The Beginning of Infinity: Explanations That Transform the World

by David Deutsch

SUMMARY Reductionism and holism are both mistakes. In reality, explanations do not form a hierarchy with the lowest level being the most fundamental. Rather, explanations at any level of emergence can be fundamental. Abstract entities are real, and can play a role in causing physical phenomena. Causation is itself such an abstraction.

First the brain was supposed to be like an immensely complicated set of gears and levers. Then it was hydraulic pipes, then steam engines, then telephone exchanges – and, now that computers are our most impressive technology, brains are said to be computers. But this is still no more than a metaphor, says Searle, and there is no more reason to expect the brain to be a computer than a steam engine. But there is. A steam engine is not a universal simulator. But a computer is, so expecting it to be able to do whatever neurons can is not a metaphor: it is a known and proven property of the laws of physics as best we know them.

Without error-correction all information processing, and hence all knowledge-creation, is necessarily bounded. Error-correction is the beginning of infinity.

The jump to universality The tendency of gradually improving systems to undergo a sudden large increase in functionality, becoming universal in some domain.

SUMMARY All knowledge growth is by incremental improvement, but in many fields there comes a point when one of the incremental improvements in a system of knowledge or technology causes a sudden increase in reach, making it a universal system in the relevant domain.

At the present state of the field, a useful rule of thumb is: if it can already be programmed, it has nothing to do with intelligence in Turing’s sense. Conversely, I have settled on a simple test for judging claims, including Dennett’s, to have explained the nature of consciousness (or any other computational task): if you can’t program it, you haven’t understood it.

The Turing-test idea makes us think that, if it is given enough standard reply templates, an Eliza program will automatically be creating knowledge; artificial evolution makes us think that if we have variation and selection, then evolution (of adaptations) will automatically happen. But neither is necessarily so. In both cases, another possibility is that no knowledge at all will be created during the running of the program, only during its development by the programmer.

Quale (plural qualia) The subjective aspect of a sensation.

SUMMARY The field of artificial (general) intelligence has made no progress because there is an unsolved philosophical problem at its heart: we do not understand how creativity works. Once that has been solved, programming it will not be difficult. Even artificial evolution may not have been achieved yet, despite appearances. There the problem is that we do not understand the nature of the universality of the DNA replication system.

Every room is at the beginning of infinity. That is one of the attributes of the unbounded growth of knowledge too: we are only just scratching the surface, and shall never be doing anything else.

Hence I conjecture that, in mathematics as well as in science and philosophy, if the question is interesting, then the problem is soluble.

The biologist Peter Medawar described science as ‘the art of the soluble’, but the same applies to all forms of knowledge. All kinds of creative thought involve judgements about what approaches might or might not work.

Infinite (mathematical) A set is infinite if it can be placed in one-to-one correspondence with part of itself. Infinite (physical) A rather vague concept meaning something like ‘larger than anything that could in principle be encompassed by experience’.

Singularity A situation in which something physical becomes unboundedly large, while remaining everywhere finite.

Multiverse A unified physical entity that contains more than one universe.

Proof A computation which, given a theory of how the computer on which it runs works, establishes the truth of some abstract proposition.

The unpredictability of the content of future knowledge is a necessary condition for the unlimited growth of that knowledge.

SUMMARY We can understand infinity through the infinite reach of some explanations.

if unlimited progress really is going to happen, not only are we now at almost the very beginning of it, we always shall be.

whether a task or pattern is simple or complex depends on what the laws of physics are.

The misconception that evidence can play no legitimate role in philosophy is a relic of empiricism. Objective progress is indeed possible in politics just as it is in morality generally and in science.

Induction, instrumentalism and even Lamarckism all make the same mistake: they expect explanationless progress. They expect knowledge to be created by fiat with few errors, and not by a process of variation and selection that is making a continual stream of errors and correcting them.

The Principle of Optimism All evils are caused by insufficient knowledge.

Like every other destruction of optimism, whether in a whole civilization or in a single individual, these must have been unspeakable catastrophes for those who had dared to expect progress. But we should feel more than sympathy for those people. We should take it personally. For if any of those earlier experiments in optimism had succeeded, our species would be exploring the stars by now, and you and I would be immortal.

The principle of optimism All evils are caused by insufficient knowledge.

