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Toxic Mathematics

Toxic Mathematics. Jerome Ravetz JMI July 30 2008. For two and a half thousand years, since the time of Pythagoras, mathematics has been the paradigm of real knowledge in our civilisation.

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Toxic Mathematics

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  1. Toxic Mathematics Jerome Ravetz JMI July 30 2008

  2. For two and a half thousand years, since the time of Pythagoras, mathematics has been the paradigm of real knowledge in our civilisation. • The depth of pure mathematics, and the power of applied mathematics, combine to make a tool of unique quality. • But now it is time to think again.

  3. It is possible for a mathematical science to be vacuous. I call this ‘GIGO science’ - for ‘Garbage in, garbage out’. • One sign of this condition is when results are stated with no ‘error bars’. • A measurement without an error bar is like a bet without the odds - hanging nowhere.

  4. More generally, GIGO is detected when the precision of the numerical outputs exceeds the accuracy of the quantitative inputs. • The description of Economics, as the science with one-digit inputs and three-digit outputs, amounts to GIGO.

  5. Of course, Statistics enables us to increase our certainty about the properties of sets of numbers. • But we all know the saying, ‘There are lies, damned lies, and statistics’. • It is important to know how this can happen. See the book by Darryl Huff.

  6. More serious perversions of mathematics occur when it is applied to decision making in social affairs. • A classic case is the ‘Theory of Games and Economic Behavior’ of von Nuemann and Morgenstern. • This was applied to Nuclear Strategy by Herman Kahn, in On Thermonuclear War’

  7. Kahn did not invent thermonuclear war. • He was trying to apply the best contemporary social science to a terrible dilemma. • Both the Americans and the Soviets had enough bombs and missiles to destroy civilisation. • How could they be deployed rationally?

  8. …Our calculations indicate that … the restoration of our prewar GNP should take place in a relatively short time - if we can hold the damage to the equivalent of something like 53 (sic) metropolitan areas destroyed.

  9. That was in 1960; not long afterwards came the Cuba Crisis. • Subsequently, both the Americans and the Russians adopted a policy of Mutual Assured Destruction. • The acronym was deliberate; they had realised that Kahn’s calculations were mathematical madness.

  10. Now fast-forward to the present. • The present ‘credit crunch’ is the result of unregulated greed and fraud, enabled by Information Technology and guided and justified by toxic mathematics.

  11. We all know about the ‘subprime mortgages’ fraudulently sold, dishonestly evaluated, and then ‘diced and sliced’ into securities whose true value was, and still is, impossible to ascertain.

  12. In order for there to be a market in these entities, there needed to be mathematical ‘models’ of their hypothetical price. • The uncertainties were all assumed to be ‘Gaussian’, with very thin tails. • And the markets were assumed to be perpetually rising; declines were ruled out of the software.

  13. Very clever people engaged in these mathematised fantasies. • If they expressed doubts, they would lose their bonuses and their jobs. • The world financial system came close to meltdown with Bear Stearns. It may yet do so. • What would Pythagoras say now?

  14. The moral of my tale? • ‘Figures can’t lie, but liars can figure’. • When we put our uncritical trust in Mathematics and Science, are we less naïve than those who put their uncritical trust in Holy Writ?

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