the beginning of infinity

notes on david deutsch's (fascinating) the beginning of infinity (2011), about infinity & universality, memetics and philosophy of science.


Sep 22, 2021 → Jan 16, 2022

  • "we do not know why the laws of physics seem fine-tuned, why various forms of universality exist, or why the world is explicable. but eventually we shall. And when we do, there will be infinitely more left to explain."
  • "if the question is interesting, the problem is soluble."

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curiosity: thinking existing explanations don't fully capture the ideas behind them, being unsatisfied with current stories.

  • guessing is ∴ the single process thought which all knowledge originates: wonder → guessing → conjecture → speculation, which is vital for discovery.
  • when stories/explanations can't be changed anymore, we have understood objective truth, and, like magic, what we understand we then control.
  • the only path for knowledge creation is then error-correcting → finding good explanations (conjecture+criticism+experiment) = progress.
  • there can ∴ be no aspects of reality beyond our brain's capacity: if (brain capacity==computational speed + memory) we can use the computer, just like we have used pen and paper to understand the world for centuries.

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creativity: ability to create and replicate ideas to increase the amount of usable knowledge.

  • parrots copy sounds, apes copy movements, but humans create: it's (conjecture+criticism+experiment) to form good explanations of other's behaviour and the world → this is creativity.
  • must be an evolutionary process within brains since it depends on conjecture (variation) and criticism (selection).
  • human brains are physical objects that evolved to replicate ideas (Blackmore). thoughts are computations permitted under the laws of nature.

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ideas: information that can be stored in human brains and affects behaviour.

  • knowledge is created by human thought, preserved and transmitted by human culture (not genetically, which is why some humans are able to survive in jungle and others in the arctic)
  • abstract language, explanations, wealth above subsistence and long-range trade gave power to ideas. by the time history began to be recorded, it was the history of ideas.

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culture: set of ideas that cause holders to behave alike.

  • ideas are rarely expressed with the same words and can vary in both written and spoken language. yet, they stay the same idea.
  • if a parrot repeats Aristotle, sound is there but knowledge (replicator) isn't → replicators of ideas are abstract, they're the knowledge itself.
  • reach of ideas in world of abstraction is a property of knowledge they contain. theory can have infinite reach even if person is unaware.
  • for centuries, people have tried to explain the mind in mechanical terms, using metaphors based on the most complex machines of the day (complicated set of gears, hydraulic pipes, steam engines, telephone exchanges, and now, the computer.)
  • but "brain=engine" ≠ "brain=computer": computers are universal simulators. expecting them to behave like neurones is not a metaphor, it's a known proven property of physics and computers

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some aspects of nature (night sky, waterfalls, sunsets) seem to be beautiful to humans but show no signs of being designed with this intention. However, flowers do seem to have an apparent design for beauty.

  • flowers need insects to bring them pollen and insects need flowers to get. how these 2 wildly distinct species evolve to communicate this?
  • flower evolved genes to make their shape attractive to insects, which bring pollen. insects evolved genes that attract them to flowers with the best nectar (most beautiful ones)
  • nature seems to have used beauty to allow these 2 wildly distinct species to communicate.

humans recognizing that flowers are beautiful even though they evolved this way for unrelated purposes is evidence that some beauty is objective: it can be found in all places from the flower's genome to human minds.

  • flowers have to create objective beauty and insects have to recognize objective beauty.
  • beauty then must exist in 2 kinds: subjective(local to species/culture/individuals, parochial) and objective(universal).
  • ⤷ local and subjective/parochial criteria of beauty evolved within a species to produce something that looks beautiful to us.

  • if beauty can be objective like the laws of nature and mathematical theorems, then new works of art must add new knowledge to the world just like scientific theories do.

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optimism: all failures are due to insufficient knowledge.

