Possible vs impossible

Week 3: constructor theory · constructor-theory

Possible vs impossible

Use the possible/impossible dichotomy as a more fundamental ground than initial-conditions+laws.

In this lesson

  1. Read the core idea (2 min).
  2. Walk through one worked example.
  3. Take the 4-question quiz; pass with 4/4 or better.

Hook

Once tasks and constructors are on the table, the central move of constructor theory is to take seriously a dichotomy that orthodox physics keeps in the basement: every task is either possible or impossible according to the laws of physics. Possible means there is some constructor — some physical setup, however contrived — that can perform it with arbitrary reliability. Impossible means the laws forbid such a constructor from existing.

This sounds harmless until you notice what it does. It reframes a law of physics not as a sentence about how things evolve, but as a sentence about which transformations the world will let you accomplish, given enough cleverness. Marletto, in The Science of Can and Can't, calls these the laws of "can and can't."