Tuesday, August 24, 2004

Geek Musings I

Exponential scales are amazingly concise number representations. So concise that you can begin to believe you can actually comprehend some of the numbers bandied about.
For instance, modern physics theories suggest that the universe consists of a quantum foam, whose graininess (bubbliness?) is referred to as the 'Planck Length', and is about 1E-43 metres. Neat when put like that, isn't it?

Try it like this:
0.0000000000000000000000000000000000000000001 metres

That looks a bit more bubbly but, even if I missed out a zero here or there, it's still only a half line of text.

Now consider what we think of as ordinary matter. The smallest component would be the proton, whose diameter is typically 1E-15 m, or (more bubbly?):
0.000000000000001 metres.

If you've ever theought about this at all, you would probably just lump these values in under the 'very, very, small' category. Relative neighbours, regardless of the fact that a proton is 1E28 times greater than the Planck length. ie:
10,000,000,000,000,000,000,000,000,000 times greater.

(These things really are best expressed in Chinese, where they can stream vertically up from the bottom of the glass, don't you think?)

Where all this is leading to is a relative comparison. Let's take piece of the ultimate Planck bubbly, and blow it up by 28 orders of magnitude to the size of a real proton. On the same scale, a proton would be 1E(28-15) = 1E13 metres in diameter.

Put another way, that's a sphere about the size of Jupiter's orbit.

You could fit an awful of protons in a space like that!

It just goes to show you know even less than you think!


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