too difficult to understand. I think.
                                        >
                                        > !!
                                        > I think it might be!
                                        >
                                        But you can ask any question. Elliot was OK with the first six points
                                        of UDA, are you?
                                        The reversal appears already at the seventh, and I am waiting for
                                        Elliot's reply.



                                        >
                                        > > It means we have
                                        > > to extend Everett phenomenology to arithmetic and derive the wave
                                        > > itself from machine's self-reference. Advantage: we can use
                                        > > incompleteness-like phenomena to justify the quanta/qualia
                                        > difference.
                                        >
                                        > Thanks again,
                                        >
                                        You are welcome,

                                        Bruno.


                                        >
                                        >

                                        http://iridia.ulb.ac.be/~marchal/





                                        [Non-text portions of this message have been removed]
                                      • Bruno Marchal
                                        ... For a platonist, reality is not necessarily WYSIWYG. (What you see is what you get). We cannot decide ontology by observation. It is enough to remember
                                        Message 19 of 28 , Jan 8, 2012
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                                          On 07 Jan 2012, at 23:10, Peter D wrote:

                                          >
                                          >
                                          > --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal
                                          > <marchal@...> wrote:
                                          > >
                                          > >
                                          >
                                          > > I totally agree with you on this. That makes my point: N exists.
                                          > It is
                                          > > part of reality.
                                          >
                                          > Not part of mine. I've never seen the set of positive integers.
                                          >

                                          For a platonist, reality is not necessarily WYSIWYG. (What you see
                                          is what you get).

                                          We cannot decide ontology by observation. It is enough to remember
                                          dream to guess that.
                                          Conscious observation proves only the existence of consciousness, not
                                          of what is observed.

                                          And then arithmetic contains a web of universal dreamers. UDA suggests
                                          that physics has to be redefined by some self-referential quotient of
                                          that web, so that we can compare the universal physics of the
                                          universal machine with ours, leading to a technology capable of
                                          measuring our possible non null degree of non-computationalism. In
                                          case comp is false. The point is technical, as computer science makes
                                          it possible with the comp hypothesis.

                                          Bruno

                                          http://iridia.ulb.ac.be/~marchal/





                                          [Non-text portions of this message have been removed]
                                        • Peter D
                                          ... Then your assumptions are COMP and Platonism, not just comp. Non-Platonist computationalists can resist your conclusions.
                                          Message 20 of 28 , Jan 8, 2012
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                                            --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal <marchal@...> wrote:
                                            >
                                            >
                                            > On 07 Jan 2012, at 23:10, Peter D wrote:
                                            >
                                            > >
                                            > >
                                            > > --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal
                                            > > <marchal@> wrote:
                                            > > >
                                            > > >
                                            > >
                                            > > > I totally agree with you on this. That makes my point: N exists.
                                            > > It is
                                            > > > part of reality.
                                            > >
                                            > > Not part of mine. I've never seen the set of positive integers.
                                            > >
                                            >
                                            > For a platonist, reality is not necessarily WYSIWYG. (What you see
                                            > is what you get).



                                            Then your assumptions are COMP and Platonism, not just comp.
                                            Non-Platonist computationalists can resist your conclusions.
                                          • Bruno Marchal
                                            ... COMP is not even defined without arithmetical platonism. If you can define to me a version of comp which is not platonist, then give it to me. I recall
                                            Message 21 of 28 , Jan 9, 2012
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                                              On 09 Jan 2012, at 05:44, Peter D wrote:

                                              >
                                              >
                                              > --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal
                                              > <marchal@...> wrote:
                                              > >
                                              > >
                                              > > On 07 Jan 2012, at 23:10, Peter D wrote:
                                              > >
                                              > > >
                                              > > >
                                              > > > --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal
                                              > > > <marchal@> wrote:
                                              > > > >
                                              > > > >
                                              > > >
                                              > > > > I totally agree with you on this. That makes my point: N exists.
                                              > > > It is
                                              > > > > part of reality.
                                              > > >
                                              > > > Not part of mine. I've never seen the set of positive integers.
                                              > > >
                                              > >
                                              > > For a platonist, reality is not necessarily WYSIWYG. (What you see
                                              > > is what you get).
                                              >
                                              > Then your assumptions are COMP and Platonism, not just comp.
                                              > Non-Platonist computationalists can resist your conclusions.
                                              >

