The Fine-Tuning Argument, in terms of probability

Argument by Robert O’Brien, based on Probability, Statistics and Theology by David J. Bartholomew:
“As far as I know, there is no reason to believe the values of the physical constants are necessary, in which case, we have the following likelihood ratio:

P(physical constants and the universe in which we exist|God)/P(physical constants and the universe in which we exist|no God) =

P(physical constants|God)P(the universe in which we exist|physical constants and God)/
P(physical constants|no God)P(the universe in which we exist|physical constants and no God)

“Now, P(the universe in which we exist|physical constants and God)/P(the universe in which we exist|physical constants and no God) is essentially one since it does not seem likely that our universe depends on whether the physical constants we observe arose by design or not. Therefore, the likelihood ratio takes the form:

P(physical constants|God)/
P(physical constants|no God)

which I argue is large since it is easy to conceive of God wishing to create a particular universe and choosing the appropriate values of the physical constants whereas a random selection would be very unlikely to achieve the correct values.”

Answer:
The point of the argument doesn’t actually require most of the mathematical notation, so we can skip a lot of the above. We’ll concentrate on the last expression of the ratio of probability:

P(physical constants|God)/
P(physical constants|no God)

For those who haven’t seen this kind of thing before, here’s a crash course. P(something) means the probability of that thing happening. If you toss a fair coin, P(heads) is one half or 0.5 and so is P(tails). The | in the middle, which is called a pipe, means “given” or “given that” or “in the case of” or just “if”. For example, if you take the bus to work, P(getting to work on time|catching the bus) is higher than P(getting to work on time|missing the bus and walking).

So, O’Brien’s final expression is the probability of the universe’s fundamental constants having their present values if there’s a God (note the capital G – he means a god like the Christian one) divided by the probability of the same constants if there’s no God. The reason why the former is much higher than the latter, he argues, is that “it is easy to conceive of God wishing to create a particular universe and choosing the appropriate values of the physical constants whereas a random selection would be very unlikely to achieve the correct values.”

Let’s transfer the argument sideways. Which is higher,

P(last week’s lottery numbers|God) or
P(last week’s lottery numbers|no God)?

One would have to argue the former using O’Brien’s logic, because whether or not it happened, it’s really easy to conceive of God wishing to make a particular person rich and choosing the right numbers whereas a random selection would be very unlikely to match a given person’s numbers. Many winners do thank God, after all.

So why are there winners all the time, then? Because any combination could be a winner, and you don’t necessarily need last week’s specific lottery numbers.

Similarly, while some combinations of the fundamental constants are unworkable, many others are. Most who argue that they aren’t make the mistake of varying just one constant at a time. Even within that limitation, the gravitational constant for example would have to vary by a factor of about 3000 to preclude the formation of stars.

Without the limitation, as Victor Stenger discovered, “changes to one parameter can be easily compensated for by changes to another, leaving the ingredients for life in place.”

The fundamental constants are set in one of potentially infinite combinations which permit life. They don’t even seem terribly conducive to life, given that it has only apparently emerged on the surface of this one rock within hundreds of light years. They’re no better than a Division 3 lottery win.

One may consider it a low or even negligible probability that an unsculpted universe will be life-ready. Assuming there are six major fundamental constants (and you may want to consider others), the entire six-dimensional sample space would have to be analysed, not just slight variations of our set, or there’s no basis for this.

And that’s without even considering a multiverse or the anthropic principle.

– SmartLX