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Showing posts with the label applied mathematics

The simplest form of utilitarianism

I've heard it said that utilitarianism has this pragmatic benefit: it could constitute a plausible ethical consensus (even if we're all only pretending to believe it?) that could lessen the intensity of moral conflicts.  In other words, it is better to argue over non-fundamental things than over fundamental things, because we're more likely to go to war over the latter than the former.     Thinking this through: reaping this benefit would require us, I suppose, to give our consent to the simplest possible form of utilitarianism, because only that one can promise to turn serious substantive moral conflicts into mere mechanical computations.  In the spirit of Jeremy Bentham, portrayed above, then, let us suppose that pleasure could be measured in, say "positive hedons." Pain could be treated as negative hedons. Consider whether the govt should require a vaccine. Add up all the positive hedons the policy will create (discounting for uncertainties), subt...

Real Clothes, No Emperor

  There is a dispute among economists that seems at first a mere superficial matter of prose style and presentation, but that may have a greater significance. The dispute is this: should economists use the paraphernalia of the quantitative sciences? Should they use formulae with lots of Greek letters, and graphs with clearly defined curves? One body of thought – found amongst self-identified Austrian school economists especially though not uniquely – suggests that such paraphernalia are inherently misleading. P.T. Bauer has phrased it well . Econometrics, he said, has “contributed to the disregard or neglect of evident reality” because the use of highly quantitative methods leads to unwarranted concentration on the variables that fit most readily into a formal analysis, and leads to “the neglect of influences which, even when highly pertinent, are not amenable to such treatment.”  Bauer, the distinguished-looking fellow above, wrote this in 1987. He...

The identity of Euler and Euler's Identity

Leonhard Euler (1707-1783) was surely one of the most prolific of great mathematicians. Among his contributions, we need to mention two, each of which comes down to us as a single letter: the letter e and the letter i .  E uler was born in Basel, Switzerland, so his life and work might fittingly be considered a riposte to the old anti-Swiss jibe (originally from The Third Man ) that Switzerland has produced nothing for all its years of peace and democracy more than the humble cuckoo clock.   Since Euler’s day and because of his work, i stands for the simplest of the numbers that Descartes had called “imaginary.” This i refers to the square root of -1. We don’t need to bother ourselves further with the question “ what is the square root of -1?” It is simply  i , by stipulation. We don't end there, of course, but we can start from there and build something new and important.   Also since Euler’s day and because of his work, e stands for perhaps the m...