Thursday, 6 October 2016

The King of Spades and the Strong Anthropic Principle

I was introduced to the works and thoughts of Max Andrews by Skydive Phil.  In this, and at least one other article, I'll be addressing some issues that I have with Max' published take on the multiverse and fine-tuning.  Note that unlike some others that we won't mention, Max is upfront about being theist (and Christian) but, as is the case with Jeff Zweerink, his support of fine-tuning as an argument for god has faded of recent times.  It should be noted that what I address below was written quite some time in the past and does not necessarily represent Andrews' current position.  Therefore, I am not arguing against Andrews per se, but rather against a position that he no longer holds (at least not in its entirety).  Keep in mind that it's quite likely that there are apologists out there who would be more than happy to call upon the 2013 version of Max Andrews in support of their argument for god, while totally ignoring the fact that the 2016 version of the same person no longer agrees with everything that the 2013 version had to say.

For an insight into Andrews' most recent position (at time of writing), listen to his appearance with Luke Barnes (yes, that Luke Barnes) on Justin Brierley's Unbelievable show.

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Max writes at his blog, in the article Do Multiverse Scenarios Solve the Problem of Fine-Tuning?:

The role probability serves in this argument does not favor the non-fine-tuning hypothesis (either chance, necessity, or a combination of the sort) in multiverse scenarios.  If the objector to a fine-tuner argues that the odds of having a finely tuned universe, which harbors life, increases given the vast number of universes there is bound to be one with the values we have.  This is an abuse of probability and commits the gambler’s fallacy.  This claim assumes a general disjunction rule of probability.  For example, this rule of probability suggests that the probability of drawing a king from a deck of cards increases when each card drawn is not replaced.  If the deck has all the cards it is supposed to have the probability of eventually drawing a king is 1.  The multiverse is like the restricted or general conjunction rule of probability. By simply increasing the number of possibilities, one does not increase the probability of selection.  For example, say you randomly draw a card from the deck and you want the king of spades.  The odds of you drawing a king of spades are 1/52.  Say you draw the three of hearts.  When you replace the card and draw another card from random the odds of you getting the king of spades is not increased by the first selection.

What Max writes about cards is true, but it misses the point.  A multiverse is more like multiple decks of cards.  With each deck there is a 1/52 chance of drawing the king of spades from the top - assuming that they have all been randomised by thorough shuffling such that there is an equal likelihood of any particular card being on top.  This is equivalent to using the one deck of cards, selecting a card at random, replacing it, and then selecting another card at random - so long as we use a probability measure such that each of the 52 cards has an equal likelihood of being selected (this comment is intended to pacify mathematicians, just in case they are reading).

But while each random draw from a single deck and each draw from the top of a randomised deck has a 1/52 chance of resulting in a king of spades, across all the draws, the chance of one of them resulting in a king of spades is higher.  By the time you have drawn 1066 cards, using either method, there is one about a 1 in a billion chance that you have not drawn a king of spades (by the way, I am not implying that William the Bastard [aka William the Conqueror] was a dastardly king of spades, it's just a happy coincidence).  Draw 10000 cards and that becomes about 2 in 1084.

In other words, as the number of universes in the multiverse increases, the likelihood of any unlikely event happening in at least one of them also increases.  If there is an infinite number of universes, then anything that is at the very least possible must happen.

Interestingly, this lends credence to a formulation of the Strong Anthropic Principle that I don’t normally favour.  The argument goes a little like this (per Carter):

(at least one) universe (and hence the fundamental parameters on which it depends) must be such as to admit the creation of observers within it at some stage

We know that life is possible (if you doubt this check your pulse, if you don't have one, try looking out your window and you'll probably see either a tree or some grass and possibly both).  If there is an infinite number of universes then we know that life must therefore be instantiated in at least one of them.  And it would appear that we are in one of them.  Therefore, life becomes less miraculous, it's just something that we'd expect.  (This is the case even if there is a finite but very large number of universes.  Andrei Linde and Vitaly Vanchurin calculate that there are in the order of ten to the power of ten to power of ten to the power of 7 (1010^7)) universes.  While this might not make very very very very very unlikely (yet possible) things certain, the odds of possible things that are merely very very unlikely happening are pretty high.

This seems a little circular, which is why I don’t give it too much credence, but it does seem to speak rather strongly against many probability-based (ie appeal to ignorance) arguments for the existence of god.

If there is an infinite or extremely high number of universes …

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