Physicists trying to cling to a single-universe world-view sometimes try to explain quantum interference phenomena as follows: ‘No shadow photons exist,’ they say, ‘and what carries the effect of the distant slits to the photon we see is — nothing. Some sort of Action at a distance (as in Newton’s law of gravity) simply makes photons change course when a distant slit is opened.’ But there is nothing ‘simple’ about this supposed action at a distance. The appropriate physical law would have to say that a photon is affected by distant objects exactly as if something were passing through the distant gaps and bouncing off the distant mirrors so as to intercept that photon at the right time and place. Calculating how a photon reacts to these distant objects would require the same computational effort as working out the history of large numbers of shadow photons. The computation would have to work its way through a story of what each shadow photon does: it bounces off this, is stopped by that, and so on. Therefore, just as with Dr Johnson’s rock, and just as with Galileo’s planets, a story that is in effect about shadow photons necessarily appears in any explanation of the observed effects. The irreducible complexity of that story makes it philosophically untenable to deny that the objects exist.
The physicist David Bohm constructed a theory with predictions identical to those of quantum theory, in which a sort of wave accompanies every photon, washes over the entire barrier, passes through the slits and interferes with the photon that we see. Bohm’s theory is often presented as a single-universe variant of quantum theory. But according to Dr Johnson’s criterion, that is a mistake. Working out what Bohm’s invisible wave will do requires the same computations as working out what trillions of shadow photons will do. Some parts of the wave describe us, the observers, detecting and reacting to the photons; other parts of the wave describe other versions of us, reacting to photons in different positions. Bohm’s modest nomenclature — referring to most of reality as a ‘wave’ — does not change the fact that in his theory reality consists of large nets of complex entities, each of which can perceive other entities in its own set, but can only indirectly perceive entities in other sets. These sets of entities are, in other words, parallel universes.
I have described Galileo’s new conception of our relationship with external reality as a great methodological discovery. It gave us a new, reliable form of reasoning involving observational evidence. That is indeed one aspect of his discovery: scientific reasoning is reliable, not in the sense that it certifies that any particular theory will survive unchanged, even until tomorrow, but in the sense that we are right to rely on it. For we are right to seek solutions to problems rather than sources of ultimate justification. Observational evidence is indeed evidence, not in the sense that any theory can be deduced, induced or in any other way inferred from it, but in the sense that it can constitute a genuine reason for preferring one theory to another.
But there is another side to Galileo’s discovery which is much less often appreciated. The reliability of scientific reasoning is not just an attribute of us, of our knowledge and our relationship with reality. It is also a new fact about physical reality itself, a fact which Galileo expressed in the phrase ‘the Book of Nature is written in mathematical symbols’. As I have said, it is impossible literally to ‘read’ any shred of a theory in nature: that is the inductivist mistake. But what is genuinely out there is evidence, or, more precisely, a reality that will respond with evidence if we interact appropriately with it. Given a shred of a theory, or rather, shreds of several rival theories, the evidence is available out there to enable us to distinguish between them. Anyone can search for it, find it and improve upon it if they take the trouble. They do not need authorization, or initiation, or holy texts. They need only be looking in the right way — with fertile problems and promising theories in mind. This open accessibility, not only of evidence but of the whole mechanism of knowledge acquisition, is a key attribute of Galileo’s conception of reality.
Galileo may have thought this self-evident, but it is not. It is a substantive assertion about what physical reality is like. Logically, reality need not have had this science-friendly property, but it does — and in abundance. Galileo’s universe is saturated with evidence. Copernicus had assembled evidence for his heliocentric theory in Poland. Tycho Brahe had collected his evidence in Denmark, and Kepler had in Germany. And by pointing his telescope at the skies over Italy, Galileo gained greater access to the same evidence. Every part of the Earth’s surface, on every clear night, for billions of years, has been deluged with evidence about the facts and laws of astronomy. For many other sciences evidence has similarly been on display, to be viewed more clearly in modern times by microscopes and other instruments. Where evidence is not already physically present, we can bring it into existence with devices such as lasers and pierced barriers — devices which it is open to anyone, anywhere and at any time, to build. And the evidence will be the same, regardless of who reveals it. The more fundamental a theory is, the more readily available is the evidence that bears upon it (to those who know how to look), not just on Earth but throughout the multiverse.
Thus physical reality is self-similar on several levels: among the stupendous complexities of the universe and multiverse, some patterns are nevertheless endlessly repeated. Earth and Jupiter are in many ways dramatically dissimilar planets, but they both move in ellipses, and they are made of the same set of a hundred or so chemical elements (albeit in different proportions), and so are their parallel-universe counterparts. The evidence that so impressed Galileo and his contemporaries also exists on other planets and in distant galaxies. The evidence being considered at this moment by physicists and astronomers would also have been available a billion years ago, and will still be available a billion years hence. The very existence of general, explanatory theories implies that disparate objects and events are physically alike in some ways. The light reaching us from distant galaxies is, after all, only light, but it looks to us like galaxies. Thus reality contains not only evidence, but also the means (such as our minds, and our artefacts) of understanding it. There are mathematical symbols in physical reality. The fact that it is we who put them there does not make them any less physical. In those symbols — in our planetariums, books, films and computer memories, and in our brains — there are images of physical reality at large, images not just of the appearance of objects, but of the structure of reality. There are laws and explanations, reductive and emergent. There are descriptions and explanations of the Big Bang and of subnuclear particles and processes; there are mathematical abstractions; fiction; art; morality; shadow photons; parallel universes. To the extent that these symbols, images and theories are true — that is, they resemble in appropriate respects the concrete or abstract things they refer to — their existence gives reality a new sort of self-similarity, the self-similarity we call knowledge.