18592Re: [ai-philosophy] On mathematics
- Oct 28, 2013> 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
Eray Ozkural, PhD. Computer Scientist
Founder, Gok Us Sibernetik Ar&Ge Ltd.
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