TB: The Beginning of Infinity (Deutsch)

Core Thesis

All progress — theoretical and practical — comes from creating better explanations. This is both uniquely human and a fundamental fact about reality at the most impersonal cosmic level; the connection between the cosmic and the human is a hint of the central role of people in the scheme of things. Good explanations are hard to vary while still accounting for the phenomena they explain. Bad explanations are easy to vary — and therefore useless even when testable. The quest for good explanations is unlimited: progress has no end, only an ongoing beginning of infinity. Three assumptions underpin the book: there are no contradictions in reality, the world is fundamentally explicable (all regularities have explanations; nothing is supernatural), and our brains are universal computers.

Key Takeaways

Good explanations vs. bad explanations

  • A good explanation is hard to vary. The hardness of varying it is precisely what makes it powerful; the harder a good explanation is to find, the harder it is to vary once found.
  • A bad explanation can be adjusted to accommodate any evidence (the ancient myth of the seasons) — it is therefore useless even if testable, because experimental testing is almost useless for correcting its errors.
  • The criterion for reality: a particular thing is real if and only if it figures in our best explanation of something. Abstract entities can be real and can cause physical phenomena.
  • Most scientific progress is not driven by testing or refuting theories; it is driven by seeking better explanations. Occam's razor is one way to strip arbitrariness from a bad explanation.
  • A problem is a situation of conflicting ideas; since reality has no contradictions, every problem signals that our knowledge is flawed.

Fallibilism — the engine of knowledge growth

  • Scientific theories are not derived from experience — they are guesses, bold conjectures. Experience is needed to choose among guesses already made, not to generate them. First understood by Popper.
  • Empiricism was a great step forward but set up two false authorities: "raw" sensory experience and "induction" from it.
  • What is needed for sustained rapid growth of knowledge is a tradition of criticism. This happened in the Enlightenment, a rebellion against authority over knowledge.
  • Fallibilism — expecting even your best theories to contain misconceptions — is what enables unlimited improvement; mere rejection of authority is not enough.
  • All observation is theory-laden: we perceive nothing as it really is. To "observe" a thing is to accurately attribute evidence (always ultimately inside our brains) to it.
  • Instrumentalism denies that explanation exists at all (still influential in QM). Prediction is not and cannot be the purpose of science.

The cosmic significance of people

  • Humans are Universal Constructors: in principle we can transform anything into anything permitted by physics. The set of possible transformations divides into three: impossible (forbidden by physics), spontaneous, and achievable with sufficient knowledge — and that is all.
  • The biosphere is not a life-support system for humans; it only achieves stability by constantly harming individuals. It is a heap of dangerous raw materials that we have partially converted using knowledge. Biological evolution did not give us enough knowledge to survive.
  • Astrophysics is incomplete without a theory of people: to predict what a star will do you must know whether people are near it and what they know and intend. Knowledge is the only phenomenon whose effects do not fall off with distance.
  • Both Spaceship Earth (we are precariously special) and the Principle of Mediocrity (we are typical) are parochial and mistaken. Mediocrity implies our explanatory ability is parochial, hence the universe is inexplicable — always a bad explanation.
  • Humans and knowledge are the most significant phenomena in nature — the only ones whose behavior cannot be understood without understanding everything of fundamental importance.

The reach of explanations

  • The "reach" of an explanation is its ability to solve problems beyond those it was created to solve.
  • The explanatory conception of science is why we can know about phenomena our senses cannot detect — neutrinos, quasars, the quantum realm.
  • Scientific instruments are conjuring tricks in reverse: they fool our senses into perceiving what is really there. All measurement uses chains of proxies, each correctable only via an explanatory theory.
  • Only explanatory knowledge can be universal; non-explanatory (rule-of-thumb) knowledge like genes is inherently bounded and parochial and cannot cross the conceptual gap that conjecture does.
  • There can be no ultimate explanation: nothing can be explained only in terms of itself, so the deeper an explanation, the more problems it creates.

