14 November 2010

Georg Cantor's Infinities (Part Two)

Continuing the last post on Cantor and how he overturned the entire world, this story comes from UD and is called "Infinitely Wrong."

Cantor demonstrated that some infinities are bigger than others (infinitely so). Robert Sheldon, in the post linked above, attempts to demonstrate that cardinality can be used to show how the multiverse can't save Darwinism.

As Roger Penrose pointed out, in order to avoid conflicting with the second law of thermodynamics, the Big Bang had to be insanely precise. According to Penrose (who now believes that after all the matter in the universe is swallowed up by black holes, and after they evapourate leaving behind nothing but photons, everything gets bigger and somehow the universe starts over again, forever, but that's a different story), the force causing the expansion of the universe has to match the force of gravity to at least one part in 10^(10^123) or the universe would have either exploded into nothing or collapsed back right after it banged. I'm not sure just how many zeroes are in that number, but think of it like this: if the universe had one more or one less proton (or probably less mass than that) at the Big Bang it wouldn't be here right now for us to talk about (or me to bore you about). Hawking, who was balked in September, places the ratio at a more reasonable one part in 10^60.

The Hawking solution to this seemingly fine-tuned feature? Infinite time + infinite space. Hawking et al. propose universes popping into existence all the time in their bubble multiverse. With infinite universes being created in a process that has infinite duration anything that can happen will happen, no matter how improbable, including gravity matching the expansion of the universe to that whole stack of tens. However, at least one part in 10^(10^123) does not mean that the fine-tuning is exactly that precise, just that that is the minimum precision of the fine-tuning. It could be more. It could even be infinite.

To deal with this, according to Sheldon, the anti-design folks ask Hugh Everett for help with creating infinitely more universes. Doing some fancy mathematics, if I'm reading it right, the anti-design folks can get an Aleph-naught infinite number of universes out of their quantum fudgery to solve a design problem with an Aleph-one cardinality, something that is impossible because the fine-tuning is now infinitely larger than the attempts at explaining it away by chance.

So, if all that made sense to you, it should have clearly been demonstrated that an infinite multiverse cannot solve the problem caused by the fine-tuning of the physical constants.

-Dee

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