Can we define randomness by the length of a computer program?
In short: Kolmogorov Complexity offers a precise way to measure randomness by looking at how much a piece of information can be compressed. This video explains the concept and uses it to provide a unique proof for the existence of infinite prime numbers.
Kolmogorov Complexity is defined as the length of the shortest possible computer program required to produce a specific string of data. If a string cannot be significantly shortened into a program, it is considered Kolmogorov random, or incompressible. This means the shortest program to output the string is essentially as long as the string itself.
The video uses this framework to explore mathematical properties, specifically providing a proof that there are infinitely many prime numbers. By understanding the relationship between information length and complexity, we can derive fundamental truths about number theory.
Opens the Intellect+ feed with this card first. Swipe up for the next one.
Sources
- Summary by Intellect · source: Intro to Kolmogorov Complexity
To cite this card, link to https://intellectplus.co.uk/app/science-intro-to-kolmogorov-complexity.
How we source, check and correct cards: Editorial standards.
General information, not professional advice. Spotted an error? Flag the card or see corrections and complaints.
Intellect Plus is a visual educational discovery platform for exploring fascinating facts and ideas. Brain Food, Not Brain Rot. What is Intellect Plus?
Related
More in Science · Latest · A–Z · All topics
