The Beginning of Infinity: Explanations That Transform the World

Behind it all is surely an idea so simple, so beautiful, that when we grasp it – in a decade, a century, or a millennium – we will all say to each other, how could it have been otherwise?

Its neutrino radiation alone would kill a human at a range of billions of kilometres, even if that entire distance were filled with lead shielding.

We do not read them in nature, nor does nature write them into us. They are guesses – bold conjectures.

For millennia people dreamed about flying, but they experienced only falling.

To the extent that experiencing dots ‘writes’ something into our brains, it does not write explanations but only dots.

It converts the quest for truth into a quest for certainty (a feeling) or for endorsement (a social status).

There is nothing more deceptive than an obvious fact.

Discoveries such as fire, clothing, stone tools, bronze, and so on, happened so rarely that from an individual’s point of view the world never improved.

The usual sequel has merely been that new authorities replaced the old. What was needed for the sustained, rapid growth of knowledge was a tradition of criticism.

That leaves no term for assertions about reality itself, except perhaps ‘useful fiction’.

That is why a trick that mystifies an adult may be uninteresting to a young child who has not yet learned to have the expectations on which the trick relies.

The refutation of a scientific theory has, from the point of view of someone who expected it to be true, the same logic as a conjuring trick – the only difference being that a conjurer does not normally have access to unknown laws of nature to make a trick work.

He made that choice – and all his substantive choices as author – for cultural and artistic reasons, and not because of the attributes of winter at all.

If an explanation could easily explain anything in the given field, then it actually explains nothing.

It is the feature that distinguishes those approaches to knowledge from all others, and it implies all those other conditions for scientific progress I have discussed: It trivially implies that prediction alone is insufficient.

If their guess was easy to vary, they might just as well have saved themselves the boat fare, stayed at home, and tested the easily testable theory that winter can be staved off by yodelling.

You have never experienced any seasons other than Mediterranean ones. You have never read, nor heard tell, of seasons that were out of phase with the ones you have experienced. But you know about them.

The theory reaches out, as it were, from its finite origins inside one brain that has been affected only by scraps of patchy evidence from a small part of one hemisphere of one planet – to infinity.

If you find a nugget of gold anywhere in the universe, you can be sure that in its history there was either a supernova or an intelligent being with an explanation.

The real source of our theories is conjecture, and the real source of our knowledge is conjecture alternating with criticism.

Feeling insignificant because the universe is large has exactly the same logic as feeling inadequate for not being a cow.

I had overestimated the mass of what I was looking at by some fifty powers of ten.

The primary function of the telescope’s optics is to reduce the illusion that the stars are few, faint, twinkling and moving.

Like conjuring tricks in reverse, such instruments fool our senses into seeing what is really there.

So, winter might be attributed to someone’s sadness, harvests to someone’s generosity, natural disasters to someone’s anger, and so on.

As the physicist Stephen Hawking put it, humans are ‘just a chemical scum on the surface of a typical planet that’s in orbit round a typical star on the outskirts of a typical galaxy’.

It may well be that the interiors of refrigerators constructed by physicists are by far the coldest and darkest places in the universe.

The nearest star would be so far away that if it were to explode as a supernova, and you were staring directly at it when its light reached you, you would not see even a glimmer.

The biosphere only ever achieves stability – and only temporarily at that – by continually neglecting, harming, disabling and killing individuals.

Before the designs created by humans, it was not a vehicle, but only a heap of dangerous raw materials.

In a sense their whole problem was that they were not arrogant enough: they assumed far too easily that the world was fundamentally incomprehensible to them.

For an inexplicable world is indistinguishable from one ‘tricked out with capricious ad hoc magic’.

That is to say, every putative physical transformation, to be performed in a given time with given resources or under any other conditions, is either impossible because it is forbidden by the laws of nature; or achievable, given the right knowledge.

In theory a knowledgeable zoologist, presented with the complete transcript of a genome, should be able to reconstruct the environmental circumstances that did the carving.

In the unique case of humans, the difference between a hospitable environment and a deathtrap depends on what knowledge they have created.

As Einstein remarked, ‘My pencil and I are more clever than I.’