                                              COMP is not even defined without arithmetical platonism. If you can
                                              define to me a version of comp which is not platonist, then give it to
                                              me.
                                              I recall that by platonism I mean the belief that the arithmetical
                                              propositions, or closed sentences, are either true or false.
                                              Technically this can be weaken into an intuitionist Church thesis. We
                                              need only the idea that for all i, and j, phi_i(j) is either defined
                                              or not defined, with phi_i(j) denoting the possibly existing, or not,
                                              output of the ith Turing machine applied on j.

                                              The "platonism" used in the definition of comp is much weaker than the
                                              platonist conception of reality which follows, by UDA, from the comp
                                              assumption. They should not be confused.

                                              Bruno


                                              >
                                              >

                                              http://iridia.ulb.ac.be/~marchal/





                                              [Non-text portions of this message have been removed]
                                            • Peter D
                                              ... Yes it is. ... In philosophy, the computational theory of mind is the view that the human mind is an information processing system and that thinking is a
                                              Message 22 of 28 , Jan 11, 2012
                                              • 0 Attachment
                                                --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal <marchal@...> wrote:
                                                >
                                                >
                                                > On 09 Jan 2012, at 05:44, Peter D wrote:
                                                >
                                                > >
                                                > >
                                                > > --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal
                                                > > <marchal@> wrote:
                                                > > >
                                                > > >
                                                > > > On 07 Jan 2012, at 23:10, Peter D wrote:
                                                > > >
                                                > > > >
                                                > > > >
                                                > > > > --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal
                                                > > > > <marchal@> wrote:
                                                > > > > >
                                                > > > > >
                                                > > > >
                                                > > > > > I totally agree with you on this. That makes my point: N exists.
                                                > > > > It is
                                                > > > > > part of reality.
                                                > > > >
                                                > > > > Not part of mine. I've never seen the set of positive integers.
                                                > > > >
                                                > > >
                                                > > > For a platonist, reality is not necessarily WYSIWYG. (What you see
                                                > > > is what you get).
                                                > >
                                                > > Then your assumptions are COMP and Platonism, not just comp.
                                                > > Non-Platonist computationalists can resist your conclusions.
                                                > >
                                                >
                                                > COMP is not even defined without arithmetical platonism.

                                                Yes it is.

                                                >If you can
                                                > define to me a version of comp which is not platonist, then give it to
                                                > me.

                                                "In philosophy, the computational theory of mind is the view that the human mind is an information processing system and that thinking is a form of computing. "

                                                > I recall that by platonism I mean the belief that the arithmetical
                                                > propositions, or closed sentences, are either true or false.


                                                That isn't what Platonism means, that is what bivalence means.

                                                > Technically this can be weaken into an intuitionist Church thesis. We
                                                > need only the idea that for all i, and j, phi_i(j) is either defined
                                                > or not defined, with phi_i(j) denoting the possibly existing, or not,
                                                > output of the ith Turing machine applied on j.
                                                >
                                                > The "platonism" used in the definition of comp is much weaker than the
                                                > platonist conception of reality which follows, by UDA, from the comp
                                                > assumption. They should not be confused.
                                                >
                                                > Bruno
                                                >


                                                There can be no UDA without a UD. There is no physical UD. So
                                                strong Platonism is required to supply a non-physical UD.

                                                > >
                                                > >
                                                >
                                                > http://iridia.ulb.ac.be/~marchal/
                                                >
                                                >
                                                >
                                                >
                                                >
                                                > [Non-text portions of this message have been removed]
                                                >
                                              • Bruno Marchal
                                                ... Show it. I doubt you could because you will need the notion of computable functions from N to N. You will need the idea that a program stop or does not
                                                Message 23 of 28 , Jan 13, 2012
                                                • 0 Attachment
                                                  On 11 Jan 2012, at 15:42, Peter D wrote:

