Monday, 28 January 2008

Safety in Numbers

An extract from Euclid's Elements


I'm reading "Pythagorean Murders" by Tefkros Michailidis at the moment. It is set in the 1920s, where a mathematician is trying to find out who murdered his friend (a maths teacher). As his friend didn't get out much, this is a bit of a mystery, but it may be that the novel's interludes, which talk about the Pythagoreans thousands of years ago keeping quiet about a terrible secret, have something to do with it.

The Pythagoreans were a little bit odd. They believed in reincarnation, and so did not eat meat, since it was possible that the animal would turn out to be one of their long deceased relatives. They also did not eat beans. I read somewhere years ago that this was because it was also possible that you were reincarnated as a bean.
Pythagoras (top left) with some of his followers.


So far in the book, one of these ancient Greeks has discovered something awful. They don't have enough numbers. They've got numbers like 1,2,3,4, and so on. They also have numbers like 1/2, 78/96, and so on. There are infinitely many of these, so what's the problem?

The problem is that a new recruit to the sect has realised that if he draws a square, say, 1 metre by 1 metre, he can't work out the length of the diagonal. It's none of the numbers I've mentioned. In fact, it's irrational.

This can't be the reason that our guy gets bumped off in the 20s, because even Plato knew about irrational numbers. These aren't numbers that need to see a shrink, or female numbers, or numbers which are odder than odd numbers. They are numbers which can't be written as fractions.

Some of these irrational numbers are transcendental (don't ask). These have nothing to do with Doctor Who, or Oriental Meditation. If I draw a circle, say, 1 metre in diameter, then the circumference will be a transcendental number of metres long.

We also have complex numbers, each of which is part real, and part imaginary. Funnily enough, these are used by engineers, who you'd have thought wouldn't have much imagination. Some groups of numbers are friendly, others amicable or sociable, and a special few are perfect.

I still can't think (imagine?) why someone killed the novel's victim. Maybe it was an irate neighbour, complaining about the smell. He probably ate too many beans and stank out his block of flats. Come to think of it, the Pythagoreans may not have been completely crazy...

14 comments:

Bee said...

"Pythagoras (top left) with some of his followers." BWAHAHAHA!

Have I told you before that math was my most hated subject? But now I'm remembering all the names for numbers and it cracks me up!
I'm going to calculate myself to figure out what number I would be.
Let's see...
blah blah blah =
I would be an irrational number.

Brian o Vretanos said...

Since you remember some of it, you can't have been that bad at it. You're right, irrational numbers go on forever without repeating themselves ;-)

Jean Knee said...

Well now, reincarnation is not something we wnat to get into in this house. Drew rented a movie called Fluke and watched it with Lean so now she believes in it...hey it might make a slightly interesting post, never mind.

second, I'm sending you a nice romance novel for your birthday you have too many number type things on your mind (you know how I dwell on the spew and Father Al and all) it's good to broaden your obsessions

Brian o Vretanos said...

Jean Knee:

Fluke:

It would have been more of a challenge if they'd made a film about coming back as a kidney bean. These people have no imagination.

Yes, it would make a great post. You could write about it from the point of view of yourself reincarnated as an animal. Please?

Romance:

You're so thoughtful... Is it in Greek?

Brian o Vretanos said...

Actually, the Prologue in the light book says:

"It must be admitted from the start, out of resepct for the reader, that the autobiography of light is basically a love story. At some long-forgotten moment, light entered, unprompted, into the centre of the author's life."

And so on, for 450 pages...

If they ever translate it into English I'll get you a copy.

Dan said...

the dead guy was a math teacher ?
Maybe they murdered him beacuse of his long boring math lessons.
Quick, Brian hide !!!!
Dan

Jean Knee said...

snort

Jean Knee said...

Oh yeah the picture of the bean guys is upside down.

Bee said...

Danny that was so rude!
Funny but Rude! ;o)

Bee said...

And also, Dan is really good at math so he should talk!

Brian o Vretanos said...

Dan:

I hadn't thought of that, it just seemed so unlikely ;-)

Brian o Vretanos said...

Jean Knee:

I thought you might notice the picture. I just did that to see if you were paying attention. (no-one else was, apparently).

Mirella said...

Well said.

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