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• CommentRowNumber1.
• CommentAuthorPeter Heinig
• CommentTimeAug 2nd 2017
• (edited Aug 2nd 2017)

To comply with

With few exceptions, all edits to the nLab (either the creation of a new page or the revision of an extant one) should be announced at the nForum, in the “Latest Changes” category.

and with

The only real exceptions are very minor edits such as correction of spelling mistakes or obvious typos or indisputable grammatical errors. However, because of this rule there can at times be a large volume of Latest Changes posts; thus a corollary is that Latest Changes posts at the forum should generally be kept very short and to the point. They should also include a link to the nLab page in question (links at the nForum are created with the same syntax as on the nLab itself).

in the rather new writing in the nLab I think I have to announce that a few days ago I added terminological comments to the pre-existing vertex.

• CommentRowNumber2.
• CommentAuthorTodd_Trimble
• CommentTimeAug 2nd 2017
• (edited Aug 2nd 2017)

I’m not in favor of including linguistic etymologies in articles, certainly not for very commonplace words like “vertex”. (For a more unusual word like ’adinkra’ I might find a brief explanation of the origin justified.) Discussions about terminology can occasionally be useful, especially to give guidance on correct usage or on how others use terms within mathematics (physics, philosophy) – but much past that point and it becomes an unnecessary digression.

I also question whether “vertex” is so overwhelmingly the term of choice in graph theory as is asserted. I see “node” being used an awful lot as well.

• CommentRowNumber3.
• CommentAuthorPeter Heinig
• CommentTimeAug 2nd 2017

Re 2: Thanks for the advice.

I also question whether “vertex” is so overwhelmingly the term of choice in graph theory as is asserted. I see “node” being used an awful lot as well.

Well, this is a subjective and/or statistical matter.

I can assure you that in what I perceive as pure graph theory proper, “vertex” is used much more frequently nowadays than “node”. My subjective perception is node gets more usual the more one gets into the literature on more “decorated” graphs, like networks.

(And then there is the irrelevant personal factor that GermanWord(node)=GermanWord(knot), homonymously,

while node and knot are rather different.)

1. I can assure you that in what I perceive as pure graph theory proper, “vertex” is used much more frequently nowadays than “node”. My subjective perception is node gets more usual the more one gets into the literature on more “decorated” graphs, like networks.

I think that “node” is very common among computer scientists.

I agree with Todd about including linguistic etymologies. I’m also having trouble following what exactly is the “canonical etymological explanation” for the mathematical terminology. It makes sense that the terminology is motivated by the connections between graph theory and the classical study of polyhedra (though one should always be wary of etymological explanations that “make sense” without a proper historical/linguistic source), but why does this depend on Steinitz’s theorem on 3-connected planar graphs? Were people using a different terminology for vertices before then?

• CommentRowNumber5.
• CommentAuthorNoam_Zeilberger
• CommentTimeAug 2nd 2017
• (edited Aug 2nd 2017)

I’m also having trouble following what exactly is the “canonical etymological explanation” for the mathematical terminology.

I see that this explanation is also included at edge. Could you clarify what you mean by the “legacy of Steinitz’s theorem”?

• CommentRowNumber6.
• CommentAuthorMike Shulman
• CommentTimeAug 2nd 2017

On the principle of doing something rather than talking about it, I’ve edited vertex to take this discussion into account.

• CommentRowNumber7.
• CommentAuthorPeter Heinig
• CommentTimeAug 3rd 2017
• (edited Aug 3rd 2017)

Could you clarify what you mean by the “legacy of Steinitz’s theorem”?

Noam, thanks for the question. To avoid performatively contradicting that I do not think this particularly important, I keep it brief:

• I wrote “legacy” to mean that Steinitz’ theorem, and more generally the role of graph theory in the study of polyhedra, is what seems to me the reason why this geometric-sounding term “edge” (think of the standard word straightedge while many applications of graphs requiring “edges” which are not straigth by any stretch of the imagination) has come to be a usual technical term
• “edge” does e.g. not appear in Petersen’s classic Die Theorie der regulären graphs, which is a German, yet English-literature-aware work, and Petersen’s papers predates (the reception of) Steinitz’s theorem
• I agree that “legacy” was not the best choice or words, not neutral enough.
• During my quotation-work phase I also remembered some quotation within a mathematical-historical context which explicitly comments on “edge” and “Steinitz theorem”, and gives the latter as the canonical explanation of the former; I did not find the quote in the time I allowed myself for it, intended to search for it once more, yet have now abandonded searching for this historical reference, in view of the mixed reception here.

So in one sentence: I wrote “legacy” because someone told me, in writing, that “edge” is a legacy of Steinitz’ theorem, yet did not find that reference before writing it in the article (not best practice of me).

• CommentRowNumber8.
• CommentAuthorUrs
• CommentTimeAug 3rd 2017

I keep it brief

That’s funny.

• CommentRowNumber9.
• CommentAuthorPeter Heinig
• CommentTimeAug 3rd 2017
• (edited Aug 3rd 2017)

Urs,

That’s funny.

Maybe. It was not meant to be funny though. If one takes this issue seriously one would have to plough through all old anglo-saxon papers on graphs (which Petersen alludes to in his 1891 article, and check them for “edge”. I am not interested in doing so.

For what it’s worth, there is good old

Earliest Known Uses of Some of the Words of Mathematics

whose scientific trustworthiness I cannot estimate

which currently tells us

EDGE (of a polyhedron). Euler used the Latin word acies. In a letter to Goldbach in 1750, he described “the junctures where two faces come together along their sides, which, for lack of an accepted term, I call acies.” Acies is a Latin term which is comonly used for the sharp edge of a weapon, a beam of light, or an army lined up for battle. [Dave Richeson]

So a fixation on Steinitz’ theorem in this matter is probably beside the point, and “edge” is a “legacy” of Euler’s, and more generally of the importance of polyhedra, and in particular of simplicial complexes (and their geometric realizations) in twentieth century mathematics.

This will be my last post on edge for a while, unless asked to say more about it.

Briefly, I was suprised that “edge” even had an nLab page in the first place, thought “What could usefully go in there?”, and though my additions there to be useful to some readers.

• CommentRowNumber10.
• CommentAuthorUrs
• CommentTimeAug 3rd 2017

Peter, you are forcing me to be blunt. The problem I was referring to is that you consistently fail to be brief and to the point. You got banned from editing the $n$Lab because you were filling entries with baroque, meandering off-topic insubstantial side-comments. In view of this it is funny to see you lead-in another such by “I keep it brief”. You are still not keeping it brief. But you’ll need to learn to do that, or else find another online forum that is open to extensive non-mathematical ramblings.

• CommentRowNumber11.
• CommentAuthorRodMcGuire
• CommentTimeAug 4th 2017