← Archive

David Deutsch / The Beginning of Infinity / An instrument

Hard to Vary

There is a test that separates knowledge from a story that merely fits. It is not evidence, and it is not consensus. It is this: how much of the explanation could you change and have it still explain the thing?

Instrument I — The variation test

Click any underlined phrase to change it

Two explanations of the same fact: the earth gets cold for part of every year. Both were believed. Both fit. Start swapping parts out of each and watch what happens.

Explanation A Greece, c. 700 BC

Still explains winter Parts changed: 0 · Broken: 0
    Nothing has broken yet. Nothing will.
    Explanation B Established, 17th c.

    Still explains winter Parts changed: 0 · Broken: 0
      Intact. Change one word and it will start contradicting the sky.

      The myth is not wrong because it involves gods. It is worthless because it is unconstrained — every part of it can be replaced by something else that explains winter equally well, which means none of its parts are doing any explaining at all. The tilt account has almost no free parts. That is not a weakness. That is the entire reason it counts as knowledge.

      I

      The criterion nobody taught you

      You were probably taught that science works by evidence: gather observations, and the true theory emerges from them. It doesn't work, and Deutsch's opening move is to show you why with the seasons.

      Both explanations above fit every observation available in ancient Greece. Every one. The myth predicts cold winters, warm summers, an annual cycle, and it does so with total accuracy for the entire Mediterranean. Evidence could not separate them — because a bad explanation can be adjusted to fit any evidence at all. That is what makes it bad.

      The thing that separates them is structural, and you can check it from your armchair before a single measurement arrives. A good explanation is hard to vary while still accounting for what it accounts for. Every component is load-bearing. Pull one out and the whole thing stops working.

      The ease of variability is the sign of a bad explanation. Ch. 1 — The Reach of Explanations

      Now run that test over the things you actually believe — about markets, about people, about why last year went the way it did. Most of them are Persephone. They fit, they feel explanatory, and every part of them could be swapped for something else without losing a thing.

      II

      Knowledge does not come from observation

      The story where you watch the world carefully and the truth accumulates is called induction, and Deutsch's position — Karl Popper's before him — is that it has never once happened. Not in any laboratory, not in any human head. It is not a slow method. It is not a method.

      You cannot start from observations because there is no such thing as an observation without a theory already in it. Something has to tell you which of the infinite facts in front of you is worth writing down. That something is a conjecture you already had.

      What actually happens is this:

      01 Problem A conflict between what you expected and what happened. Everything starts here — never with data.
      02 Conjecture A guess at the explanation. Creative, unjustified, and allowed to be wild. Where it came from is irrelevant.
      03 Criticism Attack it. Look for internal contradiction, for a variant that works as well, for the observation that would kill it.
      04  →  back to 01 A better problem Success is not arriving at truth. Success is that the problem you now have is more interesting than the one you started with.

      There is no arrow here from "observations." Experiment enters only at step 03, and only as a way of killing things. It never generates the conjecture. This is why a room full of data produces nothing without someone in it willing to guess.

      Two consequences follow, and both are uncomfortable.

      Every one of your beliefs is a conjecture. There is no foundation underneath, no source of certainty — not the senses, not authority, not the data. This is fallibilism, and it is not the same as saying all views are equal. Some conjectures have survived enormous criticism and some have survived none, and telling the difference is the whole job.

      Errors are not the failure mode. Errors are the medium. A system that expects to be right is fragile. A system built to find and correct its own errors compounds. The question worth asking about any process you run — a method, a business, a book of trades — is never is it correct. It is how fast does it find out when it isn't.

      III

      Reach: the part you can't take credit for

      Here is the strangest fact in the book. When you find a genuinely good explanation of a small thing, it turns out to explain enormous numbers of other things you were not thinking about and could not have anticipated.

      This is reach, and it is unearned. Nobody put it in. It arrives because a good explanation is about what is really out there, and what is really out there does not stop at the edges of your problem.

      ExplanationBuilt to solveReached, unasked, to
      Newtonian
      gravitation
      Why planets trace the orbits Kepler measured Tides. The shape of the Earth. An unseen eighth planet, calculated from wobbles in the seventh and found where the arithmetic said it would be. Every trajectory ever flown.
      Quantum
      theory
      Why hot objects don't radiate infinite energy The whole of chemistry. Semiconductors. The transistor. And then, decades later, a new theory of what computation itself is.
      The genetic
      code
      Nothing. It was designed by no one, for no purpose. Every organism that has ever lived, in one shared alphabet — including organisms it never encountered, on a planet it never anticipated changing.
      Axial tilt Why Greece is cold in January That when Greece is cold, the antipodes must be hot. Nobody in Greece had been there. The explanation knew anyway.

      Reach is the strongest signal available to you that you have touched something real rather than curve-fitted something local. A model that only ever explains the cases it was tuned on has told you about your tuning. A model that starts answering questions you never posed to it has told you about the world.

