experiencefestival.com
The roots of chaos theory date back to about 1900, in the studies of Henri Poincaré on the problem of the motion of three objects in mutual gravitational attraction, the so-called three-body problem. Poincaré found that there can be orbits which are nonperiodic, and yet not forever increasing nor approaching a fixed point.
(The three-body problem is solved by considering that given two massive bodies in circular orbits around a common center of mass there are five positions in space where a third body, of comparatively negligible mass, could be placed which would then maintain its position relative to the two massive bodies. These are called Lagrangarian points and are marked in green above. -AM)
Chaos theory progressed more rapidly after mid-century, when it first became evident for some scientists that linear theory, the prevailing system theory at that time, simply could not explain the observed behavior of certain experiments like that of the logistic map.
(Wiki:A rough description of chaos is that chaotic systems exhibit a great sensitivity to initial conditions. . A common source of such sensitivity to initial conditions is represented on a logistic map as a repeated folding and stretching of the space on which it is defined.
This stretching-and-folding does not just produce a gradual divergence, but an exponential divergence. In fact, exponential divergence explains the connection between chaos and unpredictability:
a small error in the supposed initial state of the system will tend to correspond to a large error later in its evolution.
Hence, predictions about future states become progressively {indeed, exponentially} worse when there are even very small errors in our knowledge of the initial state. -AM)
An early pioneer of the theory was Edward Lorenz whose interest in chaos came about accidentally through his work on weather prediction in 1961. Lorenz was using a basic computer, a Royal McBee LGP-30, to run his weather simulation. He wanted to see a sequence of data again and to save time he started the simulation in the middle of its course. He was able to do this by entering a printout of the data corresponding to conditions in the middle of his simulation which he had calculated last time.
To his surprise the weather that the machine began to predict was completely different to the weather calculated before. Lorenz tracked this down to the computer printout. The printout rounded variables off to a 3-digit number, but the computer worked with 6-digit numbers. This difference is tiny and the consensus at the time would have been that it should have had practically no effect.
However Lorenz had discovered that small changes in initial conditions produced large changes in the long-term outcome.
WSJ
October 8, 2009
Speaking with PBS's Charlie Rose on Monday, Mrs. Pelosi mused publicly about the rising possibility of enacting a value-added tax, or VAT, as part of broader tax reform. "Somewhere along the way, a value-added tax plays into this," she said. "Of course, we want to take down the health-care cost, that's one part of it. But in the scheme of things, I think it's fair to look at a value-added tax as well."
The allure of a VAT for politicians is that it applies to every level of production or service, rakes in piles of money, and is largely hidden from those who ultimately pay it—namely, consumers.
Nearly every European country that has passed national health care has also eventually imposed a VAT, and it's foolish to think the U.S. will be different.
Mrs. Pelosi is the second prominent Democrat to call for a VAT in recent weeks. John Podesta, an adviser to President Obama and president of the very liberal Center for American Progress, called in September for a "small and more progressive" VAT.
Of course, VATs always start "small" and get bigger.
Allacademic.com: The Underwood-Simmons tariff legislation of 1913 included a graduated income tax provision. The income tax only affected 2% of the workforce, but established the fiscal tool long advocated by economic reformers and popularly supported. Rate progressivity was only part of the historic legacy of the 1913 revenue bill. “It is much safer to begin upon somewhat moderate lines” wrote Wilson.
Saturday Evening Post
by Benton McMillin
May 17, 1913
President Wilson is deeply interested in a thorough reform of our tax system. He has studied it carefully and has called an extra session of Congress to consider the whole question. He is keeping in close touch with the House and the Senate, and is urging remedial legislation. His past record demonstrates that he may be relied on to carry out party pledges and the platform on which he was elected. He has the courage of his convictions and is not afraid to act.
We may also judge, from both his declaration and his record, that he stands ready to initiate reform whenever and wherever the public weal demands it. It may be predicted with perfect confidence that, whatever other tax fails, the income tax will not fail. Wherever there is a revolution it will be against some other form of taxation instead of this.
It is founded on the rock- not the sand- and will stand against all storms.
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