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Finite and Infinite Games: Difference between revisions
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=== The Global Financial Crisis and the lives of the universe === | === The Global Financial Crisis and the lives of the universe === | ||
[[File:25 sigma event.png|center|thumb|600x600px|Expect a global financial crisis to happen once in several trillion trillion trillion times this long. ''[subs: can we check that?]'']] | |||
<blockquote>“We were seeing things that were 25 [[standard deviation]] moves, several days in a row”.<ref>David Viniar, Chief Financial Officer, [[Goldman|Goldman Sachs]], August 2007.</ref></blockquote>Like the [[common law]], markets are dispositionally historic ''until they aren’t''. Finite techniques work well enough, much of the time, because infinite environments can resemble finite games, much of the time. | <blockquote>“We were seeing things that were 25 [[standard deviation]] moves, several days in a row”.<ref>David Viniar, Chief Financial Officer, [[Goldman|Goldman Sachs]], August 2007.</ref></blockquote>Like the [[common law]], markets are dispositionally historic ''until they aren’t''. Finite techniques work well enough, much of the time, because infinite environments can resemble finite games, much of the time. | ||
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Suddenly probability metaphors fail. ''One'' twenty-five standard-deviation move is preposterous. You would not expect one in several trillion trillion lives of the universe, let alone “several days in a row”.<ref>You would expect a “25-sigma move” on one in 1.3 billion billion billion billion billion billion billion billion billion billion billion billion billion billion days, which is several trillion trillion trillion trillion times as long as the life (to date) of the known universe. More on this fascinating topic on our [[normal distribution]] article.</ref> | Suddenly probability metaphors fail. ''One'' twenty-five standard-deviation move is preposterous. You would not expect one in several trillion trillion lives of the universe, let alone “several days in a row”.<ref>You would expect a “25-sigma move” on one in 1.3 billion billion billion billion billion billion billion billion billion billion billion billion billion billion days, which is several trillion trillion trillion trillion times as long as the life (to date) of the known universe. More on this fascinating topic on our [[normal distribution]] article.</ref> | ||
[[File:Normal vs fat-tailed distribution.png|center|thumb|600x600px|The green bit: normal, but dull. Most events happen here, whether in a finite or infinite game. The orange bit: normal but entertaining. Most non-dull events happen here (if an infinite game); almost all of them (if a finite game). The red bit: terrifying/thrilling. Almost no such events happen in a finite game; a small but significant number will happen in an infinite game.]] | |||
Finite games are concerned with risk. Infinite ones are concerned with uncertainty. But risk and uncertainty are hard to tell apart in normal times. For the parts of a [[normal distribution]] that roughly resemble a “fat-tailed” distribution — most of it — historical approaches will work passably well for both, as long as the events fall within the middle, which for the most part they do. | Finite games are concerned with risk. Infinite ones are concerned with uncertainty. But risk and uncertainty are hard to tell apart in normal times. For the parts of a [[normal distribution]] that roughly resemble a “fat-tailed” distribution — most of it — historical approaches will work passably well for both, as long as the events fall within the middle, which for the most part they do. | ||
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Form is an axiom; substance is its articulation with numbers. If you have right equation you will get the right answer. This depends on the universe being bounded, all rules determined, all [[Unknowns|knowns known.]] It depends, therefore, on ''the conditions existing for a [[finite game]]''. | Form is an axiom; substance is its articulation with numbers. If you have right equation you will get the right answer. This depends on the universe being bounded, all rules determined, all [[Unknowns|knowns known.]] It depends, therefore, on ''the conditions existing for a [[finite game]]''. | ||
Where the universe is not bounded, where rules change, where unknowns swamp knowns[[ | Where the universe is not bounded, where rules change, where unknowns swamp knowns<ref>[[Signal-to-noise ratio|All data is from the past]]. Seeing as there is an infinite amount of data from the future, the portion of the available data we have is, effectively, nil.</ref> — where the [[Infinite game|game is ''infinite'']] — ''substance is not a function of form''. There are no equations, axioms or formulae to follow when interacting with [[Complex system|complex adaptive systems]]. | ||
== It’s all well in theory == | == It’s all well in theory == | ||