Is there a googol of anything?

Matt - A googol is a great number in that, it is a number that exists just because it has a nice name. There's nothing that we really have a googol of, but someone thought, "wouldn't a 1 with 100 zeros be a great number?" so they called it a googol. You could hear him emphasising gooGOL because it's spelled G O O G O L. The Google search engine is named after this but they spelled it differently. He's absolutely correct. If you're going to try to count objects, you won't find a googol of anything. So, even going right up to number of protons in the universe, which I think is - physicists argue between 10⁷⁹ to 10⁸¹, so it's a 1 with somewhere between 79 and 81 zeros. But I have found one thing which we have more than a googol of in the Universe.

Chris - Well, should we ask Ginny if she can guess what it is?

Ginny - I don't know. I mean, I was thinking about neurons because they make an awful lot of connections, but I think when we are thinking about this, it probably wouldn't be quite that many, even if you include all the animals on the Earth.

Chris - 10¹¹ nerve cells in the brain, 1,000 connections per nerve cells per brain, so that would probably be about 10¹⁴; so we're still a long way short of Matt's googol...

Matt - Actually, you're not far off from what I decided on, because when you're talking about connections, well, suddenly, you're looking at different ways of combining things. And so I looked at how many ways you can shuffle a pack of cards. So if you got a pack of 52 cards and you shuffle it, you can work out there's about 10⁶⁷, It's 8 times 10⁶⁷ ways to shuffle a pack of cards, which is a lot more than the number of grains of sand in the Sahara. In fact, if you've got a pack of cards with just 27 cards, you would have about 10²⁸ different ways to shuffle them. If you want a googol, if you get a pack of cards with 70 cards - so you're going to need your normal pack and then get 18 from a pack maybe with a different colour on the front or the back so you can tell them apart - if you shuffle 70 cards, there's a googol of possible ways to arrange them!

Chris - Beautiful. I was thinking of a similar example, Matt, because I was looking at the power of passwords on the internet. Someone was asking a question on our forum and they were discussing the power of encryption and saying, "if I took a brute-force attempt to crack a password just by taking random choices, how many possible combinations of a password encrypted with a certain number of bits of encryption?" And you end up with something which will take trillions of centuries to solve and the number of solutions I think is way more than a googol.

Matt - Yes, and again, you're looking at number of possible combinations. So in fact, a password is pretty close to a pack of cards because you've got the alphabet, upper and lower case and then you do actually get extra symbols, and bits and pieces. So, if you've got a password of even just 8 characters, you're already up in the very high tens of thousands and much bigger than that, you're into millions, billions and well off very quickly!