The Beginning of Infinity: Explanations That Transform the World

by David Deutsch

However, that was not properly understood until the mid twentieth century with the work of the philosopher Karl Popper. So historically it was empiricism that first provided a plausible defence for experimental science as we now know it. Empiricist philosophers criticized and rejected traditional approaches to knowledge such as deference to the authority of holy books and other ancient writings, as well as human authorities such as priests and academics, and belief in traditional lore, rules of thumb and hearsay. Empiricism also contradicted the opposing and surprisingly persistent idea that the senses are little more than sources of error to be ignored.

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.

The laws of physics that explain it bear no resemblance to any rules of thumb that were ever in our ancestors’ genes or in their culture. Yet human brains today know in considerable detail what is happening there.

inside jet of a quasar

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. That is scientific knowledge.

the faithfulness with which the one structure resembles the other is steadily increasing. That constitutes the creation of knowledge. Here we have physical objects very unlike each other, and whose behaviour is dominated by different laws of physics, embodying the same mathematical and causal structures – and doing so ever more accurately over time. Of all the physical processes that can occur in nature, only the creation of knowledge exhibits that underlying unity.

the SETI instrument is exquisitely adapted to detecting something that has never yet been detected. Biological evolution could never produce such an adaptation. Only scientific knowledge can.

intergalactic thought experiment, we imagined ‘priming’ a typical cube, and as a result intergalactic space itself began to produce a stream of ever-improving explanations.

like all knowledge-creating systems, the transformed cube corrects errors.

good adaptations, like good explanations, are distinguished by being hard to vary while still fulfilling their functions.

biological knowledge is non-explanatory, and therefore has limited reach; explanatory human knowledge can have broad or even unlimited reach. Another difference is that mutations are random, while conjectures can be constructed intentionally for a purpose.

the eyes of vertebrates have their ‘wiring’ and blood supply in front of the retina, where they absorb and scatter incoming light and so degrade the image. There is also a blind spot where the optic nerve passes through the retina on its way to the brain. The eyes of some invertebrates, such as squids, have the same basic design but without those design flaws.

most animals have a gene for synthesizing vitamin C, but in primates, including humans, though that gene is recognizably present, it is faulty: it does not do anything.

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.

The most general way of stating the central assertion of the 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.

The physicist Brandon Carter calculated in 1974 that if the strength of the interaction between charged particles were a few per cent smaller, no planets would ever have formed and the only condensed objects in the universe would be stars; and if it were a few per cent greater, then no stars would ever explode, and so no elements other than hydrogen and helium would exist outside them.

gravitational attraction rather than electromagnetic? theyre just analgous, not rigorously related

the existence of an unsolved problem in physics is no more evidence for a supernatural explanation than the existence of an unsolved crime is evidence that a ghost committed it.

For instance, infinitely many of them contain nothing other than one bison, in various poses, and last for exactly 42 seconds. Infinitely many others contain a bison and an astrophysicist.

It will be, as Wheeler put it, ‘an idea so simple…that…we will all say to each other, how could it have been otherwise?’

if a supernatural creator were to have created the universe at the moment when Einstein or Darwin or any great scientist (appeared to have) just completed their major discovery, then the true creator of that discovery (and of all earlier discoveries) would have been not that scientist but the supernatural being. So such a theory would deny the existence of the only creation that really did take place in the genesis of that scientist’s discoveries.

what science – and creative thought in general – achieves is unpredictable creation ex nihilo. So does biological evolution. No other process does.

Creationism, therefore, is misleadingly named. It is not a theory explaining knowledge as being due to creation, but the opposite: it is denying that creation happened in reality, by placing the origin of the knowledge in an explanationless realm. Creationism is really creation denial

the neo-Darwinian theory, like the Popperian theory of knowledge, really does describe creation, while their rivals, beginning with creationism, never could.

Evolution (Darwinian) Creation of knowledge through alternating variation and selection. Replicator An entity that contributes causally to its own copying. Neo-Darwinism Darwinism as a theory of replicators, without various misconceptions such as ‘survival of the fittest’.

The main similarities: genes and ideas are both replicators; knowledge and adaptations are both hard to vary. The main difference: human knowledge can be explanatory and can have great reach; adaptations are never explanatory and rarely have much reach beyond the situations in which they evolved.

All those doctrines are irrational for the same reason: they advocate accepting or rejecting theories on grounds other than whether they are good explanations.

