Audio note: this article contains 61 uses of latex notation, so the narration may be difficult to follow. There's a link to the original text in the episode description.

A lot of our work involves "redunds". A random variable _Gamma_ is a(n exact) redund over two random variables _X_1, X_2_ exactly when both

_X_1 rightarrow X_2 rightarrow Gamma_

_X_2 rightarrow X_1 rightarrow Gamma_

Conceptually, these two diagrams say that _X_1_ gives exactly the same information about _Gamma_ as all of _X_, and _X_2_ gives exactly the same information about _Gamma_ as all of _X_; whatever information _X_ contains about _Gamma_ is redundantly represented in _X_1_ and _X_2_. Unpacking the diagrammatic notation and simplifying a little, the diagrams say _P[Gamma|X_1] = P[Gamma|X_2] = P[Gamma|X]_ for all _X_ such that _P[X] > 0_.

The exact redundancy conditions are too restrictive to be of much practical relevance, but we are [...]

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Outline:

(02:31) What We Want For The Bounty

(04:29) Some Intuition From The Exact Case

(05:57) Why We Want This

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Narrated by TYPE III AUDIO.

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