On any clear night, the chances are that your roof will be struck by evidence falling from the sky which, if you only knew what to look for and how, would win you a Nobel prize.

An unproblematic state is a state without creative thought. Its other name is death.

Neither the human condition in particular nor our explanatory knowledge in general will ever be perfect, nor even approximately perfect. We shall always be at the beginning of infinity.

It is empty, cold and dark. Or is it? Actually, that is yet another parochial misconception.

All people in the universe, once they have understood enough to free themselves from parochial obstacles, face essentially the same opportunities.

Outside our parochial perspective, astrophysics is incomplete without a theory of people, just as it is incomplete without a theory of gravity or nuclear reactions.

Somehow that jet happens in such a way that billions of years later, on the other side of the universe, a chemical scum can know and predict what the jet will do, and can understand why.

Thus the study of the behaviour of champagne corks and other proxies for what people do is logically equivalent to the study of everything significant.

Like an explosive awaiting a spark, unimaginably numerous environments in the universe are waiting out there, for aeons on end, doing nothing at all or blindly generating evidence and storing it up or pouring it out into space.

The fact that everything that is not forbidden by laws of nature is achievable, given the right knowledge. ‘Problems are soluble.’

A being who was ‘just there’ would serve no explanatory purpose (in regard to the biosphere), since then one could more economically say that the biosphere itself ‘just happened’.

At that point, a supposed designer of our biosphere will seem not only morally deficient, but intellectually unremarkable.

I ask you, when you see all these things constructed with such show of foresight, can you doubt whether they are products of chance or design?

A good design is hard to vary: If the different parts had been differently shaped from what they are, or placed after any other manner, or in any other order, than that in which they are placed, either no motion at all would have been carried on in the machine, or none which would have answered the use now served by it.

There cannot be design without a designer; contrivance without a contriver; order without choice; arrangement without anything capable of arranging.

If a tiger is placed in a habitat in which its colouration makes it stand out more instead of less, it takes no action to change the colour of its fur, nor would that change be inherited if it did.

There will be evolutionary pressure to make the genes become less well adapted to that function.

The early-nesting gene that replaced it may still be tolerably functional, but it is fittest for nothing except preventing variants of itself from procreating.

Organisms are the slaves, or tools, that genes use to achieve their ‘purpose’ of spreading themselves through the population.

The most important source of variation in explanatory theories is creativity.

Given the supposed evidence, that is still an infinitely better explanation than, for instance, creationism or Lamarckism, neither of which gives any account of the origin of the apparent knowledge in the rabbit.

Therefore 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.

Whatever anthropic reasoning predicts about the values of multiple constants, it predicts will only just happen.

Fermi’s problem is that we do not see any such civilizations, probes or signals.

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

Creationism is really creation denial – and so are all those other false explanations.

The existence of a force of gravity is, astonishingly, denied by Einstein’s general theory of relativity, one of the two deepest theories of physics.

Thus we explain a low-level physical observation – the presence of a copper atom at a particular location – through extremely high-level theories about emergent phenomena such as ideas, leadership, war and tradition.

A scrambled egg never becomes unscrambled by the whisk, and never extracts energy from the pan to propel itself upwards into the shell, which never seamlessly reseals itself.

From Kepler to Newton to Einstein we have successively: no force needed to explain orbits; an inverse-square-law force responsible for every orbit; and again no force needed.

As Popper put it, ‘We can let our theories die in our place.’

The observer points at [that domino] and asks with curiosity, ‘How come that domino there is never falling?’

The second type of answer would be, ‘Because 641 is prime.’

Regarding microphysical explanations as more fundamental than emergent ones is arbitrary and fallacious.

The growth of knowledge does not consist of finding ways to justify one’s beliefs. It consists of finding good explanations.

Those are purely factual misconceptions, yet they bear the imprint of moral wrongness just as clearly as a fossil – made of purely inorganic material – bears the imprint of ancient life.

My guess is that morality is more autonomous than that, and so it makes sense to say that such laws of physics would be immoral.

That tiny change in the rules would make the system universal. It is thought that the earliest alphabets evolved from rules like that.

A 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.

Hence the process that we call ‘using Roman numerals to do arithmetic’ also consists of the Roman-numeral system using us to do arithmetic.

