Tuesday, December 21, 2010
Scale and scales
There is a story from Oriental religion that is widely repeated in the western world: a teacher points at the moon and what his students see is just his fingernail. This story is assumed to be about the gap between words and what the words signify. But a different interpretation would not invalidate the standard meaning. Here is what occurred to me. Perhaps this teacher MEANT his students to see his fingernail AND the moon. Maybe his story was about the gap in size between the sliver of nail at the end of a finger and the size of the crescent in the sky. The gap between what man thinks he knows and what is to be known, or even, between what a man doesn't know, and what there is actually in terms of the unknown.
Monday, December 20, 2010
Winking at Complexity
This link is to an interesting article by a theoretical biologist, at Scipps Oceanogrphy Institute. He talks about what large changes in various systems have in common. He is attempting to link the financial collapse, the climate change evidence, and other similar events. He talks about synchronization between parts of a system, about a slowness just before the collapse, and the kind of generalization. The guy is on the verge of seeing something real. I would recommend anyone to read this article. Let me just quote a couple of parts here.
...Examples of catastrophic and systemic changes have been gathering in a variety of fields, typically in specialized contexts with little cross-connection. Only recently have we begun to look for generic patterns in the web of linked causes and effects that puts disparate events into a common framework—a framework that operates on a sufficiently high level to include geologic climate shifts, epileptic seizures, market and fishery crashes, ....
The main themes of this framework are twofold: First, they are all complex systems of interconnected and interdependent parts. Second, they are nonlinear, non-equilibrium systems that can undergo rapid and drastic state changes.
... there is emerging agreement that ignoring the seemingly incomprehensible meshing of counterparty obligations and mutual interdependencies (an accountant’s nightmare, more recursive than Abbott and Costello’s “Who’s on first?”) prevented real pricing of risk premiums, which helped to propagate the current crisis.
A parallel situation exists in fisheries, where stocks are traditionally managed one species at a time. Alarm over collapsing fish stocks, however, is helping to create the current push for ecosystem-based ocean management. ... Though the geological record tells us that global temperatures can change very quickly, the models consistently underestimate that possibility. This is related to the next property, the nonlinear, non-equilibrium nature of systems.
Most engineered devices, consisting of mechanical springs, transistors, and the like, are built to be stable. That is, if stressed from rest, or equilibrium, they spring back. Many simple ecological models, physiological models, and even climate and economic models are built by assuming the same principle: a globally stable equilibrium. A related simplification is to see the world as consisting of separate parts that can be studied in a linear way, one piece at a time. These pieces can then be summed independently to make the whole. Researchers have developed a very large tool kit of analytical methods and statistics based on this linear idea, and it has proven invaluable for studying simple engineered devices. But even when many of the complex systems that interest us are not linear, we persist with these tools and models. It is a case of looking under the lamppost because the light is better even though we know the lost keys are in the shadows. Linear systems produce nice stationary statistics—constant risk metrics, for example. Because they assume that a process does not vary through time, one can subsample it to get an idea of what the larger universe of possibilities looks like. This characteristic of linear systems appeals to our normal heuristic thinking.
Nonlinear systems, however, are not so well behaved. They can appear stationary for a long while, then without anything changing, they exhibit jumps in variability—so-called “heteroscedasticity.” For example, if one looks at the range of economic variables over the past decade (daily market movements, GDP changes, etc.), one might guess that variability and the universe of possibilities are very modest. This was the modus operandi of normal risk management. As a consequence, the likelihood of some of the large moves we saw in 2008, which happened over so many consecutive days, should have been less than once in the age of the universe.
Our problem is that the scientific desire to simplify has taken over, something that Einstein warned against when he paraphrased Occam: “Everything should be made as simple as possible, but not simpler.” Thinking of natural and economic systems as essentially stable and decomposable into parts is a good initial hypothesis, current observations and measurements do not support that hypothesis—hence our continual surprise. Just as we like the idea of constancy, we are stubborn to change. The 19th century American humorist Josh Billings, perhaps, put it best: “It ain’t what we don’t know that gives us trouble, it’s what we know that just ain’t so.”
