The Beginning of Infinity: Explanations That Transform the World

by David Deutsch

Discovering a new explanation is inherently an act of creativity.

To this day, most courses in the philosophy of knowledge teach that knowledge is some form of justified, true belief, where ‘justified’ means designated as true (or at least ‘probable’) by reference to some authoritative source or touchstone of knowledge. Thus ‘how do we know…?’ is transformed into ‘by what authority do we claim…?’ The latter question is a chimera that may well have wasted more philosophers’ time and effort than any other idea. It converts the quest for truth into a quest for certainty (a feeling) or for endorsement (a social status). This misconception is called justificationism.

The quest for authority led empiricists to downplay and even stigmatize conjecture, the real source of all our theories.

Starting from empiricism, they drew the inevitable conclusion (which would nevertheless have horrified the early empiricists) that science cannot validly do more than predict the outcomes of observations, and that it should never purport to describe the reality that brings those outcomes about. This is known as instrumentalism. It denies that what I have been calling ‘explanation’ can exist at all. It is still very influential. In some fields (such as statistical analysis) the very word ‘explanation’ has come to mean prediction, so that a mathematical formula is said to ‘explain’ a set of experimental data. By ‘reality’ is meant merely the observed data that the formula is supposed to approximate. That leaves no term for assertions about reality itself, except perhaps ‘useful fiction’.

If we ignore all the parts of both myths whose role could be easily replaced, we are left with the same core explanation in both cases: the gods did it.

Focus on edges instead of nodes to make ideas more concise.

That is what makes good explanations essential to science: it is only when a theory is a good explanation – hard to vary – that it even matters whether it is testable.

Most accounts of the differences between myth and science make too much of the issue of testability – as if the ancient Greeks’ great mistake was that they did not send expeditions to the southern

hemisphere to observe the seasons. But in fact they could never have guessed that such an expedition might provide evidence about seasons unless they had already guessed that sea...

Had they been seeking good explanations, they would immediately have tried to improve upon the myth, without testing it. That is what we do today.

Science would be impossible if it were not for the fact that the overwhelming majority of false theories can be rejected out of hand without any experiment, simply for being bad explanations.

When a formerly good explanation has been falsified by new observations, it is no longer a good explanation, because the problem has expanded to include those observations. Thus the standard scientific methodology of dropping theories when refuted by experiment is implied by the requirement for good explanations.

Suppose for the sake of argument that you thought of the axis-tilt theory yourself. It is your conjecture, your own original creation. Yet because it is a good explanation – hard to vary – it is not yours to modify. It has an autonomous meaning and an autonomous domain of applicability. You cannot confine its predictions to a region of your choosing. Whether you like it or not, it makes predictions about places both known to you and unknown to you, predictions that you have thought of and ones that you have not thought of.

This reach of explanations is another meaning of ‘the beginning of infinity’. It is the ability of some of them to solve problems beyond those that they were created to solve.

Thus the reach of an explanation is neither an additional assumption nor a detachable one. It is determined by the content of the explanation itself.

The universe is not there to overwhelm us; it is our home, and our resource. The bigger the better.

But a heap of raw materials is not the same thing as a life-support system. It takes knowledge to convert the one into the other, and biological evolution never provided us with enough knowledge to survive, let alone to thrive.

But the biosphere no more provides humans with a life-support system than it provides us with radio telescopes.

From the outset, it was only human knowledge that made the planet even marginally habitable by humans, and the enormously increased capacity of our life-support system since then (in terms both of numbers and of security and quality of life) has been entirely due to the creation of human knowledge.

To the extent that we are on a ‘spaceship’, we have never been merely its passengers, nor (as is often said) its stewards, nor even its maintenance crew: we are its designers and builders. Before the designs created by humans, it ...

Nor was it arrogance that prevented people from realizing their mistake for so long: they didn’t realize anything, because they did not know how to seek better explanations.

the ‘perspiration’ phase can be automated – just as the task of recognizing galaxies on astronomical photographs was.

And the more advanced technology becomes, the shorter is the gap between inspiration and automation.

Once enough knowledge has been embodied in the lunar colony, the colonists can devote their thoughts and energies to creating even more knowledge, and soon it will cease to be a colony and become simply home.

The only uniquely significant thing about humans (whether in the cosmic scheme of things or according to any rational human criterion) is our ability to create new explanations, and we have that in common with all people.

If it depends on having more memory capacity, or speed, than a human brain, then the outcome would depend on whether we could build computers to do the job. Again, such things are already commonplace in technology.

Here is another misconception in the Garden of Eden myth: that the supposed unproblematic state would be a good state to be in. Some theologians have denied this, and I agree with them: an unproblematic state is a state without creative thought. Its other name is death.

In all cases, the class of transformations that could happen spontaneously – in the absence of knowledge – is negligibly small compared with the class that could be effected artificially by intelligent beings who wanted those transformations to happen. So the explanations of almost all physically possible phenomena are about how knowledge would be applied to bring these phenomena about.

That means that one physical system – say, an astrophysicist’s brain – contains an accurate working model of the other, the jet.

