+ Brian:

You write:

If there is one white ball in a total collection of a million balls, what is the chance of drawing a white ball? … If a million draws are done, the chance of a "one in a million" event happening at least once is roughly 63%.

This is helpful. If we’re trying for one white ball out a million, our chances of success are only about 2/3

*even with a million tries!* If we get only

*one* try, our chances must drop drastically.

Considering the Penrose number, philosopher Robin Collins puts it this way: he says that

*one* try out of 10

^{10 (123)} would be like trying to hit a single photon if the entire universe were a dartboard (The Teleological Argument: An Exploration of the Fine-Tuning of the Universe, in

*The Blackwell Companion to Natural Theology,* W L Craig & J P Moreland, eds. p 220).

So, as you say, we need to know what the sample size is.

… How many "failed" universes spontaneously arose before this one, from pure random space-time fluctuation?

("Failed" in this context means “life-prohibiting.”)

As you say, “ ‘Size’

*[that is, 'extension' or 'space' --H]* and ‘time’ are only valid

*within* a single universe.” Fr Aidan, too, says that “It's not as if one can compare our cosmos over against other cosmoses. There is just our cosmos.” I agree. So since spacetime is a constituent part of the only physical reality we know or can know, since it would be meaningless to conceive of spacetime independently of some existing universe, answering the question

*How many "failed" universes spontaneously arose before this one* is like trying to summarize John Kerry’s first State of the Union Address. Spacetime “unelected” (all on its own) has no executive powers or duties—not even the power to fluctuate (since it doesn’t exist “all on its own”). Multiverse theories (which we’ll criticize in the next paragraph) try to overcome this in various ways. But we can answer the question of

*how many (hypothetical) life-prohibiting universes spontaneously arose before the actual universe* in one of two ways:

If we’re willing to settle for a purely speculative result, and if we have our hearts set on actualizing a life-sustaining universe

*just by chance,* our best bet is to set the number as high as we can—let’s say at infinity. No actual number can beat infinity! Infinity is not any

*particular* number, however great: infinity is number

*without end.* With an infinite number of tries it is

*guaranteed *that every possible combination of constants and quantities must be actualized

*an infinite number of times*. If a viable multiverse or many-worlds theory should ever arise it would provide us with the numbers we need for this. But such theories are highly speculative; they’re inherently non-verifiable (since we have no way of peering beyond the observable universe); they violate the law of parsimony (“Occam’s razor”) on a monumental scale; and they’re beset by workability problems (see Robert J Spitzer,

*New Proofs for the Existence of God*).

Well, speculation works wonders. But if we wish to extend our knowledge of what is, we can't begin from fantasy: we have to begin from knowledge already acquired. And since at this time we have no reason to believe that there has

*ever *been any universe other than our own beloved cosmos, we must assume the number of non-lifesustaining “failed” universes to be zero.

So:

… let’s accept the unverifiable odds of 1:10^10^123 (really just a guess--is Mr. Penrose possessed of Omniscience?).

There must be some misunderstanding here. First, I’m sure there’s nothing as eminently verifiable as mathematics. Anyone correctly performing the same operations with the same numbers will infallibly arrive at the same result. Dr Penrose doesn’t need omniscience. He just needs math & numbers. Secondly, no scientist achieves the status of someone like “Mr” Penrose by publishing mere guesswork.

But I should correct a mistake I think I made earlier. The Penrose calculation is not based on

*all* the various constants and quantities that constitute the fine-tuning problem. It's based on

*only one:* the fact that our universe began in a low-entropy state. This allows time for stars, and consequently carbon, to form. An initial

*high*-entropy state would have brought the universe to complete equilibrium long before stars could form, and hence would be life-

*prohibiting*. If someone were to calculate based on the two dozen or so parameters I've seen mentioned in the literature I've come across, our result would be one part in some very much larger number than 10

^{10 (123)}.

The fine-tuning problem as I've tried (however poorly) to sketch it here is, as I said in an earlier post, in itself insufficient to allow the inference to a transcendent designer. What it does is to defeat the hypothesis of a life-sustaining universe arising by chance—a hypothesis that

*is* pure guesswork.

H