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.