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18594Re: [ai-philosophy] On mathematics

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  • Sergio Navega
    Oct 29, 2013
      Eray, I understand what you say, but in order to
      construct a mapping between that bunch of organic
      molecules and those high level constructs of a
      universal 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 essential
      part of any computer, memory in "brain terms" is a complex
      (and highly distributed) pattern of connections between
      neurons that not only changes through time, but is subject
      to many external influences (such as the state of "arousal"
      of the remainder of the body). The net result is that when
      we say that brains have "memory" we are in fact discarding
      the majority of the biochemical processes that happen in
      that organ.
      This mapping usually works, but only because our abstraction
      from "biological chemistry" to the level of "the concept
      of memory" is coarse enough (which means, we are discarding
      many things). Sure, we are discarding many irrelevant stuff.
      But perhaps some of the things we are discarding can be very
      important in a different kind of theoretical construct (a
      different conceptual mapping), one which advances over the
      concept of universal computers.
      I may argue that science, in general, does this simplification
      all the time. After all, without doing it we couldn't think
      of Newtonian mechanics anymore, because of quantum details or
      relativistic effects. We just discard quantum and relativistic
      stuff when building bridges and cars. However, maybe there's
      some danger in doing this for any kind of system.
      A satellite in orbit of the Earth could be thought as being a
      purely newtonian system. But in practice we know that there are
      some satellites that require a broader model: GPS systems, for
      instance, needs that we consider relativistic effects in order
      to work correctly. In other words, if we were constrained to use
      only 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, so
      as not to lose the "big picture" and the eventual possibility
      of doing more things with a new theoretical substrate, maybe
      beyond what we're considering to be the "ultimate model".
      Sergio Navega
      Sent: Monday, October 28, 2013 10:55 PM
      Subject: Re: [ai-philosophy] On mathematics

      I think the analogy is misleading, at least for the reason that the brain isn't just a computer, it is a *universal* computer.

      On Mon, Oct 28, 2013 at 8:12 PM, Sergio Navega <snavega@...> wrote:

      > It is a computer, it has processing and memory elements, etc
      I may agree with that, but in order to do so one has to
      establish a mapping between the theoretical view of what a computer
      is (an abstract definition of memory, processing elements, etc) and
      a physical system (hormones, neurotransmitters, synapses, non-linear
      behavior of neurons, etc.). What I'm saying is that if one is doing
      that for the brain, then using a sufficiently well built mapping one
      can also do that for a  hurricane (although it would be a little bit
      odd to determine what exactly a hurricane is computing).
      I'm saying all this because there's a big chasm between the
      theoretical definition of what a computer (and computation) is
      and the real implementation of such a device. And IMHO there's
      a big danger to forget that distinction: it is too easy to fall
      prey 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 the
      operations being performed on the neocortex. Much of the
      "quality" and peculiarity of our reasoning process is due to
      emotional concerns. This has been the focus of attention of many
      researchers for some decades now. And that's my point: emotional
      processes are terribly non-computational (that's quite an assertion,
      I know!). So modeling what the brain does (in order to be
      capable of building intelligent machines) is a small, tiny
      part of the whole endeavor. There's a non-computational
      part that makes me somewhat skeptic we will be able of
      building (at least using current strategies). AI keeps giving
      us reasons to believe that we're on a race to build "the fastest
      idiots on earth".
      Sergio Navega
      Sent: Monday, October 28, 2013 1:46 PM
      Subject: Re: [ai-philosophy] On mathematics
      That'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 COMPUTATION
      I must confess that I'm changing my mind about this
      subject. I used to think that thinking was just
      computation. Now I'm inclined to consider that thinking
      can be modelled computationally, but it is NOT a
      computation per se.
      Thinking is a physical process just like a hurricane: it
      could be (in principle) modeled computationally, but it
      is not a computation. Unless, of course, we adhere
      to the idea that all material reality (below the level of
      quarks and gluons) is just an informational substrate,
      being executed by an extra-galactic humongous computer
      of some sort.
      But that's too much, isn't it? Or is it?
      Sergio Navega
      Sent: Monday, October 28, 2013 1:20 AM
      Subject: [ai-philosophy] On mathematics

      [The return of the positivist]

      Greetings all,

      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.

      Eray Ozkural, PhD. Computer Scientist
      Founder, Gok Us Sibernetik Ar&Ge Ltd.
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