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by Prof John Webb

Prof Webb of the Department of Mathematics and Applied Mathematics is a key role player in the International Mathematics olympiad as well as the Pan African Maths Olympiad. Here he gives us his viewpoint on the pseudoscience of numerology.

Numerology is a pseudoscience that claims to be able to predict a person's future based on a single digit. In an article in a popular woman's magazine, (December 2000), the author says that we live in nine-year cycles, and your position in the cycle is determined by a single "personal number" calculated from your birthdate.

Suppose you are born on 23 June, and want to know your fortune for the year 2001. June is the 6th month, so you write down the number 2362001. Add up all the digits: 2+3+6+2+0+0+1 = 14, and if (as in this example) you get a two-digit number, add the digits again so that you get a single digit: 1+4 = 5. That is your personal number. When you have worked it out, you then you can refer to the magazine's relevant column to find out what 2001 holds for you (and about half a billion other people around the world with the same personal number).

There is a certain mathematical interest in the way the personal number is calculated. It is in fact the remainder when the original date is divided by 9. In our example, 2362001 = 262444 times 9 + 5. 

In general, to find the remainder when a number is divided by 9, you simply add the digits of the number, and repeat the process until you get a single digit. This will be the required remainder. In particular, if the remainder is 0, the original number is divisible by 9. 

The proof that this process works is quite easy. If N is an integer, we denote by S(N) the sum of the digits of N. So if N is for example a five-digit number abcde, then S(N) = a + b +c + d + e.

Now N = 10000a + 1000b + 100c + 10d + e,
so N - S(N) = 9999a + 999b + 99c + 9d,
which is clearly divisible by 9. 

It follows that N and S(N) have the same remainder when divided by 9. Thus repeating the process of summing the digits of a number until you get a single digit gives you the remainder when the original number is divided by 9.

This is an interesting little piece of mathematics, and is the first step into some very important ideas such as check digits and error-correcting codes, which are central to the information revolution. But that is not the subject of this article, numerology. Unfortunately, there is no more mathematics in numerology than what has just been described. 

Numerology is a bogus and essentially worthless subject, even more so than astrology. There is no basis for the belief that everybody born on January 1 has the same future as everybody born on January 10 or January 19 or January 28, but that is what the author of this article would have you believe. On what basis does she base her advice to a woman with personal number 1 to be cautious about changing her shampoo, or have a baby if her personal number is 3, or take up religion if her personal number is 7? 

Numerology is the field of cranks and charlatans. It is quite possible that the article was published in the full knowledge of the author and the editor of this magazine that it is all hokum, but fun. Never mind, they say, it will be read avidly by our more gullible readers and boost the magazine's sales. 

But there is a more serious question. Is there a connection between the tendency of women's magazines to promote pseudoscientific rubbish and the fact that the professions based on mathematics and the hard sciences are dominated by men? 

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