Paul Davies Responds

Response to John McCarthy:

John McCarthy asks how animal behavior is encoded in DNA. May I sharpen the question? One of the most remarkable manifestations of inherited behavior is the way birds navigate accurately whilst migrating over vast distances. I understand that part of this skill lies with the bird's ability to use the positions of stars as beacons. Does this imply that some avian DNA contains a map of the sky? Could a scientist in principle sequence the DNA and reconstruct the constellations?

Response to Martin Rees's response to my question:

Sir Martin Rees has eloquently outlined the key issues concerning the status of multiverse theories. I should like to make a brief response followed by a suggestion for further research.

Sir Martin raises the question of whether what we consider to be fundamental laws of physics are in fact merely local bylaws applicable to the universe we perceive. Implicit in this assumption is the fact that there are laws of some sort anyway. By definition, a law is a property of nature that is independent of time. We still need to explain why universes come with such time-independent lawlike features, even if a vast and random variety of laws is on offer. One might try to counter this by invoking an extreme version of the anthropic theory in which there are no laws, just chaos. The apparent day-by-day lawfulness of the universe would then itself be anthropically selected: if a crucial regularity of nature suddenly failed, observers would die and cease to observe. But this theory seems to be rather easily falsified.

As Sir Martin points out, if a particular remarkable aspect of the laws is anthropically selected from a truly random set, then we would expect on statistical grounds the aspect concerned to be just sufficient to permit biological observers. Consider, then, the law of conservation of electric charge. At the atomic level, this law is implied by the assumed constancy of the fine-structure constant. (I shall sidestep recent claims that this number might vary over cosmological time scales.) Suppose there were no such fundamental law, and the unit of electric charge varied randomly from moment to moment? Would that be life-threatening? Not if the variations were small enough. The fine-structure constant affects atomic fine-structure, not gross structure, so that most chemical properties on which life as we know it depends are not very sensitive to the actual value of this number.

In fact, the fine-structure constant is known to be constant to better than one part in a hundred million. A related quantity, the anamolous magnetic moment of the electron, is known to be constant to even greater accuracy. Variations several orders of magnitude larger than this would not render the universe hostile to carbon-based life. So the constancy of electric charge at the atomic level is an example of a regularity of nature far in excess of what is demanded by anthropic considerations. Even a multiverse theory that treated this regularity as a bylaw would need to explain why such a bylaw exists.

I now turn to my meta-question of whether the multiverse might be no better than theism in modern scientific language. It is possible that this claim can be tested using a branch of mathematics known as algorithmic information theory, developed by Kolmogorov and Chaitin. This formalism offers a means to quantify Occam's Razor, by quantifying the complexity of explanations. (Occam's Razor suggests that, all else being equal, we should prefer the simplest explanation of the facts.)

On the question of how to explain certain fine-tuned bio-friendly aspects of the universe, the crude response "God made it that way" is infinitely complex (and therefore very unsatisfying), because God might have made one of an infinite number of alternative universes. Put differently, the selection set — the "shopping list" of universes available to an omnipotent Deity — contains an infinite amount of information, so the act of selection from this set involves discarding this infinite quantity of information. In the same way, the multiverse contains an infinite amount of information. In this case we observers are the selectors, but we still discard an infinite quantity of information by failing to observe the other universes. A proper mathematical parameterization of various multiverse theories and various theological models should enable this comparison to be made precise.

Even if the two modes of explanation — theistic and multiverse — turned out to be mathematically equivalent — one might still argue (as Sir Martin has done) for the superiority of the multiverse theory on the grounds that the other universes, whilst not directly observable, are nevertheless strongly implied by extrapolation from the structure of our physical theories. But a theist would readily counter that the existence of God, whilst not directly obervable, is nevertheless strongly implied by extrapolation from the nature of the world, human wisdom, mystical revelation, moral awareness, etc.

I argued in my book The Mind of God that most attempts at ultimate explanations run into this "tower of turtles" problem: one has to start somewhere in the chain of reasoning, with a certain unproved given, be it God, mathematics, a physical principle, revelation, or something else. That is because of an implied dualism common to scientific and theistic explanations alike. In science the dualism is between states of the world and abstract laws. In theism it is between creature (i.e. the physical universe) and Creator.

But is this too simplistic? Might the physical world and its explanation be ultimately indecomposable? Should we consider alternative modes of description than one based on linear reasoning from an unproved given, which after all amounts to invoking a magical levitating superturtle at the base of the tower? That is what I meant by the "Third Way" in my original question.