The Man from the Future

1. Made in Budapest

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2. To Infinity and Beyond

• Von Neumann rigorously defines a class as a collection of sets that share a property. In his theory it is no longer possible to speak meaningfully of either a "set of all sets" or a "class of all classes"; only a "class of all sets". His formulation elegantly avoids the contradictions of Russell's paradox without all the restrictions of type theory. There is no "set of all sets that are not members of themselves" but there is a "class of all sets that are not members of themselves." Crucially, this class is not a member of itself because it is not a set (it's a class!).

3. The Quantum Evangelist

• "Mathematical Foundations of Quantum Mechanics" (1932)
• "We are obliged always to divide the world into two parts, the one being the observed system, the other the observer.
• Quantum entanglement - spooky action at a distance.
• Everett: All the particles in the universe are entwined in a single massive superposition of all possible states, the "universal wave function". Every time a measurement is made, the universe "splits" to create a crop of alternative realities, in which each of the possibilities play out (so Schrodinger's cat is alive in one universe and dead in another. Or in several.)
• Most physicists now believe that there is no instantaneous wave function collapse. instead, the wave function "decays" in a small but finite amount of time into a classical state through a process called "decoherence". Another point of view, "spontaneous collapse" posits that wave function collapse occurs on a time scale that is inversely related to the size of the object in question. The wave function of an electron may not collapse for 100m years, but a cat's would collapse almost instantly.

4. Project Y and the Super

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5. The Convoluted Birth of the Modern Computer

• "First Draft of a Report on the EDVAC" (1945) would become the most influential document in the history of computing, listing five distinct parts or organs of the von Neumann architecture:
  • A central arithmetic unit
  • A central control unit
  • A memory
  • Input (sensory neuron ) units
  • Output (motor neuron) units
• In 1930, Gödel had written a computer program long before any machine capable of running it would exist. He had dissolved in one fell swoop the rigid distinction between syntax and data.
• Words coding the orders are handled in the memory just like numbers. That is the essence of modern-day coding

6. A Theory of Games

• "On the Theory of Parlor Games" (1926) - Proof of the minimax theorem, established game theory as a discipline, framing human cooperation and conflict in mathematical terms.
• Utility scores (utils) - To calibrate a utility scale, pick a pair of events, your most feared calamity (0 utils) and the most marvelous experience you can realistically imagine (100 utils). In between are all the intermediate payoffs, giving a rigorous way to assign numbers to nebulous human desires and predilictions. The most important theory in the social sciences according to Daniel Kahneman.
• Chess and tic-tac-toe are games of "perfect information" with all moves visible to both players, and all two-player, zero-sum games of perfect information have a solution, as long as the game does not go on forever. They must end in a wind or a draw and, critically, there is always only one optimal move for each player at each node of the game tree.
• "If the theory of Chess were really fully known there would be nothing left to play."
• von Neumann "solves" Sherlock Holmes' "impossible problem" and "proves" that Moriarty's optimal strategy is to take the fast train to Dover (60%), while Holmes' strategy is to get out at Canterbury (60%).
• Poker is in many ways "the" game of imperfect information - von Neumann determines that the minimax strategy for both players is, naturally, to bid high with a good hand, and to bid low most of the time when they have a poor hand, with the occasional high bid.
• The point of bluffing is not so much that you might win with a bad hand, as that you want to encourage the opposition to bet with middle-range hands when you have a good hand.
• Price and Maynard-Smith use game theory to define an "evolutionarily stable strategy" for different species to comingle in an environment (Hawk-Dove game)
• Prisoner's dilemma - The logical outcome is a bad deal for everyone.

