Martin Gardner, Don Knuth, John Wheeler and G. Spencer Brown

Today I got in the mail the March issue of the Notices of the AMS, and in its cover there is an interesting frament of a letter from Martin Gardner to Don Knuth. I had already seen (years ago, at the suggestion of Fernando Tohmé) that strange section of Wheeler's book, but I didn't know about G. Spencer Brown and his "Laws of Form".
 Looking for information on it, I found this page, where a critique is offered. I quote:

John D. Collier wrote:

"The Laws of Form are equivalent to propositional calculus. Spencer Brown showed LoF -> PC in his book. B. Banaschewski showed the opposite entailment in Notre Dame Journal of Formal Logic, 3, (1977): 507-509.[...] As I guess people will start to wonder by now why we need Spencer-Brown then, if his algebra is merely equivalent to something which is very well-known, I want to remark that the axiom system of LoF is much simpler than the usual axiom systems for PC. Moreover, these axioms are derived from 2 extremely simple and intuitively understandable properties of the act of making a distinction.''

That is intriguing enough to merit looking at those axioms. Another quote from the same page:

Laws of Form has received a mixed reception. Although in some circles it is treated with something approaching awe, there are detractors who dismiss Spencer Brown with extreme prejudice. Some dismiss him because of the formal equivalence between his logic and the Boolean / propositional logic it supposedly surpassed (cf. Collier's remarks above). Others are frank about having been put off by Spencer Brown's penchant for being cryptic -- both in his writings and in his behavior at meetings and lectures. 

Big question: could one find Spencer-like axioms for intuitionistic logic?

Pereval, Fomenko and the media post-scarcity

Pereval

A few days ago someone had the good idea to display interesting books from the math library, books otherwise lost in the stacks, but are appealing to anybody interested in mathematics. Among these books was Mathematical Impressions, an illustrated book by A. T. Fomenko. (Google doesn't show any illustrations in its entry for the book but you can see some of Fomenko's images here:  

Fomenko is a mathematician who draws and is also famous because of his theory that a whole milennium is missing in history: http://en.wikipedia.org/wiki/New_Chronology_(Fomenko) . (Thanks to Octavio Mendoza Hernandez and Hernan Cendra for introducing me to the works by Fomenko).

Reading the introduction to the book, I learned of an animated movie made by someone named Tarasov. A few minutes after learning of its existence, I had googled and found out more details about the  movie:http://www.imdb.com/title/tt0259499/plotsummary and I could watch it as well:http://video.yandex.ru/users/taribulba/view/112/

This proved once again that we are living in a post-scarcity society with regards to cultural goods such as movies, books and music. This is a shift as big as the invention of printing. It also puts responsibility on your shoulders: you can watch/read/listen to almost any work produced by humankind. What are you going to do next?

Para convertir los dvi a pdf sin perder los dibujos ni el formato A4.


1. latex mydocument.tex
2. dvips -t A4 mydocument.dvi
3. ps2pdf mydocument.ps