                                                  >
                                                  >
                                                  > --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal
                                                  > <marchal@...> wrote:
                                                  > >
                                                  > >
                                                  > > On 09 Jan 2012, at 05:44, Peter D wrote:
                                                  > >
                                                  > > >
                                                  > > >
                                                  > > > --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal
                                                  > > > <marchal@> wrote:
                                                  > > > >
                                                  > > > >
                                                  > > > > On 07 Jan 2012, at 23:10, Peter D wrote:
                                                  > > > >
                                                  > > > > >
                                                  > > > > >
                                                  > > > > > --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal
                                                  > > > > > <marchal@> wrote:
                                                  > > > > > >
                                                  > > > > > >
                                                  > > > > >
                                                  > > > > > > I totally agree with you on this. That makes my point: N
                                                  > exists.
                                                  > > > > > It is
                                                  > > > > > > part of reality.
                                                  > > > > >
                                                  > > > > > Not part of mine. I've never seen the set of positive
                                                  > integers.
                                                  > > > > >
                                                  > > > >
                                                  > > > > For a platonist, reality is not necessarily WYSIWYG. (What you
                                                  > see
                                                  > > > > is what you get).
                                                  > > >
                                                  > > > Then your assumptions are COMP and Platonism, not just comp.
                                                  > > > Non-Platonist computationalists can resist your conclusions.
                                                  > > >
                                                  > >
                                                  > > COMP is not even defined without arithmetical platonism.
                                                  >
                                                  > Yes it is.
                                                  >
                                                  Show it.
                                                  I doubt you could because you will need the notion of computable
                                                  functions from N to N. You will need the idea that a program stop or
                                                  does not stop to explain CT and the closure of the set of partial
                                                  computable function for diagonalization.



                                                  >
                                                  > >If you can
                                                  > > define to me a version of comp which is not platonist, then give
                                                  > it to
                                                  > > me.
                                                  >
                                                  > "In philosophy, the computational theory of mind is the view that
                                                  > the human mind is an information processing system and that thinking
                                                  > is a form of computing. "
                                                  >
                                                  Define "computing" without arithmetical realism.



                                                  >
                                                  > > I recall that by platonism I mean the belief that the arithmetical
                                                  > > propositions, or closed sentences, are either true or false.
                                                  >
                                                  > That isn't what Platonism means, that is what bivalence means.
                                                  >
                                                  I agree, and that is why I do not use the term "platonism", which can
                                                  be also confused with the Platonist (in a deeper sense) consequence of
                                                  comp, where arithmetical realism is used instead. You are the one
                                                  using systematically Platonism for arithmetical realism (and indeed
                                                  mathematician called it arithmetical platonism, but it is only
                                                  bivalence of arithmetical truth).
                                                  Comp is "yes doctor + Church thesis", and Church thesis is the
                                                  classical CT which makes sense through some amount of bivalence of
                                                  some arithmetical truth. Comp, as I used the term, is the weakest form
                                                  of comp in the literature.


                                                  >
                                                  > > Technically this can be weaken into an intuitionist Church thesis.
                                                  > We
                                                  > > need only the idea that for all i, and j, phi_i(j) is either defined
                                                  > > or not defined, with phi_i(j) denoting the possibly existing, or
                                                  > not,
                                                  > > output of the ith Turing machine applied on j.
                                                  > >
                                                  > > The "platonism" used in the definition of comp is much weaker than
                                                  > the
                                                  > > platonist conception of reality which follows, by UDA, from the comp
                                                  > > assumption. They should not be confused.
                                                  > >
                                                  > > Bruno
                                                  > >
                                                  >
                                                  > There can be no UDA without a UD. There is no physical UD. So
                                                  > strong Platonism is required to supply a non-physical UD.
                                                  >
                                                  Which exist in the same sense that prime number exist. In the comp
                                                  ontology, existence is very well defined. It is defined through the
                                                  truth of existential sentences, with the shape "ExP(x)", and that is
                                                  true if there exist a natural number n such that it is the case that
                                                  P(n). The UD exists in that precise sense, and we don't need any other
                                                  form of existence to explain the "persistent illusion" of material/
                                                  physical realms.

