Michael Joswig pointed my attention to the following unbelievable front page of the Frankfurter Allgemeine.

The headline is the square root of 21 and it refers to the claims of the opponents of the “Stuttgart 21” peoject that the project is the root of all evil.

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NickIf 21 is the root of all evil, then surely all evil would in fact be 21 squared, or 441?

They’ve made a terrible abuse of mathematics in the name of an eye-catching headline.

Gil KalaiPost authorDear Nick, I did not find anything terrible about it. In fact it is quite funny.

Nate Mammansqrt of 21, not 21. My German is poor! Just realized I can barely read it anymore.

gowersThere used to be an advertisement for some guru, which frequently appeared in British newspapers, claiming that if just

the square root of one percentof the population of the world were to follow his teachings, then we would usher in the new golden age, or whatever it was he wanted. There were three interpretations I could think of. (The square root of one) percent just means one percent. Or it could mean ten percent. Or, finally, it could mean that you take the population of the world, divide by 100, and take the square root of the resulting number. The last interpretation is the only half-sensible one but I don’t like the unit human-being-to-the-half.sebastianThere is also the possibility that the guru was using units of (person)^{1/2}.

Gil KalaiPost authorDear Tim, The claim you are referring to is called “The extended Maharishi effect,” and indeed your third interpretation “devide the number of people by a hundred and take the square root” is the correct one. See this webpage.

Quoting from that website: “The Maharishi Effect is a phase transition to a more orderly and harmonious state of life in society as measured by decreased crime, violence, accidents, and illness, and improvements in economic conditions and other sociological indicators. This is supposed to happen when a critical sub-population of individuals – 1% – experienced and stimulated the field of pure consciousness through the Transcendental Meditation Programme.

In 1976, with the introduction of the more advanced TM-Sidhi Programme, including Yogic Flying, a more powerful effect was expected based on a new formula: the square root of one percent of a population practising Transcendental Meditation and the TM-Sidhi Programme, morning and evening together in one place, is sufficient to neutralise negative tendencies and promote positive trends throughout the whole population.”

Surprisingly, research supporting this phenomenon found its way to respectable scientific journals including a paper published in 1988 in the Journal of Conflict Resolution. This paper describes an experiment that took place in Jerusalem of all places showing remarkable correlation between the number of Yogi flyers that took part in the experiment every week and various events that occured the same week.

(I offered it as an interesting puzzle in this web page (from the late 90s) dealing with other surprising results that can be explained via the familiar phenomenon of biased selection.)

I think the “research” regarding Yogi flying has two positive aspects. First this group regards peace as positive which by itself is a positive thing. Second, it gives us a good way to relate to other scientific claims about trencendental meditation (sometimes by the same authors) which are not apriori as absurd as these square-root-one-percent claims.