This is a Koan written after the publication of Cosmological Koans, addressing and concerning the hypothesis that simulations of minds have the same moral value as the original physical and biological minds. It can be enjoyed whether or not you’ve read the book, but it perhaps a bit more fun if you have. It’ll also be more enjoyable if you’ve studied quantum mechanics and/or thought a lot about simulating things, but that’s not strictly necessary either.

A Simulacrum of Revenge

The djinn is thirsty for revenge. But not just any garden-variety revenge. Death was too good — simple single physical suffering too good — for this intolerable human. No, the djinn needs the human to suffer many many ways, over and over and over.

Partly by nature, the djinn firmly believes that capturing the computational equivalent of something is just as good as the original thing. So it just needs to create the computation that is the human’s experience of suffering. Granted, the djinn has given up trying to figure out exactly what computation a human brain is running (what a mess!). But it is confident that it does not have to understandthe brain, just simulate it with enough fidelity: the right simulation of the matter in the brain will necessarily instantiate whatever computation the brain is doing.

So the djinn fires up some Djinnium and gets simulating. Through prodigious effort it has built up enough data, supplementing its initial scans from the cave, to feel that it can reliably replicate the human and its brain in a nice pure Djinnium computation. When this is done, the whole thing can then be tweaked just a bit, to include immense suffering. The djinn toys around for a while with a classical-physic simulations, thinking this might be sufficient. But what if classical physics is not good enough? The djinn wants to be completely sure of capturing everything, so it decides to go the full quantum route. It comes up with an appropriate wavefunction describing the human and a sufficiently large environment, and starts evolving via the Schrödinger equation.

This is extraordinarily tiresome. The human and environment has a N=10^163648237883787348374483743874.3 dimensional state-space so each step of evolution is a prodigious calculation (even using the djinn’s precious reserve of Zenonnium Djinnium that can do infinitely many computations in a finite time.) But it’s worth it, the djinn assures itself, knowing the human is in there suffering away in agony; wiping some proverbial sweat from its brow, the djinn cranks through the computation necessary to evolve the human for a few seconds once, then again with some pain mixed in.

The djinn is, though, is ever-so-slightly troubled. It’s taken the approach of “collapsing” the wavefunction by regularly – in fact really rather frequently – choosing a single branch of the branching wavefunction and trimming the others away. This is important so that the djinn does not quickly end up tracking a quickly-proliferating tangle of possibilities. But it does not really have a terribly solid prescription for when to do the trimming. So it decides not to. Why not? There are just more of the human in there suffering in different ways if they are all kept around, and even better, the wavefunction’s evolution stays nice and simple, with nothing but Schrödinger’s equation operating.

So the djinn does this. But it is, and this cannot be emphasized enough, very tiring, so the djinn has a think and realizes a wonderful idea. It does not have to evolve the state one time-step at a time. It can do it all at once! It’s exactly mathematically equivalent to write the human’s quantum state as a sum over states of definite energy, weighted by some set of complex numbers. This form has an enormous advantage, though, which is that each term in this sum evolves both independently and also very, very simply: it is just a “rotation” of the direction of the complex number. So once the set of energy states and complex weightings is computed, to get the human’s state at any later time, all the djinn needs to do is compute this rotation, apply it to each complex number, and re-do the summation of the states.

This is terrific. After, granted, a matrix diagonalization problem that is truly hellish, the djinn is all set with its energy states and weightings, and merrily starts plugging-and-chugging to get the human’s quantum state at a sequence of times.

The djinn, though, now has an uneasy thought. How many timesteps does it have to compute? When evolving using the Schrödinger equation, the djinn simply computed as many timesteps as it needed to maintain accuracy. But now it could compute the state at any time at all, without the intervening steps. So it could space them out by nanoseconds, seconds, or even minutes according to the clock of the human being simulated.

This starts to make the djinn really nervous as it thinks more. It wants the human to suffer, but if only 1/10th of the timesteps are computed, does the human suffer 1/10th as much? If the djinn just computes a single timestep at which the human remembers suffering does that count? But then, could the human experience anything at just a single timestep? Seems unlikely, but then how many timesteps does it take for the experience to appear?

The djinn keeps telling itself that the whole computation has to be equivalent to its earlier one, where it seemed clear what exactly was going on. But it can’t help but wonder, with more and more consternation: at what point does the suffering come into being? Does the suffering come into existence when the timesteps are evaluated? When the matrix is diagonalized? What about one step before completion of the (iterated) diagonalization? What about two steps?

And worse, the diagonalization is just a basis change, which, like a coordinate change, should have no physical effect. So does the suffering come into being the moment the state and Hamiltonian are chosen, without any computation? Does just imagining those two mathematical entities make the suffering come into being? That seems a bit tenuous to the revenge-thirsty djinn.

And then djinn, without really meaning to, imagines a slightly tweaked wavefunction according to which the human turns out extremely happy. Oh no! By imagining this did the djinn create a huge amount of happy experience for the human?! This feels like too much power even for an all-powerful djinn to believe that it has.

The djinn is perplexed as to where its treasured suffering went. It imagined the human as a computation, then as an accurately-simulated classical system instantiating that computation, then as a superior quantum version, then as a perfectly equivalent quantum calculation. But at the end, the djinn had just a bunch of uncomputed abstract mathematics that really did not seem to be suffering at all. At what point in this chain of improvements did the fidelity to reality disappear?