[PhDifferent (OP)]

A drunken scientist considers the probability of the existence of god.

When I was young I was a devout Catholic, and an altar server at the church which probably has the longest name in Britain.  The Cathedral Church of Our Lady help of Christians and St. Peter of Alcantara.  I loved God.  I spoke to him and sometimes I thought that he spoke back.  I loved the liturgy, the music and the rolling power of the Latin words.  The nuns that taught me had me lined up to be a priest by the age of nine.  Fortunately I had already made up my mind to be a Scientist - can you imagine what a crap priest I might have made?

As I grew older doubts started to creep in.  Two things in particular set me on a different path.  First, as everybody does I discovered sex.  Now that was supposed to be a mortal sin, but it didn't feel like it - in fact quite the reverse, it felt sort of holy, and exactly what I ought to be doing.  Secondly there was Vatican II, where pope John took a hammer to my beloved Tridentine mass, and hired somebody with less poetic sense than William Topaz McGonagle to translate the Latin words into English.  It made my gorge rise, and I stopped going to mass.  Another mortal sin, but by now I didn't care.

I had begun to think about other religions, and had concluded that they're all a load of toss.  Judaism, Christianity and Islam all trace their origins back to Abraham, who is one of the less appealing characters in the holy scriptures.  This is a man who raped his female slaves, a man who believed that God wanted him to murder his son, and only desisted when the Almighty changed his mind at the last moment.  He should have been sectioned.  And even if the story were true, what kind of God would pull such a cruel stunt?

And they all hate each other, spending their time arguing over obscure and trivial points of belief with no possibility of resolution except by fighting wars over it.  I concluded that the true purpose of organised religion was to amass power and wealth in the hands of the bishops, rabbis and ayatollahs.  They're all no better than the Church of Scientology.

So I grew up to be a scientist, and learned not to believe in anything, as a good scientist should..  Don't however run away with the idea that I'm an atheist though.  An atheist is a person who believes that God does not exist, and as I've just told you, I don't believe in anything.  Oh all right, if you insist I have to concede that I believe that I exist, otherwise who is writing this drivel?  It's hard to get past Descartes.

Rene Descartes was a boring old fart
I drink therefore I am.

Having said that, I'm not entirely sure about you lot though.  Maybe I made you all up.  Mind you, I would have to be impossibly creative to come up with such a weird and disparate bunch of folks, so I'll just have to treat you as if you were real.

But I don't believe in (e.g.) the Big Bang, Darwin's theory of Evolution or the Higg's boson.  All scientific theories are open to being disproved, that's how Science works.  The trick is to consider the probability of the theory concerned before you put your money on it.  In the case of the Big Bang, it explains an awful lot of observations, and a whole slew of modern cosmology depends on it.  But in order to make sense of that we've had to throw in a couple of things - "dark matter" and "dark energy" for which there is very little evidence.  Those two darks sound to me like phlogiston, caloric and the ether, all of them inventions introduced to prop up current theories which subsequently disappeared when a better theory came along.  So I'll give the Big Bang about a 90% chance of being correct.

Darwin does much better (perhaps because as a biologist I know a lot more about evolution than I do about cosmology).  The closer you look at living organisms, the more examples you find of things which don't look as if they were designed, but instead just happened, and were found to work and got kept.  So let's give Darwin about 99.9%.  (Creationism I'd give a score somewhere just above zero.)

The Higgs boson is much easier, because the clever chaps at CERN designed a proper experiment which yielded the statistics as part of the results, and carried on collecting particles until they acheved a five sigma level of significance.  What that means is there's about a one in three and a half million chance of getting that result by chance.  So that's 99.99997% for the Higgs boson, which is a pretty staggering level of confidence.

So back to God then.  What are the odds against God existing.  I haven't much to go on, but to put it in betting terms, I've long thought that the odds were about six to four, i.e. it's about one and a half times more likely that God does not exist than that he does.  That's kind of intuitive, like the odds that I put on the Big Bang, and Darwin above, and I thought, wouldn't it be nice to have an accurate calculation, as we have for the Higgs boson?

