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:
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
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
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...
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