Re: [-empyre-] metaphor
In response to your last post.
The world you suggest seems, to me, a dead world. If a rock has no
consciousness, why is our claim to consciousness not delusional?
Consciousness is not about language or computations. It's not about
measuring devices or philosophy. It's about a world in which magic is still
the driving cultural force. A model of reality without it's shadow, its
mystery, its poetry, its eros, doesn't satisfy me.
----- Original Message -----
From: "Henry Warwick" <email@example.com>
To: "soft_skinned_space" <firstname.lastname@example.org>
Sent: Sunday, November 23, 2003 6:23 PM
Subject: Re: [-empyre-] metaphor
> --- Alan Sondheim <email@example.com> wrote:
> > There is no resolution really; I take a more or less
> > neo-platonic position
> > (Godel also had this) - for me, for example,
> > infinitesimals are 'real.'
> There are a number of different takes on it, and some
> of them are mutually exclusive. Some have *serious*
> inernal consistency problems (esp. Hilbertian
> formalists) some have problems with materialist
> neuroscience (neoplatonists) and some have problems
> with the amazing accuracy of mathematics, etc.
> A neuroscientific vision of numbers, and one I tend to
> agree with is discussed in this interview with
> Stanislas Dehaene, who wrote a wonderful book called
> "The Number Sense."
> He has a paper here:
> WHAT ARE NUMBERS, REALLY? A CEREBRAL BASIS FOR NUMBER
> SENSE by Stanislas Dehaene
> and here is a rough description of his position:
> >From Edge.org:
> Dehaene claims that number is very much like color.
> "Because we live in a world full of discrete and
> movable objects, it is very useful for us to be able
> to extract number. This can help us to track predators
> or to select the best foraging grounds, to mention
> only very obvious examples. This is why evolution has
> endowed our brains and those of many animal species
> with simple numerical mechanisms. In animals, these
> mechanisms are very limited, as we shall see below:
> they are approximate, their representation becomes
> coarser for increasingly large numbers, and they
> involve only the simplest arithmetic operations
> (addition and subtraction). We, humans, have also had
> the remarkable good fortune to develop abilities for
> language and for symbolic notation. This has enabled
> us to develop exact mental representations for large
> numbers, as well as algorithms for precise
> calculations. I believe that mathematics, or at least
> arithmetic and number theory, is a pyramid of
> increasingly more abstract mental constructions based
> solely on (1) our ability for symbolic notation, and
> (2) our nonverbal ability to represent and understand
> numerical quantities."
> He argues that many of the difficulties that children
> face when learning math and which may turn into
> full-blown adult "innumeracy" stem from the
> architecture of our primate brain, which has not
> evolved for the purpose of doing mathematics.
> It is his view that the human brain does not work like
> a computer and that the physical world is not based on
> mathematics -- rather math evolved to explain the
> physical world the way that the eye evolved to provide
> > And I see this inextricably tied into the fabric of
> > being and the
> > universe. The fact that fundamental particles'
> > attributes can be literally
> > exhausted by mathesis amazes me and points to the
> > fabric itself.
> Again, I don't know about that... is it the universe
> that is mathematical? I have my doubts.
> > There are numerous logics and mathematics, but
> > they're all fundamnetally
> > related.
> Agreed, but they are all flawed (Goedel) and it has
> not been determined whether or not our brain is even
> capable of understanding anything of what it purports
> to understand about everything, anyway.
> I guess I'm a bit of an agnostic that way. I agree
> with Dehaene: higher math is a product of our brain's
> lanugage function based on quantities we find in the
> universe. One could say that countable quantities are
> real, but something like tensor equations are not.
> It is a complicated issue, and the passions run high
> all around it, for such a dry subject. I remember
> being on a board for a while re: higher dimensions,
> and we'd get these "new age" types who come in with a
> load of mystical claptrap about "hgiher dimensions"
> (WwOOOooOOOOoooo) and then hardcored math heads would
> sit and laugh at them, explaining that it's just
> another line of equations describing extra degrees of
> freedom, etc. and there's nothing "magical" about it
> at all, so kindly go away. I'd chime in with a more
> neuroscientific line from Dehaene et al, and then it
> broke out into open warfare. The NeoPlatonists got
> into high dudgeon going on about the reality of their
> equations and how math pre-existed and humans
> discovered these truths, bla bla bla, and then the
> constructivists would go on about it being a product
> of human behaviour and pointed at the unending
> inaccuracies and the logical contradictions
> constructed by such a position, and well, it got
> A lot of smoke, very little light.
> So, rather than re-live that little episode, I agree
> with Alan insofar as I am willing to agree that it is
> a complicated subject, and I don;t know how far or how
> fruitful sucha discussion could be in the context of
> Also: re: observer/observed issues: it works on
> subatomic particles but scale changes everything...
> empyre forum
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