A Few Notes on Multiple Theories and Conceptual Jump Size

These are a few notes about some of Ray Solomonoff’s foundational work in algorithmic probability, focussing on the universal prior and conceptual jump size, including a few illustrations of how he thought. His induction theory uses Bayes rule to measure and compare the likelihood of different theories describing observations. Can we find good theories? Lsearch is a very good way to search and the conceptual jump size is a measure for this. 1 Understanding and Learning 1. Ray taking apart a scooter. 2. Working on the house he built. 3. An “experiment” (Ray is on the right). The first thing Ray did when he acquired something was to take it apart. Here’s a picture of Ray taking apart a scooter he found in the trash. He took many notes. They were like a program, so that the scooter could be remade. Ray built a house from descriptions in a book, like a recipe. What was made in Ray’s lab in the cellar? Ray [Sol97] wrote: My earliest contact with modern scientific philosophy may have been P.W. Bridgman’s [Bri27] concept of “operational definition”. An operational definition of anything is a precise sequence of physical operations that enable one to either construct it or identify it with certainty.