*The Improbability Principle,*mathematician David J. Hand looks at the issue of apparent cosmic fine-tuning, the many ways in which the universe seems to be tailor-made for the existence of intelligent beings such as us. Hand attempts to explain this away in keeping with his overall thesis that we should not be surprised when incredibly improbable things happen.

Hand looks at the fact that the existence of stars requires an exquisite balance between two of the fundamental forces of the universe, the gravitational force and the electromagnetic force. He suggests that thinking there is such a balance results from the mistake of considering that just one of the two has been fine-tuned to just the right value. When we consider the possibility of both varying, Hand suggests, then the situation is not so amazing. As Hand says on page 214-215 of his book:

*We saw that changing the value of either one of these values would mean that the universe would not be suitable for life. But what if we changed them both? What if we increased the electromagnetic force a little, to match the increase in the gravitational force? Do this approximately, and the equilibrium within stars is maintained, so perhaps planets still form and life evolve. Fine-tuning, yes, but with much, much more scope for a pair of values which will lead to life than if the forces must separately take highly specific values.*

Hand's reasoning is incorrect. When we have a case in which two fundamental constants of nature are exquisitely balanced, there is no greater likelihood that both will balance if we allow for the possibility of both of them varying. We can see this clearly by considering the case of the proton charge and the electron charge.

There is an exquisite and unexplained balance between the proton charge and the electron charge, in that all protons have a charge of exactly 1.602176565 X 10

^{-19}coulomb, and all electrons have a charge of exactly -1.602176565 X 10

^{-19}coulomb (which is quite amazing given that each proton has a mass 1836 times greater than the mass of each electron). As the astronomer Greenstein has pointed out, there are reasons why stars and planets would not be able to exist if the absolute value of the proton charge and the electron charge differed by even 1 part in 1,000,000,000,000,000,000. Since electromagnetism is a force more than a trillion trillion trillion times greater than the gravitational force, even a tiny change in either the proton charge or the electron charge would mean that electromagnetic effects acting on a large body would overwhelm gravitational effects, and gravitation would be insufficient to keep stars and planets together.

But suppose we imagine random changes in both the electron charge and the proton charge. Would that increase the probability of the two of them matching in the way that is necessary for stars and planets to hold together? No, it wouldn't. If we imagine both constants randomly changing, it is true that this would open up many new possibilities that might be compatible with the existence of stars and planets, such as one in which the proton charge was 3.378921 X 10

^{-12 }coulomb and the electron charge was an exactly opposite value of -3.378921 X 10

^{-12}coulomb. But the overall likelihood of an exact match when both constants vary is not any greater than if one allows only one constant to vary.

Similarly, imagine I am playing a casino "million dollar jackpot" game of chance, and start with one random number between 1 and a million. To win, I have to get from the casino another number that matches the first number. If only the second number varies, the chance of success is 1 in a million. Now the casino employee may tell me: increase your chances by letting both numbers be random. But that's a fallacy – my chances of success will not be increased. The probability of getting a match if you start with one number and then get a random number is 1 in a million. The probability of getting a match if you get two random numbers is one million out of a trillion (because there are one million possible matches of two numbers between 1 and a million, and a trillion different possible combinations of two numbers between 1 and a million). But one million out of a trillion is a probability exactly the same as 1 in a million.

Hand then asks us to consider another possibility – that there may be some hidden reason why a change in one fundamental constant might cause a corresponding change in another very different fundamental constant. This might help to explain the exquisite balances within nature, Hand suggests. But this suggestion is an appeal to an imaginary possibility, and Hand provides no facts to back up such a suggestion. To the best of our knowledge, fundamental constants on which life depends (such as the speed of light, the gravitational constant, Planck's constant, the proton charge, and the electron charge) are entirely independent. There's no reason to think that having one such constant be compatible with life would increase the chance that other such constants would be compatible with life.

Hand tries to pass off his groundless imaginary idea as an example of what he calls the “law of the probability lever.” Similarly, if a husband had failed to save enough money for retirement, and his wife complained, the husband could imagine that fairies will give him a million dollars when he reaches the age of 62, and he might call such a fantasy “the law of the fairy contributions.” Imaginary concepts for which there is no factual basis should not be referred to as laws.

Hand then refers to a scientific paper in which one physicist claimed to show that it's not all that unlikely that stars should exist in random universes. Hand summarizes the paper by Adams as follows:

*Fred C. Adams, of the Michigan Center for Theoretical Physics, investigated varying the gravitational constant, the fine-structure constant, and a constant determining nuclear reaction rates. He found that about a quarter of all possible triples of these three values led to stars which would maintain nuclear fusion – like the stars in our universe. As he said, “[We] conclude that universes with stars are not especially rare (contrary to previous claims).”*

The previous claims Adams referred to are numerous claims made in the scientific literature along the lines that the chance is incredibly low of a random universe allowing stars like ours. There are some reasons why such claims were actually correct, and why Adams is wrong on this issue.

The first reason is that to have any stars at all you need to have a fine-tuning of not just the three constants Adams considered, but other constants he did not consider. For example, Adams completely fails to consider the very precise match between the proton charge and the electron charge needed for the stability of large bodies like planets and stars (previously discussed), a match that would not occur by chance in 1 in 1,000,000,000,000 universes in the parameter space he considers.

The second reason is that the real question is not the likelihood of some type of stars, but yellow stars like the sun, which offer better prospects for the evolution of intelligent life than other types of stars such as red dwarfs or blue giants. Scientists such as Paul Davies have concluded that very small changes in the fundamental constants would preclude the existence of stars like the sun. It's kind of like this: nature must thread one needle hole for there to exist some type of stars, but nature must thread a much tinier needle hole for there to be stars like the sun.

The third reason is that Adams is guilty of a fallacy that we might call the fallacy of the “ant near the needle hole.” Consider an ant that somehow wanders into your sewing kit. If it were smart enough to talk, the ant might look at the eye of a needle hole in your sewing kit, and say, “Wow, that's a big needle hole!” Such an observation will only be made if you have a perspective looking a few millimeters away from the needle hole.

Similarly, Adams has given us graphs in which his “camera” is placed a few millimeters from the needle hole that must be threaded for stars to exist. He has imagined a parameter space in which fundamental constants are merely tripled. But physicists routinely deal with a difference of 40 orders of magnitude (10,000,000,000,000,000,000,000,000,000,000,000,000,000), which, for example, is roughly the difference between the strength of the strong nuclear force and the gravitational force. So if we are imagining a parameter space of alternate universes, we must imagine a parameter space infinitely larger than the relatively microscopic parameter space Adams considered. Rather than just imagining a possible tripling of the fundamental constants Adams considers, we should imagine that any of them could vary by a trillion times or a quadrillion times or a quintillion times.

Taking that correct perspective, we can see how marvelous it was that nature managed to thread the needle holes necessary for our existence. You can visualize it this way. The parameter space is the vast Sahara desert. The needle holes that nature needed to thread for a habitable universe are in different random positions scattered throughout that vast desert. The likelihood of those needle holes being threaded successfully by chance is therefore infinitely smaller than the probability figure reached by Adams.