18605Re: Re: [ai-philosophy] On mathematics
- Nov 4, 2013Perhaps the phenomena must overlap? A kind of fuzzy phenomenon that whilst being fuzzy is also curious in meaning and not special in form.
Say knowing that numbers continue in infinity but you only noting the change as relevant.2013/11/3 <john_j_gagne@...>
Sergio Navega said
"I used to think that thinking was justcomputation. Now I'm inclined to consider
that thinking can be modelled computationallybut it is NOT a computation per se.Thinking is a physical process just like a hurricane:"But this implies that computation is, somehow, not a physical
process (like a hurricane) and as you point out above, just like
thinking. It is...
Certainly, any statement about what "thinking" is--suffers
a drop in precision when compared with the statement "thinking
is computation". Its all too popular to take an anti-computational
philosophical position with respect to brain/biological processes.
But every time this approach is established the result seem to be
to replace the precises language of computation/mathematics
with vague statements about highly non-computational emotional
states... What does that even mean?
Any "process" which is "claimed" to be non-computational is also
certainly a process which can (in the same breath) be said to be
less than "understood". By the same token, any process which can
be "modeled computationally" precisely defines not only the language
but also the level of understanding achieved with respect to the subject
I'm not saying computation will never be superseded by a better
theory (as Newton was superseded by Einstein). I'm am saying
no such superposition has presented itself to date.
John J. Gagne
---In firstname.lastname@example.org, <email@example.com> wrote:
it> You are not "making a mapping" that's the wrong way to think aboutSo what is the right way to think about it?What is the name of the process of discardingdetails from one level of analysis (or groupingmany of them into a single name) and link all theseto a higher level abstract construct? Because inscience we do that all the time.Sergio NavegaYou are not "making a mapping" that's the wrong way to think about it, and where I stopped reading.On Tue, Oct 29, 2013 at 2:29 PM, Sergio Navega <snavega@...> wrote:Eray, I understand what you say, but in order toconstruct a mapping between that bunch of organicmolecules and those high level constructs of auniversal computer we have to discard a lot of things.That's what I'm afraid of doing!Take the concept of memory, for instance. An essentialpart of any computer, memory in "brain terms" is a complex(and highly distributed) pattern of connections betweenneurons that not only changes through time, but is subjectto many external influences (such as the state of "arousal"of the remainder of the body). The net result is that whenwe say that brains have "memory" we are in fact discardingthe majority of the biochemical processes that happen inthat organ.This mapping usually works, but only because our abstractionfrom "biological chemistry" to the level of "the conceptof memory" is coarse enough (which means, we are discardingmany things). Sure, we are discarding many irrelevant stuff.But perhaps some of the things we are discarding can be veryimportant in a different kind of theoretical construct (adifferent conceptual mapping), one which advances over theconcept of universal computers.I may argue that science, in general, does this simplificationall the time. After all, without doing it we couldn't thinkof Newtonian mechanics anymore, because of quantum details orrelativistic effects. We just discard quantum and relativisticstuff when building bridges and cars. However, maybe there'ssome danger in doing this for any kind of system.A satellite in orbit of the Earth could be thought as being apurely newtonian system. But in practice we know that there aresome satellites that require a broader model: GPS systems, forinstance, needs that we consider relativistic effects in orderto work correctly. In other words, if we were constrained to useonly newtonian mechanics, GPS would not be possible.So I'm not against doing that kind of simplification,I just propose that we remember that we're doing this, soas not to lose the "big picture" and the eventual possibilityof doing more things with a new theoretical substrate, maybebeyond what we're considering to be the "ultimate model".Sergio NavegaI think the analogy is misleading, at least for the reason that the brain isn't just a computer, it is a *universal* computer.Regards,On Mon, Oct 28, 2013 at 8:12 PM, Sergio Navega <snavega@...