Buffeted by claims that her campaign cannot hope to overcome “the math” that gives Barack Obama an almost certain lead in pledge delegates as the Democratic National Convention draws ever nearer, Hillary Clinton today struck back, citing the controversial work of MIT mathematician Ian Malcolm as grounds for her supporters to hold out hope.
Mr Malcolm sees himself as the heir to pioneering mathematical genius Kurt Gödel, whose seminal “Incompleteness Theorem” proved that formal logical systems—such as Bertrand Russell and A.N. Whitehead’s attempt to reduce mathematics to set theory in “Principia Mathematica”—could not simultaneously be “consistent” (free of logical contradiction) and “complete” (allowing the derivation of all true theorems within the system). Gödel’s theorem dealt a blow to a mathematical community still reeling from the effects of Bernhard Reimann’s demonstration that Euclid’s system of geometry—previously regarded as simply the one true geometry—was only one of many incompatible but internally consistent such systems, each resting on different assumptions about the fundamental nature of space.
Recent papers by Mr Malcolm combine the insights of Riemann and Gödel, showing that depending the notoriously intractable “P=NP”problem in computational theory can be solved in at least two contradictory ways depending on subtle (and normally irrelevant) variations in the interpretive schema used to provide a semantics for the “=” symbol. “It all depends,” Mr Malcolm writes in his latest white paper, “what the definition of ‘is’ is.”
Comparing the semantics of ordinary arithmetic to the caucus system, which she has long claimed tends to favor Mr Obama, Mrs Clinton argued that “the math” itself carries an implicit pro-Obama bias. But, invoking the work of philosopher Ludwig Wittgenstein on rule following, Mrs Clinton observed that no finite series of uses of the symbol “+” for “plus” is sufficient in itself to determine future practice. Historical usage cannot distinguish, for instance, between the operation “plus” which yields “2024″as the result of summing “1632″ and “392″, and another operation, call it “quus”, which yields that result for all t prior to August 2008, but yields a smaller sum for t after that date. Mrs Clinton hinted that she may be prepared to ask the Supreme Court to rule on whether the familiar semantics for “+” run afoul of the Fourteenth Amendment, as it seems likely to yield an unequal result in the Democratic primary contest.