Baby talk

I just got an email from my nephew (really!). I hope he won't mind me posting it up here:

--------------------------------
Hello Uncle Rich,

Thank you very much for the card you sent me - I got it this morning. Sadly, I don't have the co-ordination yet to open it myself, but Mum did it for me.

Guess what, this is my first ever email!

I hear you're an actuary? So you may have a reasonably good knowledge of mathematics?

I couldn't sleep well last night as I was pondering over a few problems that are based on the infinite. Mum thought I was just hungry, but at one point, I was specifically crying over whether Zeno of Elea's argument that motion is impossible was true or not? He seemed to think that if a body moves from A to B then before it reaches B it passes through the mid-point, say B1 of AB. Now to move to B1 it must first reach the mid-point B2 of AB1. He thought that continuing this argument shows that A must move through an infinite number of distances and so cannot move.

This is probably basic to you, but being only in my 6th day of life, I'm sure you won't mind explaining this to me some point soon.

Anyway, looking forward to meeting you,

Love from Barney

--------------------------------

I'm sure that you'll agree that he seems to be quite advanced for his age, and his spelling and grammar are both really spot on.

Here is my response to the wee Barn:

--------------------------------
Hello Barney,

I'm glad you were able to find help opening your card - I realise that hand to eye co-ordination is difficult, but it's a skill that I hope you'll be able to find time to learn. And well done on sending your first email. It's good to see that you have your own email address - that should give you some element of privacy in your dealings with the rest of the world. Hey, maybe you'll be blogging soon!

You're correct in assuming that as an actuary I have a good grasp of mathematics. In fact I have published many volumes of mathematical texts and am generally reputed to be one of the most intelligent evolved monkeys on this planet (which is called "Earth" by the way, in case you haven't come across the name yet). You have come to the right person for help with your problem.

You are not the only one who has lost sleep by pondering the infinite. Infinity is such a big thing that it can sometimes take nearly half an hour to accurately visualise it all at once. However, it seems your lack of sleep is caused not by the infinite, but by the infinitesimal. This is like the infinite, but much much smaller.

Zeno was born in around 490bc and as such, lived most of his life before the invention of Proper Maths. Also, people were much less evolved in those days, and his brain, unlike yours, ill-equipped to deal with the notions he was thinking about. You have been losing sleep since it seems totally obvious to you that bodies can move through space. You see your mother's arm do this all the time, as she moves the gin bottle to and from your mouth.

The resolution to Zeno's paradox is actually quite simple: Zeno was supposing that space is infinitely divisible, that you can take a length and split it in half as many times as you want. Modern science has shown this to be complete nonsense. In fact, if you start with any length, it is not possible to divide it in half more than around eight times. This is exactly analogous to attempting to fold paper in half lots of times. As an experiment, why not take your birth certificate and fold it in half, then in half again. You may need to get Mummy to help you with this unless your co-ordination has improved over the last few days. Count how many times you can fold it. Not as many as you thought, eh?

Well, space is exactly like that. As a body moves from A to B, it does indeed first have to pass through B1, and B2 before that. But if you keep dividing the space, you hit the space-splitting limit (at around B7) and then the body does not have any further checkpoints to hinder it - it will zip straight through. Since then there will only be a finite number of distances to travel, the body has no problem moving from A to B in finite time.

I hope this helps your understanding of the world in which we live in. If you have any further questions on the topic, then do not hesitate to write again - that's what uncles are there for! If you have trouble sleeping in the future, then I recommend getting really "hammered". You'll drop to sleep as soon as your little head touches your cot.

I look forward to meeting you soon,

Lots of love,

Uncle Rich

PS - don't try and understand how gyroscopes work - that will really f**k your mind up.

--------------------------------

Hopefully the little lad will sleep better tonight.