## Monday, 30 October 2017

### Statistical Argument for the Non-Existence of a God

Here’s a simple statistical argument as to why any given theist’s god probably doesn't exist.  The argument is possibly a variation on the problem of evil, but it's combined with the divine hiddenness issue and the inefficacy of prayer.

Let's suppose that theism was true and that scriptural instructions were true, but only applicable to those who are saved.  Let's further suppose that there is some necessary evil in the world, for whatever reasons a theist might posit and that suffering includes a certain number of children not being born (due to infertility, illness that kills a youth before being able to breed, death of children during childbirth and possibly even some number of abortions).  Say also that a theist takes the instruction from her god literally and "goes forth and multiplies", but not so literally as to become a mathematician.  Say also that non-theists don't have such an imposition and they therefore have fewer children than theists (this seems to be statistically accurate, given than christians have 2.2 children on average,atheists have 1.6).

What efficacy of prayer would we need for there to be a significant effect on populations?

I did a little spreadsheet on this, with the following assumptions:

Theists have 4.4 children per family (matching the average of 2.2 children per christian)
Atheists have 3.2 children per family (matching the average of 1.6 children per atheist
Start with a population of 100,000 evenly divided between theists and atheists
A generation is 25 years
Average lifespan is 75 years
The base probability of making it to maturity (and producing children) is 30%
A millennium is a good period to check out

Note that I assume a rather low base probability of making it to maturity to take into account wars, plagues and so on, and I picked that figure because if I go too far above that, the population after a mere 1000 years is ridiculous.  Note also that I am assuming no transfer from the atheist ranks to the theist ranks and vice versa.  I’m simplifying things by assuming even numbers of males and females make it to breeding age and assuming that all those who can couple up do so thus ignoring the possibility of non-breeding couples.

I'm aware that the 2.2 and 1.6 figures could possibly be per family, but I am thinking of pre-modern societies, like the ones that we have lived in for the vast majority of human history.  In the past, and even today in the third world, parents have more children as a sort of insurance policy against all the vectors of death pointing at them.  We need also to remember that the theist's god has told them to go forth and multiply, not to go forth and maintain something that is slightly above a steady population.

So, what was the outcome?  After 1000 years, there are a little over 5000 atheists and 1.5 billion theists if prayer is totally ineffective.  The atheists are, in fact, on their way to extinction – they do linger for a quite a while though, only disappearing entirely around Year 3600).  Note that this is assuming that prayer is totally ineffective, that theists are only benefitting from a tendency to produce more children.  If we introduce a very minor efficacy of prayer, making it so that 31% of children grow up to be parents, then after 1000 years, there’ll be 5.7 billion theists.  If we say that prayer is 25% effective, saving a quarter of the children who would otherwise have died, then there’d be 142 million billion theists compared to the 5000 atheists.

We can fiddle with the numbers in other ways.  We could assume, for example that all families, theist or atheist, had the same average number of children.  Let’s take the median, at 3.8.  If prayer is totally ineffective, then the numbers of atheists and theists will remain about equal – after 1000 years, there’ll be almost 5 million of each.  So, what happens if we make prayer effective in a minor way (30%->31%)?  After 1000 years, there will be 3.7 times more theists than atheists.  And if prayer is 25% effective (30%->48%), then there’ll be 647 thousand billion theists compared to the 5 million atheists, or 13.8 million times more theists than atheists.

There is, therefore, a very low-key way for a good god to not get too involved, still maintain plausible deniability (so as to remain hidden), not making prayer appear too effective (again perhaps to remain hidden) and still effectively wipe out the atheists over an extended period.  All the god needs to do is demotivate the atheists from breeding, decrease the base rate of survival to breeding age and bump up the effectiveness of prayer (from the current rate of 0%).  Note that I am not suggesting that theists want atheists to be effectively wiped out, but if atheists are going to suffer for eternity, then a good god would have some motivation for minimising the number of atheists.  For example, in the original scenario with prayer being very slightly effective, over the 1000 years, there be about 15 billion theists and only 370 thousand atheists, quite a good ratio of eternally saved to eternally damned at 41,500:1.)

Of course, this is just a simple model.  A good god could also touch some of the atheists to shift the balance.  Say that in each generation, there was a one-way defection rate of 10%.  That results not only in almost total eradication of atheists, who are now down to only 54 after 1000 years, but a quintupling the number of theists, to 7.25 billion, and a saved to damned ratio of more than 125,000:1 over the period!  Make prayer 25% effective and that ratio goes to 2,190,000,000,000:1.

So, why does the theist’s god not do something like this?  Such a small effort could make a huge difference.  The theist could fiddle with the figures to make it less impressive, if they liked, but remember that their god is apparently in control, so it can choose to make the results even better than I have suggested.  But it doesn't, which is a very real problem for a world view that contains a god that is supposed to be even slightly good, slightly powerful and has the vaguest clue about what is going on in this universe.