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Re: Abstract mathematical development versus particle physics analysis
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Hi again,
 In FabricofReality@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.
> >
> >  InFabricofReality@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 "waveparticle 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 wavelike nature of single particles but rather how many particles are distributed. David Deutsch himself explains this better:
http://groups.yahoo.com/group/FabricofReality/message/7552
This is very succinct:
http://groups.yahoo.com/group/FabricofReality/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/FabricofReality/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. 0 Attachment
> ________________________________________________________________________
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 multiverse. Travel along that direction for any distance takes you to a different world of the multiverse.
> 4b. Re: Abstract mathematical development versus particle physics analys
> Posted by:"brhalluk@..." brhalluk@... brhallway
> Date: Sun Jan 1, 2012 2:26 am ((PST))
>
>
>
>  InFabricofReality@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.
>>> > >
>>> > > InFabricofReality@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 "waveparticle 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 wavelike nature of single particles but rather how many particles are distributed. David Deutsch himself explains this better:
>
> http://groups.yahoo.com/group/FabricofReality/message/7552
> This is very succinct:
> http://groups.yahoo.com/group/FabricofReality/message/8375
>
> Brett said:
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.
> 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.
> Brett says: Yes  relationships between ideas works. So mathematics
You have effectively argued me away from my hypothesis that analysis of mathematics and physics needed to be considered equivalent.
> 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/FabricofReality/message/5198
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:
:) I did not perceive badgering. I perceived that you gave a thoughtful response.
>> > :)
>> >
>> > 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:)
>
> :)
Probably I do embrace a weak relativism. More explanation of what is meant by "weak relativism" may either confirm or disconfirm. 0 Attachment
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 FabricofReality@yahoogroups.com, "gich7" <gich7@...> wrote:
>
>
>  Original Message 
> From: <brhalluk@...>
> To: <FabricofReality@yahoogroups.com>
> Sent: Sunday, January 01, 2012 12:41 AM
> Subject: Re: Abstract mathematical development versus particle physics analysis
>
> Hi again,
>
>  In FabricofReality@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.
> > >
> > >  InFabricofReality@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 realworld 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
> 0 Attachment
 In FabricofReality@yahoogroups.com, Kermit Rose <kermit@...> wrote:>
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
> > ________________________________________________________________________
> > 4b. Re: Abstract mathematical development versus particle physics analys
> > Posted by:"brhalluk@..." brhalluk@... brhallway
> > Date: Sun Jan 1, 2012 2:26 am ((PST))
> >
> >
> >
> >  InFabricofReality@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.
> >>> > >
> >>> > > InFabricofReality@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 "waveparticle 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 wavelike nature of single particles but rather how many particles are distributed. David Deutsch himself explains this better:
> >
> > http://groups.yahoo.com/group/FabricofReality/message/7552
> > This is very succinct:
> > http://groups.yahoo.com/group/FabricofReality/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 multiverse. Travel along that direction for any distance takes you to a different world of the multiverse.
http://rspa.royalsocietypublishing.org/content/458/2028/2911.full.pdf or here:
http://arxiv.org/pdf/quantph/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. :)
>
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 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.
>
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:
>
> > 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/FabricofReality/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.
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.
>
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.
>
> >> > 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.
Brett.
>
 0 Attachment
On 01 Jan 2012, at 15:34, gich7 wrote:
>
It depends on your hypotheses, notably in the cognitive science. If
>  Original Message 
> From: <brhalluk@...>
> To: <FabricofReality@yahoogroups.com>
> Sent: Sunday, January 01, 2012 12:41 AM
> Subject: Re: Abstract mathematical development versus particle
> physics analysis
>
> Hi again,
>
>  In FabricofReality@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.
> > >
> > >  InFabricofReality@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'.
