Isomorphism is a strange word

Ooh I need your love babe, guess you know it's true....hope you need my love babe, just like I need you.

Typing lyrics from the song that's playing is a good blog icebreaker. I do find blogging very difficult - like one of those awkward conversations at parties, without even facial cues from my conversational partner so I can try to adapt what I'm saying. What should I talk about? A lot happens in life, all the time. Some of it I don't want to think about, some I don't want to publish to the internet, some I don't want to publish to anyone. Most would just be boring.

Do you know what's not boring, however? Maths!

From the depths of my heart, I urge all of you to go to http://mathworld.wolfram.com, click on a few random articles, till you find one that looks interesting. Click on terms you don't understand to find entries defining them, and so on, until you reach the bare bones of the subject.

I love reading about mathematics (and reading in general). Strangely, at university, some of the elder maths students seem shocked like this. I, in turn, was shocked at their shock. I have no doubt that they love mathematics, but we all show our love for something in different ways. I seem to do it through reading, and research. When I love something, I want to understand it. To know it.

Every integer is expressible as the sum of four squares:
81 = 9^2 + 0^2 + 0^2 + 0^2
34 = 4^2 + 4^2 + 1^2 + 1^2
Etc.

Is every integer expressible as the sum of eight cubes? Oddly enough, every integer except 23 and 239 are. That's -every- integer. Which is a lot. Except those two.
Every integer is expressible as the sum of nine cubes, however.
Also, every integer except for 15, 22, 23, 50, 114, 167, 175, 186, 212, 231, 238, 239, 303, 364, 420, 428, and 454 can be expressed as the sum of seven cubes.

Numbers are a strange and fascinating thing. Some savants say every number has its own personality, or colour.

I love Julia. I've done some terrible things, but I know that I love her. I don't know why she loves me back, but I'm very grateful. It'll be different from now on. I'll remember. I will love her every day, in my own charmingly inept way.

I'll blog for her.