Statistical Theodicy

[Contains spoilers for Unsong.]

Since time immemorial, people have asked how evil can exist in a world created by an omnipotent and benevolent God[1].

And since time immemorial, God has remained silent.

In his absence, Scott Alexander provides an elegant solution. God created every net-positive universe. He created the perfect one, the almost perfect ones, the less perfect ones… all the way down to our universe which is full of misery and suffering, but still, on balance, worthy of existence. As Scott explains on God’s behalf:

I CREATED MYRIADS OF SUCH UNIVERSES. WHEN I HAD EXHAUSTED ALL POSSIBLE UNIVERSES WITH ONE FLAW, I MOVED ON TO UNIVERSES WITH TWO FLAWS, THEN UNIVERSES WITH THREE FLAWS, THEN SO ON, AN ENTIRE GARDEN OF FLAWED UNIVERSES GROWING ALONGSIDE ONE ANOTHER…

YOUR WORLD IS AT THE FARTHEST EDGES OF MY GARDEN… FAR FROM THE BRIGHT CENTER WHERE EVERYTHING IS PERFECT AND SIMPLE. THERE IS A WORLD MADE OF NOTHING BUT BLISS, WITH A GIANT ALEPH IN THE CENTER. THERE IS ANOTHER WORLD MADE OF NOTHING BUT BLISS WITH A GIANT BET IN THE CENTER. AND SO ON, BUT MAKE A MILLION MILLION WORLDS LIKE THOSE, AND YOU START NEEDING TO BECOME MORE CREATIVE.

This is a good start, but it only kicks the can down the road. Why are we at the edge of the garden? Even if we buy that all universes except the single flawless one will contain some evil, it sure seems like our universe contains an awful lot of it. Is that just by chance?

The easy answer is selection bias, and the anthropic principle in particular[2]. Were we in the flawless universe, we would not bother asking about evil, since no such thing would exist[3]. So given that we’re asking at all, it’s because we’re in a universe with evil, and thus the question provides its own answer.

But again, we’re not talking about dust specks or platypuses or other minor oddities, we’re talking about the unfathomably abhorrent evils of our universe. Given that there is a wide range of universes with sufficient evil to provoke questions, it still seems peculiar that we ended up in one so far along the spectrum.

Maybe theodicy is possible in all flawed universes, but more common in the worse ones? I don’t think so. Were we to exist in a universe where precisely one person suffered immensely, would that not be even more troubling than our own? It is at least possible to dismiss the evils in our universe as the product of chaos. It would be far stranger to live in a world that is nearly perfect but still contains evil. As Dostoyevsky once asked:

answer me: imagine that you yourself are building the edifice of human destiny with the object of making people happy in the finale, of giving them peace and rest at last, but for that you must inevitably and unavoidably torture just one tiny creature, that same child who was beating her chest with her little fist, and raise your edifice on the foundation of her unrequited tears—would you agree to be the architect on such conditions?

A better answer comes to us from information theory and entropy. Namely: there are simply more disordered states than there are ordered ones.

Consider the perfect universe as described by a bit-string of length N. The universities with one flaw are thus described by the same bit-string, but with a single error. Omitting duplicates, there are N one-error universes:

Next we get to two-error universes, and the possibilities explode rapidly. Formally, there are n! / (2! (n-2)!) two-error universes, and in general, n! / (k! (n-k)!) k-error universes. Or defined recursively, the number or k-error universes is equal to the number of (k-1)-error universes multiplied by (n-k)/k. For large n and small k, this grows exponentially.

Taking this to its logical conclusion, we get that the space of possible universes looks less like a neat circular garden we happen to be towards the edge of, and more like a very very skewed distribution in which nearly all universes that exist are really flawed:

That’s all to say: As you add flaws to the perfect universe, the number of possible universes expands really quickly, such that if you are being randomly placed in a universe, the bulk of the probability lands on the set of maximally flawed universes that are still net-positive. And this fact is sufficient to explain the problem of evil without having to resort to weird appeals to free will or the necessity of evil.

Addendum

Astute readers will notice that the binomial theorem does not expand forever. As k reaches n/2, the function begins to contract. Just as there is only one perfect universe, there is only one maximally flawed universe. And even before the function contracts, it begins to slow, violating the assumption that the vast majority of possible existences cluster right around the worst possible net-good universe.

There are two ways to avoid these inconvenient aspects of our model.