>
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 + selfreference. 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
http://iridia.ulb.ac.be/~marchal/
> *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 realworld 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
>
>
[Nontext portions of this message have been removed] 0 Attachment
 In FabricofReality@yahoogroups.com, brhalluk@... wrote:>
________________________________________________________________________
>
>
>  In FabricofReality@yahoogroups.com, Kermit Rose kermit@ wrote:
> >
> > >
> > > 4b. Re: Abstract mathematical development versus particle physics
analys
> > > Posted by:"brhalluk@" brhalluk@ brhallway
wrote:
> > > Date: Sun Jan 1, 2012 2:26 am ((PST))
> > >
> > >
> > >
> > >  InFabricofReality@yahoogroups.com, Kermit Rose<kermit@>
> > >> >
physics analys
> > >>> > > 7a. Re: Abstract mathematical development versus particle
> > >>> > > Posted by:"brhalluk@" brhalluk@ brhallway
wrote:
> > >>> > > Date: Sat Dec 31, 2011 4:46 am ((PST))
> > >>> > >
> > >>> > > Hi Kermit!
> > >> > :)
> > >> > Hello Brett.
> > >>> > >
> > >>> > > InFabricofReality@yahoogroups.com, Kermit Rose<kermit@>
> > >>> >
particles in the sense that we say that protons are composed of quarks,
> > >>> > Even if we show that electrons cannot be composed of other
how do we explain the nature of the electron?> > >>> >
electron nature.
> > >>> > We have advanced wave particle duality ideas to explain
> > > Brett said: This is counter to the MWI where there's no such thing
as the mysterious "waveparticle 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
wavelike nature of single particles but rather how many particles are
distributed. David Deutsch himself explains this better:> > >
be spread out over four space dimensions. The density of the particle at
> > > http://groups.yahoo.com/group/FabricofReality/message/7552
> > > This is very succinct:
> > > http://groups.yahoo.com/group/FabricofReality/message/8375
> > >
> >
> > Ahh.... This suggests another picture to me. I imagine a particle to
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 multiverse. Travel along that direction for any
distance takes you to a different world of the multiverse.>
say you haven't read FoR or BoI as you don't have access. Okay. Well
> I don't think that's science. I think this is your own conjecture. You
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/quantph/0104033>
> http://arxiv.org/pdf/quantph/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
nonacceptance 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?
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On 03 Jan 2012, at 20:15, gich7 wrote:
>
It shows that, contrary to what you said, pure mathematics might have
>  Original Message 
> From: "Bruno Marchal" <marchal@...>
> To: <FabricofReality@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: <FabricofReality@yahoogroups.com>
> > Sent: Sunday, January 01, 2012 12:41 AM
> > Subject: Re: Abstract mathematical development versus particle
> > physics analysis
> >
> > Hi again,
> >
> >  In FabricofReality@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.
> > > >
> > > >  InFabricofReality@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.
>
>
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 metalevel to make comp comprehensible at the epistemological
level. The ontology becomes pure number theory though.
Bruno
http://iridia.ulb.ac.be/~marchal/
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On 05 Jan 2012, at 10:31, gich7 wrote:
>  Original Message 
You are right. It does not have to have anything to do with the real
> From: "Bruno Marchal" <marchal@...>
> To: <FabricofReality@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'.
>
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.
>
You are right. I agree with you on that point. But IF mechanism is
> In other words, investigations in pure mathematics do not *have* to
> have
> anything to do with 'the real world'.
>
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"?
>
Some are even proud that their theories have no applications. Some
> 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.
>
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
Yes. Like a rocket scientist who does not want his rocket to be
> because* the problems interest them!
>
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
Sure.
> in the real world then fine, but this is *not* the objective of the
> activity.
>
>
But it has something to do with your statement that pure mathematics
> > 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.
>
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
Correct.
> *postulations* of the sort you have in mind in pure mathematics.
>
> You are
Not correct. The postulation makes disappear the frontier between
> studying (or inventing) a new system but this system is *not* pure
> mathematics,
> nor does it have anything to do with pure mathematics.
>
applied and pure mathematics.
And once you postulate, perhaps at some metalevel, 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
Sure.