7. The Think Tank by the Sea

• The RAND corporation ran game theory simulations of duels, where each player wanted to get the best shot by holding off firing as long as possible - but sooner than their opponent.
• Shapley values - The best payouts each player can get from a game
• Gale-Shapley deferred acceptance algorithm - for matching applicants to colleges.
• Nash equilibria - In any type of game with any number of players there are certain outcomes in which no player can do any better by unilaterally changing their strategy.
• It is arguably Nash's conception of game-theory that more closely embodies the kill-or-be-killed paranoia of the early Cold War.
• The Cold War came to be seen by many as the ultimate game that game theory was meant to analyze.
• Operations research was a science of the possible: what can be achieved with the equipment and supplies available? Systems analysis, by contrast, was goal-oriented - what future weapons and strategies would be necessary to a specified mission? With its tacit commitment to considering every "rational" eventuality, systems analysis is almost megalomaniac in its ambition.
• The Russians got to ICBMs first, in 1957. The first US Atlas rocket launched in 1958

8. The Rise of the Replicators

• "Theory of Self-Reproducing Automata" (1966). These machines need:
  • A set of instructions that describe how to build another like them.
  • A construction unit that can build a new automaton by executing these instructions.
  • A unit to copy the instructions and insert them into the new machine
• These requirements predate and foresee the mechanism of DNA and cell replication
• Dyson: "So far as we know, the basic design of every microorganism larger than a virus is precisely as von Neumann said it should be."
• Conway's game of "Life" with blinkers, oscillators, R-pentominos, and gliders.
• Wolfram's "A New Kind of Science". Cellular automata are defined by rules and divided into four classes:
  • Class I (including rule 0 or 255) - Rapidly converge to a uniform final state no matter what the initial input.
  • Class 2 - May end up in one of a number of states. The final patterns are all either stable or repeat themselves every few steps; like the fractal produce by rule 90
  • Class 3 (including rule 30) - Show essentially random behavior.
  • Class 4 (including rule 110) - Produce disordered patterns punctuated by regular structures that move and interact. This class is home to all cellular automata capable of supporting universal computation.
• Barricelli - Believed in symbiogenesis, in which two different organisms work so closely together that they effectively merge into a single, more complex creature, and in which genes themselves were originally virus-like organisms that had, in the past, combined and paved the way to complex, multi-cellular organisms. Symbiogenesis is now the leading explanation of how plant and animal cells arose from simpler, prokaryotic organisms.
• Langton: "The ultimate goal is to extract the logical form of living systems" from artificial life experiments. His experiments include "loops" which reproduce outward like a coral reef. He proposed a lambda parameter:
  • Near to zero - Information is frozen in repetitive patterns, like class 1 and 2 automata.
  • Near to one - Information moves too freely for any kind of meaningful computation to occur (like class 3)
  • Class 4 automata are poised at a value of lambda that allows information to be both stably stored and transmitted. All of life is balanced on that knife edge, below which the process of synthesis is degenerative but above which, it can become explosive.
• Venter - Has copied gneomes into new cells and created a new life form "Synthia".
• von Neumann probes are self-replicating machines sent into space to harvest materials and maybe support human migration.
• Laing - Showed that an automaton need not start with a complete description of itself if it is equipped with the means to inspect itself.
• Nanotechnology - The word is coined by Drexler in "Engines of Creation"
• Gray goo - An apocalyptic scenario where dangerous replicators escape from a lab: "they could spread like blowing pollen, replicate swiftly, and reduce the biosphere to dust in a matter of days."
• A brain must build itself from the boom up without a blueprint. The several billion base-paris-worth of data held by chomosomes inside every human cell are not sufficient to describe the brain (or any complex organ) by themselves. A neuron must interact with other neurons through some set of rules that allow the brain's incredible organization to grow from simple beginnings in the womb. This makes them in some ways kin to cellular automata
• McCarthy coined the term "artificial intelligence".
• "The Computer and the Brain"
• Teller: "To most people thinking is painful. Some of us are addicted to thinking. Some of us find it a necessity. Johnny enjoyed it. I even have the suspicion that he enjoyed practically nothing else.
• Klari: "I would like to tell about the man, the strange contradictory and controversial person; childish and good-humored, sophisticated and savage, brilliantly clever yet with a very limited, almost primitive lack of ability to handle his emotions - an enigma of nature that will have to remain unsolved.