By that argument, it is slavery to escape from slavery.

It is as though everyone in the ancient world was avoiding universality on purpose.

In all those cases, universality was being sought deliberately, as a desirable feature in its own right – even a necessary feature for an idea to be true – and not just as a means of solving a parochial problem.

At the time, they were compiled by armies of clerks known as ‘computers’ (which is the origin of the word), and were notoriously error-prone.

And so the Analytical Engine became one of the tragic might-have-beens of history.

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.

Error-correction is the beginning of infinity.

Assigning meanings to the whole continuum of angles would nominally have allowed each wheel to carry (infinitely) more information; but, in reality, information that cannot be reliably retrieved is not really being stored.

But there came a moment when the code stopped evolving yet the organisms continued to do so.

If intelligent extraterrestrials had visited Earth at any time during those billion years they would have seen no evidence that the genetic code could specify anything significantly different from the organisms that it had specified when it first appeared.

Only people can rely on themselves into the unbounded future.

In retrospect, I am quite amazed at how much genuine intelligence I was willing to accept as somehow having been implanted in the program.

This is how much success the quest for ‘machines that think’ had achieved in the fifty-eight years following Turing’s paper: nil.

But it can no more think than Turing’s slide rule could.

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.

Thus the very same utterance by the program – the joke – can be either evidence that it is not thinking or evidence that it is thinking depending on the best available explanation of how the program works.

Becoming better at pretending to think is not the same as coming closer to being able to think.

When you have identified and solved as many of these sub-problems as you can, you will have created a code, or language, that is highly adapted to making statements about how your robot should walk.

Even if you yourself are the programmer, you are in no position to judge whether you created that relatively small amount of knowledge or not.

Specifically, we do not know why the DNA code, which evolved to describe bacteria, has enough reach to describe dinosaurs and humans.

The reach of explanations cannot be limited by fiat.

But in Infinity Hotel, where the number of rooms is infinity, all the rooms have numbers infinitely far below infinity.

What happens at the last room? There is no last room, and hence no problem about what happens there.

Almost all ways in which the guests could, as a matter of logic, be distributed among the rooms are unattainable.

It was no exaggeration to say that the bags are nowhere. They have not been stuffed into a mythical ‘room number infinity’. They no longer exist; nor does the puppy.

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.

At our whim, we can number them in such a way that astrophysicists seem to be the rule, or the exception, or anything in between.

If there was no first universe or universes, but the whole ensemble has already existed for an infinite time, then the theory has an infinite regress problem.

It is a single physical entity, a multiverse with internal interactions that relate different parts of it to each other and thereby provide a unique meaning, known as a measure, to proportions and averages over different universes.

If he is complaining that there is something inconsistent about motion because one could not experience each point along a continuous path, then he is simply confusing two different things that both happen to be called ‘infinity’.

In general terms, the mistake is to confuse an abstract attribute with a physical one of the same name.

The laws of physics provide us with only a narrow window through which we can look out on the world of abstractions.

Quantum computation drives a coach and horses through the classical notion of a ‘simple’ or ‘elementary’ operation.

Proof theory is a science: specifically, it is computer science.

The whole point of universality is lost if one conceives of computation as being somehow prior to the physical world, generating its laws.

One does not understand a mathematical proposition merely by proving it true.

The most important of all limitations on knowledge-creation is that we cannot prophesy: we cannot predict the content of ideas yet to be created, or their effects.

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

The future of civilization is unknowable, because the knowledge that is going to affect it has yet to be created.

Observations are theory-laden. Given an experimental oddity, we have no way of predicting whether it will eventually be explained merely by correcting a minor parochial assumption or by revolutionizing entire sciences.

But blind pessimism is a blindly optimistic doctrine. It assumes that unforeseen disastrous consequences cannot follow from existing knowledge too (or, rather, from existing ignorance).

Very few, if any, could have been saved by greater caution about innovation. In fact most had enthusiastically implemented the precautionary principle.

The idea that there could be beings that are to us as we are to animals is a belief in the supernatural.

In reality they were all allowing themselves to be misled by the ineluctable fact of the human condition that we do not yet know what we have not yet discovered.

People must have died of exposure literally on top of the means of making the fires that would have saved their lives, because they did not know how.