> investigates some system in pure mathematics, possible applications
> in the 'real
> world' are of no concern to him.
>
>
I disagree. When you do group theory you assume axioms. Those are
> 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.
>
scientific postulations. We believe in them because we have examples,
but to make those example existent, we need other postulations (like
classes, sets, selfconsistency, etc.). The situation is not different
from theoretical physics, which you can seen indeed as pure mathematics.
>
You have to assume they exist.
> 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.
>
> The *symbols*, a, b, c, d are just *labels* and have *no*
You assume that your interlocutor can distinguish those labels, and
> 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.
>
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.
>
Of course, ... in the formal deductive theory. But group theorists are
> 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.
>
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.
>
This is not different than any theoreticians. They build theories and
> 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.
>
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
>
http://iridia.ulb.ac.be/~marchal/
> For those interested in pursuing this further a useful introduction
> to the Klein
> fourgroup and other groupconcepts will be found at.
> http://en.wikipedia.org/wiki/Klein_fourgroup
>
> Gich
>
>
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On 06 Jan 2012, at 11:50, gich7 wrote:> marchal wrote:
[I meant might be false]
> > 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
I totally agree with you on this. That makes my point: N exists. It is
> > 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.
>
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.
> 
Totally OK with this.
> [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
They confuse numbers with the human conception of numbers. But with
> 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.
>
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
>
> > 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.
>
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.
> 
I agree with this, although I do not assume it to be true in the
> [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.
>
reasoning mentioned above.
> Is there a possible world in which there is no number two (but all
Well, there are certainly theories without natural numbers. We cannot
> 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.
>
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.
> >>
It is the result of 30 years of hard work. Look at the SANE04 paper
> >> 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.
>
referred above. The result is counterintuitive, 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
As I said above, you cannot prove the existence of the natural
> mechanism *leads to*
> the existence of the natural numbers.
>
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.
>
As I knew from your post, we are very close on this.
>
>
> I think all human knowledge in theoretical physics stems from number
> theory.
> Mathematics rules!
>
> But I don't think we need a postulation of the sort you're
The conclusion is technical and constructive: it makes mechanism
> promoting to reach this conclusion.
>
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
You are right. But the result is that IF we are machine THEN
> >> 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, selfconsistency, 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.
>
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 PostChurchTuring sense).
> The *axioms* in pure mathematical systems are simply *definitions*
The theory explains where such "mathematician's intellect" comes from.
>  products
> of the mathematician's intellect.
>
>
I can agree. It is not entirely true. The axioms have to be
> 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?"
>
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.
>
That's not entirely true. They want examples and instantiation of
> The pure mathematician deals with questions like, "if suchandsuch
> is true
> (which, initially, would be one of his axioms) does it then follow
> that
> soandso 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
> andsuch or,
> indeed, whether it makes any sense (in the realworld) is of no
> concern to him.
>
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.
>
I am saying that IF we are digitalizable machine, THEN the ontological
> 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.
>
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.
>
When I believe that I am a machine, I stop to believe in the natural
> >
> >
> >
> >>
> >> 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.
>
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 Gï¿½del 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 ...).
>
In practice you do assume, at the metalevel some interlocutor, even
> >
> >
> >
> >> 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.
>
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
>
http://iridia.ulb.ac.be/~marchal/
> >
> >
> >>
> >> 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
> >> fourgroup and other groupconcepts will be found at.
> >> http://en.wikipedia.org/wiki/Klein_fourgroup
> >>
> >> Gich
> >>
> >>
>
> Gich
>
>
[Nontext portions of this message have been removed] 0 Attachment
> I totally agree with you on this. That makes my point: N exists. It is
Hi Bruno et al,
> 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).
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. 0 Attachment
 In FabricofReality@yahoogroups.com, Bruno Marchal <marchal@...> wrote:>
Not part of mine. I've never seen the set of positive integers.
>
> I totally agree with you on this. That makes my point: N exists. It is
> part of reality.
