Is God a Mathematician_ - Mario Livio [115]
Recall that selection effects are distortions introduced in the results of experiments either by the apparatus being used or by the way in which the data are collected. For instance, if in a test of the efficiency of a dieting program the researcher would reject everyone who drops out of the trial, this would bias the result, since most likely the ones who drop out are those for whom the program wasn’t working. In other words, Hamming suggests that at least in some cases, “the original phenomenon arises from the mathematical tools we use and not from the real world…a lot of what we see comes from the glasses we put on.” As an example, he correctly points out that one can show that any force symmetrically emanating from a point (and conserving energy) in three-dimensional space should behave according to an inverse-square law, and therefore that the applicability of Newton’s law of gravity should not be surprising. Hamming’s point is well taken, but selection effects can hardly explain the fantastic accuracy of some theories.
Hamming’s second potential solution relies on the fact that humans select, and continuously improve the mathematics, to fit a given situation. In other words, Hamming proposes that we are witnessing what we might call an “evolution and natural selection” of mathematical ideas—humans invent a large number of mathematical concepts, and only those that fit are chosen. For years I also used to believe that this was the complete explanation. A similar interpretation was proposed by physics Nobel laureate Steven Weinberg in his book Dreams of a Final Theory. Can this be the explanation to Wigner’s enigma? There is no doubt that such selection and evolution indeed occur. After sifting through a variety of mathematical formalisms and tools, scientists retain those that work, and they do not hesitate to upgrade them or change them as better ones become available. But even if we accept this idea, why are there mathematical theories that can explain the universe at all?
Hamming’s third point is that our impression of the effectiveness of mathematics may, in fact, be an illusion, since there is much in the world around us that mathematics does not really explain. In support of this perspective I could note, for instance, that the mathematician Israïl Moseevich Gelfand was once quoted as having said: “There is only one thing which is more unreasonable than the unreasonable effectiveness of mathematics in physics, and this is the unreasonable ineffectiveness [emphasis added] of mathematics in biology.” I don’t think that this in itself can explain away Wigner’s problem. It is true that unlike in The Hitchhiker’s Guide to the Galaxy, we cannot say that the answer to life, the universe, and everything is forty-two. Nevertheless, there is a sufficiently large number of phenomena that mathematics does elucidate to warrant an explanation. Moreover, the range of facts and processes that can be interpreted by mathematics continually widens.
Hamming’s fourth explanation is very similar to the one suggested by Atiyah—that “Darwinian evolution would naturally select for survival those competing forms of life which had the best models of reality in their minds—‘best’ meaning best for surviving and propagating.”
Computer scientist Jef Raskin (1943–2005), who started the Macintosh project for Apple Computer, also held related views, with a particular emphasis on the role of logic. Raskin concluded that
human logic was forced on us by the physical world and is therefore consistent with it. Mathematics derives