*To*: soft_skinned_space <empyre@lists.cofa.unsw.edu.au>*Subject*: Re: [-empyre-] metaphor*From*: Henry Warwick <henry.warwick@sbcglobal.net>*Date*: Sun, 23 Nov 2003 18:23:40 -0800 (PST)*Delivered-to*: empyre@bebop.cofa.unsw.edu.au*In-reply-to*: <Pine.NEB.4.58.0311232045240.11372@panix3.panix.com>*Reply-to*: soft_skinned_space <empyre@lists.cofa.unsw.edu.au>

--- Alan Sondheim <sondheim@panix.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: http://www.edge.org/3rd_culture/dehaene/dehaene_p2.html 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 sight. ====================================== > 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 messy. 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 empyre. Also: re: observer/observed issues: it works on subatomic particles but scale changes everything... HW

**Follow-Ups**:**Re: [-empyre-] metaphor***From:*Alan Sondheim <sondheim@panix.com>

**Re: [-empyre-] metaphor***From:*"Joel Weishaus" <weishaus@pdx.edu>

**References**:**Re: [-empyre-] metaphor***From:*Alan Sondheim <sondheim@panix.com>

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