Wealth The repertoire of physical transformations that one is capable of causing.

SUMMARY Optimism (in the sense that I have advocated) is the theory that all failures – all evils – are due to insufficient knowledge. This is the key to the rational philosophy of the unknowable.

truth does exist in all those fields, and progress towards it is made by seeking good explanations. Problems are inevitable, because our knowledge will always be infinitely far from complete. Some problems are hard, but it is a mistake to confuse hard problems with problems unlikely to be solved.

is also our custom to give a hearing to anyone who offers us honest criticism, seeking to persuade us freely to change our minds. For we want to do what is right.

SOCRATES: What? I’m sorry, but that was too convoluted a comment for my allegedly wise mind to comprehend.

the thing they call ‘knowledge’, namely justified belief, is a chimera. It is unattainable to humans except in the form of self-deception; it is unnecessary for any good purpose; and it is undesired by the wisest among mortals.

We agree among ourselves (to the extent that we do) because, through our tradition of endless critical debate, we have discovered some genuine knowledge.

You doubted and criticized fallibilism itself, as a true fallibilist should.

Moreover, had I not criticized it, I could not have come to understand why it is true. My doubt improved my knowledge of an important truth – as knowledge held immune from criticism never can be improved!

Here we sit, for ever imprisoned in the dark, almost-sealed cave of our skull, guessing.

[A group of Socrates’ COMPANIONS is approaching. Sprinting eagerly ahead of the rest is the teenage poet Aristocles, whom his friends call PLATO (‘the Broad’) because of his wrestler’s build.]

epistemology – knowledge about knowledge, which also has implications for morality and other fields.

Those two overarching concerns are these: we Athenians are concerned above all with improvement; the Spartans seek only – stasis. Two opposite objectives.

Sparta has no philosophers. That’s because the job of a philosopher is to understand things better, which is a form of change, so they don’t want it. Another difference: they don’t honour living poets, only dead ones. Why? Because dead poets don’t write anything new, but live ones do. A third difference: their education system is insanely harsh; ours is famously lax. Why? Because they don’t want their kids to dare to question anything, so that they won’t ever think of changing anything.

Socrates and his circle were among the foremost contributors to the ‘Golden Age of Athens’, which should have become a beginning of infinity but did not.

In reality, the communication of new ideas – even mundane ones like directions – depends on guesswork on the part of both the recipient and the communicator, and is inherently fallible.

The immediate reason is that the original sources of scientific theories are almost never good sources. How could they be? All subsequent expositions are intended to be improvements on them, and some succeed, and improvements are cumulative.

Crucially, this is the same objective that the originator of the theory had. If it is a good theory – if it is a superb theory, as the fundamental theories of physics nowadays are – then it is exceedingly hard to vary while still remaining a viable explanation. So the learners, through criticism of their initial guesses and with the help of their books, teachers and colleagues, seeking a viable explanation, will arrive at the same theory as the originator. That is how the theory manages to be passed faithfully from generation to generation, despite no one caring about its faithfulness one way or the other. Slowly, and with many setbacks, the same is becoming true in non-scientific fields. The way to converge with each other is to converge upon the truth.

The idea of a ‘doppelgänger’ (a ‘double’ of a person) is a frequent theme of science fiction.

All fiction that does not violate the laws of physics is fact.

Fungible Identical in every respect.

Quantum interference Phenomena caused by non-fungible instances of a multiversal object becoming fungible.

Quantum computation Computation in which the flow of information is not confined to a single history.

The physical world is a multiverse, and its structure is determined by how information flows in it. In many regions of the multiverse, information flows in quasi-autonomous streams called histories, one of which we call our ‘universe’. Universes approximately obey the laws of classical (pre-quantum) physics. But we know of the rest of the multiverse, and can test the laws of quantum physics, because of the phenomenon of quantum interference. Thus a universe is not an exact but an emergent feature of the multiverse. One of the most unfamiliar and counter-intuitive things about the multiverse is fungibility. The laws of motion of the multiverse are deterministic, and apparent randomness is due to initially fungible instances of objects becoming different. In quantum physics, variables are typically discrete, and how they change from one value to another is a multiversal process involving interference and fungibility.

Let me define ‘bad philosophy’ as philosophy that is not merely false, but actively prevents the growth of other knowledge.