 0 Attachment
On 07 Jan 2012, at 08:21, brhalluk@... wrote:
> > I totally agree with you on this. That makes my point: N exists.
OK. I don't think we can program person, but we might be unable to
> 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.
>
enslave universal machine a long time enough, and virtual person might
develop in virtual realities, yes.
>
Not necessarily. But you will have to provide memories regularly to
> Two somewhat unrelated questions:
>
> Firstly, would this mean that the discoveries simulated people make
> is inherently bounded?
>
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
This is delicate to answer. Those person, as seen by you, will
> would be able to discover our world  the one in which the computer
> on which they are being simulated  is running?
>
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*
Except the existence of an external global physical reality is an open
> 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.
>
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 UDAstep7.
>
This will happen if you stop to trick them purposefully.
> 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
We don't know if our stuff is real. If comp is correct, it real with
> 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).
>
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.
>
It is physical realism, and some amount of it is consistent with comp,
> 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.
>
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).
>
Yes. But they can extract the physics from that, and then compare with
> 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.
>
the observations.
> Namely  they are *obviously* machines who have *invented* the real
But they have a different perspective, and "belongs" to infinities of
> world (from our perspective).
>
computations like us. The trick to confuse them will have a quickly
growing price.
> From our perspective, the ultimate explanation of their world is
Not if you install democracy and freethinking. Either you don't trick
> some instantiation of arithmetic (a program running on a computer).
>
> Is this correct?
>
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!
>
Not really. The physical worlds is not emulable, normally. Its 'shape"
> 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?
>
comes from the fact that below our substitution level, we are in
infinities of computations at once.
>
It is more complex. Our world is a sum on infinities of simulations.
> In other words under digital mechanism, our world is a virtual
> world, only there's no programmer?
>
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 selfreference. Advantage: we can use
incompletenesslike phenomena to justify the quanta/qualia difference.
 Bruno Marchal
>
http://iridia.ulb.ac.be/~marchal/
[Nontext portions of this message have been removed] 0 Attachment
On 07 Jan 2012, at 18:05, gich7 wrote:
>
The "correct" physical laws/theories are anything relating "correctly"
>  Original Message 
> From: "Bruno Marchal" <marchal@...>
> To: <FabricofReality@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 observation I can do. More deeply, it is related of what is
persistent and invariant in those observations.
>
I kind of agree, but they have interesting "beliefs" (theories,
> 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'.
>
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, at least, has intuited that consciousness might have some
> [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."
>
role. Alas, he defended a noncomp theory of consciousness, where the
comp theory fits much better with both GÃ¶del's theorem, QM, cognitive
science, etc.
Penrose remains physicalist. And, this, I argue, can't be defended in
the comp frame.
>
Because, like many, they stick to an aristotelian conception of reality.
> GICH: This is why people like Susskind and Hawking ban the word
> 'reality' from
> scientific discussion and why Penrose entitled his 1094page magnum
> opus, "The
> Road to reality . . .", but failed to come to any conclusions
> concerning what
> this "reality" might be.
>
It is very common (to say the least).
> He ended his book with the following paragraph:
Yeah. I think that science is deeply sleepy since we close Plato
>
> [Penrose] "The spacetime 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 presentday theories are
> powerless to
> describe. . . . there are other deeply mysterious issues about which
> we have
> little comprehension. . . ."
>
academy in Athena. The most interesting questions and concepts (life,
soul, death, etc.) are still offered to the authoritativeargument,
pseudoreligious, 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/
[Nontext portions of this message have been removed] 0 Attachment
 In FabricofReality@yahoogroups.com, "Peter D" <peterdjones@...> wrote:>
Have you seen gravity?
>
>
>  In FabricofReality@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.
>
 0 Attachment
Hi Bruno, thanks for your response...
 In FabricofReality@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 UDAstep7.
>
>
>
>
> >
> > 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 freethinking. 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 selfreference. Advantage: we can use
> incompletenesslike phenomena to justify the quanta/qualia difference.
