Sunday, September 28, 2008
Tuesday, September 23, 2008
Chaos Theory -- Part 2
Strange Attractor:
An attractor is informally described as strange if it has non-integer dimension or if the dynamics on it are chaotic. The term was coined by David Ruelle and Floris Takens to describe the attractor that resulted from a series of bifurcations of a system describing fluid flow. Strange attractors are often differentiable in a few directions, but some are like a Cantor dust, and therefore not differentiable.
The recognition of strange attractors fed the revolution in chaos by giving numerical explorers a clear program to carry out. They looked for strange attractors everywhere, wherever nature seemed to be behaving randomly. Many argued that the earth's weather might lie on a strange attractor. Others assembled millions of pieces of stock market data and began searching for a strange attractor there, peering at randomness through the adjustable lens of a computer.
For now, the excitement went beyond pure science. Ruelle, for example: "I have not spoken of the esthetic appeal of strange attractors. These systems of curves, these clouds of points suggest sometimes fireworks or galaxies, sometimes strange and disquieting vegetal proliferations. A realm lies there of forms to explore, and harmonies to discover."
An attractor is informally described as strange if it has non-integer dimension or if the dynamics on it are chaotic. The term was coined by David Ruelle and Floris Takens to describe the attractor that resulted from a series of bifurcations of a system describing fluid flow. Strange attractors are often differentiable in a few directions, but some are like a Cantor dust, and therefore not differentiable.
The recognition of strange attractors fed the revolution in chaos by giving numerical explorers a clear program to carry out. They looked for strange attractors everywhere, wherever nature seemed to be behaving randomly. Many argued that the earth's weather might lie on a strange attractor. Others assembled millions of pieces of stock market data and began searching for a strange attractor there, peering at randomness through the adjustable lens of a computer.
For now, the excitement went beyond pure science. Ruelle, for example: "I have not spoken of the esthetic appeal of strange attractors. These systems of curves, these clouds of points suggest sometimes fireworks or galaxies, sometimes strange and disquieting vegetal proliferations. A realm lies there of forms to explore, and harmonies to discover."
....to be continued
Friday, September 19, 2008
Thursday, September 4, 2008
Guru Yoga of Milarepa Retreat by Shangpa Rinpoche
We had a two-day retreat of Guru Yoga of Milarepa by Shangpa Rinpoche in August at M.B.A. The assistant sitting next to Rinpoche is Lama Jampa.
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