I have been reading a fascinating book called Meta Math: The Quest for Omega by the well-known mathematician Gregory Chaitin. In it he describes his own (successful) efforts to take Gödel’s Incompleteness Theorem a step further. Here is a very good review of the book by Jaron Lanier in American Scientist, and here is another, including a summary of the main ideas, in Scientific American.
The book has interesting takes on a lot of things, but I just want to adduce one as a small example of the sorts of brilliant things that Chaitin reports: as you know, human DNA is a digital information code composed of a sequence of four bases. This means that each base can be represented using two bits of information, and since the human genome has about 3 billion bases, this is equal to 6 gigabits. So you can think of your own genetic information as something that would easily fit on an Ipod Nano! Now the interesting thing is that you get half that information from your mother, and the other half from your father. But your father’s part of the information had to be transmitted to your mother through an act of sexual congress (unless you are a test tube baby), and given the amount of time it took him to “transmit,” you can calculate the bandwidth of the connection between your mom and dad. Here’s Chaitin:
Jacob Schwartz once surprised a computer science class by calculating the bandwith of human sexual intercourse, the rate of information transmission achieved in human lovemaking. I’m too much of a theoretician to care about the exact answer, which anyway depends on details like how you measure the amount of time that’s involved, but his class was impressed that the bandwidth that’s achieved is quite respectable! (p. 67)
There are many such fascinating asides in the book, which I recommend highly. Here is one last review by Marianne Freiberger in the Cambridge University Millenium Mathematics Project. Check it out.