Thanks again,
Brett.
>
>  Bruno Marchal
>
> >
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
>
>
> [Nontext portions of this message have been removed]
> 0 Attachment
 In FabricofReality@yahoogroups.com, brhalluk@... wrote:>
I've felt it.
>
>
>  In FabricofReality@yahoogroups.com, "Peter D" <peterdjones@> wrote:
> >
> >
> >
> >  In FabricofReality@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?
>
 0 Attachment
On 08 Jan 2012, at 09:26, gich7 wrote:
>  Original Message 
With comp physics is, to be short, reduced to an weighting on paths
> From: "Bruno Marchal" <marchal@...>
> To: <FabricofReality@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!
>
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.
>
For a rational computationalist "pure mathematics" is the real world.
> 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 blackholes. 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'."
>
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 metalevel, like all mathematicians and physicists). Like you,
I see below. (And I think Peter too perhaps).
>
Not sure. Peter might say that N does not exist *anywhere*, but in the
> **************************
> 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.
>
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
I can't agree more with you.
> a planet Earth, if the human race had never existed, N would still
> exist.
>
>
I agree with all this.
> 
> [ 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.
>
>
> Moreover, they do not act on anything, so as to produce results.
I don't assume a natural world. I assume only natural numbers. N.
> They are 'powerless' in the natural world, and leave no trace
> there. . . .
>
"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 multiuser dreams appears in deep
(in Bennett sense) and thus *long*, computations, making necessary
sharable first person plural realities (the physical worlds).
And thanks to GÃ¶del 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 manyworlds 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/
[Nontext portions of this message have been removed] 0 Attachment
On 08 Jan 2012, at 01:40, brhalluk@... wrote:
>
No. The laws here are explicable, but they are not really effective.
> > >
> > > 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?
>
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.
>
Is QM testable? yes. Comp shows "the matrix" is testable, and that QM
> >
> >
> >
> >
> > >
> > > 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.
>
might be the reflect of the digital seen by itself.
>
They will know that they are virtually elsewhere, but they might still
> 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.
>
ask you to make it possible to share your reality with you.
>
Yes it is the error of all dictator sand prohibitionist doctrines.
> >
> >
> >
> >
> >
> > > 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 UDAstep7.
> >
> >
> >
> >
> > >
> > > 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?
>
>
Hmm... Physical can be opposed to non physical. Non physical can be
> >
> >
> >
> >
> > > 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?
>
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
Yes. The 'real one', when you look close to them, you get the trace of
> 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?
>
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.
>
Physical realism? Primitive physical realism (physicalism/weak
> >
> >
> >
> > >
> > > 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?
>
materialism) is inconsistent with mechanism (UDA).
> In fact, doesn't it demand it? I'm not saying that *only* the
With comp any physical reality is embarrasing. It is like an invisible
> physical exists 
>
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
Both are real, but which one is the more fundamental?
> 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'.
>
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.
>
OK.
> >
> >
> > >
> > > 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.
>
> >
Yes.
> >
> >
> > > 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.
>
>
Nice.
> >
> >
> >
> >
> > > 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 freethinking. 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.
>
>
Since Deutsch coin the terms, I have use it. I use often the idea that
> >
> >
> >
> >
> > >
> > > 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?
>
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
I think they should be identical. QM is quite solid, and smells number
>  are different at the level of metaphysical reality but much
> remains the same (identical, even?).
>
theory a lot. And then the compphysics extracted from selfreference
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 selfreference/number theory.
> There are many fungible copies of me in the multiverse which *I* am.
I would say so. OK.
> 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?
>
>
But you can ask any question. Elliot was OK with the first six points
> >
> >
> >
> > >
> > > 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!
>
of UDA, are you?
The reversal appears already at the seventh, and I am waiting for
Elliot's reply.
>
You are welcome,
> > It means we have
> > to extend Everett phenomenology to arithmetic and derive the wave
> > itself from machine's selfreference. Advantage: we can use
> > incompletenesslike phenomena to justify the quanta/qualia
> difference.