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?’

Thus the very question ‘Who should rule?’ begs for violent, authoritarian answers, and has often received them.

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

The prisoner understands that, while his immediate problems have to do with prison bars and the king and his horse, ultimately the evil he faces is caused by insufficient knowledge.

We choose to go to the moon in this decade and do the other things, not because they are easy, but because they are hard.

The end of pessimism is potentially a beginning of infinity.

Thus almost the entire effort of the society was devoted to preserving itself in its existing state – in other words, to preventing improvement.

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.

If benevolent, then what do I have to fear? If malevolent, then I disdain to fear you.

I can think of nothing more boring – no offence meant, wise Apollo – than to attain the state of being perfectly secure in one’s beliefs, which some people seem to yearn for.

So 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.

I am not sure what is in front of my eyes – ever – with my eyes open or closed, asleep or awake.

Their whole way of life misleads and traps them – because one of their mistaken beliefs is that they must take no steps to prevent their way of life from misleading and trapping them!

My doubt improved my knowledge of an important truth – as knowledge held immune from criticism never can be improved!

This is a rare and deadly sort of error: it prevents itself from being undone.

What matters in all cases is the explanation you create, within your own mind, for the facts, and for the observations and advice in question.

‘For all is but a woven web of guesses.’ Guesses!

And then we hone our guesses, and then fashion the best ones into a sort of waking dream of reality.

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

We were up all night, wrestling by candlelight. I’ve never done that before. They’re really good! Though they do sometimes cheat as well.

How sneaky Apollo is! It’s the Spartan Socrates who’s the wisest man in the world – though only by the breadth of a hair, I’ll bet!

Perhaps it is significant that the statue of Ares that stands outside Sparta represents him chained, so that he will always be there to protect the city.

We might do well to put up a statue of democracy chained, to symbolize the fundamental safeguard of our city.

Theorem: a king who’s a philosopher is the same as a philosopher who’s a king. So, what if a philosopher became king?

What is the point of writing down things that are going to be endlessly tinkered with and improved?

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 way to converge with each other is to converge upon the truth.

And if two identical human bodies were to coincide even approximately, they would explode simply because water at double its normal density exerts a pressure of hundreds of thousands of atmospheres.

Since a wizard could equally well have been said to conjure any events, in any story, it is a bad explanation; and that is why the fan is exasperated by it.

We should not be surprised that good fictional science is hard to invent: it is a variant of real science, and real scientific knowledge is very hard to vary.

This is to stress that a universe is not a receptacle containing physical objects: it is those objects.

It is an even weirder attribute than Leibniz guessed – much weirder than multiple universes for instance, which are, after all, just common sense, repeated.

It is not merely that we cannot know whether it was the same dollar, or have decided not to care: because of the physics of the situation there really is no such thing as taking the original dollar, nor such a thing as taking the one added subsequently.

It is not that they coincide in anything, such as an external space: they are not in space. An instance of space is part of each of them.

The third – which had never been imagined before quantum theory – is that two or more initially fungible instances of the observer become different.

And if you have such a theory, then perhaps you have no need to be skulking in transporter rooms.

Thus, starting with the voltage happening in only one universe, a wave of differentiation between the universes spreads in all directions through space.

There is only one known phenomenon which, if it ever occurred, would have effects that did not fall off with distance, and that is the creation of a certain type of knowledge, namely a beginning of infinity.

It is remarkable how much subtlety there can be in the apparently straightforward, binary distinction between ‘same’ and different’ – or between ‘affected’ and ‘unaffected’.

The same words, printed in the same column in the same newspaper, are fungible between the two histories; but they are fiction in one history and fact in the other.

The ‘naive’ audience’s mistake is a form of parochialism: they observe a phenomenon – people phoning in because their watches stopped – but they are failing to understand it as part of a wider phenomenon, most of which they do not observe.

The upshot is that our laws of physics must also say that every object carries within it information about which instances of it could interact with which instances of other objects.

This is rather like the doppelgängers merging with their originals in some phantom-zone stories, except that here we do not need to repeal the principle of the conservation of mass.

When a photon strikes such a mirror, it bounces off in half the universes, and passes straight through in the other half.

