Some researchers dream of solving all mysteries with a common method—but a mathematical paradox may keep such solutions out of reach
What did you dream of doing when you were 16 years old? I wanted to drive a car and travel the world. But American mathematician Ray Solomonoff had more ambitious goals at that age. He wanted to find a method to solve every conceivable scientific problem.
Solomonoff was looking for a rule that would select the simplest of all possible descriptions. Such a rule could be translated into a computer program. Any data could be passed to this program, and after a certain amount of time, the simplest explanation for the origin of these values could be obtained. It would be a veritable miracle machine.First things first: Solomonoff’s simplest-description finder does not exist—and it never will.
The Kolmogorov complexity thus depends on the programming language used. A certain program might turn out shorter in Python than in C++ and vice versa. Every computer program can be expressed in machine code, which in turn consists of a sequence of 0’s and 1’s. The length of the shortest sequence of 0’s and 1’s for which a computer calculates the desired result corresponds to the Kolmogorov complexity.
But a paradox puts a wrench in the works. Philosopher Bertrand Russell attributed the problem in question to librarian G. G. Berry in 1908 —long before Solomonoff and Kolmogorov published their ideas. An example of Berry’s thought experiment is as follows: Suppose you have a dictionary with just 20 words, and you try to describe different numbers using these words—very similar to what Kolmogorov had in mind with computer programs. You can start to gradually define numbers using these 20 words.
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