The question of how many tickets are drawn is a tough one. If only one is drawn, your present Now, which does exist, must be the one and only instant realized and experienced. All your memories are then illusions in the sense that you never experienced them. That seems very hard to believe. What is more, memories are legion. If you believe you did actually experience them all, then lots of Nows have been drawn. From this it is a small step to saying that all Nows in Platonia are drawn. In quantum mechanics, this is called the many-worlds hypothesis. But then the theory seems to become vacuous: everything that can be is, no predictions appear to be made. The root of the problem is the assumption, neat and clean in itself, that each experienced instant is always tied to a single Now and that the distribution of the mist over Platonia is determined by a law indifferent to the workings of the cosmic lottery. Whether or not particular Nows are drawn has no effect on the mist intensity. The rules of the scheme make it quite impossible to say how many, if any, of your memories are real. All we know is that the present Now is real. You can see how Descartes’s dilemma is revived in such a scheme. I suspect that it is a problem we just have to live with.
The theory is still testable because only Nows with high mist intensity (and therefore high probability) are likely to be experienced, and such Nows have characteristic properties: above all, they are time capsules. We can therefore test our own experiences and see if they verify the predictions of the theory. This is something that in principle can be settled by mathematics and observations. For if physicists can determine or guess the structure of Platonia and formulate the law that determines how the mist is distributed over it, then it is simply a matter of calculation to find out where in Platonia the mist is most intense. If the mist is indeed concentrated on structures that are time capsules, the theory will make a very strong prediction – any Now that is experienced will contain structures that seem to be records of a past of that Now. It will also contain other characteristic structures.
The huge number of things that can coexist simultaneously in one Now is significant here. It means that many independent tests can be made on a single time capsule to see whether the predictions are confirmed. The laws of nature are usually tested by repeating experiments in time. If the same initial state gives the same outcome, the law is confirmed. However, for an object as richly structured as the Earth (which in any instant belongs to one of the Nows in Platonia), repeating experiments in time can be replaced by repeating them in space. As it happens, even confirming a theory by repeating experiments in time as normally understood boils down to comparing records in one Now. The precondition of all science is the existence of time capsules. All the Nows we experience are time capsules. The question is whether we can explain why this is so from first principles: can the strong impression of time emerge from timelessness? It is a logical possibility, but the real test must await mathematical advances. Unfortunately, they are not likely to be easy.
Strange as a timeless theory may seem, it has the potential to be very powerful. Boltzmann’s work highlighted two difficulties inherent in any theory of time – initial conditions must be imposed arbitrarily; and dull, unstructured situations are far more probable than the interesting structured things we find all around us. Interestingly structured Nows are an extreme rarity among all the Nows that can be. If the mist does pick out time capsules in Platonia, it must be very selective. Since all possible structures are present in Platonia, the vast majority of Nows do not contain any structures at all that could be called records. Even then, the apparent records will be mutually consistent in only a tiny fraction of what is already a tiny fraction. Only our habitual exposure to the time capsules we experience blinds us to the magnitude of the phenomenon that needs to be explained. Stars in real space give us only an inkling of how thinly time capsules are spread. Any scheme that does select them will be very powerful. But more than that, it will be more fully rational than classical physics, with its need to invoke a very special initial condition, can ever be. Once the law that governs the distribution of the mist over Platonia has been specified, nothing more remains to be done. The mist gathers where it does for only two reasons: the structure of the law and the structure of Platonia.
So where is the mist likely to gather? The mathematics needed to answer this question will certainly be difficult, but there are some hints (which I shall elaborate in the final chapters). They suggest that mist is likely to be distributed along thin, gossamer-like filaments that bifurcate and form a tree-like structure (Figure 6).
A tendency to bifurcation is deeply rooted in quantum mechanics. In principle, it could happen in both directions along a filament. However, the Nows we experience all seem to have arisen from a unique past. There seems to be no branching in that direction. Within quantum mechanics, as presently formulated in space and time, this fact is not impossible, but it is as puzzling as the low entropy that so exercised Boltzmann. It does seem improbable. I suspect that everything will look different if we learn to think about quantum mechanics in Platonia. For one thing, the arena has a very different shape. This is why I was keen to show you at this early stage the diagrams of Triangle Land (Figures 3 and 4) and my representation of Platonia (Figure 5). It opens out in one direction from nothing. I suspect that the branching filaments of mist in Figure 6 arise because they reflect this overall, flower-like structure of Platonia. If that is so, the great asymmetries of our existence – past and future, birth and death – arise from a deep asymmetry in being itself. The land of possible things has one absolute end, where it abuts onto mere nothing, but it is unbounded the other way, for there is no limit to the richness of being.
Who knows what experiences are possible in the oases of richly structured Nows strung out along the trade routes that cross the deserts of Platonia? The plurality of experience is remarkable and suggestive. In any instant, we are aware of many things at once. Through memories we are, as it were, present simultaneously in many different Nows in Platonia. Richness of structure permits this. One grand structure contains substructures that are ‘pictures’ – simplified representations that capture the essential features – of other structures. Our memories are pictures of other Nows within this Now, rather like snapshots in an album. Each Now is separate and a world unto itself, but the richly structured Nows ‘know’ about one another because they literally contain one another in certain essential respects. As consciousness surveys many things at once in one Now, it is simultaneously present, at least in part, in other Nows. This awareness of many things in one could well exist in a much more pronounced form in other places in Platonia.
Figure 6. The conjectured filamentary distribution of mist in Platonia. The instant you experience now is marked NOW. To its left lie Nows of which you have memories in NOW. There is no bifurcation in this direction, matching our conviction that we have a unique past. In the other direction there is a branching into different alternative ‘futures’ of NOW. In all of them, you think you have advanced into the future by the same amount from NOW. These different filaments are ‘parallel worlds’ that seem to have a common past, to which NOW belongs. Note that the filaments have a finite width, unlike a Newtonian string of successive instants. All around NOW, along the filament and to either side of it, are other Nows with slightly different versions of yourself. All such Nows are ‘other worlds’ in which there exist somewhat different but still recognizable versions of yourself. In other filaments are worlds you would not recognize at all.