Archive for June, 2007

14th June
written by simplelight

If you haven’t watched the documentary on Fermat’s Last Theorem you should set aside 45 minutes as soon as you can. The documentary is a splendid testament to what happens when passion and perseverance are coupled with a stunningly sharp mind. Here are some notes from the producer:

There is a brilliant genius from the past who solves an apparently impossible problem. He dies without revealing the solution. This becomes buried treasure, and every subsequent mathematician goes in search of it. There are heroes, villains, rivals, rich prizes, a duel at dawn, a suicide and an attempted suicide, but after 300 years the problem remains intact. The greatest minds on the planet failed to solve it. Undaunted, however, a young boy promises to devote the rest of his life to solving this notorious problem. After thirty years he suddenly identifies a strategy that might work. For seven years he works in secret. He reveals his proof, only to learn that he has made a mistake. He hides away again, humiliated and ashamed, but he returns a year later, this time triumphant. The problem has been solved. His journey is over.

The documentary was about mathematics and mathematicians, but it was also about childhood dreams, ambition, obsession, passion, failure and triumph. Not surprisingly, there was a time when one of the Hollywood studios put in a serious bid to make a feature film, but somewhere along the line the project faded away.

The emotion of the documentary is clear from the first minute. The opening sequence shows Professor Andrew Wiles recalling the moment when he realised that he had solved Fermat’s Last Theorem and achieved his childhood dream. The memory is so moving that he begins to stumble over his words. He then pauses, takes a breath, tries to continue, but eventually he is overcome with emotion and turns away from the camera. There are other moments in the programme that are equally emotional.

I particularly like the final comments from Iwasawa, the Japanese mathematician who came up with the conjecture which was necessary to prove the theorem.

12th June
written by simplelight

It is rare to read a book that has the potential to change one’s entire worldview. This weekend I read Genetic Entropy & the Mystery of the Genome. The author is John Sanford, a professor of genetics at Cornell University, inventor of the gene gun, and holder of 25 patents. His essential thesis is that a blind evolutionary process could not have produced humans from single cell organisms. He gives a multitude of cogent arguments why this is so.

Moreover, he makes a very compelling case that, in fact, mutation and natural selection are actually degrading the genome to such an extent that humans will eventually go extinct. The simple reason is that each generation introduces at least 100 mutations which are both deleterious (degrade the genome) and near-neutral (unlikely to be removed by natural selection). The cost of natural selection would have to be extraordinarily high to remove such a large number of mutations from the gene pool. In addition, the rare beneficial mutations are also near-neutral and consequently impossible to select for.

A lot of this resonates with my experience with genetic algorithms where the vast majority of the population has to be wiped out at each generation to prevent non-useful mutations from multiplying.

What I find fascinating, though, is that everyone I have spoken to about this book immediately dismisses it because it “sounds like Creationism”. Perhaps secularism really has risen to the level of a religion: steeped in dogma and unwilling to confront facts.