So how do we proceed? There are a number of ways to approach this tactically, including new data-intensive techniques that model each system uniquely but look for common characteristics. However, a more strategic approach is to study these systems at their most generic level, to identify universal principles that are independent of the specific details that distinguish each system. This is the domain of complexity theory.
Among these principles is the idea that there might be universal early warning signs for critical transitions, diagnostic signals that appear near unstable tipping points of rapid change. The recent argument for early warning signs is based on the following: 1) that both simple and more realistic, complex nonlinear models show these behaviors, and 2) that there is a growing weight of empirical evidence for these common precursors in varied systems.
A key phenomenon known for decades is so-called “critical slowing” as a threshold approaches. That is, a system’s dynamic response to external perturbations becomes more sluggish near tipping points. ... Another related early signaling behavior is an increase in “spatial resonance”: Pulses occurring in neighboring parts of the web become synchronized. Nearby brain cells fire in unison minutes to hours prior to an epileptic seizure, for example, and global financial markets pulse together. ...
...Examples of catastrophic and systemic changes have been gathering in a variety of fields, typically in specialized contexts with little cross-connection. Only recently have we begun to look for generic patterns in the web of linked causes and effects that puts disparate events into a common framework—a framework that operates on a sufficiently high level to include geologic climate shifts, epileptic seizures, market and fishery crashes, ....
The main themes of this framework are twofold: First, they are all complex systems of interconnected and interdependent parts. Second, they are nonlinear, non-equilibrium systems that can undergo rapid and drastic state changes.
... there is emerging agreement that ignoring the seemingly incomprehensible meshing of counterparty obligations and mutual interdependencies (an accountant’s nightmare, more recursive than Abbott and Costello’s “Who’s on first?”) prevented real pricing of risk premiums, which helped to propagate the current crisis.
A parallel situation exists in fisheries, where stocks are traditionally managed one species at a time. Alarm over collapsing fish stocks, however, is helping to create the current push for ecosystem-based ocean management. ... Though the geological record tells us that global temperatures can change very quickly, the models consistently underestimate that possibility. This is related to the next property, the nonlinear, non-equilibrium nature of systems.
Most engineered devices, consisting of mechanical springs, transistors, and the like, are built to be stable. That is, if stressed from rest, or equilibrium, they spring back. Many simple ecological models, physiological models, and even climate and economic models are built by assuming the same principle: a globally stable equilibrium. A related simplification is to see the world as consisting of separate parts that can be studied in a linear way, one piece at a time. These pieces can then be summed independently to make the whole. Researchers have developed a very large tool kit of analytical methods and statistics based on this linear idea, and it has proven invaluable for studying simple engineered devices. But even when many of the complex systems that interest us are not linear, we persist with these tools and models. It is a case of looking under the lamppost because the light is better even though we know the lost keys are in the shadows. Linear systems produce nice stationary statistics—constant risk metrics, for example. Because they assume that a process does not vary through time, one can subsample it to get an idea of what the larger universe of possibilities looks like. This characteristic of linear systems appeals to our normal heuristic thinking.
Nonlinear systems, however, are not so well behaved. They can appear stationary for a long while, then without anything changing, they exhibit jumps in variability—so-called “heteroscedasticity.” For example, if one looks at the range of economic variables over the past decade (daily market movements, GDP changes, etc.), one might guess that variability and the universe of possibilities are very modest. This was the modus operandi of normal risk management. As a consequence, the likelihood of some of the large moves we saw in 2008, which happened over so many consecutive days, should have been less than once in the age of the universe.
Our problem is that the scientific desire to simplify has taken over, something that Einstein warned against when he paraphrased Occam: “Everything should be made as simple as possible, but not simpler.” Thinking of natural and economic systems as essentially stable and decomposable into parts is a good initial hypothesis, current observations and measurements do not support that hypothesis—hence our continual surprise. Just as we like the idea of constancy, we are stubborn to change. The 19th century American humorist Josh Billings, perhaps, put it best: “It ain’t what we don’t know that gives us trouble, it’s what we know that just ain’t so.”
So how do we proceed? There are a number of ways to approach this tactically, including new data-intensive techniques that model each system uniquely but look for common characteristics. However, a more strategic approach is to study these systems at their most generic level, to identify universal principles that are independent of the specific details that distinguish each system. This is the domain of complexity theory.