> wrote:> It is a computer, it has processing and memory elements, etcI may agree with that, but in order to do so one has toestablish a mapping between the theoretical view of what a computeris (an abstract definition of memory, processing elements, etc) anda physical system (hormones, neurotransmitters, synapses, non-linearbehavior of neurons, etc.). What I'm saying is that if one is doingthat for the brain, then using a sufficiently well built mapping onecan also do that for a hurricane (although it would be a little bitodd to determine what exactly a hurricane is computing).I'm saying all this because there's a big chasm between thetheoretical definition of what a computer (and computation) isand the real implementation of such a device. And IMHO there'sa big danger to forget that distinction: it is too easy to fallprey of the "the brain is a computer" simplification.Let me expand a bit on why I've changed my mind in recent years.We know that what makes us human is not restricted to theoperations being performed on the neocortex. Much of the"quality" and peculiarity of our reasoning process is due toemotional concerns. This has been the focus of attention of manyresearchers for some decades now. And that's my point: emotionalprocesses are terribly non-computational (that's quite an assertion,I know!). So modeling what the brain does (in order to becapable of building intelligent machines) is a small, tinypart of the whole endeavor. There's a non-computationalpart that makes me somewhat skeptic we will be able ofbuilding (at least using current strategies). AI keeps givingus reasons to believe that we're on a race to build "the fastestidiots on earth".Sergio NavegaThat's the strong C-T thesis, but it is not needed actually. What matters is what the nervous system *is* and it is a biological computer, it doesn't have any other real function. If you think it is not a computer, probably your theory of computation is not wide enough. It is a computer, it has processing and memory elements, etc.On Mon, Oct 28, 2013 at 5:40 PM, Sergio Navega <snavega@...> wrote:> ... and thinking is MADE UP OF COMPUTATIONI must confess that I'm changing my mind about thissubject. I used to think that thinking was justcomputation. Now I'm inclined to consider that thinkingcan be modelled computationally, but it is NOT acomputation per se.Thinking is a physical process just like a hurricane: itcould be (in principle) modeled computationally, but itis not a computation. Unless, of course, we adhereto the idea that all material reality (below the level ofquarks and gluons) is just an informational substrate,being executed by an extra-galactic humongous computerof some sort.But that's too much, isn't it? Or is it?Sergio Navega
[The return of the positivist]
I don't think that the analytic-synthetic distinction's too relevant any more. The trouble is that mathematics cannot be captured by neither platonism nor formalism, that many mathematicians like so much. The true answer is through physicalism of course.
I think that computation is the golden standard of mathematics. That is because if mathematics is a science, it is the science of thinking, and thinking is MADE UP OF COMPUTATION. That is to say, the mathematics that lies beyond computer science (i.e. graphs with uncountably many edges) isn't science. It's a pretty harsh statement, given how many academic mathematicians make a living out of, what is essentially the empty set.
Let me say it again, mathematics always involves a kind of reasoning, a form of reasoning that is better and more precise than common sense. And as such that WAY OF THINKING underlies all science.
That is not an UNCANNY COINCIDENCE or anything like that. It happens precisely because the abstract representations in mathematics have proven themselves useful, that they exist at all. Therefore, if one "liberates" mathematics by turning it into an art form, one essentially makes an assault on the entirety of science, of which mathematics is a mostly reliable foundation.
That is to say, mathematical statements gain their meaning only by way of a computational interpretation. When such interpretation is absent, mathematics is nonsense.
Mathematics is just general purpose computations (i.e., an axionatic system of geometry).
Computer science is identical to mathematics.
Universal induction can answer any valid mathematical question.
Halting problem essentially encompasses the entirety of mathematical thought. Of which there is an infinite variety, only limited by computational resources.
Full empiricism explains mathematics: it is just experiments on computer devices. It fully reduces to the physical science of computers.
A set is just an ordered list of bitstrings.
These are the scientific facts we know as they follow from the plain and obvious fact that the brain is a computer. In summary, computational neuroscience proves Godel's silly spiritual philosophy wrong. (I dont even mention how irrelevant quine and putnam are to science of nathematics)
Eray Ozkural, PhD
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