Thus emergence is another beginning of infinity: all knowledge-creation depends on, and physically consists of, emergent phenomena.

Einstein remarked, ‘There could be no fairer destiny for any physical theory than that it should point the way to a more comprehensive theory in which it lives on as a limiting case.’

Also, in order to make progress in any field, it is the explanations in existing theories, not the predictions, that have to be creatively varied in order to conjecture the next theory.

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.

Plato. He noticed that the theorems of geometry – such as Pythagoras’ theorem – are about entities that are never experienced: perfectly straight lines with no thickness, intersecting each other on a perfect plane to make a perfect triangle.

comes from conjecture, like all our knowledge, and through criticism and seeking good explanations.

Moreover, experience does play a role in philosophy – only not the role of experimental testing that it plays in science. Primarily, it provides philosophical problems. There would have been no philosophy of science if the issue of how we can acquire knowledge of the physical world had been unproblematic.

advocates of highly immoral doctrines almost invariably believe associated factual falsehoods as well.

Progress depends on explanation, and therefore trying to conceive of the world as merely a sequence of events with unexplained regularities would entail giving up on progress.

there is a kind of infinite reach that is unique to people: the reach of the ability to understand explanations.

small change in a system to meet a parochial purpose just happened to make the system universal as well. This is the jump to universality.

system originated in India, but it is not known when. It might have been as late as the ninth century, since before that only a few ambiguous documents seem to show it in use. At any rate, its tremendous potential in science, mathematics, engineering and trade was not widely realized. At approximately that time it was embraced by Arab scholars, yet was not generally used in the Arab world until a thousand years later.

the Enlightenment, whose quintessential idea is, as I have said, that progress is both desirable and attainable.

genetic code has displayed phenomenal reach. It evolved only to specify organisms with no nervous systems, no ability to move or exert forces, no internal organs and no sense organs, whose lifestyle consisted of little more than synthesizing their own structural constituents and then dividing in two. And yet the same language today specifies the hardware and software for countless multicellular behaviours that had no close analogue in those organisms, such as running and flying and breathing and mating and recognizing predators and prey. It also specifies engineering structures such as wings and teeth, and nanotechnology such as immune systems, and even a brain that is capable of explaining quasars, designing other organisms from scratch, and wondering why it exists.

if it can already be programmed, it has nothing to do with intelligence in Turing’s sense.

Turing invented his test in the hope of bypassing all those philosophical problems. In other words, he hoped that the functionality could be achieved before it was explained.

In fact, if we had only such an explanation but had not yet seen any output from the program – and even if it had not been written yet – we should still conclude that it was a genuine AI program. So there would be no need for a Turing test. That is why I said that if lack of computer power were the only thing preventing the achievement of AI, there would be no need to wait.

experiment of a slightly different kind: eliminate the graduate student from the project. Then, instead of using a robot designed to evolve better ways of walking, use a robot that is already in use in some real-life application and happens to be capable of walking. And then, instead of creating a special language of subroutines in which to express conjectures about how to walk, just replace its existing program, in its existing microprocessor, by random numbers. For mutations, use errors of the type that happen anyway in such processors (though in the simulation you are allowed to make them happen as often as you like). The purpose of all that is to eliminate the possibility that human knowledge is being fed into the design of the system, and that its reach is being mistaken for the product of evolution. Then, run simulations of that mutating system in the usual way. As many as you like. If the robot ever walks better than it did originally, then I am mistaken.

This is a remarkable limitation on the apparently limitless power of Infinity Hotel’s management to shuffle the guests around.

Yet, taken together, those actions annihilated the puppy and cannot be reversed.

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.

The harm that can flow from any innovation that does not destroy the growth of knowledge is always finite; the good can be unlimited.

their caution about innovation and progress was as perverse as expecting a blindfold to be useful when navigating dangerous waters.

The question about the sources of our knowledge…has always been asked in the spirit of: ‘What are the best sources of our knowledge – the most reliable ones, those which will not lead us into error, and those to which we can and must turn, in case of doubt, as the last court of appeal?’ I propose to assume, instead, that no such ideal sources exist – no more than ideal rulers – and that all ‘sources’ are liable to lead us into error at times. And I propose to replace, therefore, the question of the sources of our knowledge by the entirely different question: ‘How can we hope to detect and eliminate error?