Disproving Nietzsche's Eternal Recurrence

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Ok, I know there is already a thread in here about Eternal Recurrence, but I want to concentrate on a passage from a book called “A Little Knowledge” by Michael Macrone. Now, bear in mind this book is a layman’s guide to key ideas from philosophy, physics, maths, biology, psychology and economics. (I think it’s a good book, but to give you some idea … Heisenberg’s uncertainty principle gets three pages, Godel’s incompleteness theorem gets four, Hegel’s dialectic gets three, etc)

So (according to the book) Nietzsche believed that time was infinite, but that space was finite and is composed of a finite number of ‘power quanta’. So, in time every arrangement of power quanta will repeat itself infinitely many times, which ultimately means that human history will repeat itself endlessly (and if you welcome such a thought, you are a superman – and so on).

But it’s the next passage I’m interested in, and (ahem) I quote:

“Scientists … take a pretty dim view of Nietzsche’s theory. Spitting out word permutations in linear order is one thing, but arranging matter in three-dimensional, continuous space is another – even if you accept that space is finite and time infinite. It’s quite possible, for instance, to set a small number of objects in motion so that they never repeat their initial position (or any other), even if let go on to doomdsay and beyond.”

So how is this last sentence so? Is it for a similar reason that a bounded number line contains an infinite number of real numbers (i.e., is the key phrase here “continuous space”)?

This reminds me vaguely of something I read by David Deutsch about the multiverse idea, and about how even if you accept that there are an infinite number of parallel universes, it does not mean that everything that can physically happen in the multiverse does actually. (I think he said to understand why it helps to remember that there are different degrees of inifnity, as Cantor showed.)

Well, any comments would be welcome. I’m aiming for a reply count in the “above zero” range.

Hmm...I think the idea was that each quantum event generated a universe for all the possibilities. But then I watch too much Star Trek...

I never realized Nietzsche had that much to do with physics.

It's still an interesting belief though. Perhaps it could be made into a star trek sort of story? Why not take this over to the writing forum?

nice replies different perspecctives