Thus spake Russ Abbott circa 11/01/09 11:21 PM: > I think you're agreeing with me. It's the concepts that are important, not > the equations. To the extent that you can read the equations as statements > about concepts the equations talk to you. But a computer can read and > calculate with those same equations without the concepts. The concepts are > in the mind of the person reading the equations, not in the equations > themselves.
The truth is that _both_ the formalisms and the concepts are integral to math. Equations without concepts is not math and concepts without automatically transformable sentences (e.g. equations) is not math. The same is true with any language, including English. The point is that math (like science) consists largely of an effort to formalize things so that we can think (as well as delegate, teach, and repeat) clearly about those things. I don't know what the percentage of artists is who feel themselves in the business of formalizing the creation of artifacts; but an artist who understands how important formalization is to large-scale cooperation will have no trouble understanding the relationship between equations (or, more generally, automated deduction) and mathematical concepts. My guess about art is that most people who self identify as artists are against relying on consensus methods, i.e. art is a very personal thing both for the artist and the audience. (Note that I used "personal" rather than "subjective".) To rigorize (rigorify?, rigorate?) art is to remove the art. But I also guess that each artist (or art lineage) has a set of, fairly rigorous, methods associated with her (it). The rigor may be contained in the fingers instead of in symbols on paper, but the rigor would be there somewhere for any artist capable of repeating their work. (Unless one believes in luck and a "good artist" is just a lucky person.) This tacit vs. explicit methodological dichotomy may be the major cause for incommensurance between any of the more intuitive human activities (like entrepreneurship, art, scientific speculation) vs. the more inferential/reasoned activities (like accounting, manufacturing, falsification), and those people proficient in one but not the other. -- glen e. p. ropella, 971-222-9095, http://agent-based-modeling.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