Because these two groups of instances of the particle, initially at different positions, have gone through a moment of being fungible, there is no such thing as which of them has ended up at which final position.

Furthermore, it turns out that, in the hydrogen atom, the electron in its lowest-energy state is not orbiting at all but, as I said, just sitting there like an ink blot – its uncertainty-principle tendency to spread exactly balanced by the electrostatic force.

Universes, histories, particles and their instances are not referred to by quantum theory at all – any more than are planets, and human beings and their lives and loves.

That particle must be travelling in a range of slightly different directions, because the uncertainty principle implies that in the multiverse it must spread sideways like an ink blot as it travels.

In such computations, a quantum computer with only a few hundred qubits could perform far more computations in parallel than there are atoms in the visible universe.

Forget anything that you may have read about ‘quantum jumps’: they are a myth.

It is as if a continuously variable amount of money changed ownership gradually from one discrete owner to another.

In some tiny sliver of it, the kettle transforms itself into a top hat, and the water into a rabbit which then hops away, and I get neither tea nor coffee but am very surprised.

What an observer sees as a married couple is actually just a sliver of a vast entity that includes many fungible instances of such a couple, together with other instances of them who are divorced, and others who have never married.

But let us remember that, just as we are at the top rank of significance in the great scheme of things, anything else that could create explanations would be too.

Are you claiming to be made of something other than atoms?

Instead of trying to improve and integrate those two powerful but slightly flawed explanatory theories, and to explain why the rule of thumb worked, most of the theoretical-physics community retreated rapidly and with remarkable docility into instrumentalism.

Inconsistency was defended as ‘complementarity’ or ‘duality’; parochialism was hailed as philosophical sophistication.

Here was an eminent physicist joking that he might be considered mad. Why? For claiming that his own equation – the very one for which he had won the Nobel prize – might be true.

I wonder: if Einstein had continued to take positivism seriously, could he ever have thought of the general theory of relativity, in which spacetime not only exists but is a dynamic, unseen entity bucking and twisting under the influence of massive objects?

Creating a good explanation is hard not because of what anyone has decided, but because there is an objective reality that does not meet anyone’s prior expectations, including those of authorities.

The sensations are real, but the dinosaurs were not. Or, if they were, we can never know of them.

According to it, whether one was a slave or not was once a highly ‘heritable’ trait in America: it ran in families.

The headline will say, ‘New Study Shows Happiness 50% Genetically Determined’ – without quotation marks around the technical terms.

For refusing to theorize about the mind as a causative agent is the equivalent of regarding it as a non-creative automaton.

The less competent your counting and tabulating are, the more often you will find those ‘inconsistencies with conventional physics’.

As a matter of logic, it would still be open to him to say, ‘I’m not seeing atoms, I’m only seeing a video monitor.’

In quantum theory, bad philosophy manifested itself mainly as the Copenhagen interpretation and its many variants, and as the ‘shut-up-and-calculate’ interpretation.

It is true that 5 per cent now have no representatives – so they will not be able to vote in congressional elections at all – but that still leaves them within the quota, and indeed only slightly further from their exact quota than they were.

In this way the Constitution attempted to treat the population equally by treating voters unequally.

Yet the paradoxes as a whole have the infuriating property that, no matter how firmly they are kicked out of the front door, they instantly come in again at the back.

‘God help the State of Maine when mathematics reach for her and undertake to strike her down.’

Every apportionment rule that stays within the quota suffers from the population paradox.

Arrow’s theorem appears to deny the very existence of social choice – and to strike at the principle of representative government, and apportionment, and democracy itself, and a lot more besides.

So there is no such thing as ‘the will of the people’. There is no way to regard ‘society’ as a decision-maker with self-consistent preferences.

This disproportionate power that proportional representation gives the third-largest party is an embarrassing feature of a system whose whole raison d’être, and supposed moral justification, is to allocate political influence proportionately.

They have been not outweighed, but out-argued, refuted and abandoned.

In reality, the voter is choosing between explanations, not checkboxes.

If your conception of rationality conflicts with a mathematical theorem (or, in this case, with many theorems) then your conception of rationality is irrational.

If a policy is no one’s idea of what will work, then why should it work?