I looked at the so-called proofs of the existence of God, and to be honest they're all a load of toss.  The most popular is the argument from design which goes like this;
"A man is walking in the desert and comes across a watch lying in the sand.  He picks it up and admires the workmanship and the complexity of the design which went into it.  He realises at once that the watch couldn't simply have appeared there in the desert;  somebody must have made it.  Then he looks at his own body/the world/the universe and sees that this is an even more complex piece of design, so someone must have made it, therefore God must exist."

There are a few logical holes in that argument, not the least of which is that he might have carried on and observed that God himself would have to be even more complex than the cosmos which he created, so in turn somebody must have made God, which leads to an infinite regression of gods and super-gods going on forever.  Infinite regressions are really boring.

However, let's take it at face value for the moment.  The argument hangs on the observation that it is extremely unlikely that all this could come into existence by accident, so what we have to ask is what is the probability of a zero-probability event occurring given an infinite amount of time?  (Don't tell me there's only been 13.7 billion years - I told you I don't believe in the Big Bang.)

Strangely enough it turns out to be possible to calculate that.  You kind of have to sneak up on it, as with many mathematical problems.  Start with something simple, like tossing a coin.  The chances of throwing heads are 1/2, so what are the chances if you have two tries?  That's quite easy.  On the first throw the chance is 1/2.  On the second throw it's the same, but half the time you won't get as far as the second throw because you've already succeeded on the first throw, so the probability on the second throw is halved again:

p = 1/2 +(1-1/2)/2
p = 0.75

Now consider throwing a dice - what is the probability of throwing a six, given six tries?

p = 1/6 + (1-1/6)/6  +(1-1/6-(1-1/6)/6)/6  ... six terms, each of which is one minus the sum of the previous terms divided by six.

If you can be bothered calculating it the answer is p = 0.66510202.

So now we can generalise that for a dice with any number of sides, n:

p = 1/n + (1-s2)/n + (1-s3)/n ... +(1-sn)/n
where s2, s3 etc represent the sum of all the previous terms in the series.

As n approaches infinity the value of p represents the probability of a watch "just happening" in the desert, or the universe coming into existence exactly as it is, with no divine intervention required.  And the mathematically astute of you will have spotted that that is a convergent series, and that the series sums to:

p = 1 - 1/e
p = 0.632120558828558

Thos who are not so mathematically astute will just have to take that on, er, faith, wont you.*

So the probability of the universe coming into existence exactly as it is by random chance is 1-1/e, and if that didn't happen it must have been God wot done it, so the probability of that is 1/e = 0.367879441171442.  And my original guess at 6/4 wasn't far out, was it?

And for those of you with sincere religious beliefs, you don't have to get out the stake and the faggots.  I'm not really being blasphemous here.  After all, I'm not saying that you're wrong;  in fact I have just proven conclusively that you might be right.  There is an argument that we should all accept Pascal's wager and become believers, since when we die, if we're wrong we'll never know about it.

Exit Elderly Scientist, stage left, pursued by a vast number of monkeys brandishing typewriters.

* Oh all right, I can't really get away with that can I?  If you really want to understand this stuff Google "Bernoulli Trials".  Seems I wasn't the first person to think of this after all.

[Bored chemist]

"Can we calculate the probability of the existence of God?"

Apparently not.

A drunken scientist considers the probability of the existence of god.

But I don't believe in (e.g.) the Big Bang, Darwin's theory of Evolution or the Higg's boson.

So, drunk or otherwise, you are not really a scientist, because you ignore evidence.

In particular a friend of mine (an devout Catholic) pointed out that the problem with Darin isn't that he's wrong.
Quite the reverse.
Saying that "survivors survive"- which was his distillation of the theory- is tautologically true, but meaningless.

