

A New Mathematics for Computing - rsmiller510
http://h30565.www3.hp.com/t5/Feature-Articles/A-New-Mathematics-for-Computing/ba-p/1390

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apsp
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).

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drblast
This article is light on the details. Here is the paper it's based on (I
think):

[http://users.cms.caltech.edu/~schulman/Papers/intercoding.pd...](http://users.cms.caltech.edu/~schulman/Papers/intercoding.pdf)

~~~
jberryman
I see the author is from the Imposing Wall of Text school of typesetting.

~~~
eru
It's a paper about an abstract mathematical topic. Just be glad that the whole
thing doesn't consist mostly of equations.

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klheyman
Thank you all for your thoughtful comments. You've hit the heart of the
challenge in any kind of science writing: Trying not to frighten off those
unfamiliar with a field and therefore using metaphors, such as bubble wrap,
while at least touching on some common ground for those who are (Hamming
distances).

My respectful suggestion for those truly interested in following up is to
contact either Leonard or Amit directly. Of necessity, any math that is
translated into prose is going to be imprecise, and thus, unsatisfying.

To answer a few of the specific questions that were brought up:

Yes, it is essentially an existence proof. At least for now. Yes, that paper
is a good starting point. Also take a look at Amit's work. Yes, buses inside
chips is something they think it could be useful for. (Sigh) I wish there were
a better introduction to tree codes at a lay level. Believe me, I tried very
hard to find one. FWIW, both scientists vetted the explanations.

~~~
klheyman
I got some further clarifications from Leonard Schulman:

He writes, "Yes, a tree code is a near-isomorphic image of a tree metric. No,
this has nothing to do with the Shannon capacity of graphs."

Thank you again for your comments.

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baltcode
There has to be a better introductory to tree codes than this. One that
doesn't assume you work in error correcting codes but can actually explain
things in terms of basic math and information entropy.

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ajb
So, the advantage of this scheme seems to be that you don't have to wait for
the end of a transmission block before doing error correction and extracting
your data. But, we have error correction schemes which work well with fairly
small blocks of data. It seems to me that this isn't a saving in network
comms, where the delay for a few hundred bit-times is outweighed by other
delays. Maybe it will be useful for buses inside chips.

