Tuesday, 30 September 2008

Mathematical treasures by Gregory Chaitin

My wanderings over various disciplines that usually lead mt to and fro, this time have led me back to gregory Chaitin. I have already read some of his articles while writing Country of Blindfolded bit this time the search has been started by a provocative paper How real are real numbers?.

This has directed me to Irreducible Complexity in Pure Mathematics and finally to a delightful, easy to read but very deep Meta Math! The Quest for Omega. The last one is especially worth recommending. Mathematics that is told with gusto and personal interest.

There are whole passages that are so close to my soul, that I can only quote them in extenso:
In my opinion, the view that math provides absolute certainty and is static and perfect while physics is tentative and constantly evolving is a false dichotomy. Math is actually not that different from physics. Both are attempts of the human mind to organize, to make sense, of human experience; in the case of physics, experience in the laboratory, in the physical world, and
in the case of math, experience in the computer, in the mental mindscape of pure mathematics.

And mathematics is far from static and perfect; it is constantly evolving, constantly changing, constantly morphing itself into new forms. New concepts are constantly transforming math and creating new fields, new viewpoints, new emphasis, and new questions to answer. And mathematicians do in fact utilize unproved new principles suggested by computational experience, just as a physicist would.

And in discovering and creating new mathematics, mathematicians do base themselves on intuition and inspiration, on unconscious motivations and impulses, and on their aesthetic sense, just like any creative artist would. And mathematicians do not lead logical mechanical “rational” lives. Like any creative artist, they are passionate emotional people who deeply care about their art, they are unconventional eccentrics motivated by mysterious forces, not by money nor by a concern for the “practical applications” of their work.

I know, because I’m one of these crazy people myself! I’ve been obsessed by these questions for my whole life, starting at an early age. And I’ll give you an insider’s view of all of this, a first-hand report from the front, where there is still a lot of fighting, a lot of pushing and shoving, between different viewpoints. In fact basic questions like this are never settled, never definitively put aside, they have a way of resurfacing, of popping up again in transformed form, every few generations. . .

So that’s what this book is about: It’s about reasoning questioning itself, and its limits and the role of creativity and intuition, and the sources of new ideas and of new knowledge. That’s a big subject, and I only understand a little bit of it, the areas that I’ve worked in or experienced myself. Some of this nobody understands very well, it’s a task for the future. How about you?! Maybe you can do some work in this area. Maybe you can push the darkness back a millimeter or two! Maybe you can come up with an important new idea, maybe you can imagine a new kind of question to ask, maybe you can transform the landscape by seeing it from a different point of view! That’s all it takes, just one little new idea, and lots and lots of hard work to develop it and to convince other people! Maybe you can put a scratch on the rock of eternity!

A good read ahead

Just a short note on a book I have found on the arXiv:
Complex and Adaptive Dynamical Systems: A Primer by Claudius Gros.

On first impression it looks interesting and accessible, an joind an already quite rich shelf of electronically available books on networked systems.

Sunday, 21 September 2008


A couple of news stories have drawn my worried attention to the status of medical research. The appearance of more and more bacteria strains that are highly resistive to the current generations of antibiotics is showing the difference between a natural process - such as evolution of bacteria - and the socially driven planned activity of medical research.

While it would be unjust to call the process under which bacteria reach resistance to new generations of drugs "easy" and "costless" (as the billions of dying bacteria for each one that survives and multiplies prove), the human effort, with its needed billions of dollars is much less flexible.

I recall a quote from Lem's Magellan Cloud, hwere infections are deemed to be long gone - one of very few blunders of Lem. Nope. It's a lost war.

And in the current political and social climate, the situation is even worse due to lack of concentrations, and anti-scientific sentiments. I have read some news stories in the Polish dailies - accompanied by lots of supporting WEB comments - condemning doctors and medical industry for its inability to fight "trivial diseases". Probably, many of these comments were by people who discarded their antibiotic treatment just after a couple of days, when they "felt better".

I am quite pessimistic for the next 20 years. If, as recent article in Science claims,
more people die from the methicillin-resistant Staphylococcus aureus (MRSA) bacterium than from HIV in the United States

then we need to start worrying. The number of new drugs is decreasing. The activity of bacteria is not and will not. You do the math yourself.

Revival - perhaps

Due to vacation season and lots of work I have almost abandoned the blog in the past months. Perhaps it is time to revive it? I'll try...