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Our future, our universe, and other weighty topics


Monday, January 16, 2017

The Professor's Bad Reasoning About "Bad Odds"

Our universe seems to be astonishingly fine-tuned to allow the existence of life. For example, if the absolute value of the proton charge and the electron charge were not exactly the same, gravitation would not be enough to hold planets together (since the electromagnetic force is roughly a trillion trillion trillion times stronger than the gravitational force, even a relatively tiny difference in the proton charge and the electron charge would cause repulsive effects exceeding the attractive effects of gravitation in large bodies such as planets, preventing their existence, as mentioned by Greenstein here). We know of no specific reason why such an equality between the proton charge and the electron charge should occur, and given that each proton has a mass 1836 times larger than each electron, it seems quite the amazing coincidence that the electron charge and the proton charge match exactly (experiments have shown they match to twenty decimal places, the only difference being that the signs are opposite). 

An even greater coincidence occurs in regard to the vacuum energy density, as discussed here. Straightforward calculations tell us that the quantum contributions to the vacuum should cause empty space to be extremely densely packed with mass-energy, but no such thing occurs. Somehow we have a cosmological constant or vacuum energy density more than 1060 times smaller than what quantum physics predicts, possibly because of an exact cancelling out of opposing effects. If it were not for such a coincidence, life would be totally impossible (no more possible than the evolution of life inside the sun). As discussed here, there are many similar coincidences involving the strong nuclear force, particle masses, the gravitational constant, and nuclear resonances. 

The visual below helps to illustrate the difference between the ratios of uninhabitable, barely habitable, moderately habitable, and abundantly habitable universes, although the actual ratios are almost certainly vastly greater than illustrated in this schematic visual.  I discuss these categories here, and argue that our universe must be in the rarest category (the "abundantly habitable" category shown in green).


habitable universes


Many have suggested that this cosmic fine-tuning suggests the likelihood of a cosmic fine-tuner. But Princeton philosophy professor Hans Halvorson disagrees. He came out yesterday with an essay entitled, “The Cosmos’ Fine-Tuning Does Not Imply a Fine-Tuner.”

Below is some of Halvorson's reasoning.

An analogy here might be apt. Suppose that you’re captured by an alien race whose intentions are unclear, and they make you play Russian roulette. Then suppose that you win, and survive the game. If you are convinced by the fine-tuning argument, then you might be tempted to conclude that your captors wanted you to live. But imagine that you discover the revolver had five of six chambers loaded, and you just happened to pull then [sic] trigger on the one empty chamber. The discovery of this second fact doesn’t confirm the benevolence of your captors. It disconfirms it. The most rational conclusion is that your captors were hostile, but you got lucky. Similarly, the fine-tuning argument rests on an interesting discovery of physical cosmology that the odds were strongly stacked against life. But if God exists, then the odds didn’t have to be stacked this way. These bad odds could themselves be taken as evidence against the existence of God.

Halvorson's reasoning in this essay is as careless as his proofreading.

The claim that “the odds didn't have to be stacked this way” is in error, if we are talking about the ratio between possible habitable universes and possible non-habitable universes. Regardless of whether any deity exists, it will inevitably be true that the class of all possible habitable universes is vastly outnumbered by the class of all possible universes. It is in general true that the number of ways in which one can arrange things so that a desirable functional end is achieved is vastly smaller than the number of ways in which you can arrange things so that no particular functional end is achieved.

For example, if I have a garage full of atoms, the number of ways in which I can arrange those atoms so that no functional end is achieved is always going to be 1,000,000,000,000,000 times larger than the total number of ways in which the atoms can be arranged so that a working motor vehicle is created. Similarly, the total number of ways in which the physics and constants of a universe can be arranged so that nothing special will ever happen is always going to be vastly greatly than the total number of ways in which the physics and constants of a universe can be arranged so that the very many physical requirements of life (such as stable long-burning stars, stable planets, and stable atoms) are met.

So the odds in which “nothing-special” uninhabitable possible universes vastly outnumber possible habitable universes do indeed “have to be stacked this way,” contrary to what the professor claims. Such an odds ratio is simply a logical necessity, and not at all something that can be “taken as evidence against the existence of God.” The fact that possible uninhabitable universes vastly outnumber possible habitable universes is no more evidence against the existence of God than the fact that the set of all numbers is vastly greater than the set of all numbers with consecutive digits.

Now let's look at the professor's analogy about the gun. Here he gives us a case of a false analogy, because the situation he's describing bears no resemblance to any claim that anyone is actually making. The professor imagines a person who is forced to fire at himself a six-shooter loaded with five bullets. Here are the characteristics of a person who is forced to fire at himself a six-shooter loaded with five bullets, and then survives:

Characteristic 1: The person faces a danger point, with a strong likelihood of a disastrous result.
Characteristic 2: The person fares well from this danger point, purely as a matter of luck.

Such characteristics bear no resemblance to the assumptions of a person believing that the universe was deliberately fine-tuned for life. Suppose you imagine that a benevolent deity deliberately created the universe so that it would be habitable for life. Under such a scenario, there never is any danger point in which there is a likelihood of a disastrous result. So Characteristic 1 does not hold true. There is also no point at all in which a favorable result occurs, purely as a matter of luck. If you think that the universe was set up deliberately so that it would be habitable, you do not believe this was a matter of luck. So Characteristic 2 also does not hold true.

So with his Russian roulette analogy, Halvorson is imagining some situation that bears no resemblance to the claims made by those who think the universe was deliberately fine-tuned. Halvorson has therefore committed the fallacy of false analogy.

I can imagine using reasoning similar to Halvorson's in other situations. If someone built a nice home for you to live in, you would consider that the set of all possible unlivable or dangerous ways to arrange the bricks, nails, boards, and pipes is much greater than the set of all nice livable houses; and you would conclude from these “bad odds” either that no one built the house or that someone evil built the house. Such reasoning would be as erroneous as Halvorson's.