Saturday, August 17, 2013

Slartibartfast would probably know

I am having trouble with measurements. I probably shouldn't think about these things too much but this has been on my mind for a while now. It's this business of how long something is. So the distance between some marks on my ruler is an inch or a centimetre - that's OK, I can cope with that for now. It all started with maps.

I looked at a map of the British Isles and wondered how long the coastline was - the bit around the mainland. It could have been any island - just happened to be the one I live on.

I used to have one of those smart wheel things that you could roll around a line and it would tell you how long it was. That would have been useful. A piece of string would be useful too. But there are quite a few wiggly bits. Not as bad as Norway, of course, but pretty bad none the less.

Walking around the coast with some gadget or other would provide an answer. But that misses out quite a few little ins and outs. Even if I could go around each of the little ins and outs, how far should I go up a river? OK, there could be a rule for that - up to the first crossing.

This gets tricky, though - not the rivers, I am reasonably content about them - the fiddly bits like rocks, stones, pebbles, small pebbles, tiny pebbles. Lumps on pebbles. Even if they all stayed in the same place and even if I could measure around them. The more 'accurate' I try to be, the higher the perimeter becomes. It's not the satisfying outcome of a figure that homes in towards something - these measurements just get wildly bigger and bigger the closer you get to what it is you're measuring.

I had hoped that you could have a triangle (or some other polygon that you know how to work out a perimeter for) that sort of fitted inside our national perimeter and then another that sat just outside it. Logically one would jump to the conclusion that the length we want would be somewhere between the two but no. the damn line in the margin between them wiggles around and gets even longer the longer you think about it.

There, something like that would have been nice. The answer would have been somewhere between the two. But no - all those wiggles cause so many problems.

Here's another example. A line looks simple and straight. But look closer and you see it has a bump. Look even closer and it has bumps on the bumps. Travel along the first line - say 3 units.


Travel along the second one and, if the bumps are even and a third of the line length, you'll go 5 units.

Go along the next iteration and you've got 25 bits, each say a third of the previous one, so you go 8.33 units.

I am guessing but I expect this just keeps rising rather than heading for some pleasant and mutually agreed figure. With even bumps like this it's all nice and fractal so there'll be a formula too. That would be nice to know if anyone cares to share it or I suppose I can work it out.

All this tells me, though, is that it is not possible to be very sure about how far it is along things. The numbers seem to get bigger and bigger. And yet we know that the Earth is only so big so there has to be a limit somewhere or we'd be talking about things that fall off the edge or make rockets redundant for Moon visits.

Am I missing something terribly obvious or is this measurement business just some convenient approximation we make in this Age and will one day be looked upon as a bit silly.




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