The Jump to Universality

  • The Jump to Universality: gradually improving systems suddenly leap in functionality and become universal in a domain. Before the jump, specialized tools for each use; after, one customizes/programs a single universal object (spoken languages build words from a finite set of sounds).
  • All universal computers are digital and use error correction. There is no universal analog computer: analog values cannot be error-corrected, and without error correction knowledge growth is bounded. All jumps to universality occur in digital systems.
  • Every known jump to universality was made by humans except one: DNA. The genetic code stopped evolving while still coding only for single-celled organisms, yet has enough reach to describe dinosaurs and humans — we don't know why.
  • AI must be possible because a universal computer is a universal simulator. But AGI has made no real progress because of an unsolved philosophical problem: we don't understand how creativity works. "If you can't program it, you don't understand it." Against AI supremacy: humans and AIs are both universal explainers and so will always be, in every important sense, equal.

Infinity, finitism, and orders of infinity

  • Mathematicians long ago showed one can work consistently with infinity. Finitism (only finite abstract entities exist) is instrumentalism applied to mathematics — a principled rejection of explanation that must deny the law of the excluded middle.
  • The universality of reason: every branch of inquiry has limits, but there is no bound on reason itself; believing otherwise is equivalent to believing in the supernatural. The best explanation of anything eventually involves universality, and therefore infinity.
  • There are uncountably many orders of infinity. The attributes "probable," "typical," "rare" have no meaning when comparing infinite sets — bad news for anthropic arguments, none of which supply a measure.

Computation, proof, and the math–physics link

  • The set of all functions is uncountable while the set of all programs is only countable, so almost all mathematical truths have no proof — they are unprovable, and most statements are undecidable (all undecidable statements concern infinite sets).
  • Undecidable questions are distinguished by physics, not mathematics. A computation or proof is a physical process in which objects (brains, computers) physically model abstract entities. The proposition is independent of physics; the proof is a matter of physics only. Proof theory is therefore a science (computer science), not a branch of mathematics.
  • The point of mathematics is to understand abstract entities; proof is like observation — a way of ruling out false explanations. Seeking a perfectly secure foundation is justificationism.
  • The laws of physics are fine-tuned for computation, prediction, and explanation: if they depended on non-computable functions (most are) we could not predict and could not exist. This is "the unreasonable effectiveness of mathematics."
  • P ≠ NP: some answers are easy to verify but cannot be computed easily. Conjecture: if a problem is interesting, it is soluble — and inherently insoluble problems are inherently uninteresting.

The multiverse, many-worlds, and quantum computing

  • Quantum theory is the deepest explanation known to science, yet the many-universes interpretation remains a minority view even though many phenomena have no other explanation.
  • Fungibility: identical entities (amounts of energy classically; elementary particles in QM) are identical in every way except that there are two of them. Counter-intuitively, fungible objects can become different under deterministic, symmetrical laws — this is at the heart of quantum physics.
  • Apparent randomness in QM is the third kind of unpredictability: initially fungible instances of an observer becoming different. The multiverse is deterministic. Histories can rejoin and become fungible again — interference — and the need to explain interference is the main argument that the multiverse is real (the Mach–Zehnder interferometer; quantum computation depends on different histories of the same atoms).
  • The only way for physics to be simultaneously universal, deterministic, and forbid faster-than-light communication is to have multiple universes. Different times are special cases of different universes; time is an entanglement phenomenon.
  • "Bad philosophy" (philosophy that actively prevents the growth of knowledge) reigned over QM for decades — the Copenhagen "collapse" rule of thumb was inconsistent with both Schrödinger's and Heisenberg's theories. Most physicists retreated to instrumentalism rather than improve the explanation.

Bad philosophy: positivism, postmodernism, and "because I say so"

  • "Because I say so" embodies bad philosophy: it explains anything, is about who spoke not what was said, recasts a request for truth as a request for justification, and claims to stand outside criticism.
  • Positivism (Mach) is empiricism taken literally; it led Mach to reject relativity and atoms. Logical positivism (which is not itself observable) and postmodernism (all ideas are arbitrary "narratives") are worse.
  • Bad philosophy is best countered by progress, not by logic or experience: progress makes bad philosophy harder to believe.

Popper, authority, and the problem of communication

  • Popper replaced the question "where does knowledge come from?" with "how can we detect and eliminate error?"
  • We sit imprisoned in the near-sealed cave of our skulls, guessing about the outside world; when we can improve our guesses no longer we have grasped objective truth — and what we understand we can control. Like magic, only real.
  • Communication is inherently fallible guesswork on both sides; misunderstandings are ubiquitous. The way to converge with each other is to converge on the truth.

