My dad, a fan of Chaos Theory, just sent me this interesting article about it and some of its history. Some of these things I already knew, but for the most part it was greatly revealing.
When I visit my parents home this winter, there will be a greater chance of me finally reading the pile of books he left on my desk a few months ago ;)
MATHEMATICS: CATASTROPHE THEORY, STRANGE ATTRACTORS, CHAOS
The following points are made by Nigel Calder (citation below):
1) Go out of Paris on the road towards Chartres and after 25 kilometers you will come to the Institut des Hautes Etudes Scientifiques at Bures-sur-Yvette. It occupies a quite small building surrounded by trees. Founded in 1958 in candid imitation of the Institute for Advanced Study in Princeton, it enables half a dozen lifetime professors to interact with 30 or more visitors in pondering new concepts in mathematics and theoretical physics. A former president, Marcel Boiteux, called it “a monastery where deep-sown seeds germinate and grow to maturity at their own pace.”
2) A recurring theme for the institute at Bures has been complicated behavior. In the 21st century this extends to describing how biological molecules — nucleic acids and proteins — fold themselves to perform precise functions. The mathematical monks in earlier days directed their attention towards physical and engineering systems that can often perform in complicated and unpredictable ways.
3) Catastrophe theory was invented at Bures-sur-Yvette in 1968. In the branch of mathematics concerned with flexible shapes, called topology, Rene Thom found origami-like ways of picturing abrupt changes in a system, such as the fracture of a girder or the capsizing of a ship. Changes that were technically catastrophic could be benign, for instance in the brain’s rapid switch from sleeping to waking. As the modes of sudden change became more numerous, the greater the number of factors affecting a system.
Continue reading ‘On Chaos Theory’
by Michael Shermer – Scientific American
I found this interesting read earlier this morning almost by chance on the RichardDawkins.net Twitter feed… I just finished reading it and although it doesn’t give the complete explanation about this so-called Agenticity it made me think different about certain ideas we have about some behaviors of beliefs.
Souls, spirits, ghosts, gods, demons, angels, aliens, intelligent designers, government conspirators, and all manner of invisible agents with power and intention are believed to haunt our world and control our lives. Why?
The answer has two parts, starting with the concept of “patternicity,” which I defined in my December 2008 column as the human tendency to find meaningful patterns in meaningless noise. Consider the face on Mars, the Virgin Mary on a grilled cheese sandwich, satanic messages in rock music. Of course, some patterns are real. Finding predictive patterns
in changing weather, fruiting trees, migrating prey animals and hungry predators was central to the survival of Paleolithic hominids.
The problem is that we did not evolve a baloney-detection device in our brains to discriminate between true and false patterns. So we make two types of errors: a type I error, or false positive, is believing a pattern is real when it is not; a type II error, or false negative, is not believing a pattern is real when it is. If you believe that the rustle in the grass is a dangerous predator when it is just the wind (a type I error), you are more likely to survive than if you believe that the rustle in the grass is just the wind when it is a dangerous predator (a type II error). Because the cost of making a type I error is less than the cost of making a type II error and because there is no time for careful deliberation between patternicities in the split-second world of predator-prey interactions, natural selection would have favored those animals most likely to assume that all patterns are real.
[ Seen on RichardDawkins.net ]