h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

I have been googling in a desultory manner, and arrived at the surprising information that someone has expanded the irrational (nay, transcendental) number Pi to a trillion decimal places. How much of your bookshelf would that fill, I wondered.

Well a large novel (a Harry Potter for instance) contains around a million characters (we're talking about letters and symbols here, not fictional persons). So a billion integers would fill a thousand books, and a trillion would fill a million books.

My bookcases currently hold something in the region of a thousand books, so a thousand houses like mine could house all the books of pi-to-a-trillion. Ten streets like mine. Of course a decent library such as Trinity College's in Dublin would house some five million books, so they could take care of five copies, if they held nothing else.

It is hard to visualise large numbers, but there are some vivid visual images available. In 1981, when the US national debt had reached its first trillion dollars, Ronald Reagan said: "A few weeks ago I called such a figure, a trillion dollars, incomprehensible, and I’ve been trying ever since to think of a way to illustrate how big a trillion really is. And the best I could come up with is that if you had a stack of thousand-dollar bills in your hand only 4 inches high, you’d be a millionaire. A trillion dollars would be a stack of thousand-dollar bills 67 miles high."

Of course there is no such thing as a thousand-dollar bill, so some people speak instead of a stack of dollar bills 67,00 miles high. But then, where does 67,000 miles get you?

In 1938 (that long ago!) a schoolboy came up with the name 'googol' for the number 10^100 (or 10e100) -- ten to the power of one hundred, or a one followed by a hundred noughts. It's easy to write that out as a plain number: it takes just a two lines of text, or one if you write small enough.

But a googolplex, that's ten to power of one googol: you can't write that out in zeroes at all, because there isn't enough paper in the world, or, put it another way, you can't write small enough. In fact, even if you could inscribe a zero on one atom, there just aren't that many atoms in the observable universe.