The Fabric of Reality: The Science of Parallel Universes--and Its Implications

by David Deutsch

Science seeks better explanations. A scientific explanation accounts for our observations by postulating something about what reality is like and how it works. We deem an explanation to be better if it leaves fewer loose ends (such as entities whose properties are themselves unexplained), requires fewer and simpler postulates, is more general, meshes more easily with good explanations in other fields and so on.

why should a better explanation be what we always assume it to be in practice, namely the token of a truer theory?

There is indeed no logically necessary connection between truth and explanatory power.

in that case, what justifies our relying on our best explanations as guides to practical decision-making?

Philosophers today yearn for this missing justification. They no longer believe that induction would provide it, yet they have an induction-shaped gap in their scheme of things, just as religious people who have lost their faith suffer from a ‘God-shaped gap’ in their scheme of things.

So in view of that, I repeat, the whole problem is to find what does justify the prediction. That is the problem of induction. DAVID: Well, that is the problem that Popper solved.

What justifies the prediction, if it isn’t the evidence? DAVID: Argument.

Only argument ever justifies anything — tentatively, of course. All theorizing is subject to error, and all that. But still, argument can sometimes justify theories. That is what argument is for.

I’m glad I listened carefully, as you asked, for now I see that at least part of the difference between us has been caused by a misunderstanding over terminology.

When Popper speaks of ‘rival theories’ to a given theory, he does not mean the set of all logically possible rivals: he means only the actual rivals, those proposed in the course of a rational controversy.

Languages are theories. In their vocabulary and grammar, they embody substantial assertions about the world. Whenever we state a theory, only a small part of its content is explicit: the rest is carried by the language. Like all theories, languages are invented and selected for their ability to solve certain problems.

Are you claiming to understand Popper’s theory better than he did himself? DAVID: I neither know nor care. The reverence that philosophers show for the historical sources of ideas is very perverse, you know. In science we do not consider the discoverer of a theory to have any special insight into it. On the contrary, we hardly ever consult original sources.

For example, most relativity theorists today understand Einstein’s theory better than he did.

gravity is not a force but a manifestation of the curvature of spacetime.

You might as well say that since our theories hold certain features of reality to be the same throughout space, they imply a ‘spatial principle of induction’ to the effect that ‘the near resembles the distant’.

A phenomenon is ‘fundamental’ if a sufficiently deep understanding of the world depends on understanding that phenomenon. Opinions differ, of course, about what aspects of the world are worth understanding, and consequently about what is deep or fundamental.

Not everything that can be copied is a replicator. A replicator causes its environment to copy it: that is, it contributes causally to its own copying.

But make a change in the corresponding gene (if you do it just after the bear is conceived, you need only change one molecule), and any offspring will not only have noses of the new shape, but copies of the new gene as well. This shows that the shape of each nose is caused by that gene, and not by the shape of any previous nose.

This gene-based understanding of life — regarding organisms as part of the environment of genes — has implicitly been the basis of biology since Darwin, but it was overlooked until at least the 1960s, and not fully understood until Richard Dawkins published The Selfish Gene (1976) and The Extended Phenotype (1982).

Similarly, it seems that life is a property of some parochial area, or perhaps areas, of the universe, fundamental to us because we are alive, but not at all fundamental either theoretically or practically in the larger scheme of things. But remarkably, this appearance is misleading. It is simply not true that life is insignificant

It is the survival of knowledge, and not necessarily of the gene or any other physical object, that is the common factor between replicating and non-replicating genes. So, strictly speaking, it is a piece of knowledge rather than a physical object that is or is not adapted to a certain niche.

although all known life is based on replicators, what the phenomenon of life is really about is knowledge.

However, the point I am making here does not depend on our being able to predict what will happen, but only on the proposition that what will happen will depend on what knowledge our descendants have, and on how they choose to apply it. Thus one cannot predict the future of the Sun without taking a position on the future of life on Earth, and in particular on the future of knowledge.

Astrologers used to believe that cosmic events influence human affairs; science believed for centuries that neither influences the other. Now we see that human affairs influence cosmic events.

At least, no one could conceive of it, until recently. In 1982 the physicist Richard Feynman considered the computer simulation of quantum-mechanical objects.

Chaos theory is about limitations on predictability in classical physics, stemming from the fact that almost all classical systems are inherently unstable.

So the question arises, if we know them to some reasonable degree of accuracy, can we also predict to a reasonable degree of accuracy how they will behave in the future? And the answer is, usually, that we cannot. The difference between the real trajectory and the predicted trajectory, calculated from slightly inaccurate data, tends to grow exponentially

In 1985 I proved that under quantum physics there is a universal quantum computer.

So by about 1900 there was a crisis at the foundations of mathematics — namely, that there were no foundations.

