Abstract
How do physicists discover the physics of their world?

Consider a very simple world in which some physical process - a deterministic algorithm - generates a sequence of integers. The physicists in this world can see the integers as they are generated one after the other. Their goal is to determine the algorithm, which encodes the physics of their world.

Think of physics as a game. A fixed but unknown deterministic algorithm generates an infinite sequence of numbers. The first person to correctly guess an algorithm that generates those numbers wins the game.

For example, the sequence might be
2, 11, 3, 111, 4, 1111, .... What comes next?
or
1, 2, 1, 2, 3, 2, 1, 2, 3, 4, 3, 2, 1, 2, ..... What comes next?
or
1, 1, 4, 1, 9, 2, 16, 3, 25, 5, 36, 8, 49, 13, 64, 21.... What comes next?

The Sloane Encyclopedia of Integer Sequences documents roughly 150,000 such sequences (worlds) that have been described in mathematics, combinatorics, computer science, physics, chemistry,... scientific and engineering books and journals. The encyclopedia can be used to investigate questions such as

Q: How many well-formed parenthesis strings are there of any given length?

A:
For n odd, answer is 0.
For n = 2, answer is 1: ( )
For n = 4, answer is 2: ( ( ) ), ( ) ( )
For n = 6, answer is 5: ( ( ( ) ) ), ( ) ( ( ) ), ( ( ) ) ( ), ( ) ( ) ( ), ( ( ) ( ) )
For n = 8, answer is ......

This talk will show the uses of Sloane's encyclopedia and discuss our work in creating a robotic physicist to infer those algorithmically generated sequences that arise in practice.

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