# Fractions Are Hard?

I don’t usually spend my spare time reviewing and correcting mathematical calculations by physicists, but I think yesterday evening was an exception.

In the course of an interesting reflection in the *Wall Street Journal *yesterday on the recent experiment appearing to show that neutrinos travel faster than the speed of light, Michio Kaku, a professor of theoretical physics at City College of New York, wrote:

Physicists fired a beam of neutrinos (exotic, ghost-like particles that can penetrate even the densest of materials) from Switzerland to Italy, over a distance of 454 miles. Much to their amazement, after analyzing 15,000 neutrinos, they found that they traveled faster than the speed of light—

one 60-billionth of a second faster, to be precise. In a billionth of a second, a beam of light travels about one foot. So a difference of 60 feet was quite astonishing.

If Professor Kaku means that the neutrinos arrived “one 60-billionth of a second” faster (i.e., sooner)* *than a light beam would, then the difference between the neutrinos and the light beam would be only 1/60 of one foot (or 1/5 of an inch). But from reports that the neutrinos did indeed appear to beat a light beam by 60 feet, it would appear that Professor Kaku meant to write that the neutrinos were “60 billionths of a second faster” (or, if you prefer, “60 one-billionths of a second faster”). In other words, it appears that he put the 60 in the denominator when it belongs in the numerator of the fraction.

(I have sent an e-mail inquiry to Professor Kaku.)

UPDATE: By e-mail, Professor Kaku has acknowledged the error.

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