Tags: CPU | Albert Einstein | MASPAR | William of Ockham | Univ. of Calif.

Occam's Blunt Razor

Image: Occam's Blunt Razor
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Wednesday, 07 Jan 2015 04:27 PM Current | Bio | Archive

Whenever the media reports a strange phenomenon — a Bigfoot sighting, a psychic detective finding a missing person, a sea monster photo, or what-not — a veritable conga-line of skeptics is always on hand to decry it. To them, apparitions are simple optical illusions, hallucinations or hoaxes, and legendary creatures are, well . . . just legendary.

Experts use what’s called Occam’s razor to debunk conspiracy theories; atheists even use it to debunk religion. Similarly, scientists faced with unusual results in the laboratory are encouraged to consider the least complicated hypothesis supporting the simplest theory or physical model.

This guiding principle of adhering to the simplest explanation of anything is often said to have originated in the writings of the English Franciscan friar and philosopher William of Ockham (1287–1347). Occam is the Latin spelling.

Ironically, the idea goes back at least as far as Aristotle — “Nature operates in the shortest way possible.” For example, Ptolemy (90–168) wrote, "We consider it a good principle to explain the phenomena by the simplest hypothesis possible."

Indeed, just about every major intellectual figure in human history has made a similar statement: John Duns Scotus, Maimonides, Robert Grosseteste, Thomas Aquinas, Isaac Newton, Gottfried Wilhelm Leibniz, Ernest Mach, Bertrand Russell, Ray Solomonoff, Steven Hawking, and even the Hindu philosopher Madhvacharya (1238–1317) who wrote in verse 400 of his Vishnu-Tattva-Nirnaya, “To make two suppositions when one is enough is to err by way of excessive supposition.”

Amusingly, the exact words attributed to Ockham, “entia non sunt multiplicanda praeter necessitatem” (entities must not be multiplied beyond necessity) do not appear in his works. He did, however, write, “It is futile to do with more things that which can be done with fewer.”

Through the centuries, Occam’s razor has been progressively sharpened, metaphorically speaking, into more extreme forms, such as, “Among all hypotheses equally consistent with the evidence, the simplest one is the most likely to be true,” which cautions scientists to employ the razor to “shave away” metaphysical conceptual gobbledygook from their theories.

This is not what Occam himself intended, however, and in fact does not follow from the original principle’s statement. Occam was simply criticizing the theories of his fellow medieval scholastic philosophers, whose theories were becoming increasingly elaborate without any corresponding increase in explanatory or predictive power.

Occam was also trying to use his somewhat more nebulous principle to justify statements such as, “God’s existence cannot be deduced by reason alone.” This is why modern philosophers prefer to use the term “Principle of Parsimony” or “Principle of Simplicity” instead of “Occam’s razor.”

Even so, in the modern world of parallel processing computers equipped with hundreds or thousands of CPUs, scientists can explore simulations of world-theories and models, investigating all possibilities, and therefore put the principle to the test.  The results are fascinating.

Back in 1994, researchers P. M. Murphy and M. J. Pazzani published a paper in the Journal of Artificial Intelligence Research wherein they described how the massively parallel MASPAR computer at the University of California at Irvine was used in a series of machine learning experiments to investigate Occam’s razor. The scientists grew decision trees (sets of "If-Then" rules) to construct conceptual models from training data.
Murphy and Pazzani concluded, “The results of the experiments on several artificial and two real world problems indicate that, for many of the problems investigated, smaller consistent decision trees are on average less accurate than the average accuracy of slightly larger trees.”

Thus, Occam’s razor is not so sharp after all. While sometimes useful it is not infallible and can give false or misleading results. Indeed, in the years since Murphy and Pazzani’s experiment, scores of other researchers have come to the same conclusion.

Many different definitions of simplicity are possible, making the idea of a computable definition of simplicity highly dubious.

As the University of Washington’s Pedro Domingos wrote in a 1999 issue of Data Mining and Knowledge Discovery: “. . . for every domain where a simpler model is more accurate than a more complex one, there exists a domain where the reverse is true, and thus no argument about which is preferable in general can be made.”

Unless a phenomenon is essentially simple, an accurate conceptual or mathematical model of it can be very complex, and any attempt to deal with a heuristic approximation of it comprehensible to the great benighted public is a foolish endeavor at best. This is especially true when we mere mortals attempt to discuss something on the order of the world economic system.

As Einstein said, “Everything should be made as simple as possible, but not simpler.”

Sometimes, I suppose, your favorite conspiracy theory is true and Bigfoot really is out there in the backyard.

Richard Grigonis is an internationally known technology editor and writer. He was executive editor of Technology Management Corporation’s IP Communications Group of magazines from 2006 to 2009. The author of five books on computers and telecom, including the highly influential Computer Telephony Encyclopedia (2000), he was the chief technical editor of Harry Newton's Computer Telephony magazine (later retitled Communications Convergence after its acquisition by Miller Freeman/CMP Media) from its first year of operation in 1994 until 2003. Read more reports from Richard Grigonis — Click Here Now.
 

 


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Many different definitions of simplicity are possible, making the idea of a computable definition of simplicity highly dubious.
CPU, Albert Einstein, MASPAR, William of Ockham, Univ. of Calif.
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2015-27-07
Wednesday, 07 Jan 2015 04:27 PM
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