Comments on: Treats Tropiques

By: Felipe Zaldivar

Felipe Zaldivar — Tue, 07 Jul 2009 19:54:29 +0000

Two things:

(i) The term “idempotent” means that a square of each term is the same element.

(ii) May it be that the many non-asked for explanations for the term “tropical geometry” is that the first geometrical example of a log image looks like an amoeba, an endemic disease associated to tropical climates? It seems to me that the French authors who coined this term are just having fun at a regrettable situation where sanitary conditions are not up to the standards of the developed world. Litvinov and Maslov who studied the same semi-field before the French authors
coined the name “idempotent analysis”, that perfectly describes the novel properties of this semi-field, and they also named the process (inverse to Schroedinger’s quantization) “dequantization” for the so-called “tropicalization” used by the French authors. These extra “explanations” are an attempt to be “politically correct”, very far from the intentions and name of the book you are paraphrasing, but I believe that Levi-Strauss was more sensible and intelligent.

By: Aaron Davies

Aaron Davies — Tue, 23 Jun 2009 23:55:00 +0000

interesting. reminds me somehow of polyhedral exponentiation, where the “volume of an n-dimensional cube” definition is replaced by some other solid. (i think i was introduced to this mostly in the context that fermat’s last theorem was false for octahedral exponentiation, but i can’t recall the relevant triple at the moment.)

By: Anonymous

Anonymous — Sat, 20 Jun 2009 15:16:52 +0000

I’d distinguish between four types of whimsical naming:

(1) Excellent: names that are whimsical yet descriptive. For example, the arctic circle theorem (http://front.math.ucdavis.edu/9801.5068).

(2) Good: whimsical names that are obviously not descriptive. For example, quark flavors like charm and strangeness. Even nonscientists don’t imagine that quarks actually have a taste or have any connection with the everyday meaning of charm, but the quirky terminology helps avoid overusing the same handful of standard words. There’s no way to attach actual descriptive terms to quark flavors (they are simply too abstract), and talking about “quarks of types 2a and 2b” would be much less memorable.

(3) Bad: pop culture references that eventually fade in popularity, like Sonic the Hedgehog. The hedgehog name is actually somewhat descriptive (it refers to the appearance of mutant fruitfly embryos), and I wouldn’t mind the Sonic part if I thought people in 150 years would still know who Sonic was.

(4) Terrible: whimsical names that sound like they may be descriptive but aren’t, like tropical geometry. I can’t tell you how many times I wondered what was tropical about the mathematics before I was finally able to ask someone who was able to tell me definitively that the answer was nothing.

By: John Cowan

John Cowan — Thu, 18 Jun 2009 22:57:06 +0000

Well, “tropical” with a short o is connected to “tropic”, but “tropical” with a long o is connected to “trope”. I toss out this suggestion for reinterpretation of the name for whatever it’s worth.

By: MarkusQ

MarkusQ — Thu, 18 Jun 2009 15:46:33 +0000

I’d vote for the whimsical naming. The point of naming things is to help people keep them clear in their heads–with enough distinction and structure to reattach the concepts to the name when you come back to think about it later. Whimsical naming can help a lot with memorability.

Although, for my part, I would have probably called it “golly” arithmetic, (gol = log spelled backwards), since a lot ot the structure is the opposite of what you get be taking the log. But then, I’m not French, so…

– MarkusQ