Among these principles is the idea that there might be universal early warning signs for critical transitions, diagnostic signals that appear near unstable tipping points of rapid change. The recent argument for early warning signs is based on the following: 1) that both simple and more realistic, complex nonlinear models show these behaviors, and 2) that there is a growing weight of empirical evidence for these common precursors in varied systems.
A key phenomenon known for decades is so-called “critical slowing” as a threshold approaches. That is, a system’s dynamic response to external perturbations becomes more sluggish near tipping points. ... Another related early signaling behavior is an increase in “spatial resonance”: Pulses occurring in neighboring parts of the web become synchronized. Nearby brain cells fire in unison minutes to hours prior to an epileptic seizure, for example, and global financial markets pulse together. ...
My point in the above excerpts was not to convey the cogency of his arguments, just give a sense of his approach, so click on the hyperlink above and read the whole article.
What you will not find in the article (though he verges on it at moments) is how gravely he UNDERESTIMATES the complexity of what he is trying to analyze. Notice some of those big words, he may be waving them around like a torch in a tribal dance. But for cutting edge science this thinker (George Sugihara, a theoretical biologist is the McQuown Chair in Natural Science at Scripps) has done an outstanding job.
Wednesday, December 8, 2010
Quoth the craven, evermore
Numbers are an aspect of reality---what kind, even mathematicians disagree. To a non-math person it seems that they are the backbone, the rigidity of science. All the explanations of science largley neglect the math parts I notice. Anyway, if you want to be precise you go to the right of the decimal, and, maybe, just keep moving.
So is it not odd that these same numbers let us avoid----reality? What brought this to mind was the way numbers of years can fudge an old mystical "method." The method is not one Jan Cox used himself, , though he mentioned it. He merely said, it was not helpful to him. My recollection is of an obvious sense when he spole that it was a perfectly valid method. (By method I mean the doing of the mystical search, not the talking about that pursuit.) The tool then we are discussing is (odd how long it is taking me to come to the point here) is the remembering of your own mortality. That you, the subject, whatever else you know, you know, you will die.
Assuming that is clear, and even writing about it objectively requires some steeliness, numbers can let you avoid this fact. Yes, if you think, well who knows when I will die, and you think one hundred years, who knows I could live that long, some people do, it could happen,
you are escaping, turning from, averting your consciousness from the reality of ---reality.
Obviously I am not recommending this method. And I will recall to everyone, what Jan said, if you are not smiling you did not "get it." He did not find this method helpful. It is nice though to have an example of a method, in case we forget what methods even are. Because to speak of something actively being used by the speaker, is to diminish it's value for the speaker.
Sunday, December 5, 2010
The meaning of freedom
how interesting that in a world of governments, of people with agenda, of mechanical struggle, of electronic monitoring, the main---only--??--place of external freedom should be, the geographical place where it all began, --the place where men domesticated, fire, ---
caves
caves of mexico
caves of asia
caves I don't know about
.
Notice I said external freedom.
The nature, possibilities, limits, meaning of
freedom
is at the heart of the teaching of Jan Cox.
And if you take the above to have any political slant,
you are reading the wrong blog.
Jan actually did address the world of history---he saw the individual struggle as where one sought knowledge alternatively between the world outside and that within
and he had marvelous things to say on the subject of the external.
Rather than risk wasting some energy in what he said, let me just mention one thing,
that change is,
IS,
but the cycles are beyond that of the life span of the individual.
News that is new.
Wednesday, December 1, 2010
Is Antarctica at the top or at the bottom?
When I recall the words of Jan Cox, and his description of what he chose to spend his life doing, "I call it the Work, (Way Of Real Knowledge) because that is what it is--Work, " words can seem like ice. Surface ice, the ice over a continent, a continent of mountains, all underneath a plane of unbidden white.
Sunday, November 21, 2010
Friday, November 19, 2010
Let there be....
How do you annotate a flash of light?
Such is the chore facing, not this those concerned to convey the burden of the ideas of Jan Cox, but the issue facing anyone who investigates the nature of human reality.
The sun glinting in the trees, the carlights on the bedroom wall, the juncture of the light switch...
These phrases only make sense to someone who has experienced them. What can more words add to the experience itself, except the dubious assumption that our experiences are the same?
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