Problems of the Fine-tuning Argument
The Fine-tuning Argument is a case made for the existence of a divine Creator that has arisen out of our exploration of quantum physics and relativity. At this time there are six known mathematical constants that govern everything from the size of the universe to the nature of a photon. Although the argument is broad, it is reasonably summarized by physicist Martin Rees in his acclaimed book Just Six Numbers:
“These six numbers constitute a ‘recipe’ for a universe. Moreover, the outcome is sensitive to their values: if any one of there were ‘untuned’, there would be no stars and no life. Is this tuning just a brute fact, a coincidence? Or is it the providence of a divine Creator?”
— Martin Rees
Being a good physicist in the absence of evidence, Rees makes no further speculation. However, the observation takes on a far more personal meaning as phrased by Stephen Hawking in A Brief History of Time:
“The remarkable fact is that the values of these numbers seem to have been very finely adjusted to make possible the development of life.”
— Stephen Hawking
Hawking sits relatively comfortably on the anthropic principle, but by no means rules out a Creator entirely. Obviously you can’t prove a Creator does not exist any more than you can prove light is not comprised of infinitesimally small Honey Baked Hams.
Because the argument claims that each individual number is an example of fine-tuning, the fact that there are six only serves —so they say—to improve the odds of God’s existence. Presumably one would be enough. If metaphysics can be disentangled from one it can be for all.
Of the six, N is the most convenient. N is the ratio between the electromagnetic repulsion of two protons and their gravitational attraction. It’s is number so large ( ≈ 10^36 ) that it’s very difficult to ascribe any relevant meaning to it save this: if it was considerably less or more this particular universe wouldn’t have come into being. Too small and gravity sucks all the protons into heavy elements, too big and all we get is hydrogen because the protons repel and can’t form nuclei.
The principle difficulty dealing with a number of that size is that making an analogy doesn’t simplify it. 10^36 is in the ballpark of the number of kilometers to drive across our galaxy and back again, for instance. OK, so you’ve never done that. Let’s make it a millimeter then. Now it’s just a round trip past Alpha Centauri. Going the other way is no help either. I can tell you it’s around around the number of cells in a family of three, but you have no intuitive understanding of how many cells are in one of your fingernail clippings, much less yourself.
Fortunately, large numbers that are generated out of complexity rather than magnitude force our brains into the mental corner of awe a vivid imagination can’t. Nobody has ever walked to Mars, but we’ve all looked at a math problem and walked away shaking our heads. As an example, in 1974 Emo Rubik invented the Rubik’s Cube. This infuriating little device has an absurd number of possible arrangements, and when people figured out all the tricks for solving it, the company came out with one appropriately named Rubik’s Revenge. It is a cube based on the exact same principles as the original, except instead of having three squares per edge it has four.
There are a lot of these in dumpsters.
When you pick it up, you are holding in your puny little hand an object that has precisely
7,401,196,841,564,901,869,874,093,974,498,574,336,000,000,000 different possible states, assuming that solving it means returning it to its original state, not just with all sides having the right colors. It’s approximately 7.4012 X 10^45, but for argument’s sake I’ll take an even 10^45— one hundred million times bigger than N. How is that possible?
Take a penny and a nickel and lay them side-by-side. How many different ways can you arrange them? Two obviously, unless you are creative and made a distinction between heads and tails. In that case you came up with eight, but let’s not worry about that. If you add a dime into the mix you have six different states. Add a quarter and you have 24. Add a dollar bill and you have 120. Five dollars and there are 720 different arrangements. You’ve bought a lot of combinations for $6.41.
The number of different arrangements of different objects are called permutations, and they get big fast. The math term is a “factorial”, and it looks like this:
n! (not to be confused with N above)
The “n” stands for “number of objects”, and the exclamation point means you multiply all the numbers from “n” to 1 together. 4! would mean 4x3x2x1=24. 8! is 40320. By the time you get to the ten fingers on your hands, there are 3,628,800 different ways for the mafia to sew them back on if you don’t pay your protection money. It seems extremely hard to imagine, but if you want to play the home game get ten Scrabble letters instead of a cigar cutter and start counting.
When we consider the Rubik’s Revenge, there are even more complications to figuring out how many permutations it has. The corners, for instance, can only change places with the other corners. All the other cubes move in limited ways. In fact, 10^45 is far less than the number of permutations when the cubes could go anywhere.
This brings us to the fallacy of the fine-tuning argument. Our big number N is supposedly “fine-tuned”, but any physicist will tell you that it's got wiggle room. If you take N and add one to it, we still live in the same universe. You add two, same universe. This can go on to quite some degree without any significant effect. Therefore, it’s not entirely fine-tuned, it’s just within a margin of error that allows the universe to exist in this particular state. Of the six numbers, this is an extreme example. ε, the mass lost when protons fuse into helium, is 0.007. If it’s off by, say, 0.00001, your coffee cup may be a little to the left but otherwise everything is just dandy. It’s hardly fine-tuned at all, and an object 0.007 meters long is easily visible to the naked eye.
This margin of error is of no small metaphysical or existential consequence concerning the Rubik’s Revenge. Maybe being off by a few kilometers on a trip around the galaxy isn’t large enough for a Creator to worry about, but the same is not true of the Rubik’s Revenge. That gigantic, precise number of permutations, many orders of magnitude larger than N, is fine-tuned to such a degree that if it was off by even a single permutation it would destroy the fabric of the entire universe as we know it.
Imagine if reality worked in the following way: you have five fingers on each hand, so 5x2=10 fingers. No problem. But what if you then counted them out individually and you only had nine? For something to so obviously violate all known principles of reality—particularly if it was testable and repeatedly found to be so—would be either an extraordinary piece of evidence that someone or something was dipping its fingers into the mix, or an extraordinary piece of evidence that we could use one to help tutor us on our last 10,000 years of homework.
It would be, quite literally, infinitely more miraculous if the math didn’t work but existence did, and we were all just walking Barbie Dolls that didn't need to eat or breathe to satisfy the desire of an all-powerful Creator to be worshipped night and day. When we add up all the permutations of a Rubik’s Revenge we aren’t surprised at the number because we see how it’s put together. What we do not do is thank Emo Rubik for being so benevolent and wonderful as to pick exactly 7,401,196,841,564,901,869,874,093,974,498,574,336,000,000,000 permutations with which to imbue his little toy to ensure the universe wouldn’t implode. Or explode. Come to think of it, I don’t know what would happen if 1+1=1.
We should probably get some scientists on that.