This year, which is this January month, we have quite a bit of snow (we had some also in December last year).
January is almost gone, just one week left. I’ll meet neuro-science biologists, B.Y. and another from Illinois, on January 29 (if I make it for a morning seminar :-)) and January 30. B.J. And I met twice at Glencoe Crossing Starbucks last December.
There were a number of Introduction to Mathematics which meant to introduce readers to some topics not covered at high school, and to give an idea of the general mathematical style, away from the high school mathematics. They were mostly limited affairs, not terribly ambitious, and often rather shallow. Thus when I recently started to write a text which would teach the entire mathematics (up to a level–I need only four thousand years to get my text advanced) I called it Learn Mathematics. I wrote the initial few KBytes and… stopped. I hope to continue once I finish this blog entry. So far the text resides on my Eee (PC) only, which is not a good idea. I need to upload it to wlod.net.
Once again (again and again) I have too many plans. For instance, today I participated in a meeting of writers from my senior citizen building (these meetings are conducted by a woman who is one way or another a professional writer; she does it well). Thus I already feel like starting another Tangia site, this time under ipage. This time I feel like doing it totally alone (if at all; it would me more rational to give up on this idea).
In addition to Learn Mathematics I also want to start another project, which is with me for years: defining mathematics in my own way. I want to treat mathematics like a computer, I want to define it’s architecture (like a computer architecture). There is nothing wrong with this because ordinarily one would not use the assembler language, one would use advanced languages. I mean that I am not restricting mathematics in any way by limiting its architecture. Mathematics is finite at any moment, meaning that only finitely many characters are devoted to mathematics. Thus the countable (\(\aleph_0)\) size of the architecture is not a true limitation.
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In my architecture there are functions but they don’t have any explicit parameters. There is just \(f\), and never \(f(x)\) or \(f(x\ y)\) or similar. Actually, implicitly, everything is a function of everything or at least of a countable set of variables. The mathematics/computer is always in a state. There is a countable set of variables, a countable set of constants, and the theorems make assumptions about the state of the computer (values of variables), and derive conclusions from these assumptions. That’s what happens literally. The literal description is limited. But there is also (full of imagination :-)) interpretation. Most of the true or classical mathematics happens via interpretations.
A few years ago J.M. mentioned to me Hilbert’s quantifier free logic (or logical notation, which in a sense is the same). This one statement made a great impression on me. It told me how mechanical is mathematics. Any philosophy about it should be forbidden :-). Logic is but a consequence of the mechanical nature of the Nature (of extremely simplified Nature). On one hand there is the hopeless chaos of Physics, and on the other hand there is a mechanical fragment of the World (the mechanical laws which govern the strings of characters), of some of its aspects, which allow us to study the Nature to our best. But that mechanics leads to chaos too, in more than one way. Even when we limit ourselves to the classical, so-called deterministic Newtonian mechanics (there is nothing really deterministic about it except in a fictional, formal sense), and even if we limit ourselves still much more to the mechanism of strings, we still run into Chaos very fast. Fortunately, we still have time to enjoy mathematics–and that fluctuation is a part of the Chaos as well 🙂
Enough of this disgusting rumble.