Since this is said to be the season of miracles, here's an excerpt from John C. Lennox's God's Undertaker, which neatly summarizes some of the evidence for the apparently miraculous fine-tuning of the cosmos.
After briefly discussing the “abundant supply of carbon” made possible by the very specific resonance of helium and beryllium nuclei (“if the variation were more than 1 per cent either way, the universe could not sustain life”), Lennox moves on to other matters:
In terms of the tolerance permitted, this [carbon] example pales into insignificance when we consider the fineness of the tuning of some of the other parameters in nature. Theoretical physicist Paul Davies tells us that, if the ratio of the nuclear strong force to the electromagnetic force had been different by one part in 1016, no stars could have been formed. Again, the ratio of the electromagnetic force-constant to the gravitational force-constant must be equally delicately balanced. Increase it by only one part in 1040 and only small stars can exist; decrease it by the same amount and there will only be large stars. You must have both large and small stars in the universe: the large ones produce elements in their thermonuclear furnaces; and it is only the small ones that burn long enough to sustain a planet with life.
To use Davies' illustration, that is the kind of accuracy a marksman would need to hit a coin at the far side of the observable universe, twenty billion light years away. If we find that difficult to imagine, a further illustration suggested by astrophysicist Hugh Ross may help. Cover America with coins in a column reaching to the moon (380,000 km or 236,000 miles away), then do the same for one billion other continents of the same size. Paint one coin red and put it somewhere in one of the billion piles. Blindfold a friend and ask her to pick it out. The odds are about one in 1040 that she will.
Although we are now in realms of precision far beyond anything achievable by instrumentation designed by humans, the cosmos still has more stunning surprises in store. It is argued that an alteration in the ratio of the expansion and contraction forces by as little as one part in 1055 at the Planck time (just 10-43 seconds after the origin of the universe), would have led either to too rapid an expansion of the universe with no galaxies forming or to too slow an expansion with consequent rapid collapse.
Yet even this example of precision-tuning is completely eclipsed by what is perhaps the most mind-boggling example of all. Our universe is a universe in which entropy (a measure of disorder) is increasing: a fact which is enshrined in the Second Law of Thermodynamics. Eminent mathematician Sir Roger Penrose writes: “Try to imagine the phase space … of the entire universe. Each point in this phase space represents a different possible way that the universe might have started off. We are to picture the Creator, armed with a 'pin' – which is to be placed at some point in the phase space … Each different positioning of the pin provides a different universe. Now the accuracy that is needed for the Creator's aim depends on the entropy of the universe that is thereby created. It would be relatively 'easy' to produce a high entropy universe, since then there would be a large volume of the phase space available for the pin to hit. But in order to start off the universe in a state of low entropy – so that there will indeed be a second law of thermodynamics – the Creator must aim for a much tinier volume of the phase space. How tiny would this region be, in order that a universe closely resembling the one in which we actually live would be the result?”
His calculations lead him to the remarkable conclusion that the “Creator's aim” must have been accurate to one part in 10 to the power of 10123, that is 1 followed by 10123 zeros, a “number which it would be impossible to write out in the usual decimal way, because even if you were able to put a zero on every particle in the universe there would not even be enough particles to do the job.”
Faced with not one, but many such spectacular to examples of fine-tuning, it is perhaps not surprising that Paul Davies says, “The impression of design is overwhelming.” [pp. 70, 71]