But my thoughts in Rio were not on death, they were on life! Inspired by the beautiful beaches, the beautiful women, and the tropical lushness of Rio, my mind was working well.
While in Rio I published a two-part PUC research report. The first part was my Rio breakthrough and is the subject of this book: I realized that using the ideas that I had been developing in order to define randomness or lack of structure, I could come up with an information-theoretic approach to the mysterious incompleteness phenomenon discovered by Gödel, that limits the power of formal axiomatic mathematical theories. [I told this story in an interview, my third and latest TV interview, that was broadcast by Globo News TV in Brazil in June 2001. The Globo News TV channel is simultaneously webcast to the rest of the world, so I was able to see this interview on my PC in NY at the same time that it was on TV in Brazil! Thirty years ago at the Ipanema beach, how could I have imagined that this would be possible?]
The second half of my PUC research report was an English translation of a paper that I had presented at a meeting in Buenos Aires the year before. This paper was called ``To a mathematical definition of `life','' and it was my initial attempt to apply my program-size complexity ideas to biology in order to define what a living organism is and how to measure its complexity. [I don't think that my work in this area was too successful, since it did not lead to a general, abstract mathematical theory of evolution, as I'll explain at the end of the first lecture and in the last interview. In his forthcoming A New Kind of Science, Stephen Wolfram argues that there is no essential difference between us and any universal computer, and therefore no such general theory of evolution is needed. While his thesis is interesting, I feel that it is not the whole story.]
However, the four-day weekend of Carnival all the math came to a full stop, or so I thought! I danced in the street all night to irresistible Brazilian and African rhythms, and watched the sensual Samba Parade. Now, thirty years later, I can see that this was information theory too. After all, from a biological point of view, the purpose of love-making is to exchange information, that's really what Carnival in Rio is all about, about information! [By the way, I fell in love in Rio. At PUC I bought a copy of the LISP 1.5 Programmer's Manual, which was not available in Buenos Aires. That was the beginning of my life-long love affair with LISP!]
So to me, ``information'' is definitely a sexy subject, and it includes my algorithmic information, which is measured in bits of software, biological information, which is measured in kilobases of DNA, and psychological information and thought and the soul, [As I have argued at the end of my book The Unknowable and in the last interview, one can think of the soul as software that is moving from machine to machine. But then what about feelings?] which we know very little about, but will hopefully someday understand. The ideas in this book on algorithmic information and the limits of formal reasoning may seem cold and inhuman, but I hope that they are the first step in the direction of a new, more sensual mathematics of life and creativity.
To the Future! [Regarding the reason for sex and future possibilities, see Mark Ridley, Mendel's Demon (UK title), The Cooperative Gene (US title). For an account of the role of information theory in the early work on molecular biology and DNA, see Lily E. Kay, Who Wrote the Book of Life?]
