Waking Life

Kant says somewhere: "The lunatic is a dreamer in the waking state." According to Krauss, "Insanity is a dream in which the senses are awake." Schopenhauer terms the dream a brief insanity, and insanity a long dream. Hagen describes delirium as a dream-life which is inducted not by sleep but by disease. Wundt, in his Physiologische Psychologie, declares: "As a matter of fact we ourselves may in dreams experience almost all the manifestations which we observe in the asylums for the insane."

Sigmund Freud, The Interpretation of Dreams, p. 66.

Black Swans in the Market

Modern portfolio theory is based on the assumption that changes in stock prices are normally distributed (follow a bell curve). Benoit Mandelbrot and Nassim Nicholas Taleb disagree with this assumption, and believe market crashes like that of 1987 are much more likely to occur than standard theory predicts.

For my spring 2006 U.C. Berkeley Extension Statistics class I created a presentation Are Daily Changes in Stock Prices Normally Distributed? I analyzed MSFT (used in the standard MBA Finance textbook as an example of normality!), BRKA, and the S&P 500 index over various date ranges. I found none of them satisfied statistical tests for normality.

Black Swans

"Black Swans", as unlikely or unexpected economic events, are currently in the news. This usage was popularized by Nassim Nicholas Taleb. It was based on the old European belief that all swans were white, which was contradicted by the discovery of black swans in Australia. But as I discussed earlier genus and species are human-defined categories. There is no logical contradiction inherent in a black swan, and probabilities related to finding one are really probabilities of finding individuals (animal instances) fitting into ill-defined categories.

Note the first black swan was discovered in 1697, over 150 years before publication of Darwin's On the Origin of Species (1859) and over 250 years before Watson and Crick's A Structure for Deoxyribose Nucleic Acid (DNA) (1953). So seventeenth century notions of species would not include modern concepts of evolutionary descent or DNA similarity. Instead they were based on ideas of fixed categories inherited from Aristotle.

Progress in GPGPU Ray Tracing

I've been getting traffic and questions about my pages on Cell and CUDA ray tracing. Saarland University has been doing some interesting work on Cell and CUDA ray tracing including this paper: Realtime Ray Tracing on the GPU with BVH-based Packet Traversal.