>
> Thanks again,
>
Bruno.
>
http://iridia.ulb.ac.be/~marchal/
>
[Nontext portions of this message have been removed] 0 Attachment
On 07 Jan 2012, at 23:10, Peter D wrote:
>
For a platonist, reality is not necessarily WYSIWYG. (What you see
>
>  In FabricofReality@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.
>
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 selfreferential 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 noncomputationalism. 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/
[Nontext portions of this message have been removed] 0 Attachment
 In FabricofReality@yahoogroups.com, Bruno Marchal <marchal@...> wrote:>
Then your assumptions are COMP and Platonism, not just comp.
>
> On 07 Jan 2012, at 23:10, Peter D wrote:
>
> >
> >
> >  In FabricofReality@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).
NonPlatonist computationalists can resist your conclusions. 0 Attachment
On 09 Jan 2012, at 05:44, Peter D wrote:
>
COMP is not even defined without arithmetical platonism. If you can
>
>  In FabricofReality@yahoogroups.com, Bruno Marchal
> <marchal@...> wrote:
> >
> >
> > On 07 Jan 2012, at 23:10, Peter D wrote:
> >
> > >
> > >
> > >  In FabricofReality@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.
> NonPlatonist computationalists can resist your conclusions.
>
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/
>
[Nontext portions of this message have been removed] 0 Attachment
 In FabricofReality@yahoogroups.com, Bruno Marchal <marchal@...> wrote:>
Yes it is.
>
> On 09 Jan 2012, at 05:44, Peter D wrote:
>
> >
> >
> >  In FabricofReality@yahoogroups.com, Bruno Marchal
> > <marchal@> wrote:
> > >
> > >
> > > On 07 Jan 2012, at 23:10, Peter D wrote:
> > >
> > > >
> > > >
> > > >  In FabricofReality@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.
> > NonPlatonist computationalists can resist your conclusions.
> >
>
> COMP is not even defined without arithmetical platonism.
>If you can
"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 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
That isn't what Platonism means, that is what bivalence means.
> propositions, or closed sentences, are either true or false.
> Technically this can be weaken into an intuitionist Church thesis. We
There can be no UDA without a UD. There is no physical UD. So
> 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
>
strong Platonism is required to supply a nonphysical UD.
> >
> >
>
> http://iridia.ulb.ac.be/~marchal/
>
>
>
>
>
> [Nontext portions of this message have been removed]
> 0 Attachment
On 11 Jan 2012, at 15:42, Peter D wrote:
>
Show it.
>
>  In FabricofReality@yahoogroups.com, Bruno Marchal
> <marchal@...> wrote:
> >
> >
> > On 09 Jan 2012, at 05:44, Peter D wrote:
> >
> > >
> > >
> > >  In FabricofReality@yahoogroups.com, Bruno Marchal
> > > <marchal@> wrote:
> > > >
> > > >
> > > > On 07 Jan 2012, at 23:10, Peter D wrote:
> > > >
> > > > >
> > > > >
> > > > >  In FabricofReality@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.
> > > NonPlatonist computationalists can resist your conclusions.
> > >
> >
> > COMP is not even defined without arithmetical platonism.
>
> Yes it is.
>
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.
>
Define "computing" without arithmetical realism.
> >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 agree, and that is why I do not use the term "platonism", which can
> > 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.
>
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.
>
Which exist in the same sense that prime number exist. In the comp
> > 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 nonphysical UD.
>
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.
UDA17 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 UDA8. 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 compphysics. The point is technical: it
shows that comp empirically is refutable, but it shows also that QM
withoutcollapse confirmed it, in its most weird aspect. Numbers
develop "naturally" a persistent manyworlds 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/
[Nontext portions of this message have been removed] 0 Attachment
 In FabricofReality@yahoogroups.com, Bruno Marchal <marchal@...> wrote:>
Which is bivalence, not Platonism, properly so called.
