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[new thread since vertex seems not to have had one]]
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.
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.
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.)
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?
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”?
On the principle of doing something rather than talking about it, I’ve edited vertex to take this discussion into account.
Thanks for the comments.
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:
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).
I keep it brief
That’s funny.
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.
Please note I packaged the terminological comments in a section entitled “2. Terminological comments”.
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.
Added to terminological_remarks at vertex:
in an automaton the vertices are called “states”;
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