  • optimism in civilizations has led to mini-enlightenments, traditions of criticisms that lead to patterns of human progress: art, philosophy, science, technology and open institutions.
  • Athen's Golden Age (V. bc): one of firsts democracies. home to Socrates, Plato and Aristotle, the playwrights Aeschylus, Aristophanes, Euripides and Sophocles, and the historians Herodotus, Thucydides and Xenophon.
  • democratic tradition dated back to Thales (6th C. BCE) and Xenophanes (570-480 BCE). Pericles argued (Funeral Oration, 431 BCE) it existed not because people should rule but because it promotes wise action (continual discussion, necessary condition for discovery and progress)
  • Florentine's believe of improving ancient knowledge. began in art, then philosophy, science and technology. led to humanism (knowledge > dogma, intellectual independence, curiosity, taste)
  • progress implies discoveries are inconceivable. dynamic societies are those that expect their knowledge to grow unpredictably.
  • Popper's criterion is met by societies that expect their knowledge to grow unpredictably ∴ he's an optimist, progress implies discoveries are inconceivable.

enlightenment: 1688 (English Enlightenment), inconceivable a century earlier.

  • success at making scientific discoveries implies commitment to values of progress: truth, good explanations, open to ideas and change, tolerance, integrity, openness of debate.
  • necessary condition for progress: change meant new authorities replaced old ones, so tradition of criticism was needed to sustain rapid growth of knowledge.
  • Universal theories of justices, legitimacy and morality began to take place alongside universal theories of matter and motion as philosophers set out to free institutions from arbitrary rules. (Locke→political) universality was now a desirable feature.
  • emergence of methodical rule that scientific theories must be testable, rebellion against authority of knowledge. "problems as soluble and inevitable, progress is attainable and desirable."

static societies: people could expect to die under the same values, lifestyles, technology and patterns of economic production.

  • universality needs appreciation of abstract knowledge for its own/to yield unforeseeable benefits. unnatural in static societies.
  • small populations + parochial knowledge → big ideas are set millennia apart.
  • if way of life leads to more efficient methods of living (farming, medicine...) it is not sustainable → population grows, fewer workers are needed ∴ live the solution and set about solving the new problems it creates. only progress is sustainable.

humans alone are authors of explanatory knowledge, the human behaviour called history.

  • Knowledge alone converts landscapes into resources or prevents improvements (≠Marx, Engels). ideas and not biogeographical explanations account for events: can't explain the fall of the USSR with climate, minerals or flora/fauna.
  • Marx's theory of history was evolutionary and described a progression though historical stages, determined by economic "laws of motion". He used Darwin's theory as a basis for the historical class struggle (biological species ≈ socio-economic classes). Facsist groups use this and other misinterpretations of evolution to justify violence.
  • (presence of gene is always explained as being caused by more replications than rival genes. competition in biological evolution is between variant of genes within a species: can produce violence or cooperation.)

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nature of science can be understood with theories=misconceptions

  • Einstein doesn't correct Newton but is radically different (gravitational force, uniform flow of time in respect to motion). same with Kepler and Newton. each ignores and denies its predecessors' basic means of explaining reality.
  • explanations were never true ∴ successive explanations ≠ growth of knowledge about reality.
  • Einstein's misconception of Gravity was an improvement on Newton's misconception, which was an improvement on Kepler's. neo-Darwinian evolution is an improvement on Darwin's misconception, and his on Lamarck's. No infallibility nor finality.

scientific method: increasingly difficult to ignore philosophical implications of the fact that nature had been understood in unprecedented depth, and of the methods of science and reason by which it was done.

  • perhaps it started with Galileo and became irreversible with newton. (his laws replicated themselves as rational ideas and fidelity was very high as they were so useful)
  • no way of missing rapid that progress was underway after newton. (some like Rousseau tried by arguing reason as harmful, civilization as bad and primitive live as happy).
  • No process can reveal the content and consequences of a discovery before it is made. scientific discovery is ∴ unpredictable but determined by the laws of physics

evolution: optimizes neither good of species or individual, but the relative ability of surviving variants to spread through population. it favours only genes that spread best.

  • peacock's colourful tail: diminishes viability and harder to evade predators but prominent mating ∴ offspring has more prominent tails, ↻.

genetic code as language for organisms has shown phenomenal reach.