      Instrument II — The jump to universality

      Drag to change the number

      Three systems for writing down a number. Two of them were the state of the art for millennia. One of them, by an accident of design, has no upper limit at all — and it costs no more to build.

      The number to be written 1080atoms in the observable universe
      Tally marks — one stroke, one thing
      Roman numerals — seven symbols, additive
      Positional decimal — ten symbols, and a zero

      Roman numerals do not get worse as the number grows. They stop. Past 3,999 the classical system has no representation at all — there is no symbol, and adding one only moves the wall. Positional notation has no wall, and its inventors were not reaching for one. They wanted to keep accounts. What they built can address every atom in the universe using eighty-one marks and a rule a child learns in an afternoon.

      IV

      Nothing approaches infinity gradually

      That wall is the shape of the whole pattern. Systems built for a small, parochial purpose keep hitting limits — and then one of them, without anyone intending it, crosses a threshold and becomes unlimited.

      It has happened at least four times. An alphabet: invented to write one language, and it turns out to write every sound a human can make, including in languages that did not exist yet. Movable type. Babbage's engine, designed to grind out navigation tables, whose design was universal for computation and its author had no way to know. And, four billion years ago, a molecular code that started copying and could in principle encode any organism whatsoever.

      The jump is never gradual, and it is never anticipated by the people making it. They were solving something small. They over-built by one component, and the system fell through into infinity.

      Universality can be attained by adding a small improvement to a system that already had a lot of reach. Ch. 6 — The Jump to Universality

      And there is one more universal system in the list, which is the reason any of this matters to you. People. Not a species that is good at a wide range of things — a species that is a universal explainer, capable in principle of understanding anything that can be understood and building anything the laws of physics permit. There is no category of phenomenon that is closed to us by our design. That is a claim about physics, not a compliment.

      V

      The Earth is not your life-support system

      Deutsch's most disorienting chapter takes the phrase "Spaceship Earth" and inverts it completely.

      The image is of a planet that supports us, a delicate biosphere providing what we need, which we are damaging. Every part of that is backwards. Take a modern human and put them in the Great Rift Valley — the place our species is best adapted to, where we evolved, the ancestral home — and they die. Quickly. That environment supported a few tens of thousands of hunter-gatherers living at the edge of extinction, and it did nothing to support them; they survived it using knowledge, and barely.

      Deutsch's own Oxfordshire would kill him unaided within days. It sustains him because of clothing, agriculture, buildings, refrigeration, antibiotics, sewerage — knowledge, all of it, none of it native. The biosphere does not support human life. Human life supports itself, on hostile ground, using explanations.

      The Earth's biosphere is incapable of supporting human life. Ch. 3 — The Spark

      Which makes "sustainability" a category error when it is offered as the goal. No way of life has ever been sustainable, because problems keep arriving — an ice age, a pathogen, a rock from orbit — and a static way of life has, by construction, no means of generating the solution. Every static society in history eventually met a problem it could not solve and ended. The only thing that has ever actually sustained anyone is the continued rapid creation of new knowledge, which is inherently unpredictable and cannot be planned.

      Stephen Hawking once described humans as "chemical scum on a moderate-sized planet, orbiting a very average star." Deutsch's answer is the book's spine: exactly backwards. In a universe that is almost entirely inert, the rarest and most consequential thing that exists is a system that generates explanations — because there is no bound on what it can eventually know or do. Astrophysically we are a rounding error. In the only ranking that tracks causal significance, we are the interesting part.

      VI

      Why good ideas lose to bad ones

      If knowledge grows by criticism, the obvious question is why it almost never did. For most of human history, nothing changed for centuries at a stretch. That stasis was not an absence of clever people. It was an achievement — actively maintained, and very hard to build.

      Deutsch's account is about which ideas survive. An idea can be transmitted down generations in two entirely different ways. It can be useful and true, so people keep it because it works. Or it can be structured to disable the recipient's ability to evaluate it — and that second kind spreads without needing to be true at all.

      Static society

      • Ideas survive by suppressing criticism. Doubt is punished, often by people who love you.
      • Behaviour is uniform across a lifetime and across generations. Nothing anyone does is novel.
      • Creativity still exists — it is spent entirely on conforming more precisely.
      • It feels correct from the inside. There is no vantage point within it from which it looks like a trap.
      • It ends when a problem arrives that the inherited knowledge cannot solve. This always eventually happens.

      Dynamic society

      • Ideas survive by being useful to the person holding them, which means they have to withstand being questioned.
      • Criticism is institutionalised — built into the machinery, not dependent on anyone's courage.
      • Change is rapid enough that a lifetime contains several worlds.
      • It feels unstable from the inside. That is the correct feeling and it is not a warning.
      • It survives new problems — not by having predicted them, but by generating solutions faster than problems accumulate.

