## The private life of numbers (1): are numbers just numbers?

This is Part 1 of a set of three posts adapted from Mateja Prešern’s talk at The Burn in November 2011.

Do you have a lucky number? Or a favourite number? Surprisingly many of us do, whether we’re mathematicians or not. I (MP) am particularly fond of the odd prime numbers, and I’m not sure whether this is because I’m a number theorist or whether I’m a number theorist because I’m fond of prime numbers.

In Western culture, 13 is widely seen as an unlucky number, and the fear of 13 even has a name, triskaidekaphobia, which is almost as silly as the fear itself. On the other hand, the former world chess champion Garry Kasparov regards it as his lucky number. (He was the 13th World Champion, was born on the 13th day of April in 1963 =13$\times$151, and never lost the 13th game of any World Championship match.) In traditional Chinese culture, many numbers were regarded as lucky or unlucky because they sound like words with a positive or negative meaning — for example, the words for “four” and “death” sound very similar. More unusually, MP once met someone who had eight personal “lucky” numbers, ranging from 4 to 36. That’s spreading your bets!

What all this suggests is that people find it very hard to think of numbers just as numbers — they easily start to acquire associations, or even personalities.

For some people, this goes a very long way, even shading into synaesthesia. From a forum discussion on discovery.com:

For me, numbers and letters have personalities and genders and color associated with them. In the case of numbers, their personalities are quite distinct. Many of them don’t get along with each other. 9, for example, is male and nothing but trouble, while 2 is female and motherly.

As a child, I had a great deal of trouble with math, because for me, a page of math problems was a roomful of difficult people and I had to mediate all the arguments so I could get the answer. Getting them together for addition was tough, but they REALLY hate being subtracted! It was exhausting.

(Glenngirl)

9 for me is a female who has a thing for 5, but 5 is 4’s boyfriend. That’s as complex as it gets. I did have instances as a kid where I would ask a friend whether a number was a boy or girl, and get a strange reaction. Couldn’t understand why.

(heggieq1)

I’ve always thought of numbers, letters, days of the week, months, names, and even my school subjects having colours. I find some numbers have more distinct personalities, and appearances than others. For example, 9 is cold and unfriendly male, constantly looking down on 8, who is female, while 10 is a friendly, optimistic male. Yellow, of course. 4 is a bit of a push-over.

(WhammyBar)

Elizabeth Tudor: queenly or girly?

Different people’s perceptions of the same numbers can be completely different:

1 – One is like the leader. He’s a male and has a very strong presence although he is very quiet…
3 – Is a very young female. She has a lot of energy and is very hyper…
9 – Is like the queen, she’s tall and powerful and rules alongside 8. (danom8)

1= loud and bossy (female)…
9= very girly, as in “likes to dress up and go shopping” type of girl. (female). (lizzardV)

And, in case you think this is just for people who aren’t too good at maths, here’s mathematical physicist John Baez:

Different numbers have their own personalities. If you’re a mathematician doing a calculation and you get the answer 248, it means something completely different than if you get 247 — because the number 248 shows up in all sorts of amazing places, while 247 is just dull.

(Actually, 247 is a pentagonal number, which is far from dull! We’ll look at these figurate numbers in Part 2.) John Baez gave a sequence of lectures in Glasgow in 2009 called “My Favorite Numbers”: one lecture each on 5, 8 and 24. You can view the talks starting here.

Let’s end on a more mathematical note. The sequence of “lucky numbers” can be constructed as follows.

$1,\, 2,\, 3,\, 4,\, 5,\, 6,\, 7,\, 8,\, 9,\, 10,\, 11,\, 12,\, 13,\, 14,\, 15,\, 16,\, 17,\, 18,\, 19,\, 20,\, 21, \dots$

2. Delete every second number:

$1, \, 3, \, 5, \, 7, \, 9, \, 11, \, 13, \, 15, \, 17, \, 19, \, 21, \dots$

3. The second number remaining is 3, so delete every third number.

$1, \, 3, \, 7, \, 9, \, 13, \, 15, \, 19, \, 21, \dots$

4. The next number remaining is 7, so delete every 7th number:

$1, \, 3, \, 7, \, 9, \, 13, \, 15, \, 21, \dots$

5. The next number remaining is 9, so delete every ninth number, etc. Those numbers were lucky they weren’t crossed out. The first ten are:

$1, \,3, \,7, \,9, \,13, \,15, \,21, \,25, \,31, \,33.$

As a “teaser” to end on: would you expect the lucky numbers to get more or less widely spaced as they get larger? Try your intuition on this before looking up at the Mathworld entry for lucky numbers

Coming in Part 2: figurate numbers, evil numbers and happy numbers (and even some theorems!)…

(MP/DP)