Not just a superficial image (though it contains that as well), but an explanatory theory that embodies the same mathematical relationships and causal structure.

configuration of the cork is what experimentalists call a ‘proxy’: a physical variable which can be measured as a way of measuring another variable. (All scientific measurements involve chains of proxies.)

The mass of a typical cube is spread thinly throughout its whole volume; most of the mass of the transformed cube is concentrated at its centre.

Almost any of them would, if the right knowledge ever reached it, instantly and irrevocably burst into a radically different type of physical activity: intense knowledge-creation, displaying all the various kinds of complexity, universality and reach that are inherent in the laws of nature, and transforming that environment from what is typical today into what could become typical in the future. If we want to, we could be that spark.

Religions will no longer want to claim the design of the biosphere as one of the achievements of their deities, just as today they no longer bother to claim thunder.

A conjuring trick cannot have been performed by real magic – by the magician simply commanding events to happen – but must have been brought about by knowledge that was somehow created beforehand. Similarly, biologists need only have asked: how does the knowledge to construct a mouse get to those rags, and how is it then applied to transform the rags into a mouse?

it is a rare configuration of matter.

A good design is hard to vary:

Dawkins coined the term memes

neo-Darwinian theory of evolution is that a population of replicators subject to variation (for instance by imperfect copying) will be taken over by those variants that are better than their rivals at causing themselves to be replicated.

Non-explanatory human knowledge can also evolve in an analogous way: rules of thumb are not passed on perfectly to the next generation of users, and the ones that survive in the long run are not necessarily the ones that optimize the ostensible function. For instance, a rule that is expressed in an elegant rhyme may be remembered, and repeated, better than one that is more accurate but expressed in ungainly prose. Also, no human knowledge is entirely non-explanatory.

There is always at least a background of assumptions about reality against which the meaning of a rule of thumb is understood, and that background can make some false rules of thumb seem plausible.

Curiously enough, one immediate prediction from the anthropic explanation is that the value will not be exactly 137.5. For suppose that it were. By analogy, imagine that the bull’s-eye of a dartboard represents the values that can produce astrophysicists. It would be a mistake to predict that a typical dart that strikes the bull’s eye will strike it at the exact centre.

For although any one constant is unlikely to be near the edge of its range, the more constants there are, the more likely it is that at least one of them will be. This can be illustrated pictorially as follows, with our bull’s-eye replaced by a line segment, a square, a cube…and we can imagine this sequence continuing for as many dimensions as there are fine-tuned constants in nature. Arbitrarily define ‘near the edge’ as meaning ‘within 10 per cent of the whole range from it’. Then in the case of one constant, as shown in the diagram, 20 per cent of its possible values are near one of the two edges of the range, and 80 per cent are ‘away from the edge’. But with two constants a pair of values has to satisfy two constraints in order to be ‘away from the edge’. Only 64 per cent of them do so. Hence 36 per cent are near the edge. With three constants, nearly half the possible choices are near the edge. With 100 constants, over 99.9999999 per cent of them are.

liquidity of water and the relationship between containers, heating elements, boiling and bubbles – that can be well explained in terms of each other alone, with no direct reference to anything at the atomic level or below. In other words, the behaviour of that whole class of high-level phenomena is quasi-autonomous – almost self-contained. This resolution into explicability at a higher, quasi-autonomous level is known as emergence.

There is another, even more important, advantage in that ability to criticize theories without staking one’s life on them. In an evolving species, the adaptations of the organisms in each generation must have enough functionality to keep the organism alive, and to pass all the tests that they encounter in propagating themselves to the next generation. In contrast, the intermediate explanations leading a scientist from one good explanation to the next need not be viable at all. The same is true of creative thought in general. This is the fundamental reason that explanatory ideas are able to escape from parochialism, while biological evolution, and rules of thumb, cannot.

Now Hofstadter imagines that an observer who does not know the purpose of the domino network watches the dominoes performing and notices that one particular domino remains resolutely standing, never affected by any of the waves of downs and ups sweeping by. The observer points at [that domino] and asks with curiosity, ‘How come that domino there is never falling?’ We know that it is the output domino, but the observer does not. Hofstadter continues: Let me contrast two different types of answer that someone might give. The first type of answer – myopic to the point of silliness – would be, ‘Because its predecessor never falls, you dummy!’

The second type of answer would be, ‘Because 641 is prime.’ Now this answer, while just as correct (indeed, in some sense it is far more on the mark), has the curious property of not talking about anything physical at all. Not only has the focus moved upwards to collective properties…these properties somehow transcend the physical and have to do with pure abstractions, such as primality. Hofstadter concludes, ‘The point of this example is that 641’s primality is the best explanation, perhaps even the only explanation, for why certain dominoes did fall and certain others did not fall.’

as the philosopher David Hume pointed out, we cannot perceive causation, only a succession of events.

Also, the laws of motion are ‘conservative’ – that is to say, they do not lose information. That means that, just as they determine the final state of any motion given the initial state, they also determine the initial state given the final state, and the state at any time from the state at any other time.

There is no inconsistency in having multiple explanations of the same phenomenon, at different levels of emergence. Regarding micro-physical explanations as more fundamental than emergent ones is arbitrary and fallacious.