Let's play tag - or exponential bliss

This is a post about tagging and very large numbers, and how the two come together.

Let me introduce the topic this way (you may already know it): A wise man is offered a reward for something or other by a ruler. He appears to ask a very modest amount, namely, that he be given an amount of wheat calculated as follows: one grain of wheat on the first square of a chessboard, two grains on the next, four on the next, eight on the next and so on.

It doesn't sound like a lot, but the total number of grains is one less than 2 to the power 64; a very big number. In fact it is the wheat yield of the entire earth, assuming we grew nothing but wheat, for the next 80 years. That's the nature of exponential growth.

Move on to tagging. This particular tag has you identify five blogs that you like, each of whom thus tagged must come up with another five and so on. I was tagged in this way, recently, by three utterly delightful people whose blogs I enjoy greatly: millennium housewife, ngorobobhillhouse and the times of miranda.

However I do not take this as evidence that my blog is irresistible. Rather, I think we have a slight chessboard and wheat situation developing here. If 2 to the power something is big, then 5 to the power something is even bigger. Just how big? Well have a look at this series:

The first person tags 5
Each of them tags five, so that's 5 x 5 or 25. (Actually, strictly speaking it is 25 plus the original 5, giving 30. We should accumulate as we go, but it doesn't really change the logic).
In the next it is 125 (5 x 5 x 5) ...

OK, starting from 1 again, and taking it up to 15 successive taggings we have this series:

1. 5
2. 25
3. 125
4. 625
5. 3,125
6. 15,625
7. 78,125
8. 390,625
9. 1,953,125
10. 9,765,625
11. 48,828,125
12. 244,140,625
13. 1,220,703,125
14. 6,103,515,625 (this is about the population of Earth)
15. 30,517,578,125
16. eek, my head hurts

I'm still very happy to nominate blogs that I like; but I think I'm not going to tell them they've been tagged; not enough untagged blogs left on the planet!

baino's banter
the gold puppy
not enough mud
jolly good yarn girl
working mum on the verge
little brown blog

Yes, I can count, since you ask.

PS - you can still tag me!

PPS - another fun example of exponential growth. This is physically impossible, but suppose you could fold a piece of paper in half, then in half again, and so on, for 32 times. How thick would it be? Answer - so thick that it reach the orbit of the moon. No kidding.