The Magical Qualities of the Number 7

Today is a day of sevens: 07/07/07. Seven is considered lucky by many people. There are seven days of the week, seven continents and seven brides for seven brothers. But is it magical in the world of math? Expert Keith Devlin weighs in.

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SCOTT SIMON, host:

Today is July 7, 2007. That's 07-07-07. Seven is considered lucky by many people, certainly worked out for Mickey Mantle. There are seven days of the week, seven continents, seven brides for seven brothers, et cetera. But what about in the world of math, is seven a magic number?

So we turn to our Math Guy Keith Devlin, always on the case for us, out in Palo Alto, California. Keith, thanks for being with us.

Prof. KEITH DEVLIN (Math Guy; Executive Director, Center for the Study of Language and Information, Stanford University): Hi, Scott. Good to be here.

SIMON: So does seven mean anything in particular in the human brain?

Prof. DEVLIN: Yeah, there's a couple of interesting cognitive aspects to seven. If you show someone a collection of objects randomly scattered around on a tabletop or on a computer screen…

SIMON: Yeah.

Prof. DEVLIN: …seven is the largest number of objects where they will recognize that there were seven objects. Beyond that, you have the need to count them or group them either physically or mentally. But up to seven, you can recognize them immediately.

And the other interesting thing about seven is that if you ask people to pick a number between one and 10, almost everybody picks the number seven. I don't think that tells you anything about the mathematics of seven. It tells you a little bit about how the human mind deals with things like randomness and arbitrary representations.

SIMON: Are there mathematical properties to seven?

Prof. DEVLIN: There are a couple. If you start forming all of the obvious fractions - one-seventh, two-sevenths, three-sevenths, all the way up to six-sevenths - something very interesting happens. If you work out one-of-a-seven, you get a decimal, 0.142857142857, and that pattern 1-4-2-8-5-7 repeats indefinitely.

Okay, so far so good. Work out two 7s, you get 0.2857142857142857, et cetera and you basically get that same sequence, 1-4-2-8-5-7, shifted along. And that's a curiosity, I think…

SIMON: I - do you have any idea how seven became a lucky number?

Prof. DEVLIN: I have no idea, whatsoever, except that, you know, if we forget lucky numbers, there is a mathematical notion called a happy number. To get a happy number, you look at the number and you start squaring the digits and adding the answers. If you keep on doing that, eventually either you'll end up with the number one or you will end up getting a sequence of numbers that cycles. It begins 4, 16, 37. Seven is the smallest number that gives you one.

And let me just explain the idea in terms of the calculation for seven.

SIMON: Yeah.

Prof. DEVLIN: Seven only has one digit, so you square it. That gives you 49.

SIMON: Yeah.

Prof. DEVLIN: Forty-nine has two digits, four and nine. You square four, you get 16. You square the nine; you get 81. Out of the 16 and the 81, you get 97. Do the same thing with 97, square roots digits and add them. Nine square…

SIMON: That's where they just have to check out. Keith, thanks for spending 7-7-07 with us.

Prof. DEVLIN: It's my pleasure, Scott.

SIMON: Keith Devlin, our Math Guy, speaking from Palo Alto.

And this is NPR News.

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