Monday, 1 October 2007

Infinity, The Universe and Probablity

A couple years ago I thought in an infinite universe anything that has the merest possibility of occurring, will occur. So the chance of me sitting here turning into a rock may be 0.01e99 (no maths notation on blogger:(], but assuming an infinite universe and basic probability theory:

∞ * 0.01e-99= ∞

i.e. that is something (probable) rather than nothing (impossible). Thinking of it without mathematical notation we can just use the infinte Infinite monkey theorem:

The infinite monkey theorem states that a monkey hitting keys at random on a tpewriter keyboard for an infinite amount of time will almost surely type a particular chosen text, such as the complete works of William Shakespeare

I always assumed however that:

∞ * 0 = 0

Meaning that, an event that is simply impossible, will never occur because infinity multiplied by an impossible probability (0) is still zero. However, reading The God Delusion I came over Aldous Huxley's mathematical 'proof' of the existence of god

You know the formula: m over nought equals infinity, m being any positive number? Well, why not reduce the equation to a simpler form by multiplying both sides by nought? In which case, you have m equals infinity times nought. That is to say that a positive number is the product of zero and infinity. Doesn’t that demonstrate the creation of the universe by an infinite power out of nothing? [p108 GD]

I don't think this is a decent proof for the existence of god, in googling this I came across this proof that ∞ * 0 is not 1:

no one can EVER finish multiplying zero times infinity, therefore the answer will always be undefined. Even though logic dictates that the answer will never not be zero, this answer will never be reached. Therefore, trying to multiple zero times infinity is undefined.

Therefore, postulating the universe is indeed infinite (many worlds, brane worlds parallel or sequential via big bangs/crunches) then nothing, absolutely nothing, is impossible. Because the product of 0 and infinity != 0.

I don't think this is just of philosophical significance, because many current theories in cosmology postulate infinite parallel universes/branes etc.

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