To really know you’ve created the best possible universe, you’d have to create them all

I was on my way into work this morning and started thinking about a curious question.

You may be aware of the area of theological inquiry called theodicy*.  It deals with the “problem of evil”, though I’m sure that’s an oversimplification.  In other words, it deals with the issue that, if God exists, and is infinitely powerful, and is omnibenevolent and omnipresent and omni-whatnot, then why is there evil?

We can leave aside arguments based on notions of free will and just desserts; bad things happen to “good” people in the world, whether through the actions of “evil” people or simply through the operations of the forces of nature.  Think of childhood cancers and the like, and indeed, most childhood diseases prior to the modern era, as well as the fact that many children, through no fault of their own, are born to parents who are idiots (this probably describes all children, including mine).

One potential solution to the “problem of evil” is the notion that, despite appearances, the universe in which we live is the best possible one there can be.  This idea is caricatured by Voltaire in the form of Dr. Pangloss, but it’s a serious point that is seriously made, and there is a certain logic to it.  The notion is that, if things were changed, locally, to make some particular situation better, it would overall make more things worse, by whatever criteria you might happen to choose, and so every bad thing that happens, though it may not have any local good to it, is nevertheless necessary to minimize the evil, or maximize the good, of the universe, by whatever measure happens to be used by the one doing the parsing…presumably, God.

But how would such a God know what the best possible universe was?  Such a being is assumed to have infinite intelligence**, as well as infinite power and awareness.  We could, perhaps, describe it as a sort of “computer” that is infinite in all dimensions (perhaps an infinite number of them) and with limitless processing power, constrained only to the degree that it does not lead to paradoxes and contradictions, since we must assume—or I do, at least—that logic would apply even to an omnipotent being.  Even God cannot actually make two plus two equal five without changing definitions, in which case it hasn’t actually been done.

So, how would a God know what the best of all possible universes was?  We can probably presume that there isn’t any a priori “rule of thumb” about which universes might be the best ones, such that one could know ahead of time without even having to think about the details, though we can perhaps rule out universes devoid of life.  Those universes would be free of suffering, of course—indeed, I suspect they would be the only possible universes in which there could ever be “no suffering”—but they would be rather boring, and no one would be terribly impressed by their lack of suffering…not least because there wouldn’t be anyone to be impressed.

In all possible universes in which life of any sort is possible—and there may be many more potential arrangements of laws of physics in which that could happen than seems obvious to us at first glance—how would an omniscient mind determine what the best possible universe was?

deciding paths

It would have to run the experiments.  It would have to test the many possible variations—indeed, there would be infinitely many, even if we restrict the trials to universes with laws of physics equivalent to ours.  This sort of simulation is really what we do in a much more restricted sense when we imagine possible outcomes of our own actions; we simulate the potential futures in our minds, so we can try out our various options without having to assume real risks.

However, a simulation that does not take all possibilities into account—such as the ones we always run in our own heads, being limited beings—is not capable of truly ruling out any possible choices or outcomes or events, it can only generate estimated probabilities.  If one is going to know—for certain—that an outcome will be a certain way, one needs to run a full simulation of possibilities.

The mathematics and science of chaos theory, for instance, demonstrate that, in principle, to know the long-term details of a complex system to a complete degree of specification, one cannot truncate the simulation or its variables, since in higher-order equations—such as would, presumably, be required to describe a cosmos—being anything less than perfectly precise*** would give answers that rapidly diverge in detail from actual outcomes.  And the details are where the Devil is, as the saying goes.

So, to know which possible universe is the best possible universe, a God would need to, in a sense, simulate all possible universes and see which one turns out best, by whatever criteria such a being might choose.

But as Max Tegmark discusses in Our Mathematical Universe, and in Life 3.0, and as other people such as Nick Bostrum, etc., have pointed out, we ourselves may be simulations.  Indeed, there is no functional difference between a fully simulated universe**** and an actual universe (which would mean the terms “actual” and “fully simulated” are interchangeable), just as there is no difference in the content of a story whether the words are written in ink on paper or read aloud or stored as a Kindle e-book…or carved in stone or written in DNA code or any other form of storage one might want.  Again, chaos theory is not just a function of the limits of our ability to measure things like weather—it is a mathematical phenomenon, baked into the nature of logic and calculation itself.  So even God, presumably, could not just work around it.

This would mean that, to know which was the best of all possible worlds, God would have to simulate all possible worlds, or at least a fair chunk of them.  Perhaps God could rule out, a priori, universes in which life exists only for a short period of time, or never becomes in any sense sentient, or in which life happens but is always completely just on the edge of destruction—truly nasty, brutish, and short at all levels and all times.

Even given that, there are functionally infinite variations in all possible events, even only in universes in which human beings come into existence*****, and to find out which of these was truly and definitively “best” by any chosen criteria, one would have to simulate them all.  But this would, effectively, mean simply creating them all.  In each simulation, each person would experience a real universe, a real life, however good or bad.  Which would mean that, as far as we could know, we might be living in one of the simulations of a less than optimal universe, one that will or would ultimately be discarded by God’s criteria.  But then, what’s the point of doing the trials if each trial instantiates a universe?  They would all exist, anyway.  Indeed, merely in imagining them as possible, if it did so thoroughly, a God would be creating them.

This is rather analogous to the arguments made by David Deutsch, pioneer of quantum computing, for why the “many worlds interpretation” of quantum mechanics must be the correct one.  If everything happens as if all these other quantum possibilities happen and “interact” with the “real” one, then they exist, or there would be no sense in which they could behave as if they interact.  I won’t get into that now, except to say that I find the arguments made by Deutsch, as well as Tegmark and Sean Carroll, and similar, going back to Hugh Everett, to be pretty convincing.

All of which brings me to my “conclusion”, if it can be called that, which is that there’s no logical sense in which, even if there were a God, we could know that we are living in the best possible world such a being could create.  If infinite universes are simulated, fully, then each of those infinite universes exists, and to do other than simulate them fully would be to remain uncertain—mathematically—that one had found the best possible universe, even in a universe in which nature cannot be infinitely subdivided because of quantum uncertainty and wave-related limits on the precision of knowledge/measurement/existence.

Maybe it would be better if such a God just throws the dice and sees what happens.

train track divergence

*Or, as I like to call it when I’m not feeling particularly charitable, “the idiocy”.

**Whatever that might mean.

***Again, whatever that might even mean.

****And here I do mean fully, i.e. down to the last Planck length and time.  Perhaps this is the reason, or one of them, why quantum mechanics demands that things cannot be infinitely divided.  A universe with truly continuous variables, involving infinite decimal places of the real numbers in many calculations, such as every use of pi or e, could not, in fact, be simulated at all…and therefore, perhaps, could never be instantiated.  Even a God could not simulate a universe in which fully continuous variable exist, since it would take infinite time and memory just to delineate the digits of the first irrational number brought into use.  And anyone who has worked with math and physics at all knows that both pi and e, for instance, come into play often…and because the Pythagorean theorem seems baked into the geometrical nature of reality at a fundamental level, even seemingly simple things like the square root of 2 come up quite often as well.

*****For the sake of hubris, I’ll stipulate that such are the universes in which we are interested, though there’s no good reason to think God would prefer us.  Maybe God made the universe so that cocker spaniels could come into existence, and humans are just the means by which that’s made to happen.