      The Enlightenment, on this reading, was not the discovery of a set of facts. It was a rebellion against the authority of received knowledge, and its content was almost nothing: we do not know, but we can find out. It is roughly four centuries old, it has failed and been extinguished before, and it is not guaranteed to continue.

      The test for an anti-rational idea is worth carrying with you, because they are not rare and they do not announce themselves. Ask: does this idea make me better at judging ideas, or worse? Anything that arrives with a reason you shouldn't examine it — that questioning it is disloyal, naive, dangerous, or beneath you — has told you its category.

      Problems are inevitable.

      Problems are soluble.

      David Deutsch — Ch. 3

      Two lines that have to be held together. Drop the first and you get utopianism, which shatters on contact. Drop the second and you get resignation, which is a self-fulfilling forecast. Held together they describe a permanent condition: there is no final state, no arrival, no end of trouble — and no problem in front of you that the right knowledge could not dissolve.

      VII

      Optimism is not a mood

      Deutsch means something technical by optimism and it is worth getting precise, because the word has been ruined by people using it to mean cheerfulness.

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

      That is a claim about causation. Not that things will go well — they frequently won't. Not that we will solve any particular problem in time — we may not, and failure is real and permanent for the people it lands on. The claim is narrower and stranger: every failure, examined closely enough, turns out to be a failure to have known something in time. There is no category of misfortune that is simply built into reality and immune to being understood.

      Everything that is not forbidden by laws of nature is achievable, given the right knowledge. Ch. 3 — The Spark

      Which is why optimism in this sense forbids prophecy in both directions. You cannot predict the future growth of knowledge, because to predict the content of a future discovery is to have made it. So confident forecasts of doom and confident forecasts of triumph are the same error wearing different clothes: both claim to know what will be known.

      What survives is a rule for the present. When something fails, the question is not who was at fault or was this fated. It is: what would we have needed to know? Every other framing ends the inquiry. That one continues it.

      Terms of art

      TermWhat Deutsch meansWhere it bites
      FallibilismAll knowledge is conjectural. There is no source of certainty — not the senses, not authority, not data.It is not relativism. Conjectures differ enormously in quality, and grading them is the work.
      ReachA good explanation solves problems far beyond the one it was invented for.Unearned reach is your best evidence you found something real rather than fitted something local.
      UniversalityA system built for a narrow job crosses a threshold and becomes unlimited.The jump is discrete. Nothing approaches infinity gradually — you are either below the wall or past it.
      ParochialismMistaking your local conditions for the general case.Undetectable from inside, by definition. Only a better explanation reveals it, never more of the same data.
      Anti-rational
      meme
      An idea that survives by disabling its holder's capacity to criticise it.It feels exactly like conviction. Truth is not required for it to spread, and often gets in the way.
      Bad
      philosophy
      Philosophy that actively obstructs the growth of knowledge."Don't ask what it means, just use the formula" is a philosophical position, and it has a body count in lost decades.
      The Principle
      of Optimism
      All evils are caused by insufficient knowledge.A claim about causes, not a forecast. It converts every failure into a specification for what was missing.

      Instrument III — Turn it on one of your own

      Stays on this device

      The test only does anything if you point it at something you actually believe and would defend. Pick one — about a market, a person, your own last bad year. Then answer honestly, which is harder than it sounds, because the whole point is to find out that you were holding a myth.

      State it the way you'd say it out loud, not the defensible version.
      Change a mechanism, a cause, an actor. If you find one easily, that part was never explaining anything.
      Something specific and checkable. If nothing comes, the belief is compatible with every outcome, which means it forbids nothing.
      Reach. Anything it accounts for that you weren't thinking about when you formed it.

      Readout

      Awaiting a belief.

      Fill in the first box to start. The reading updates as you type.

      This is a mirror, not a judge. Nothing here is read, scored, or sent anywhere — the verdict is assembled from which boxes you could fill and which you couldn't, and that pattern is the finding. If box 02 came easily and box 03 came hard, you already have your answer.

      The title is not a description of the universe. It is a description of where you are standing.

      Everything before the Enlightenment was the era in which explanation was parochial, criticism was fatal, and the total stock of human knowledge was roughly constant across a life. That era ended recently and unevenly, and it is not obvious it will stay ended.

      What replaced it has no known terminus. Not because progress is guaranteed — nothing is guaranteed, and the entire mechanism can be switched off by a sufficiently confident society. But because there is no discoverable point at which explanation runs out, no last problem, no final theory that closes the subject. Every solution is going to reveal problems that could not have been stated before it existed.

      Which means the honest posture is not that we know a great deal. It is that we know almost nothing, we are the first few centuries into a process with no ceiling, and the limiting factor has never once been the universe's willingness to be understood.

      We are only just beginning. Ch. 18 — The Beginning

      Go back to Instrument III. The belief you typed in is one of a few hundred you are running right now, most of which you have never looked at directly. Some of them are load-bearing and some of them are Persephone, and the only way to tell is the same test either way.