Better Intuition for Information Theory

[hardmaru]

https://www.blackhc.net/blog/2019/better-intuition-for-information-theory/

[adriantam]

Yeung (author of the article mentioned) was my teacher in school. He wrote a book more than a decade ago with a Venn diagram of four sets on the cover

https://www.amazon.com/First-Course-Information-Theory-Techn...

I remember he draw such diagram almost every lesson to explain the mathematical structure of various information theory topics.

[0-_-0 → adriantam]

I just went down the rabbit hole of Venn diagrams, and emerged with one for 7 sets:

https://i.stack.imgur.com/kImwq.png

[carapace → 0-_-0]

That's truly awesome. Cheers!

Check out Lewis Carol's Logic Game:

https://www.cut-the-knot.org/LewisCarroll/tridiagram.shtml

[knzhou]

This is nice, but I could've sworn I saw the exact same diagrams in all the old-school information theory books I originally learned it from. I've drawn the I-diagrams the author gives in my notes quite a few times. I'm guessing the point of the paper is that it goes further than that?

[kthielen → knzhou]

The paper is from 1991, when was your textbook written?

[mturmon → kthielen]

The first place I saw these diagrams is in the first edition of Tom Cover and Joy Thomas's excellent textbook - copyright 1991.

But the Venn diagrams are presented in their book as mnemonic tools, and not in terms of entropies of an underlying "I-measure" as in the article. (Of course, the book is an introduction, not in a theorem/proof format.) So you're not sure how far the notions can be extended.

The world of information theory was small then, and the author of the paper would have been well-known to both Cover and Thomas.

[knzhou → kthielen]

Ah, I see. I was under the impression the paper was new.