                                                  UDA1-7 shows that physics is a branch of computer science/number
                                                  theory in case a concrete UD exist. Do you agree so far? Then the
                                                  movie graph argument, or even just some strong occam razor, explains
                                                  why the existence of a concrete UD is not necessary to get the
                                                  reversal. That's step UDA-8. It is a constructive proof that physics
                                                  emerges from number theory, both ontologically and epistemologically.
                                                  Then AUDA illustrates what machines/numbers, relatively to universal
                                                  numbers can say about that comp-physics. The point is technical: it
                                                  shows that comp empirically is refutable, but it shows also that QM-
                                                  without-collapse confirmed it, in its most weird aspect. Numbers
                                                  develop "naturally" a persistent many-worlds interpretation of number
                                                  truth. The coupling consciousness/reality is emerging from addition
                                                  and multiplication in a verifiable way.

                                                  Bruno

                                                  http://iridia.ulb.ac.be/~marchal/





                                                  [Non-text portions of this message have been removed]
                                                • Peter D
                                                  ... Which is bivalence, not Platonism, properly so called. ... Again, you mean bivalence, which is just another formal rule for me. ... Bivalence doens t get
                                                  Message 24 of 28 , Jan 13, 2012
                                                  • 0 Attachment
                                                    --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal <marchal@...> wrote:
                                                    >
                                                    >
                                                    > On 11 Jan 2012, at 15:42, Peter D wrote:
                                                    >
                                                    > >
                                                    > >
                                                    > > --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal
                                                    > > <marchal@> wrote:
                                                    > > >
                                                    > > >
                                                    > > > On 09 Jan 2012, at 05:44, Peter D wrote:
                                                    > > >
                                                    > > > >
                                                    > > > >
                                                    > > > > --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal
                                                    > > > > <marchal@> wrote:
                                                    > > > > >
                                                    > > > > >
                                                    > > > > > On 07 Jan 2012, at 23:10, Peter D wrote:
                                                    > > > > >
                                                    > > > > > >
                                                    > > > > > >
                                                    > > > > > > --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal
                                                    > > > > > > <marchal@> wrote:
                                                    > > > > > > >
                                                    > > > > > > >
                                                    > > > > > >
                                                    > > > > > > > I totally agree with you on this. That makes my point: N
                                                    > > exists.
                                                    > > > > > > It is
                                                    > > > > > > > part of reality.
                                                    > > > > > >
                                                    > > > > > > Not part of mine. I've never seen the set of positive
                                                    > > integers.
                                                    > > > > > >
                                                    > > > > >
                                                    > > > > > For a platonist, reality is not necessarily WYSIWYG. (What you
                                                    > > see
                                                    > > > > > is what you get).
                                                    > > > >
                                                    > > > > Then your assumptions are COMP and Platonism, not just comp.
                                                    > > > > Non-Platonist computationalists can resist your conclusions.
                                                    > > > >
                                                    > > >
                                                    > > > COMP is not even defined without arithmetical platonism.
                                                    > >
                                                    > > Yes it is.
                                                    > >
                                                    > Show it.
                                                    > I doubt you could because you will need the notion of computable
                                                    > functions from N to N. You will need the idea that a program stop or
                                                    > does not stop to explain CT and the closure of the set of partial
                                                    > computable function for diagonalization.

                                                    Which is bivalence, not Platonism, properly so called.

                                                    > > >If you can
                                                    > > > define to me a version of comp which is not platonist, then give
                                                    > > it to
                                                    > > > me.
                                                    > >
                                                    > > "In philosophy, the computational theory of mind is the view that
                                                    > > the human mind is an information processing system and that thinking
                                                    > > is a form of computing. "
                                                    > >
                                                    > Define "computing" without arithmetical realism.


                                                    Again, you mean bivalence, which is just another
                                                    formal rule for me.

                                                    > >
                                                    > > > I recall that by platonism I mean the belief that the arithmetical
                                                    > > > propositions, or closed sentences, are either true or false.
                                                    > >
                                                    > > That isn't what Platonism means, that is what bivalence means.
                                                    > >
                                                    > I agree, and that is why I do not use the term "platonism", which can
                                                    > be also confused with the Platonist (in a deeper sense) consequence of
                                                    > comp, where arithmetical realism is used instead. You are the one
                                                    > using systematically Platonism for arithmetical realism (and indeed
                                                    > mathematician called it arithmetical platonism, but it is only
                                                    > bivalence of arithmetical truth).
                                                    > Comp is "yes doctor + Church thesis", and Church thesis is the
                                                    > classical CT which makes sense through some amount of bivalence of
                                                    > some arithmetical truth. Comp, as I used the term, is the weakest form
                                                    > of comp in the literature.
                                                    >


                                                    Bivalence doens't get you an existing UD. Without
                                                    that, the argument doens;;t work.