The all-or-nothing nature of the constituency elections, and the consequent low representation of small parties, makes the overall outcome sensitive to small changes in opinion.

What is the point of giving the party with the most votes the most seats, if the party with the third-largest number of seats can then put the second-largest party in power regardless – there to enact a compromise platform that absolutely no one voted for?

They converge with each other on any given issue because they are all converging on the objective truth.

Human life can improve without limit as we advance from misconception to ever better misconception.

The poet John Keats’ assertion (which I think was ironic) that ‘Beauty is truth, truth beauty’ is refuted by what the evolutionist Thomas Huxley called ‘the great tragedy of Science – the slaying of a beautiful hypothesis by an ugly fact’.

And when a ‘beautiful hypothesis’ is slain, it is more often than not replaced, as the spontaneous-generation theory was, by a more beautiful one.

But if beauty is objective, then a new work of art, like a newly discovered law of nature or mathematical theorem, adds something irreducibly new to the world.

To a skydiver, the vista from which we were born to recoil is beautiful.

So flowers have to create objective beauty, and insects have to recognize objective beauty.

Flowers are like that: they have the appearance of having been evolved for a purpose which we call ‘beauty’, which we can (imperfectly) recognize, but whose nature is poorly understood.

Signalling across the gap between two humans is analogous to signalling across the gap between two entire species.

I guess that we shall also be able to design new senses, and design new qualia, that can encompass beauty of new kinds literally inconceivable to us now.

The fact that flowers reliably seem beautiful to humans when their designs evolved for an apparently unrelated purpose is evidence that beauty is objective.

The biosphere is a grim place. It is rife with plunder, deceit, conquest, enslavement, starvation and extermination.

If a joke has evolved in that way from a non-joke, it truly has no author.

We are in the counter-intuitive (but common) position of having been mistaken about the reason for our own behaviour.

A meme cannot be downloaded like a computer program. If it is not enacted, it will not be copied.

If establishing a faithfully replicating meme were that easy, the whole adult population in our society would be proficient at algebra, thanks to the efforts made to teach it to them when they were children.

The whole of biological evolution was but a preface to the main story of evolution, the evolution of memes.

The primary method is always – and can only be – to disable the source of new ideas, namely human creativity.

Just as genes for the eye implicitly ‘know’ the laws of optics, so the long-lived memes of a static society implicitly possess knowledge of the human condition, and use it mercilessly to evade the defences and exploit the weaknesses of the human minds that they enslave.

The spirit of creativity with which we are all born is systematically extinguished in them before it can ever create anything new.

It can perpetuate itself only by suppressing its members’ self-expression and breaking their spirits, and its memes are exquisitely adapted to doing this.

The best way to seem useful to diverse people under diverse, unpredictable circumstances is to be useful.

On the contrary, the non-existence of the hobgoblin helps to make the meme a better replicator, because the story is then unconstrained by the mundane attributes of any genuine menace, which are always finite and to some degree combatable.

If their thoughts ever wander in the forbidden directions, they feel uneasiness and embarrassment, and the same sort of fear and loss of centredness as religious people have felt since time immemorial at the thought of betraying their gods.

Consider how you would be judged by other people if you went shopping in pyjamas, or painted your home with blue and brown stripes.

And so we live in a society in which people can spend their days conscientiously using laser technology to count cells in blood samples, and their evenings sitting cross-legged and chanting to draw supernatural energy out of the Earth.

Anything that says ‘Because I say so’ or ‘It never did me any harm,’ anything that says ‘Let us suppress criticism of our idea because it is true,’ suggests static-society thinking.

Either they are static, and survive only by extinguishing their members’ creativity and breaking their spirits, or they quickly lose their knowledge and disintegrate, and violence takes over.

Their ability to innovate was increasing rapidly, but they were barely innovating.

So how does one gain status, specifically by exercising more creativity than anyone else, without becoming noticeable as a taboo-violator?

There are infinitely many possible interpretations of ‘imitate Popper’, each defining a different behaviour for the imitator.

As Popper remarked, ‘It is impossible to speak in such a way that you cannot be misunderstood.’

The parrot could not be said to have acquired the memes, because it would be reproducing only one of the countless behaviours that they could produce.

