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.

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