                                                    > > > Technically this can be weaken into an intuitionist Church thesis.
                                                    > > We
                                                    > > > need only the idea that for all i, and j, phi_i(j) is either defined
                                                    > > > or not defined, with phi_i(j) denoting the possibly existing, or
                                                    > > not,
                                                    > > > output of the ith Turing machine applied on j.
                                                    > > >
                                                    > > > The "platonism" used in the definition of comp is much weaker than
                                                    > > the
                                                    > > > platonist conception of reality which follows, by UDA, from the comp
                                                    > > > assumption. They should not be confused.
                                                    > > >
                                                    > > > Bruno
                                                    > > >
                                                    > >
                                                    > > There can be no UDA without a UD. There is no physical UD. So
                                                    > > strong Platonism is required to supply a non-physical UD.
                                                    > >
                                                    > Which exist in the same sense that prime number exist.

                                                    Which is not at all as far as I am concerned. Although
                                                    doesn't stop playing the bivalence game.

                                                    > In the comp
                                                    > ontology, existence is very well defined.

                                                    It's not ontology it's pseudo ontology. Ontology
                                                    is about what really exists. Maths, and therefore
                                                    comp, is game playing. It just supposes
                                                    that various abstract objects "exist" and
                                                    explores the consequences. However, I am not
                                                    someone's supposition or formal game. So I
                                                    am not running on a hypothetical UD. The UD
                                                    is an idea in my head: I am realler than it is.

                                                    > It is defined through the
                                                    > truth of existential sentences, with the shape "ExP(x)", and that is
                                                    > true if there exist a natural number n such that it is the case that
                                                    > P(n). The UD exists in that precise sense, and we don't need any other
                                                    > form of existence to explain the "persistent illusion" of material/
                                                    > physical realms.
                                                    >
                                                    > UDA1-7 shows that physics is a branch of computer science/number
                                                    > theory in case a concrete UD exist. Do you agree so far? Then the
                                                    > movie graph argument, or even just some strong occam razor, explains
                                                    > why the existence of a concrete UD is not necessary to get the
                                                    > reversal. That's step UDA-8. It is a constructive proof that physics
                                                    > emerges from number theory, both ontologically and epistemologically.
                                                    > Then AUDA illustrates what machines/numbers, relatively to universal
                                                    > numbers can say about that comp-physics. The point is technical: it
                                                    > shows that comp empirically is refutable, but it shows also that QM-
                                                    > without-collapse confirmed it, in its most weird aspect. Numbers
                                                    > develop "naturally" a persistent many-worlds interpretation of number
                                                    > truth. The coupling consciousness/reality is emerging from addition
                                                    > and multiplication in a verifiable way.
                                                    >
                                                    > Bruno
                                                    >
                                                    > http://iridia.ulb.ac.be/~marchal/
                                                    >
                                                    >
                                                    >
                                                    >
                                                    >
                                                    > [Non-text portions of this message have been removed]
                                                    >
                                                  • Bruno Marchal
                                                    ... I repeat, you are the one using the term platonism , and I have explained why this is confusing. ... You are confusing a theory and its interpretation. Do
                                                    Message 25 of 28 , Jan 16, 2012
                                                    • 0 Attachment
                                                      On 14 Jan 2012, at 03:18, Peter D wrote:

                                                      >
                                                      >
                                                      > --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal
                                                      > <marchal@...> wrote:
                                                      > >
                                                      > >
                                                      > > On 11 Jan 2012, at 15:42, Peter D wrote:
                                                      > >
                                                      > > >
                                                      > > >
                                                      > > > --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal
                                                      > > > <marchal@> wrote:
                                                      > > > >
                                                      > > > >
                                                      > > > > On 09 Jan 2012, at 05:44, Peter D wrote:
                                                      > > > >
                                                      > > > > >
                                                      > > > > >
                                                      > > > > > --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal
                                                      > > > > > <marchal@> wrote:
                                                      > > > > > >
                                                      > > > > > >
                                                      > > > > > > On 07 Jan 2012, at 23:10, Peter D wrote:
                                                      > > > > > >
                                                      > > > > > > >
                                                      > > > > > > >
                                                      > > > > > > > --- In Fabric-of-Reality@yahoogroups.com, Bruno Marchal
                                                      > > > > > > > <marchal@> wrote:
                                                      > > > > > > > >
                                                      > > > > > > > >
                                                      > > > > > > >
                                                      > > > > > > > > I totally agree with you on this. That makes my point: N
                                                      > > > exists.
                                                      > > > > > > > It is
                                                      > > > > > > > > part of reality.
                                                      > > > > > > >
                                                      > > > > > > > Not part of mine. I've never seen the set of positive
                                                      > > > integers.
                                                      > > > > > > >
                                                      > > > > > >
                                                      > > > > > > For a platonist, reality is not necessarily WYSIWYG. (What
                                                      > you
                                                      > > > see
                                                      > > > > > > is what you get).
                                                      > > > > >
                                                      > > > > > Then your assumptions are COMP and Platonism, not just comp.
                                                      > > > > > Non-Platonist computationalists can resist your conclusions.
                                                      > > > > >
                                                      > > > >
                                                      > > > > COMP is not even defined without arithmetical platonism.
                                                      > > >
                                                      > > > Yes it is.
                                                      > > >
                                                      > > Show it.
                                                      > > I doubt you could because you will need the notion of computable
                                                      > > functions from N to N. You will need the idea that a program stop or
                                                      > > does not stop to explain CT and the closure of the set of partial
                                                      > > computable function for diagonalization.
                                                      >
                                                      > Which is bivalence, not Platonism, properly so called.
                                                      >

                                                      I repeat, you are the one using the term "platonism", and I have
                                                      explained why this is confusing.



                                                      >
                                                      > > > >If you can
                                                      > > > > define to me a version of comp which is not platonist, then give
                                                      > > > it to
                                                      > > > > me.
                                                      > > >
                                                      > > > "In philosophy, the computational theory of mind is the view that
                                                      > > > the human mind is an information processing system and that
                                                      > thinking
                                                      > > > is a form of computing. "
                                                      > > >
                                                      > > Define "computing" without arithmetical realism.
                                                      >
                                                      > Again, you mean bivalence, which is just another
                                                      > formal rule for me.
                                                      >
                                                      You are confusing a theory and its interpretation. Do you accept
                                                      bivalence for the arithmetical proposition (not the sentences). If
                                                      not, then even Church-Turing thesis becomes meaningless. CT is not a
                                                      formalizable thesis. Yet it is a refutable scientific statement.




                                                      >
                                                      > > >
                                                      > > > > I recall that by platonism I mean the belief that the
                                                      > arithmetical
                                                      > > > > propositions, or closed sentences, are either true or false.
                                                      > > >
                                                      > > > That isn't what Platonism means, that is what bivalence means.
                                                      > > >
                                                      > > I agree, and that is why I do not use the term "platonism", which
                                                      > can
                                                      > > be also confused with the Platonist (in a deeper sense)
                                                      > consequence of
                                                      > > comp, where arithmetical realism is used instead. You are the one
                                                      > > using systematically Platonism for arithmetical realism (and indeed
                                                      > > mathematician called it arithmetical platonism, but it is only
                                                      > > bivalence of arithmetical truth).
                                                      > > Comp is "yes doctor + Church thesis", and Church thesis is the
                                                      > > classical CT which makes sense through some amount of bivalence of
                                                      > > some arithmetical truth. Comp, as I used the term, is the weakest
                                                      > form
                                                      > > of comp in the literature.
                                                      > >
                                                      >
                                                      > Bivalence doens't get you an existing UD. Without
                                                      > that, the argument doens;;t work.
                                                      >
                                                      I can prove the existence of the UD even without bivalence. The UDs
                                                      exist exactly like prime number exists.