Arrow's theorem and voting systems

  • Arrow's five axioms each seem essential to a fair, rational system of social preferences, yet they are jointly inconsistent: there is no such thing as "the will of the people." Wishing for the logically impossible signals there is something better to wish for.
  • Popper's criterion: good political institutions make it as easy as possible to detect a bad ruler or policy and remove it without violence. Plurality systems make outcomes sensitive to small shifts in opinion and avoid watered-down compromises (whose failures teach no one anything); proportional representation can hand disproportionate power to the third-largest party. The essence of democracy is the ideas created between elections, not the choice at the ballot box.
  • Decision-making is not selecting from fixed options by a preference formula — its most important element is creating new options.

Objective beauty

  • Aesthetic and moral truths can be linked to physical facts through explanations; facts can criticize aesthetic theories, and artistic problems can emerge from physical situations.
  • Nature often has beautiful explanations, and wrong beautiful explanations are replaced by more beautiful ones — a regularity that must have an explanation.
  • We reliably find flowers beautiful (not roots or leaves), even ones we've never seen. Flower–insect co-evolution required a hard-to-fake signaling code across species; Deutsch's guess is that the easiest way is objective standards of beauty. Beauty comes in two forms: parochial (local to a species or culture) and universal (as objective as the laws of physics); creating universal beauty requires knowledge with universal reach.

Memes and static vs. dynamic societies

  • A culture is a set of closely related (variant) memes producing characteristic behaviors. Genes and memes are both replicators embodying knowledge, but differ enormously above that: DNA is copied indiscriminately and automatically, whereas each meme must be re-expressed as behavior to be copied. Meme evolution is vastly faster — a large fraction of all evolution on Earth has happened as memes in human brains.
  • Rational memes rely on the recipient's critical faculties to replicate; anti-rational memes rely on disabling them. Existing accounts of memes neglect this all-important distinction.
  • Static societies survive only by disabling their members' creativity, leaving them chronically balked; their long-lived memes encode real knowledge of the human condition, which is why their fear of change has truth in it. Primitive societies are an unimaginably bad place to live. Western civilization is in an unstable transition from a static society of anti-rational memes to a dynamic society of rational memes.
  • What replicates human memes is creativity. Creativity first evolved to acquire existing knowledge (to thrive in a static society one must creatively be less innovative than others); because the same mechanism creates new knowledge, selection for acquiring knowledge automatically selected for creating it. "Replicating memes is the function for which creativity evolved — and that is why our species exists."

Optimism, sustainability, and the unknowable future

  • Principle of Optimism: all evils are caused by insufficient knowledge; there is no fundamental barrier to progress. Optimism is a way of explaining failure.
  • The future of civilization is unknowable because the knowledge that will shape it has not yet been created — even the possible outcomes are unknown. Scientific prediction fundamentally fails the moment new knowledge begins to matter.
  • Existential danger is not new: most civilizations in history were destroyed, almost all of which could have been saved by more knowledge, almost none by more caution about innovation. The distinction between "natural" disaster and one caused by ignorance is parochial.
  • On climate: rather than reducing emissions at any cost, we ought to be thinking about how to lower the temperature or thrive cheaply at higher temperatures. The idea that the future can be scientifically planned reliably causes disaster; we need a vibrant research community and the wealth to fund it. Against the Domesday argument: it fails if the total number of humans (or lifetimes) becomes infinite. Illness and old age will likely be cured within a few lifetimes.

Morality

  • "You can't derive an ought from an is" is true, but you can't derive a factual theory from an "is" either. Factual evidence and moral maxims are independent, but factual and moral explanations are not — factual knowledge can criticize moral explanations (scientific success itself commits one to values: truth, good explanations, openness to change).
  • Objective progress is possible in morality and politics just as in science, by seeking good explanations. Good customs: defy anyone who seeks your submission; give a hearing to anyone offering honest criticism.
  • The Moral Imperative — possibly the only one, from which all others follow: do not destroy the means of correcting mistakes.
  • Reductionism and holism are both mistakes: explanations at any level can be fundamental. The growth of knowledge is a continual transition from problems to better problems, not from problems to solutions. Infinite ignorance is a necessary condition for infinite growth of knowledge.

Mental Models

Source note

The Beginning of Infinity (Deutsch)

Backlinks