It is a very inefficient method, requiring a lot of watching of behaviours that a human could mimic almost immediately by understanding their purpose.

In fact a student might well acquire a complex meme at a lecture without being able to repeat a single sentence spoken by the lecturer, even immediately afterwards.

The transmission of human-type memes – memes whose meaning is not mostly predefined within the receiver – cannot be other than a creative activity on the part of the receiver.

Innovation remained imperceptibly slow, even as the capacity for it was increasing rapidly.

Hence, paradoxically, it requires creativity to thrive in a static society – creativity that enables one to be less innovative than other people.

The horror of static societies, which I described in the previous chapter, can now be seen as a hideous practical joke that the universe played on the human species.

We can see the actions, but not the rules, so how do we replicate them? We replicate them by creativity.

These frozen faces, these frozen frames in a film that is running down, mark a civilization which failed to take the first step on the ascent of rational knowledge.

It sustained the values that placed forests – literally – beneath statues.

The ancient Roman ruler Julius Caesar was stabbed to death, so one could summarize his mistake as ‘imprudent iron management, resulting in an excessive build-up of iron in his body’.

The conditions for a beginning of infinity exist in almost every human habitation on Earth.

What would have happened if one of those hunters had had a different idea: to ride the beast before killing it?

It is knowledge alone that converts landscapes into resources, and humans alone who are the authors of explanatory knowledge and hence of the uniquely human behaviour called ‘history’.

The Easter Island civilization collapsed because no human situation is free of new problems, and static societies are inherently unstable in the face of new problems.

Once I realized that Ehrlich’s prophesies amounted to saying, ‘If we stop solving problems, we are doomed,’ I no longer found them shocking, for how could it be otherwise?

After all, why should nature supply elements with properties to suit our convenience?

In the pessimistic conception, that distinctive ability of people is a disease for which sustainability is the cure. In the optimistic one, sustainability is the disease and people are the cure.

The fact that reliance on specific antibiotics is unsustainable is only an indictment from the point of view of someone who expects a sustainable lifestyle. But in reality there is no such thing. Only progress is sustainable.

From society’s point of view, physicists were a luxury in 1902, like colour televisions were in the 1970s.

It is as if people were arguing about how best to prepare for the next hurricane while all agreeing that the only hurricanes one should prepare for are human-induced ones.

But if we choose instead to embark on an open-ended journey of creation and exploration whose every step is unsustainable until it is redeemed by the next – if this becomes the prevailing ethic and aspiration of our society – then the ascent of man, the beginning of infinity, will have become, if not secure, then at least sustainable.

Even Feynman cannot get round the fact that the future is not yet imaginable.

Their system of the world would for ever remain a tiny, frozen island of explanation in an ocean of incomprehensibility.

Infinite ignorance is a necessary condition for there to be infinite potential for knowledge.

Never before in the history of human thought has it been so obvious that our knowledge is tiny and our ignorance vast.

To the inhabitants – who would eventually have to upload their personalities into computers made of something like pure tides – the universe would last for ever because they would be thinking faster and faster, without limit, as it collapsed.

Everything physically possible will eventually be revealed: watches that came into existence spontaneously; asteroids that happen to be good likenesses of William Paley; everything.

Imagine that physicists discover that space is actually many-layered like puff pastry; the number of layers varies from place to place; the layers split in some places, and their contents split with them.

So my question is: is it wrong to switch the computer on, setting it executing all those programs simultaneously in different histories?

Universality implies that, in every important sense, humans and AIs will never be other than equal.

Stand up, look back on all those equations, some perhaps more hopeful than others, raise one’s finger commandingly, and give the order ‘Fly!’ Not one of those equations will put on wings, take off, or fly. Yet the universe ‘flies’.

All we can choose is whether it is an infinity of ignorance or of knowledge, wrong or right, death or life.

The objectivity of beauty 122, 353–68

humans as chemical scum 44–8, 51, 72, 73

Puzzle of what use it was in non-innovating cultures 398–402, 410–15 as a hideous joke played on humans 416.

Popper’s criterion of ridding ourselves of bad governments without violence 344–51, 352

The falseness of empiricism: the deceptiveness of the senses and the mistaken idea of theory-free observation.

