Glen, got it :-) We
all have *two* me: the one is indefinable "I am" (who thinks, the real one) and
the another is the product of thinking of the first one (me as I think about
me). The perception of the first one - mostly through intuition, imagination,...
- of "external things" is what we call *reality*. The problem is we are mostly
unaware about many details of it (they are beneath of our consciousness) or it
is very difficult to *articulate* them correctly. Falling in love with a woman
is here (try to describe this unique feeling). Another example is: it took a
quite some time to recognize the essence of people and become more predictive
about their behaviors... The second one organizes our world around his
categorization, rationality, causality,... It is the *constructed* reality.
There is a gap inside of us: we differently "know" what reality is and what we
construct in our rational minds as "reality". Here is an example from that
Chaitin's lesson: we intuitively (geometrically) "know" *all* points on the line
but rationally can name and compute... almost nothing (zero probability). Our
second me perceives everything when it appears in our rational mind as it is
created there, but the first one knows that... his companion lives inside of the
Matrix. And Godel's theorems exist only in that artificial "reality". Our
rational mind tries hard to fix these problems and it cannot. It cannot even
leave a zone of zero-probability... The artist - call him a mathematician - is a
real me who exists in reality and through his art creates another one and all
fancy stuff there like Lie groups :-) --Mikhail
From: [hidden email]To: [hidden email]Sent: Monday, July 14, 2008 9:45 PMSubject: Re: [FRIAM] Mathematics and MusicMikhail Gorelkin wrote:
>>> Glen between brackets<<
>
> 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.")
These are fine notions; but ultimately we're just trading opinions,
there, and won't really get very far, at least not over e-mail.
> An act of creation is beyond any language
OK. I explicitly disagree with the claim that an act of creation is
beyond any language. Specifically, I think linguistic constructs are
part of a larger, more general type of sensory-motor interaction that
also includes other forms of communication like pictures, fist-fights,
chair-building, etc. as well as the general interpretation and discovery
of the world around us.
This general sensory-motor category (I'll call it SMI) is the _only_
evidence we have that an external reality even exists. Hence, things in
SMI are the only things we can talk about rationally. All the other
hypothetical occult stuff behind the things in SMI are amorphous shadows
that we can only get at indirectly, if at all.
So, the claim that creation is _beyond_ (behind, more than, etc.)
language (and vision, and interactive exploration, etc.) is a very
strong, realist claim.
There's no problem being a realist and assuming there is _something_ out
there beyond SMI. But accepting such an assumption is a slippery slope.
Once you accept that, you tend to _delude_ yourself into thinking you
can somewhat accurately or precisely determine the difference between
two things hidden behind elements of SMI.
In essence, this is why the scientific method consists largely of a)
repeatability, b) falsification, and c) prediction. Because all that
stuff is on _this_ side of SMI. All else is occluded behind SMI.
So, it is much more conservative to avoid claims about what's behind SMI
and stick with talking about things like the language and the constructs
in the language. Hence, creation is the act of constructing something
in SMI, e.g. a novel, or a chair, or a rigorous statement of a theorem,
using other things in SMI.
Since there are things in SMI other than languages, it is true that math
may not be _merely_ a language. It may consist of other sensory-motor
interactions with our environments. If that's your criticism, then I
accept it and admit that we need to broaden the consideration to other
things in SMI. But I won't accept that we have to appeal to the
"supernatural" to define math.
> Are the English poetry and the English language the same?
Clearly not. Poetry is a sub-language, which is why it's so remarkable
when one sees good poetry. The best artists can do so much within very
tight constraints. (And this demonstrates why I'm not a language artist
... because I'm a wind-bag ... can't say anything in under 1000 words. ;-)
> 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.
Yes! The _act_ of transforming one thing into another thing is what
makes the things "living", which is why relational modeling seems so
much more powerful than constituent modeling (though I happen to believe
they're expressively equivalent).
But that doesn't mean we can pierce the ontological veil and directly
see what's behind the elements of SMI.
> 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
OK. Well, again, I have to argue with you (without arguing with
Chaitin). [grin] What we are capable of inferring about reality _is_
calculable and nameable. We can count the words we use. We can
categorize and name our beakers, animals, genes, shirts, etc. And we
can quantitatively compare stories (experimental protocols, poems, etc.).
And since we cannot have a clear idea what's behind the elements of SMI,
my claim is that reality _is_ what's in SMI. And, hence, reality is
calculable and nameable, at least to the extent to which we're concerned
with reality.
--
glen e. p. ropella, 971-219-3846, http://tempusdictum.com
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