Remember the jellyfish and the ocean? I have received this communication from a reader:

I happen to be friends with a jellyfish, called Jelly von Neumann. I asked Jelly about what Professor Atiyah said and she replied as follows...

'Even if one has never seen any fish, crabs or the like, one may proceed as follows. First consider the empty set, { }, the set which has no elements whatsoever. Call that 0. Next, having got 0, consider the set {0}, whose only element is 0. Call that 1. Next consider the set {0, 1}, whose elements are exactly 0 and 1. Call that 2. Next consider the set {0, 1, 2}. Call that 3.

'And so on. This gives you the infinite sequence 0, 1, 2, 3,... (One can prove that this sequence is infinite, since the operation involved is injective and never maps anything to 0.) You may even consider the whole infinite set, {0, 1, 2, 3,...}. Call this set omega. And you can go further. For consider the set {omega}. Call this omega + 1. Then consider {omega, omega + 1}, and call this omega + 2. Keep going. You get to omega + omega, and then omega + omega + omega. And so on. Eventually omega squared. Then omega cubed. And so on. Then omega to the power omega. And then omega to the power (omega to the power omega). And then keep going. Eventually, you get to epsilon-zero. It gets a bit complicated after that. The point is that you can do mathematics just by virtue of thinking. Of course, I am a rather special jellyfish in that regard.'

That jellyfish is cleverer than I am.