Mikhail 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 ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org