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.
Tuesday, August 19, 2008
Monday, August 18, 2008
Chaos Theory -- Part 1
Introduction:
I'm currently reading James Gleick's best-selling book in 1987, Chaos: Making A New Science, and chaos theory has become an increasingly popular metaphor in management literature, regarded as the "new science" of administration. While Gleick did not invent the idea of chaos, nor did he contribute to its scientific principles, he did help lift it from obscurity in the pages of scientific journals and put it into the mainstream.
Butterfly Effect:
A meteorologist, named Edward Lorenz, proved the butterfly effect in 1961. The amount of difference in the starting points of the two curves is so small that it is comparable to a butterfly flapping its wings.
The flapping of a single butterfly's wing today produces a tiny change in the state of the atmosphere. Over a period of time, what the atmosphere actually does diverges from what it would have done. So, in a month's time, a tornado that would have devastated the Indonesian coast doesn't happen. Or maybe one that wasn't going to happen, does.
The Butterfly Effect acquired a technical name: sensitive dependence on initial conditions. And sensitive dependence on initial conditions was not an altogether new notion. It had a place in folklore:
"For want of a nail, the shoe was lost;
For want of a shoe, the horse was lost;
For want of a horse, the rider was lost;
For want of a rider, the battle was lost;
For want of a battle, the kingdom was lost!"
In science as in life, it is well known that a chain of events can have a point of crisis that could magnify small changes. But chaos meant that such points were everywhere. They were pervasive. In systems like the weather, sensitive dependence on initial conditions was an inescapable consequence of the way small scales intertwined with large.
I'm currently reading James Gleick's best-selling book in 1987, Chaos: Making A New Science, and chaos theory has become an increasingly popular metaphor in management literature, regarded as the "new science" of administration. While Gleick did not invent the idea of chaos, nor did he contribute to its scientific principles, he did help lift it from obscurity in the pages of scientific journals and put it into the mainstream.
Butterfly Effect:
A meteorologist, named Edward Lorenz, proved the butterfly effect in 1961. The amount of difference in the starting points of the two curves is so small that it is comparable to a butterfly flapping its wings.
The flapping of a single butterfly's wing today produces a tiny change in the state of the atmosphere. Over a period of time, what the atmosphere actually does diverges from what it would have done. So, in a month's time, a tornado that would have devastated the Indonesian coast doesn't happen. Or maybe one that wasn't going to happen, does.
The Butterfly Effect acquired a technical name: sensitive dependence on initial conditions. And sensitive dependence on initial conditions was not an altogether new notion. It had a place in folklore:
"For want of a nail, the shoe was lost;
For want of a shoe, the horse was lost;
For want of a horse, the rider was lost;
For want of a rider, the battle was lost;
For want of a battle, the kingdom was lost!"
In science as in life, it is well known that a chain of events can have a point of crisis that could magnify small changes. But chaos meant that such points were everywhere. They were pervasive. In systems like the weather, sensitive dependence on initial conditions was an inescapable consequence of the way small scales intertwined with large.
....to be continued
Sunday, August 17, 2008
Saving Lives in the Swimming Pool
Strolling the backyard has been a morning routine since my retirement. Smelling the jasmine and listening to the birds chirping aren't all I do. Refilling the water into the pool and using leaf skimmer to lift up debris and/or worms become chores. You'll be surprised how many lives I have saved. Sometime it mounts up to 10 plus. Today, one bee and a worm got picked up to the pool side and jumped right back into the pool water in no time. It reminds me of what we understand the moth's suicidal for the fire, which is his duty-bound mission in his life span. As for our human body, we are repeating the same scenario day in and day out without knowing it. The first Noble Truth from Buddha Sakyamuni explained to us "Life entails suffering" and "suffering stops when attachment does".
佛寶歌
人天長夜，宇宙黮闇，誰啟以光明？
三界火宅，眾苦煎迫，誰濟以安寧？
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