>
> On 11 Jan 2012, at 15:42, Peter D wrote:
>
> >
> >
> >  In FabricofReality@yahoogroups.com, Bruno Marchal
> > <marchal@> wrote:
> > >
> > >
> > > On 09 Jan 2012, at 05:44, Peter D wrote:
> > >
> > > >
> > > >
> > > >  In FabricofReality@yahoogroups.com, Bruno Marchal
> > > > <marchal@> wrote:
> > > > >
> > > > >
> > > > > On 07 Jan 2012, at 23:10, Peter D wrote:
> > > > >
> > > > > >
> > > > > >
> > > > > >  In FabricofReality@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.
> > > > NonPlatonist 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
Again, you mean bivalence, which is just another
> > > 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.
formal rule for me.
> >
Bivalence doens't get you an existing UD. Without
> > > 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.
>
that, the argument doens;;t work.
> > > Technically this can be weaken into an intuitionist Church thesis.
Which is not at all as far as I am concerned. Although
> > 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 nonphysical UD.
> >
> Which exist in the same sense that prime number exist.
doesn't stop playing the bivalence game.
> In the comp
It's not ontology it's pseudo ontology. Ontology
> ontology, existence is very well defined.
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.
>
> UDA17 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 UDA8. 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 compphysics. The point is technical: it
> shows that comp empirically is refutable, but it shows also that QM
> withoutcollapse confirmed it, in its most weird aspect. Numbers
> develop "naturally" a persistent manyworlds 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/
>
>
>
>
>
> [Nontext portions of this message have been removed]
> 0 Attachment
On 14 Jan 2012, at 03:18, Peter D wrote:
>
I repeat, you are the one using the term "platonism", and I have
>
>  In FabricofReality@yahoogroups.com, Bruno Marchal
> <marchal@...> wrote:
> >
> >
> > On 11 Jan 2012, at 15:42, Peter D wrote:
> >
> > >
> > >
> > >  In FabricofReality@yahoogroups.com, Bruno Marchal
> > > <marchal@> wrote:
> > > >
> > > >
> > > > On 09 Jan 2012, at 05:44, Peter D wrote:
> > > >
> > > > >
> > > > >
> > > > >  In FabricofReality@yahoogroups.com, Bruno Marchal
> > > > > <marchal@> wrote:
> > > > > >
> > > > > >
> > > > > > On 07 Jan 2012, at 23:10, Peter D wrote:
> > > > > >
> > > > > > >
> > > > > > >
> > > > > > >  In FabricofReality@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.
> > > > > NonPlatonist 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.
>
explained why this is confusing.
>
You are confusing a theory and its interpretation. Do you accept
> > > >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.
>
bivalence for the arithmetical proposition (not the sentences). If
not, then even ChurchTuring thesis becomes meaningless. CT is not a
formalizable thesis. Yet it is a refutable scientific statement.
>
I can prove the existence of the UD even without bivalence. The UDs
> > >
> > > > 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.
>
exist exactly like prime number exists.
>
Well, if you don't believe in elementary arithmetic, then I can
> > > > 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 nonphysical 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.
>
understand that you cannot follow a reasoning based on the use of
computer science in cognitive science.
>
If you are formalist then the expression "really exists" has no sense.
> > 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
OK. But then you are not formalist. here you assume you are conscious,
> 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.
>
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
In which theory? If you say you are really real because you are made
> am not running on a hypothetical UD. The UD
> is an idea in my head: I am realler than it is.
>
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
>
http://iridia.ulb.ac.be/~marchal/
> > 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.
> >
> > UDA17 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 UDA8. 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 compphysics. The point is technical: it
> > shows that comp empirically is refutable, but it shows also that QM
> > withoutcollapse confirmed it, in its most weird aspect. Numbers
> > develop "naturally" a persistent manyworlds 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/
> >
> >
> >
> >
> >
> > [Nontext portions of this message have been removed]
> >
>
>
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