The first is simply to suggest that the net-good cutoff occurs prior to the reversal:

This is a reasonable assumption if you consider goodness to be fragile, and evil to be born from chaos. The maximally likely universe is the one with no structure of all, who’s configuration is purely random, and thus has no godly design. Hoping that it comes out net-good is like sending a tornado into a supermarket and hoping a decent meal comes out the other side.

Our second option is to claim that “introducing flaws” to a perfect universe is best modeled not as corrupting individual bits, but through some other process that grows strictly exponentially. Consider elsewhere in Unsong where Scott describes his own information theory-inspired theology:

God is one bit. The bit ‘1’… it’s easy to represent nothingness. That’s just the bit ‘0’. God is the opposite of that. Complete fullness. Perfection in every respect.

Rather than corrupting that single bit, flaws are introduced by appending new bits onto the end. It doesn’t even matter what they are, since anything other than God itself introduces an imperfection:

In this case, the number of possible universes simply increases exponentially as a function of the number of errors, again making it overwhelmingly likely that you are amongst the worst possible net-positive universes. Formally, there’s a ~50% chance we’re in the most flawed set of universes, a 25% chance we’re in the second most flawed set, and so on.

Addendum 2

Another possible answer is that we’re not far along the spectrum at all. Horrific as it may be to contemplate, maybe our universe is not bad at all, but merely average.

To be specific, not average amongst all universes that could exist, but merely amongst the ones that are good on balance. The implication is that you could double that amount of suffering in our world to get to a universe that is net-neutral: exactly as good as it is bad.

It is tempting to dismiss this outright. There is already so much evil, that doubling it would seem to obviously render the university net-negative. The holocaust as we experienced it was sufficient to make many lose faith altogether, the idea of a tragedy of double it’s magnitude existing in a merely net-neutral universe feels ludicrous[4]

Even ignoring the impossibility of summing up human welfare to figure out where we fall on the spectrum of net-positive universes, this entire line of argument seems to fail since the value of a universe is determined by its entire timeline including the future, not merely the history up until the current moment. So wherever your intuitions stand now about the balance of good and evil in our world, this is all just the prelude to a much longer history, and we can’t reasonably expect our experience thus far to be representative.

But wait, if human-history to date was net-negative, but our future will be glorious and good, couldn’t God just create the universe starting now and then implant memories, star dust, fossils, etc, to make it seem like the universe had gone on for much longer?

Come to think of it, what makes you convinced that he didn’t?

Footnotes

[1] Since one man’s modus ponens is another man’s modus tollens, we might also ask: how can God exist in a world that contains evil?

[2] You know something has gone wrong when anthropics is the easy answer.

[3] Really, if we were in the flawless universe, we would not be “beings” at all in the sense you and I understand the term, nor actually capable of asking questions. Scott again:

IN THAT UNIVERSE, THERE IS NO SPACE, FOR SPACE TAKES THE FORM OF SEPARATION FROM THINGS YOU DESIRE. THERE IS NO TIME, FOR TIME MEANS CHANGE AND DECAY, YET THERE MUST BE NO CHANGE FROM ITS MAXIMALLY BLISSFUL STATE. THE BEINGS WHO INHABIT THIS UNIVERSE ARE WITHOUT BODIES, AND DO NOT HUNGER OR THIRST OR LABOR OR LUST. THEY SIT UPON GOLDEN THRONES AND CONTEMPLATE THE PERFECTION OF ALL THINGS.

[4] Is it even more ludicrous for us to draw the line between 6 million and 12 million? First, this whole thing is predicated on us teetering on the edge of losing faith anyway. Second, everyone has their breaking point. Scott again:

He told me it didn’t work that way. Everyone’s willing to dismiss the evil they’ve already heard about. It’s become stale. It’s abstract. People who say they’ve engaged with the philosophical idea of evil encounter evil on their own, and then suddenly everything changes. He gave the example of all of the Jewish scholars who lost their faith during the Holocaust. How, they asked, could God allow six million of their countrymen to perish like that?

But read the Bible! Somebody counted up all the people God killed in the Bible, and they got 2.8 million. It wasn’t even for good reasons! He kills three thousand people for worshipping the Golden Calf. He kills two hundred fifty people for rebelling against Moses’ leadership. He kills fourteen thousand seven hundred people for complaining that He was killing too many people, I swear it’s in there, check Numbers 16:41! What right do we have to lose faith when we see the Holocaust? “Oh, sure, God killed 2.8 million people, that, makes perfect sense, but surely He would never let SIX million die, that would just be too awful to contemplate?” It’s like – what?

The lesson I learned is that everybody has their breaking point, the point where they stop being able to accept things for philosophical reasons and start kicking and screaming.

Coda