Similarly, to postulate that angels come through the other slits and deflect our photons would be better than nothing. But we can do better than that. We know exactly how those angels would have to behave: very much like photons. So we have a choice between an explanation in terms of invisible angels pretending to be photons, and one in terms of invisible photons. In the absence of an independent explanation for why angels should pretend to be photons, that latter explanation is superior.
We do not feel the presence of our counterparts in other universes. Nor did the Inquisition feel the Earth moving beneath their feet. And yet, it moves! Now, consider what it would feel like if we did exist in multiple copies, interacting only through the imperceptibly slight effects of quantum interference. This is the equivalent of what Galileo did when he analysed how the Earth would feel to us if it were moving in accordance with the heliocentric theory. He discovered that the motion would be imperceptible. Yet perhaps ‘imperceptible’ is not quite the right word here. Neither the motion of the Earth nor the presence of parallel universes is directly perceptible, but then neither is anything else (except perhaps, if Descartes’s argument holds, your own bare existence). But both things are perceptible in the sense that they perceptibly ‘kick back’ at us if we examine them through scientific instruments. We can see a Foucault pendulum swing in a plane that gradually seems to turn, revealing the rotation of the Earth beneath it. And we can detect photons that have been deflected by interference from their other-universe counterparts. It is only an accident of evolution, as it were, that the senses we are born with are not adapted to feel such things ‘directly’.
It is not how hard something kicks back that makes the theory of its existence compelling. What matters is its role in the explanations that such a theory provides. I have given examples from physics where very tiny ‘kicks’ lead us to momentous conclusions about reality because we have no other explanation. The converse can also happen: if there is no clear-cut winner among the contending explanations, then even a very powerful ‘kick’ may not convince us that the supposed source has independent reality. For example, you may one day see terrifying monsters attacking you — and then wake up. If the explanation that they originated within your own mind seems adequate, it would be irrational for you to conclude that there really are such monsters out there. If you feel a sudden pain in your shoulder as you walk down a busy street, and look around, and see nothing to explain it, you may wonder whether the pain was caused by an unconscious part of your own mind, or by your body, or by something outside. You may consider it possible that a hidden prankster has shot you with an air-gun, yet come to no conclusion as to the reality of such a person. But if you then saw an air-gun pellet rolling away on the pavement, you might conclude that no explanation solved the problem as well as the air-gun explanation, in which case you would adopt it. In other words, you would tentatively infer the existence of a person you had not seen, and might never see, just because of that person’s role in the best explanation available to you. Clearly the theory of such a person’s existence is not a logical consequence of the observed evidence (which, incidentally, would consist of a single observation). Nor does that theory have the form of an ‘inductive generalization’, for example that you will observe the same thing again if you perform the same experiment. Nor is the theory experimentally testable: experiment could never prove the absence of a hidden prankster. Despite all that, the argument in favour of the theory could be overwhelmingly convincing, if it were the best explanation.
Whenever I have used Dr Johnson’s criterion to argue for the reality of something, one attribute in particular has always been relevant, namely complexity. We prefer simpler explanations to more complex ones. And we prefer explanations that are capable of accounting for detail and complexity to explanations that can account only for simple aspects of phenomena. Dr Johnson’s criterion tells us to regard as real those complex entities which, if we did not regard them as real, would complicate our explanations. For instance, we must regard the planets as real, because if we did not we should be forced into complicated explanations of a cosmic planetarium, or of altered laws of physics, or of angels, or of whatever else would, under that assumption, be giving us the illusion that there are planets out there in space.
Thus the observed complexity in the structure or behaviour of an entity is part of the evidence that that entity is real. But it is not sufficient evidence. We do not, for example, deem our reflections in a mirror to be real people. Of course, illusions themselves are real physical processes. But the illusory entities they show us need not be considered real, because they derive their complexity from somewhere else. They are not autonomously complex. Why do we accept the ‘mirror’ theory of reflections, but reject the ‘planetarium’ theory of the solar system? It is because, given a simple explanation of the action of mirrors, we can understand that nothing of what we see in them genuinely lies behind them. No further explanation is needed because the reflections, though complex, are not autonomous — their complexity is merely borrowed from our side of the mirror. That is not so for planets. The theory that the cosmic planetarium is real, and that nothing lies beyond it, only makes the problem worse. For if we accepted it, then instead of asking only how the solar system works we should first have to ask how the planetarium works, and then how the solar system it is displaying works. We could not avoid the latter question, and it is effectively a repetition of what we were trying to answer in the first place. Now we can rephrase Dr Johnson’s criterion thus:
If, according to the simplest explanation, an entity is complex and autonomous, then that entity is real.
Computational complexity theory is the branch of computer science that is concerned with what resources (such as time, memory capacity or energy) are required to perform given classes of computations. The complexity of a piece of information is defined in terms of the computational resources (such as the length of the program, the number of computational steps or the amount of memory) that a computer would need if it was to reproduce that piece of information. Several different definitions of complexity are in use, each with its own domain of applicability. The exact definitions need not concern us here, but they are all based on the idea that a complex process is one that in effect presents us with the results of a substantial computation. The sense in which the motion of the planets ‘presents us with the results of a substantial computation’ is well illustrated by a planetarium. Consider a planetarium controlled by a computer which calculates the exact image that the projectors should display to represent the night sky. To do this authentically, the computer has to use the formulae provided by astronomical theories; in fact the computation is identical to the one that it would perform if it were calculating predictions of where an observatory should point its telescopes to see real planets and stars. What we mean by saying that the appearance of the planetarium is ‘as complex’ as that of the night sky it depicts is that those two computations — one describing the night sky, the other describing the planetarium — are largely identical. So we can re-express Dr Johnson’s criterion again, in terms of hypothetical computations:
If a substantial amount of computation would be required to give us the illusion that a certain entity is real, then that entity is real.
If Dr Johnson’s leg invariably rebounded when he extended it, then the source of his illusions (God, a virtual-reality machine, or whatever) would need to perform only a simple computation to determine when to give him the rebounding sensation (something like ‘if leg-is-extended then rebound …’). But to reproduce what Dr Johnson experienced in a realistic experiment it would be necessary to take into account where the rock is, and whether Dr Johnson’s foot is going to hit or miss it, and how heavy, how hard and how firmly lodged it is, and whether anyone else has just kicked it out of the way, and so on — a vast computation.