If you say you don't believe in Evolution, you need to come up with something which would stop it.

[PhDifferent (OP)]

Who says I ignore evidence?  I said that I'll give Darwin 99.9%.  If you had been alive at the beginning of the 20th century you would have claimed that Newton's laws of motion were 100% correct.  You would have been wrong as it turned out.  And if Einstein had had a closed mind like you then relativity would not have been discovered.

The belief that any theory is absolutely true is disastrous for Science.  Belief belongs in religion, not Science.

[Bored chemist]

The belief that any theory is absolutely true is disastrous for Science.

Not believing them is worse.
If you didn't believe in Newtonian physics, you couldn't have sent a rocket to the moon.

You seem to be muddling up the conditional belief that science uses with the irrational belief (in things which are known to be false) which characterises religion.

[Origin]

'Can we calculate the probability of the existence of God?"
No, there is no logical way you could.

[alancalverd]

To estimate the probability of something existing, you need to (a) define your target and (b) show that there is no evidence of its not existing as defined, before you start doing any arithmetic.

So far I haven's seen a definition of a god that is consistent with what we know and see every day.   

[Colin2B]

There have been a number of responses saying you can’t calculate this, but let’s be a little more specific on the problem.

so what we have to ask is what is the probability of a zero-probability event occurring given an infinite amount of time?

Strangely enough it turns out to be possible to calculate that. 

No, a zero probability event will never occur even given an infinite amount of time. That’s what we mean by zero probability.

Start with something simple, like tossing a coin.  The chances of throwing heads are 1/2, so what are the chances if you have two tries?  That's quite easy.  On the first throw the chance is 1/2.  On the second throw it's the same, but half the time you won't get as far as the second throw because you've already succeeded on the first throw, so the probability on the second throw is halved again:

p = 1/2 +(1-1/2)/2
p = 0.75
............
Etc
............
So the probability of the universe coming into existence exactly as it is by random chance is 1-1/e, and if that didn't happen it must have been God wot done it, so the probability of that is 1/e = 0.367879441171442. 

There are a number of problems with this calculation.
You have assumed that if the universe didn’t form by chance then god must have done it, but that’s not so.
Let’s take the example of you winning the lottery. We can calculate the probability as p, but 1-p is not the probability of someone else winning it, just the probability that you don’t. Everyone entering has the same chance. So your calculation should be the universe came into being by chance vs it never came into being - the fact that it has come into being is second guessing the outcome. The fact that a coin has come down heads doesn’t change the probability that it might not have done.
Even if you did assume 2 possibilities (chance vs god) your calculation is wrong. Let’s go back to the coin toss. You are correct that for 2 tries the probability of a head is 0.75, but the probability of a tail is not 0.25 it is 0.75; 0.25 is the probability that you don’t get a head ie 2 tails. So in your chance vs god, both have the same probability. In fact, based on the calculation you did you could insert almost any event eg unicorns happening by chance!

And for those of you with sincere religious beliefs, you don't have to get out the stake and the faggots.  I'm not really being blasphemous here. 

Oh but you are.
For someone who believes in an omnipotent god (who gets things right 1st time) you have just suggested that the god needs an infinite number of tries and then is worse than pure chance. I’d hide the matches if I were you.

The overall problem here is that when we speak of, say, the "probability" that England will win the the world cup this year, we are using the word "probability" in a colloquial sense, not its mathematical sense. This is because England winning the world cup in a given year is not a repeatable experiment, we can only derive an estimate based on previous performance. Coin tossing is repeatable and we can easily calculate a mathematical probability based on the number of favourable occurrences, we don’t have that information for either the universe or god. You have chosen to seed the formula with an infinite sided dice, but we could choose any number.

Thought: given an infinite number of tries it might be possible for England to win.

[Zer0]

Re: Can we calculate the probability of the existence of God?

Religion ain't Mathematics.