This sounds like an interesting topic, but the article itself was more confusing than enlightening to me. It seems that the actual explanation (using Hamming d

This sounds like an interesting topic, but the article itself was more confusing than enlightening to me. It seems that the actual explanation (using Hamming distances) could be used instead of the bubble-wrap analogy (in the same amount of space, without making more assumptions about the reader). I felt it didn't represent the trade-off (or rather the strict improvement in this case) very well. In fact, it seems to suggest something that is false (that the two methods are fundamentally different). They also start using graphs without an (informal) definition. I didn't know about tree codes before so this could have been interesting but I still don't know much about them. The article alludes to some kind of uniqueness theorem but remarkably Leonard showed there is actually one out there that’s useful but the end suggests that we do not actually know the optimal strategy (so I guess its just an existence proof?). a set of structured binary strings, in which the metric space looks like a tree, doesn't tell me much either. How should I interpret "look like"? Do I approximately embed the space in R^n? Do they mean that its close to a tree metric? Finally, the article also didn't mention how little we actually know about, say, the Shannon capacity of many (small) fixed graphs. The impression I got is that we already know all there is to know about "classical" Shannon capacity (which I believe is false).