Audio note: this article contains 182 uses of latex notation, so the narration may be difficult to follow. There's a link to the original text in the episode description.

Suppose random variables <span>_X_1_</span> and <span>_X_2_</span> contain approximately the same information about a third random variable <span>_Lambda_</span>, i.e. both of the following diagrams are satisfied to within approximation <span>_epsilon_</span>:

"Red" for redundancy

We call <span>_Lambda_</span> a "redund" over <span>_X_1, X_2_</span>, since conceptually, any information <span>_Lambda_</span> contains about <span>_X_</span> must be redundantly represented in both <span>_X_1_</span> and <span>_X_2_</span> (to within approximation).

Here's an intuitive claim which is surprisingly tricky to prove: suppose we construct a new variable Lambda' by sampling from <span>_P[Lambda|X_2]_</span>, so the new joint distribution is