Thanks to Gödel, we know that there will never be a fixed method of determining whether a mathematical proposition is true, any more than there is a fixed way of determining whether a scientific theory is true. Nor will there ever be a fixed way of generating new mathematical knowledge. Therefore progress in mathematics will always depend on the exercise of creativity.

still does not help us to explain the alleged certainty of the knowledge that we acquire by doing mathematics.

First of all, Plato tells us that since we have access only to imperfect circles (say) we cannot thereby obtain any knowledge of perfect circles. But why not, exactly?

If, say, the only way of learning about circles from experience were to examine thousands of physical circles and then, from the accumulated data, to try to infer something about their abstract Euclidean counterparts, Plato would have a point.

but even in virtual reality we cannot measure all triangles, and so we cannot verify the theorem. How do we verify it? We prove it. A proof is traditionally defined as a sequence of statements satisfying self-evident rules of inference, but what does the ‘proving’ process amount to physically?

The answer is that we must use rules of inference which, to the best of our understanding, will cause our symbols to behave, in the relevant ways, like the abstract entities they denote. How can we be sure that they will? We cannot.

All we can do is explain.

Any physical experiment can be regarded as a computation, and any computation is a physical experiment.

proof is a physical process. In fact, a proof is a type of computation. ‘Proving’ a proposition means performing a computation which, if one has done it correctly, establishes that the proposition is true. When we use the word ‘proof’ to denote an object, such as an ink-on-paper text, we mean that the object can be used as a program for recreating a computation of the appropriate kind.

proof theory is not a branch of mathematics — it is a science. Proofs are not abstract. There is no such thing as abstractly proving something, just as there is no such thing as abstractly calculating or computing something.

Mathematics, the study of these relationships and properties, is therefore the study of absolutely necessary truths. In other words, the truths that mathematics studies are absolutely certain. But that does not mean that our knowledge of those necessary truths is itself certain, nor does it mean that the methods of mathematics confer necessary truth on their conclusions. After all, mathematics also studies falsehoods and paradoxes. And that does not mean that the conclusions of such a study are necessarily false or paradoxical. Necessary truth is merely the subject-matter of mathematics, not the reward we get for doing mathematics. The objective of mathematics is not, and cannot be, mathematical certainty. It is not even mathematical truth, certain or otherwise. It is, and must be, mathematical explanation.

the human eye and its controlling software implicitly embody the false theory that yellow light consists of a mixture of red and green light (in the sense that yellow light gives us exactly the same sensation as a mixture of red light and green light does). In reality, all three types of light have different frequencies and cannot be created by mixing light of other frequencies. The fact that a mixture of red and green light appears to us to be yellow light has nothing whatever to do with the properties of light, but is a property of our eyes. It is the result of a design compromise that occurred at some time during our distant ancestors’ evolution.

Grammarians nowadays try not to make value-judgements about how language is used; they try only to record, analyse and understand it. Therefore Quirk et al. are in no way to blame for the quality of the theory of time that they describe. They do not claim that it is a good theory. They claim only, and I think quite correctly, that it is our theory. Unfortunately it is not a good theory.

We do not experience time flowing, or passing. What we experience are differences between our present perceptions and our present memories of past perceptions. We interpret those differences, correctly, as evidence that the universe changes with time. We also interpret them, incorrectly, as evidence that our consciousness, or the present, or something, moves through time.

Perhaps ‘paradox’ is a better word than mystery, for we have here a blatant conflict between two apparently self-evident ideas. They cannot both be true. We shall see that neither is true.

We are getting dangerously close to nonsense here

Therefore we know that even though some events can be predicted from others no event in spacetime caused another. Let me stress again that this is all according to pre-quantum physics, in which everything that happens, happens in spacetime. What we are seeing is that spacetime is incompatible with the existence of cause and effect. It is not that people are mistaken when they say that certain physical events are causes and effects of one another, it is just that that intuition is incompatible with the laws of spacetime physics. But that is all right, because spacetime physics is false.

Let me sum up the elements of the quantum concept of time. Time is not a sequence of moments, nor does it flow. Yet our intuitions about the properties of time are broadly true. Certain events are indeed causes and effects of one another. Relative to an observer, the future is indeed open and the past fixed, and possibilities do indeed become actualities. The reason why our traditional theories of time are nonsense is that they try to express these true intuitions within the framework of a false classical physics. In quantum physics they make sense, because time was a quantum concept all along.

Each version of us is not directly aware of the others, but has evidence of their existence because physical laws link the contents of different universes. It is tempting to suppose that the moment of which we are aware is the only real one, or is at least a little more real than the others. But that is just solipsism. All moments are physically real. The whole of the multiverse is physically real. Nothing else is.

Why should we expect every visitor we receive from the future to hail from the particular future snapshots in which we shall eventually find ourselves? We really should not expect this.

Arguments from virtual reality help in understanding time travel because the concept of virtual reality requires one to take ‘counter-factual events’ seriously, and therefore the multi-universe quantum concept of time seems natural when it is rendered in virtual reality.