The key discovery in the omega-point theory is that of a class of cosmological models in which, though the universe is finite in both space and time, the memory capacity, the number of possible computational steps and the effective energy supply are all unlimited. This apparent impossibility can happen because of the extreme violence of the final moments of the universe’s Big Crunch collapse. Spacetime singularities, like the Big Bang and the Big Crunch, are seldom tranquil places, but this one is far worse than most. The shape of the universe would change from a 3-sphere to the three-dimensional analogue of the surface of an ellipsoid. The degree of deformation would increase, and then decrease, and then increase again more rapidly with respect to a different axis. Both the amplitude and frequency of these oscillations would increase without limit as the final singularity was approached, so that a literally infinite number of oscillations would occur even though the end would come within a finite time. Matter as we know it would not survive: all matter, and even the atoms themselves, would be wrenched apart by the gravitational shearing forces generated by the deformed spacetime. However, these shearing forces would also provide an unlimited source of available energy, which could in principle be used to power a computer. How could a computer exist under such conditions? The only ‘stuff’ left to build computers with would be elementary particles and gravity itself, presumably in some highly exotic quantum states whose existence we, still lacking an adequate theory of quantum gravity, are currently unable to confirm or deny. (Observing them experimentally is of course out of the question.) If suitable states of particles and the gravitational field exist, then they would also provide an unlimited memory capacity, and the universe would be shrinking so fast that an infinite number of memory accesses would be feasible in a finite time before the end. The end-point of the gravitational collapse, the Big Crunch of this cosmology, is what Tipler calls the omega point.
Now, the Turing principle implies that there is no upper bound on the number of computational steps that are physically possible. So, given that an omega-point cosmology is (under plausible assumptions) the only type in which an infinite number of computational steps could occur, we can infer that our actual spacetime must have the omega-point form. Since all computation would cease as soon as there were no more variables capable of carrying information, we can infer that the necessary physical variables (perhaps quantum-gravitational ones) do exist right up to the omega point.
A sceptic might argue that this sort of reasoning involves a massive, unjustified extrapolation. We have experience of ‘universal’ computers only in a most favourable environment which does not remotely resemble the final stages of the universe. And we have experience of them performing only a finite number of computational steps, using only a finite amount of memory. How can it be valid to extrapolate from those finite numbers to infinity? In other words, how can we know that the Turing principle in its strong form is strictly true? What evidence is there that reality supports more than approximate universality?
This sceptic is, of course, an inductivist. Furthermore, this is exactly the type of thinking that (as I argued in the previous chapter) prevents us from understanding our best theories and improving upon them. What is or is not an ‘extrapolation’ depends on which theory one starts with. If one starts with some vague but parochial concept of what is ‘normal’ about the possibilities of computation, a concept uninformed by the best available explanations in that subject, then one will regard any application of the theory outside familiar circumstances as ‘unjustified extrapolation’. But if one starts with explanations from the best available fundamental theory, then one will consider the very idea that some nebulous ‘normalcy’ holds in extreme situations to be an unjustified extrapolation. To understand our best theories, we must take them seriously as explanations of reality, and not regard them as mere summaries of existing observations. The Turing principle is our best theory of the foundations of computation. Of course we know only a finite number of instances confirming it — but that is true of every theory in science. There remains, and will always remain, the logical possibility that universality holds only approximately. But there is no rival theory of computation claiming that. And with good reason, for a ‘principle of approximate universality’ would have no explanatory power. If, for instance, we want to understand why the world seems comprehensible, the explanation might be that the world is comprehensible. Such an explanation can, and in fact does, fit in with other explanations in other fields. But the theory that the world is half-comprehensible explains nothing and could not possibly fit in with explanations in other fields unless they explained it. It simply restates the problem and introduces an unexplained constant, one-half. In short, what justifies assuming that the full Turing principle holds at the end of the universe, is that any other assumption spoils good explanations of what is happening here and now.
Now, it turns out that the type of oscillations of space that would make an omega point happen are highly unstable (in the manner of classical chaos) as well as violent. And they become increasingly more so, without limit, as the omega point is approached. A small deviation from the correct shape would be magnified rapidly enough for the conditions for continuing computation to be violated, so the Big Crunch would happen after only a finite number of computational steps. Therefore, to satisfy the Turing principle and attain an omega point, the universe would have to be continually ‘steered’ back onto the right trajectories. Tipler has shown in principle how this could be done, by manipulating the gravitational field over the whole of space. Presumably (again we would need a quantum theory of gravity to know for sure), the technology used for the stabilizing mechanisms, and for storing information, would have to be continually improved — indeed, improved an infinite number of times — as the density and stresses became ever higher without limit. This would require the continual creation of new knowledge, which, Popperian epistemology tells us, requires the presence of rational criticism and thus of intelligent entities. We have therefore inferred, just from the Turing principle and some other independently justifiable assumptions, that intelligence will survive, and knowledge will continue to be created, until the end of the universe.
The stabilization procedures, and the accompanying knowledge-creation processes, will all have to be increasingly rapid until, in the final frenzy, an infinite amount of both occur in a finite time. We know of no reason why the physical resources should not be available to do this, but one might wonder why the inhabitants should bother to go to so much trouble. Why should they continue so carefully to steer the gravitational oscillations during, say, the last second of the universe? If you have only one second left to live, why not just sit back and take it easy at last? But of course, that is a misrepresentation of the situation. It could hardly be a bigger misrepresentation. For these people’s minds will be running as computer programs in computers whose physical speed is increasing without limit. Their thoughts will, like ours, be virtual-reality renderings performed by these computers. It is true that at the end of that final second the whole sophisticated mechanism will be destroyed. But we know that the subjective duration of a virtual-reality experience is determined not by the elapsed time, but by the computations that are performed in that time. In an infinite number of computational steps there is time for an infinite number of thoughts — plenty of time for the thinkers to place themselves into any virtual-reality environment they like, and to experience it for however long they like. If they tire of it, they can switch to any other environment, or to any number of other environments they care to design. Subjectively, they will not be at the final stages of their lives but at the very beginning. They will be in no hurry, for subjectively they will live for ever. With one second, or one microsecond, to go, they will still have ‘all the time in the world’ to do more, experience more, create more — infinitely more — than anyone in the multiverse will ever have done before then. So there is every incentive for them to devote their attention to managing their resources. In doing so they are merely preparing for their own future, an open, infinite future of which they will be in full control and on which, at any particular time, they will be only just embarking.