Counterintuition

Not everything is as it appears at first glance.

Socrates’ whole shtick was based on demonstrating that much, most, or even all of what we think we “know” is hardly knowledge at all, and that it is often surprisingly easy to find a path to contradiction or absurdity even when starting from very basic and obvious-seeming assumptions or principles.

A great deal can be learned from those moments where your intuition failed you and your first instinct pointed in the wrong direction. On that note, here’s a (quite far from comprehensive) collection of a few concepts worthy of the “surprising” label.

In Math…

• Some infinities are larger than others
• e^iπ = -1
• “a pea can be chopped up and reassembled into the Sun”
• Finite volume, infinite surface area objects are mathematically coherent
• Godel made math “eat itself”; language can speak to the limits of language
• All horses are the same color and induction is broken (no, not really)
• There are numbers with number theoretical relevance that are too big for the observable universe to even express
• Hercules cannot lose the hydra game
• Imaginary numbers are useful; in fact, i has been called “the most important single invention of mathematics”
• A well-shuffled deck of cards produces an arrangement of cards never before seen in the universe. The number of possible deck-orderings (52!) is mind-bogglingly large.
• In practice, you only really need ~38 digits of pi
• 18 point problem^[1]

In Bitcoin…

• More energy consumption is good, not bad
  • Energy Beacon
  • Bitcoin’s Energy Consumption: A shift in perspective
  • The Anatomy of Proof-of-Work
• Making proof-of-work secondarily useful is bad^[1]
  • Andreas Antonopoulos’ speech
  • Security Through Purity
• Sometimes your greatest strengths can backfire
  • Nakamoto Rationality
  • Innovation Slipstream
• A stable store of value might look really volatile for a while
• Bitcoin-based exchanges may not have Bitcoin’s best interests at heart
• The ability to “do more” at the base layer isn’t necessarily a good thing

Elsewhere…

• Identity ain’t so easy
• Free will
• Relativity
• The “Problem” of Evil
• Information is physical
• The 3 Gods riddle is solvable

In this surprise-filled world, then, perhaps a healthy dollop of humility is in order. May each of us, with grace, remember that we are error-prone beings who are all-too-wrong about oh-so-many things, and in so remembering be better prepared to adjust our mental models to accommodate, learn, and grow along our way.