                                                      >
                                                      > > > > Technically this can be weaken into an intuitionist Church
                                                      > thesis.
                                                      > > > We
                                                      > > > > need only the idea that for all i, and j, phi_i(j) is either
                                                      > defined
                                                      > > > > or not defined, with phi_i(j) denoting the possibly existing, or
                                                      > > > not,
                                                      > > > > output of the ith Turing machine applied on j.
                                                      > > > >
                                                      > > > > The "platonism" used in the definition of comp is much weaker
                                                      > than
                                                      > > > the
                                                      > > > > platonist conception of reality which follows, by UDA, from
                                                      > the comp
                                                      > > > > assumption. They should not be confused.
                                                      > > > >
                                                      > > > > Bruno
                                                      > > > >
                                                      > > >
                                                      > > > There can be no UDA without a UD. There is no physical UD. So
                                                      > > > strong Platonism is required to supply a non-physical UD.
                                                      > > >
                                                      > > Which exist in the same sense that prime number exist.
                                                      >
                                                      > Which is not at all as far as I am concerned. Although
                                                      > doesn't stop playing the bivalence game.
                                                      >
                                                      Well, if you don't believe in elementary arithmetic, then I can
                                                      understand that you cannot follow a reasoning based on the use of
                                                      computer science in cognitive science.




                                                      >
                                                      > > In the comp
                                                      > > ontology, existence is very well defined.
                                                      >
                                                      > It's not ontology it's pseudo ontology. Ontology
                                                      > is about what really exists.
                                                      >
                                                      If you are formalist then the expression "really exists" has no sense.




                                                      > Maths, and therefore
                                                      > comp, is game playing. It just supposes
                                                      > that various abstract objects "exist" and
                                                      > explores the consequences. However, I am not
                                                      > someone's supposition or formal game.
                                                      >
                                                      OK. But then you are not formalist. here you assume you are conscious,
                                                      and I assume no more in the reasoning. Then the $conclusion* of the
                                                      reasoning makes elementary arithmetic the theory of everything. It
                                                      explains why numbers believe correctly in God, consciousness, matter,
                                                      etc.



                                                      > So I
                                                      > am not running on a hypothetical UD. The UD
                                                      > is an idea in my head: I am realler than it is.
                                                      >
                                                      In which theory? If you say you are really real because you are made
                                                      of primitive matter, then UDA shows that you will not survive
                                                      (assuming your premise is correct) with a digital artificial brain
                                                      (even if primitively material).

                                                      Bruno


                                                      >
                                                      > > It is defined through the
                                                      > > truth of existential sentences, with the shape "ExP(x)", and that is
                                                      > > true if there exist a natural number n such that it is the case that
                                                      > > P(n). The UD exists in that precise sense, and we don't need any
                                                      > other
                                                      > > form of existence to explain the "persistent illusion" of material/
                                                      > > physical realms.
                                                      > >
                                                      > > UDA1-7 shows that physics is a branch of computer science/number
                                                      > > theory in case a concrete UD exist. Do you agree so far? Then the
                                                      > > movie graph argument, or even just some strong occam razor, explains
                                                      > > why the existence of a concrete UD is not necessary to get the
                                                      > > reversal. That's step UDA-8. It is a constructive proof that physics
                                                      > > emerges from number theory, both ontologically and
                                                      > epistemologically.
                                                      > > Then AUDA illustrates what machines/numbers, relatively to universal
                                                      > > numbers can say about that comp-physics. The point is technical: it
                                                      > > shows that comp empirically is refutable, but it shows also that QM-
                                                      > > without-collapse confirmed it, in its most weird aspect. Numbers
                                                      > > develop "naturally" a persistent many-worlds interpretation of
                                                      > number
                                                      > > truth. The coupling consciousness/reality is emerging from addition
                                                      > > and multiplication in a verifiable way.
                                                      > >
                                                      > > Bruno
                                                      > >
                                                      > > http://iridia.ulb.ac.be/~marchal/
                                                      > >
                                                      > >
                                                      > >
                                                      > >
                                                      > >
                                                      > > [Non-text portions of this message have been removed]
                                                      > >
                                                      >
                                                      >

                                                      http://iridia.ulb.ac.be/~marchal/





                                                      [Non-text portions of this message have been removed]
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