Gnomon's Guide

In a school classroom, mathematician Edward Kasner was talking with some school children about very large numbers. The class came up with a new number, a 1 with a hundred zeroes after it. One child, Milton Sirotta, the 9-year-old nephew of Kasner, made up the name 'Googol' for it, and later it was decided that a 'Googolplex' should be a 1 followed by a googol zeroes.

Written out in long-hand, a googol is:

10, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000,
000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000,
000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000

The googol achieved a certain level of fame in the UK when it was the answer to the million-pound question on ITV's 'Who wants to be a Millionnaire?', in which Major Charles Ingram cheated his way to the top, relying on coughs from a knowledgeable accomplice in the audience to identify the correct answers.

It also provided the name for the well-known search engine Google, which attempts to 'organize the immense, seemingly infinite amount of information available on the web'.

Just how big is a Googol?

It is easy enough to write this number, with a little patience. But it is very difficult to imagine just how big such a number is. Some attempt will be made here to give you a feel for it.

• Imagine a tiny silver ball, about 3 millimetres in diameter. It is made of sugar and is used to decorate cakes with fancy icing. Get used to the thought of that tiny mirrored sphere, because we're going to encounter rather a lot of them!
• Now imagine a cubical box which is 1 metre along each side. That's a cubic metre. It would hold approximately 50 million silver balls. That's 50,000,000.
• Let's up the scale a bit and build a wall around the island of Great Britain. Now we'll cover the entire island with silver balls, to a depth of 1 metre. (OK, they'd roll off some of the steeper bits, but don't worry, the wall around the outside will keep them in). Now we're talking a seriously big number of balls, 11,000,000,000,000,000,000. That's big enough that there isn't any name for it in normal English. Mathematicians call it eleven quintillion. It's easier, however, if we just write it like this: 11 x 10¹⁸. This means there are 18 zeroes after it. It's still pretty insignificant compared with a googol.
• Try hollowing out the inside of the Earth and filling the entire planet with silver balls. We get 6 x 10²⁸ balls. That's 6 with 28 zeroes after it. Still way too small.
• How about a sphere the size of the Solar System, packed tightly with silver balls: a mere 5 x 10⁴⁶, a 5 with 46 zeroes after it.
• A sphere the size of the galaxy? That's a total of 2 x 10⁷⁰ silver balls.
• How about the Universe? Well the farthest thing ever seen by humankind is a quasar which is about 10 billion¹ light years away. So the observable universe is a sphere with a radius of 10 billion light years. Fill 'er up! We can pack in 2 x 10⁸⁶ silver balls into the universe. That's 200, 000, 000, 000, 000, 000, 000, 000,000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000, 000.

So we've filled the entire observable universe with tightly-packed balls and we're still nowhere near a Googol. Even multiplying this number by a trillion², we're still short.

So how can we reach the big 100 zeroes? Here's a way. Imagine the entire universe full of silver balls. One second later, remove them all and replace them with another set of identical balls. Do this every second for 4000 years. The total number of silver balls is a googol! And that's a load of balls!