Glen, 1) >>I maintain my
claim that math is a living language by which we describe aspects of
reality.<< and >>But I disagree that an accurate definition of math
is equal to doing math.<< I don't know a better definition of math
than: it is an *art*. Even more: there is no math but mathematicians who perform
their *indefinable* art ("The other sort [of mathematicians] are guided by
intuition..." --Henri Poincare "Intuition and Logic in Mathematics"; or "a
mathematician who is not something of a poet will never be a good
mathematician.") An act of creation is beyond any language but to communicate
their ideas, models, results, yes, they need a language and, from this point, it
*appears* that math is a language, or, at least, that there is an isomorphism
between math and a language. Are the English poetry and the English language the
same? Studying only French, can we write, for example, "In Search of Lost
Time"?... When we cannot put something into a language, we try to extend and
change it. A language is living because an artist (or the Artist, it
depends on a point of view) is performing. 2) >>on the Chaitin talk is
that there were many things said in the talk<< My perception is: he told
about one thing: reality of things is incalculable and even un-nameable with
probability one (Borel). It is, probably, why philosophers talk about its divine
nature. --Mikhal
----- Original Message -----
From: [hidden email]To: [hidden email]Sent: Monday, July 14, 2008 5:08 PMSubject: Re: [FRIAM] Mathematics and MusicMikhail Gorelkin wrote:
> I would like to return to that Chaitin lesson:
Well, the problem with focusing on the Chaitin talk is that there were
many things said in the talk, not all of which point in the same
direction. So, it would be better if you would single out a specific
aspect of the talk that bears discussion.
> it seems that a full
> and correct definition of mathematics is *impossible*... like a full
> axiomatization of arithmetic. Mathematics is so complex that an
> accurate definition of it is equal to doing math (no compression in
> Chaitin's terminology). It means that all our descriptions are just
> *references* to discussed subjects. --Mikhail
Hmmm. I maintain my claim that math is a living language by which we
describe aspects of reality. That means I agree completely that a
complete and consistent definition of math is impossible.
But I disagree that an accurate definition of math is equal to doing
math. Because I believe math is a language, defining math is
linguistics (and anthropology and history). Granted, to be specific
about the actual language, one has to know and do some math. After all,
describing, say, the history of the concept of "infinity" requires
enough mathematical understanding to follow the historical thread.
But such "doing math" is a side-effect of the linguistic work. I
suspect that, in defining math, the linguist only has to about the same
amount of math as a linguist has to do when defining, say, French or
Swahili.
Then I again agree that all our descriptions are just references to
discussed objects, because that's the fundamental role of languages.
They provide us with the ability to _refer_ to things (albeit the
"things" that can be referred to may not actually exist or they may be
an artifact of the language being used).
So, I'm in the odd position of having to agree with the beginning of
your argument, disagree with the middle, and agree with the end. [grin]
--
glen e. p. ropella, 971-219-3846, http://tempusdictum.com
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