01.30.08

44 Orders of Magnitude

Suppose you worked really hard to earn a billion dollars, and you traded it in on a special penny. Bad deal, huh? Now suppose you did it again, and again, and again. You are up to four cents. Now keep doing a hundred billion times. Hey, you are back to a billion dollars in special pennies. That's what eleven orders of magnitude means.

If you are very clever and can earn $11574 per second every second day and night, you will earn a special penny every day! You will earn a regular penny in less than a microsecond, so you can collect a billion in special pennies in less than 2.7 million years. The difference between that microsecond and that 2.7 million years is about twenty-two orders of magnitude.

Now take your special pennies, a billion dollars worth, and trade them in on an extra-special penny. Now start over and earn another extra -pecial penny by earning a hundred billion special pennies, each of which costs a billion regular dollars. Cool. Now you are up to two extra-special pennies.

Don't rest until you have a billion dollars in extra-special pennies. If you are very clever and can earn $11574 regular dollars a second in regular money (or a bit more than a regular penny per microsecond) , you will have your extra special billion in 270 million billion years, which will require a fair amount of patience. (Most scientists believe the universe is much, much, much younger than that, about 40 billion years old if I recall right.) That's what thirty-three orders of magnitude means.

You see where this is going, right? Suppose you got a raise; to make the numbers come out right you are now earning about 14 times as much, $164280 regular dollars per second. And suppose you got everyone on earth to get the same salary, and they all gave everything they earned to you. And suppose you traded every extra-special billion in on a super-extra-special penny. Now with that raise in salary and everybody on earth helping, you can earn a super-extra-special billion in that same 270 million billion years.

So now you have a super-duper-whizbang penny, (which you can now contemplate saving up to get to your super-duper-whizbang billion if you like), which is worth 44 orders of magnitude more than the penny you started with in your first sixteenth of a microsecond.

In regular money (assuming I did this all correctly; please do check) you will have accumulated:

$1,000,000,000,000,000,000,000,000,000,000,000,000,000.00

What a ridiculously large number 44 orders of magnitude is!

Yet that is the span of science; the number of the smallest subatomic scale phenomena that we are interested in that span the largest cosmological scale. There was an excellent short movie made back in 1977 to illustrate this. The excellent Long Now blog has come up with a link to it on a site hosted by Toyota. Go have a look (click "Watch Powers of 10").

People like Clifford like to think at the extremes of that scale. People like me like to be in the middle. What we end up doing is very similar in some ways and very different in others.

Tags: powers of ten

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