David Deutsch

Science in the 20th century has become focussed on the what, with scant regard for the why. Deutsch wants explanation put back into our way of doing science -- science is our way of understanding the world, not just tersely describing what it does. This book is his attempt to describe what An Explanation of Everything might look like (as contrasted with physicists' quest for a theory of everything, by which they mean one single equation to describe fundamental physics). This explanation is structured around four theories central to modern science:

• Hugh Everett's Many Worlds interpretation of quantum theory
• Richard Dawkins' approach to Darwin's Theory of Evolution
• Karl Popper's philosophy of science
• Alan Turing's Theory of Universal Computation

He argues these theories should be 'taken seriously'; that is, scientists should be exploring their (possibly extreme) logical consequences, not just applying them in narrow domains.

In all [four] cases the theory that now prevails, though it has definitely displaced its predecessor and other rivals in the sense that it is being applied routinely in pragmatic ways, has nevertheless failed to become the new 'paradigm'. That is, it has not been taken on board as the fundamental explanation of reality by those who work in the field.

Despite the fact that they are not taken seriously, usually because the consequences are disliked, there are no better alternatives. Deutsch argues that this results in some people supporting worse alternatives, leading to a lot of wasted effort.

so long as the proponents of our best theories of the fabric of reality have to expend their intellectual energies in futile refutation and re-refutation of theories long known to be false, the state of our deepest knowledge cannot improve.

I like the rigorously rational view Deutsch takes:

there is no room for magic in a comprehensible reality. Anything that seems incomprehensible is regarded by science merely as evidence that there is something we have not yet understood, be it a conjuring trick, advanced technology or a new law of physics.

He also has little time for those who artificially handicap themselves:

intuitionism is precisely the expression, in mathematics, of solipsism.

He makes it clear that what we like to think of as purely abstract computation is in fact deeply grounded in physics, with the physics affecting the kinds of computers we can build, and therefore the kinds of models of computation we devise. Analogue classical physics gives us a fundamentally different model of computation.

the continuous motion of classical systems would have allowed for 'analogue' computation which did not proceed in steps and which had a substantially different repertoire from the universal Turing machine. Several examples are known of contrived classical laws under which an infinite amount of computation (infinite, that is, by Turing-machine or quantum-computer standards) could be performed by physically finite methods. Of course, classical physics is incompatible with the results of countless experiments, so it is rather artificial to speculate on what the 'actual' classical laws of physics 'would have been'; but what these examples show is that one cannot prove, independently of any knowledge of physics, that a proof must consist of finitely many steps.

[This focus on what we mean by proof in 'finite proof' contrasts rather nicely with Lavine's focus on what we mean by finite.] Similarly, the discrete 'classical' physics of Turing machines also gives us an incorrect model of computation.

Turing hoped that his abstracted-paper-tape model was so simple, so transparent and well defined, that it would not depend on any assumptions about physics that could conceivably be falsified, and therefore that it could become the basis of an abstract theory of computation that was independent of the underlying physics. 'He thought,' as Feynman once put it, 'that he understood paper.' But he was mistaken. Real, quantum-mechanical paper is wildly different from the abstract stuff that the Turing machine uses. The Turing machine is entirely classical, and does not allow for the possibility the the paper might have different symbols written on it in different universes, and that those might interfere with one another. ... That is why the resulting model of computation was incomplete.

Quantum computation is fundamentally different from classical computation. Deutsch states quite clearly that there are quantum programs that cannot be run on a classical Turing machine.

Quantum computation is more than just faster, more miniaturized technology for implementing Turing machines. A quantum computer is a machine that uses uniquely quantum-mechanical effects, especially interference, to perform wholly new types of computation that would be impossible, even in principle, on any Turing machine and hence on any classical computer.

This statement confused me when I first read it: I have listened to quantum computing researchers describe their emulations of quantum computations on classical computers, they just require exponentially increasing resources (either processors, or time). These two statements seem incompatible. But then a few pages later I came across a paragraph that affects his meaning of 'in principle' in the quote above.

... not only are universal [computers] possible, it is possible to build them so that they do not require impracticably large resources to [compute]. From now on, when I refer to universality I shall mean it in this sense...

Now, a universal computer must, by definition, be able to emulate any other computer using only a 'similar' amount of resources (where 'similar' has a technical meaning that excludes 'exponentially more'). But a 'Universal' Turing Machine does need exponentially more resources than a quantum computer in order to emulate one, and so is not truly 'Universal' by this definition.

So Deutsch, being firmly grounded in physical law and the universe we are living in, argues that there are certain computations that cannot be performed classically in a tractable time, because there are insufficient resources in our single universe, but that can be performed quantumly, when the resources of exponentially many parallel universes can be brought to bear. There are computations that require exponential resources on classical computers, and so are intractable, but are are tractable on quantum computers. One such kind of computation is that of calculating the state of a multi-particle quantum system itself.

... with several interacting particles, such a computation could easily ... become 'intractable'. Yet since we could readily obtain its result just by performing this experiment, it is not really intractable after all.

Deutsch weaves together his four strands, and comes up with some rather interesting, and sometimes startling, conclusions. In particular, his use of the Turing principle to define a universal virtual reality renderer, and to use that to infer consequences for the laws of physics, in particular, for time travel, is quite ingenious. And one has to admire the author who can conclude that his view

is the conservative view, the one that does not propose any startling change in our best fundamental explanations

a mere 15 pages after describing Tipler's omega-point argument that it is possible to perform an infinite amount of computation in a universe with a particular configuration, inferring that we are in such a universe, and further inferring

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

This is an excellent book, with some fascinating ideas. It is particularly nice to find a real practicing physicist who is willing to come out and admit that explanation is what it's all about. Most of the book is solid scientific extrapolation, but his description, in the last chapter, of a universe full of beings who must continue to evolve and grow in knowledge for ever, is particularly exhilarating. (I found it made an optimistic contrast to Chaitin's slightly gloomy view of the place of randomness in increasing knowledge.)

I do have one area where I have some confusion, however, and would have liked more explanation. That is of the Many Worlds interpretation itself. It certainly does give an intuitive explanation of how quantum computers work (or rather, where they do all their work), but I am less convinced that it is the inevitable explanation of quantum interference experiments. (Deutsch is a much better physicist than I am, however.) Cramer's Transactional interpretation, in particular, seems to offer equally plausible explanations of these experiments, without being so profligate with universes. I would also have liked a little more detail of what the Many Worlds interpretation is: before reading this I had a vague picture of a universe branching at every decision point; Deutsch talks of reams of pre-existing identical universes subsequently evolving in different ways depending on the choice.

Despite my area of doubt and uncertainly, I highly recommend this book. It is very well written (the dialogue between Deutsch and the crypto-inductivist is particular fun), brings together some important ideas, avoids the excesses of Penrose and Tipler (whilst exploiting their good parts), and gives a view onto a humane and rational explanation of the world.