The quest for good explanations: good (hard to vary) vs. bad (easy to vary).

significance of knowledge and 70–75, 76

The infinite reach of ideas 167–93; our infinite ignorance 447.

anti-rational 81, 381, 385, 388–90, 391–3, 394–396, 397, 413, 428, 457

fictional variations on the doppelganger idea 258–62, 270

people as universal explainers 146, 164, 416, 429; cosmic significance of 72–74, 458, 459; as a disease or cure 435

Popper’s criterion of ridding ourselves of bad governments without violence; letting theories die in our place.

Problems are inevitable, but problems are soluble.

reach: always has an explanation; and the jump to universality.

scum, humans as chemical 44–8, 51, 72, 73

The mistake of separating prediction from explanation leads to a view of science as a mere tool for tallying, rather than a quest for truth.

Zeno’s mistake (confusing abstract attributes with physical ones of the same name)

Our experience of the world is indeed a form of virtual-reality rendering which happens wholly inside the brain.

Behind it all is surely an idea so simple, so beautiful, that when we grasp it – in a decade, a century, or a millennium – we will all say to each other, how could it have been otherwise?

Its neutrino radiation alone would kill a human at a range of billions of kilometres, even if that entire distance were filled with lead shielding.

We do not read them in nature, nor does nature write them into us. They are guesses – bold conjectures.

For millennia people dreamed about flying, but they experienced only falling.

To the extent that experiencing dots ‘writes’ something into our brains, it does not write explanations but only dots.

It is the feature that distinguishes those approaches to knowledge from all others, and it implies all those other conditions for scientific progress I have discussed: It trivially implies that prediction alone is insufficient.

The theory reaches out, as it were, from its finite origins inside one brain that has been affected only by scraps of patchy evidence from a small part of one hemisphere of one planet – to infinity.

That is to say, every putative physical transformation, to be performed in a given time with given resources or under any other conditions, is either impossible because it is forbidden by the laws of nature; or achievable, given the right knowledge.

In the unique case of humans, the difference between a hospitable environment and a deathtrap depends on what knowledge they have created.

Neither the human condition in particular nor our explanatory knowledge in general will ever be perfect, nor even approximately perfect. We shall always be at the beginning of infinity.

Outside our parochial perspective, astrophysics is incomplete without a theory of people, just as it is incomplete without a theory of gravity or nuclear reactions.

Creationism is really creation denial – and so are all those other false explanations.

The observer points at [that domino] and asks with curiosity, ‘How come that domino there is never falling?’

In all those cases, universality was being sought deliberately, as a desirable feature in its own right – even a necessary feature for an idea to be true – and not just as a means of solving a parochial problem.

Error-correction is the beginning of infinity.

If intelligent extraterrestrials had visited Earth at any time during those billion years they would have seen no evidence that the genetic code could specify anything significantly different from the organisms that it had specified when it first appeared.

Thus the very same utterance by the program – the joke – can be either evidence that it is not thinking or evidence that it is thinking depending on the best available explanation of how the program works.

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

So 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.

This is a rare and deadly sort of error: it prevents itself from being undone.

This is rather like the doppelgängers merging with their originals in some phantom-zone stories, except that here we do not need to repeal the principle of the conservation of mass.

In such computations, a quantum computer with only a few hundred qubits could perform far more computations in parallel than there are atoms in the visible universe.

They have been not outweighed, but out-argued, refuted and abandoned.

If a policy is no one’s idea of what will work, then why should it work?

So flowers have to create objective beauty, and insects have to recognize objective beauty.

The best way to seem useful to diverse people under diverse, unpredictable circumstances is to be useful.

The transmission of human-type memes – memes whose meaning is not mostly predefined within the receiver – cannot be other than a creative activity on the part of the receiver.

The horror of static societies, which I described in the previous chapter, can now be seen as a hideous practical joke that the universe played on the human species.

The fact that reliance on specific antibiotics is unsustainable is only an indictment from the point of view of someone who expects a sustainable lifestyle. But in reality there is no such thing. Only progress is sustainable.

Universality implies that, in every important sense, humans and AIs will never be other than equal.

All we can choose is whether it is an infinity of ignorance or of knowledge, wrong or right, death or life.