  • genes replicate themselves by an indirect chemical route, being templates for similar molecules. evolved to specify organisms without having a nervous system, organs, senses, ability to exert force or move.
  • knowledge embodied in genes describes how to get replicated and functionality is achieved by encoding regularities in environments. complexity ≠ evolutionary adaptation. Darwin crystallized this: random mutations are discarded by natural selection.
  • might not be universal since it relies on specific chemicals (proteins) but could be universal constructor (created from inorganic materials like calcium phosphate in bones, programs organisms to construct outside their bodies: nests, dams, houses...)
  • RNA acts as the program which directs the synthesis of enzymes (catalysts, promotes change to other chemicals while remaining unchanged itself) catalysts control all chemical production and regulatory functions of an organism ∴ ≔ organism itself.

evolution of biological adaptations and creation of human knowledge are similar (ideas and genes are replicators, knowledge and adaptation hard to vary) yet distinct (human knowledge as explanatory and with reach, contrary to adaptations.)

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quantum physics

quantum theory discovered independently by Heisenberg and Schrödinger between 1935 and 1927.

  • Heisenberg: physical variables of a particle are matrices, not values. we now know multiplicity of information is due because a variable has different values for different instances of the object in the multiverse.
  • Heisenberg uncertainty principle: for any fungible collection of instances of a physical object, some of their attributes must be diverse.
  • Schrödinger: mathematical equations that describes a single wave moving in a higher-dimensional space, when applied to an individual particle.
  • Bohr: Copenhagen interpretation, quantum theory as the complete description of reality and only outcomes of observations count as phenomena, they can't exist objectively.
    • proposed the principle of complementarity: phenomena can only be stated in classical language, anthropocentric language, meaning that the transition is caused by human consciousness ∴ acting at a fundamental level in physics.
    • Nothing is ever derived from observation: Mach (positivist), influenced Einstein to eliminate untested assumption from physics, including Newton's idea the time flows at the same rate for all observers.
    • Einstein soon rejected positivism in favour of realism, which explains why he never accepted the Copenhagen interpretation.

issue: not consistent when applied to the case of an observer performing quantum measurements on another observer.

  • classical physics measures change in quantifiable quantities, quantum physics measures change in discrete variables and their proportions.
  • new type of motion, information flow and structure of the physical world: all objects contain information about which instances of it can interact with instances of other objects and different times are special cases of different universes → time is an entanglement phenomenon which places all equal clock readings into the same history.

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history of computers

  • → calculations used to be done by clerks called "computers".

computational universality should have happened with Babbage's Difference Engine (1820s), which had rules of arithmetic built into hardware to to automate log, cos, sin (used in navigation and engineering).

  • Lovelace argued that The Analytical Engine has no pretensions whatever to originate anything. It can do whatever we know how to order it to perform. can follow analysis but no power of anticipating any analytical truths. Alan Turing called this mistake ‘Lady Lovelace’s objection’. Lovelace failed to appreciate not computational universality, but the universality of the laws of physics.
  • addition of memory and control over which cards to read next (Analytical Engine) → jump to universality.

193# electrical relays for the analytical engine were just being used for the first applications of electromagnetism and were about to be mass produced for the telegraphy revolution.

Turing Test: The general-purpose sense of Intelligence that Turing meant (constellation of attributes of the human mind) puzzled philosophers for a millennia. (others are consciousness, free will and meaning).

  • requiring a program to pretend to be human is biased and not relevant to know whether it can think, but it is easy to identify it as a computer if it doesn't.
  • if it can be programmed, it has nothing to do with intelligence –in Turing's sense (can't program it → haven't understood it.)
  • 1936: Turing develops his definitive theory of universal classical computer. His intention is to use the theory to study the nature of mathematical proof, not universality. The development of the first universal computers was for wartime applications.
  • Colossus (🇬🇧, Turing): code breaking → dismantled.
  • ENIAC (🇺🇸): equations -> universality (weather, h-bomb forecast)
  • the early telegraph system, even before the computer, did create an internet-like phenomenon among the operators, with ‘hackers, on-line romances and weddings, chat-rooms, flame wars... and so on’.
  • 1970s: Electronic technology has been miniaturized since WW2, this led to a jump to universality with silicon chips.
  • From then on, designers start with a microprocessor and program it to do specific tasks: washing machines are controlled by a computer that could be programmed to do astrophysics or word processing with enough memory.

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

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