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January 10, 2005
The Occultism of Stock-Picking
There is no contradiction between apparent lack of mathematically-tractable pattern and the existence of "exploitable opportunities" for prediction. If the market is not totally random (that is, if it has some 'memory', if every movement is not causally isolated from those that precede it) then such opportunities should exist. But these opportunities may be in the form of inexplicable, and probably impermanent, correlations between apparently unrelated factors.
In Paulos' view if a tip was good traders would not find the want of explanation troubling (they may even quietly admit that the situation was similar with their analytical systems...) Making superlative hyperstitional use of Plato, he states that traders would not care whether the shadows in the cave were 'real' or not so long as they turned a profit, and would regard the cave as a "bargain basement"
Given this, Paulos suggests that the supposedly rational, but scarcely successful, predictions of technical analysis might profitably be replaced by a "counterintuitive investment strategy" based on Parrondo's paradox.
Parrondo's paradox states that two dice-games in which the trend is towards loss can be combined randomly to produce an game where the definite trend is in the opposite direction. The two games represent in abstract two types of ratchet mechanism, which combine in this unexpected way. The paradox has a direct physical analog in a process whereby grains on a sloped surface, when shaken in a certain repetitive way, counterintuitively move upwards rather than down the slope.
In Parrondo's paradox the rules of the two games are apparently arbitrary: they have no special relation to the playing 'surface'. Paulos suggests then that a successful trading strategy may well take a similar form "depend[ing] in some way on the cross-correlation between a pair of stocks or...on some value being a multiple of 3:" ...that is, occult numerology, simply trusting blindly in pattern-matching, may be the most mathematically-informed approach to the stock-market!
By forcing apart explanation and prediction (the only rational course), we have made our stockpicking procedure by definition clairvoyant or magical.
The cause of so many people avowedly believing numbers to be "boring", and money to be a vacuous circulatory medium must be the learnt conviction that the actual amounts, sums, exchanges of number in everyday life, and their relationships, are "arbitrary", that there is nothing to say about them. Whereas this may seem a thoroughly rational position, it is fairly obvious that it militates against some basic cognitive instincts (pythagorean intuitions, we might say). Indeed it is arguably the role of mathematical education to beat such tropisms toward numerological play out of us, to make numbers work for us rather than enchant us with their limitless combinatorial richness. All the 'superstitious' qualities of number-relation are supressed in favour of a utilitarian approach to quantitative calculation. We are all aware that superstitious or irrational approaches to number abound in our 'inner life' (especially with respect to money) but it is not generally considered polite or sane to propose them as being socially or politically significant. To the extent they are acknowledged at all, they remain faintly embarassing and deplorable infantile tendencies with regard to the serious business of number-crunching.
My father, who taught mathematics to children for over a decade, conducted research with primary-school-age children which showed that many of them developed private methods for carrying out mathematical operations differing procedurally from those they had been taught; the children created well-defined working patterns, coping prcedures that made things work for them, and sometimes displayed intuitive insights into numerical relationships beyond what was strictly required for the operation in question. Such "vernacular mathematics" or popular numeracy will maintain a stubborn social inexistence unless one actually sets out to expose it, because it is systematically supressed by "royal" mathematics, which would have all qualitatively distinct routes reducible to one analytical truth, and any remaining difference marked as trivial or arbitrary. A huge variety and richness is concealed beneath the metanarratives of royal mathematics. (The introduction of 'investigational mathematics' into schools is IMHO a rare example of truly progressive change in the [UK] schools curriculum, that is if it hasn't already been reversed by those regular anticounter-revolutionaries' back-to-basics campaigns.)
A telling symptom of the deep ingrainedness of the received principle of the 'uninterestingness' of number qua number is that laypeople asked to simulate the result of random coinflips tend to make them overly featureless: They do not include enough of the 'surprisingly' long runs of heads or tails which would occur in a truly random sequence. Inversely, when presented with actual random data displaying these 'patterns' the non-statistician is tempted to furnish unwarranted explanations (the flipside of the occult stockpickers "unwarranted success").
Paulos suggests that in particularly intractable situations, the autocensored vagabond arithmetic of "popular numeracy" may be of as, if not more, effective than its imperial captor.
Posted by robin at January 10, 2005 06:34 PM