Shannon's Information Theory

June 9, 2020

Shannon’s theory of information is usually just called information theory, but is it deserving of that title? Does Shannon’s theory completely capture every possible meaning of the word information? In the grand quests to creating AI and understanding the rules of the universe (i.e. grand unified theory) information may be key. Intelligent agents search for information and manipulate it. Particle interactions in physics may be viewed as information transfer. The physics of information may be key to interpreting quantum mechanics and resolving the measurement problem. If you endeavor to answer these hard questions, it is prudent to understand existing so-called theories of information so you can evaluate whether they are powerful enough and to take inspiration from them. Shannon’s information theory is a hard nut to crack. Hopefully this primer gets you far enough along to be able to read a textbook like Elements of Information Theory. At the end I start to explore the question of whether Shannon’s theory is a complete theory of information, and where it might be lacking. This post is long. That is because Shannon’s information theory is a framework of thought. That framework has a vocabulary which is needed to appreciate the whole. I attempt to gradually build up this vocabulary, stopping along the way to build intuition. With this vocabulary in hand, you will be ready to explore the big questions at the end of this post. …

Visualizing Quantum Field States

January 10, 2020