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I don't think descriptive names per se would be especially helpful. The challenge of understanding a concept typically dwarfs the challenge of remembering a nam

I don't think descriptive names per se would be especially helpful. The challenge of understanding a concept typically dwarfs the challenge of remembering a name. Some people, though, have so many things named after them that Googling for concepts can become challenging. In my thesis, I needed to use something called the Steiner point, which is sometimes also called the Steiner curvature centroid, although I didn't know about this name at first. For a convex set K, this is the limit, as R goes to infinity, of Bar(K + B(0,R)), where Bar(L) denotes the barycenter of L. This is the unique continuous map S on convex sets with the two properties (i) S(K) is in K for all K (ii) S(aK + bL) = a S(K) + b S(L). It is also the map on convex sets satisfying (i) which has the smallest possible Lipschitz constant when the space of compact convex sets is endowed with the Hausdorff metric. It took me a while to get a thorough enough grasp on the literature to learn these things, though, because when you Google "Steiner point", you mostly get stuff about a triangle center, also named after Steiner, which is a totally different concept. It's not that I thought this other triangle center was the Steiner curvature centroid, it was that I literally didn't know what to search for in order to get results on the Steiner point I was interested in.

abnry 6y ago
I don't see how your example proves your point. It is not plausible to think about curvature when discussing triangles (you may discuss curvature of constructed circles, but that's tautological to the size of the circles...) so searching for "Steiner Curvature Point" should help find what you need faster.
- woopwoop 6y ago
  But at the time I didn't know the phrase "Steiner curvature centroid", I just knew "Steiner point". The definition I knew was not in terms of the curvature, or in the terms I gave above, but as a certain integral of the support function. As an aside, the Steiner curvature centroid has a perfectly reasonable interpretation in terms of the "curvature" of a triangle. For a convex set in the plane with smooth boundary, the Steiner curvature centroid is equal to the barycenter of the probability measure on the boundary weighted proportionally to the curvature. Given a triangle, take a sequence of smooth convex sets converging in Hausdorff metric to the triangle, and the limit of the Steiner points of these will converge to the following thing: the average of the vertices of the triangle weighted proportionally to pi - the angle. This is the analogue of the barycenter of the curvature-weighted perimeter for triangles.
  - abnry 6y ago
    The thrust of the original article's point is that more descriptive names for theorems and definitions is better. "Steiner curvature centroid" is more descriptive than "Steiner Point", and by the metric of being able to Google for relevant information, it is indeed better. I see now, rereading, that you were in fact making two points. First, that understanding the definition dwarfs learning the name. (I'd argue that a better name won't make you instantly understand a definition, but it can help but the very example of Steiner point vs Steiner curvature centroid.) Second, that sometimes multiple defintions and theorems are named for the same person, which causes confusion. So you were making a for-and-against argument.
tzs 6y ago
Georg Steller (1709-1746) was like that, but in biology rather than math. Things named after him: Steller's jay, Steller's eider, Steller's sea eagle, Steller's sea cow, Steller's sea lion, and the Stellera genus of flowing plants. Oh, also the mineral Stellerite. He's also in the scientific names of a couple others: Cryptochiton stelleri (a marine mollusc) and Atremisia stelleriana (a plant in the sunflower family). And a school: Steller Secondary School in Anchorage, Alaska. https://en.wikipedia.org/wiki/Georg_Wilhelm_Steller https://en.wikipedia.org/wiki/Georg_Wilhelm_Steller
JdeBP 6y ago
Part of the problem is the "Googling for concepts" idea. What did Google Scholar tell you? And did adding the word "barycentre" improve that?

abnry 6y ago

I don't see how your example proves your point. It is not plausible to think about curvature when discussing triangles (you may discuss curvature of constructed circles, but that's tautological to the size of the circles...) so searching for "Steiner Curvature Point" should help find what you need faster.

woopwoop 6y ago
But at the time I didn't know the phrase "Steiner curvature centroid", I just knew "Steiner point". The definition I knew was not in terms of the curvature, or in the terms I gave above, but as a certain integral of the support function. As an aside, the Steiner curvature centroid has a perfectly reasonable interpretation in terms of the "curvature" of a triangle. For a convex set in the plane with smooth boundary, the Steiner curvature centroid is equal to the barycenter of the probability measure on the boundary weighted proportionally to the curvature. Given a triangle, take a sequence of smooth convex sets converging in Hausdorff metric to the triangle, and the limit of the Steiner points of these will converge to the following thing: the average of the vertices of the triangle weighted proportionally to pi - the angle. This is the analogue of the barycenter of the curvature-weighted perimeter for triangles.
- abnry 6y ago
  The thrust of the original article's point is that more descriptive names for theorems and definitions is better. "Steiner curvature centroid" is more descriptive than "Steiner Point", and by the metric of being able to Google for relevant information, it is indeed better. I see now, rereading, that you were in fact making two points. First, that understanding the definition dwarfs learning the name. (I'd argue that a better name won't make you instantly understand a definition, but it can help but the very example of Steiner point vs Steiner curvature centroid.) Second, that sometimes multiple defintions and theorems are named for the same person, which causes confusion. So you were making a for-and-against argument.

tzs 6y ago

Georg Steller (1709-1746) was like that, but in biology rather than math. Things named after him: Steller's jay, Steller's eider, Steller's sea eagle, Steller's sea cow, Steller's sea lion, and the Stellera genus of flowing plants. Oh, also the mineral Stellerite. He's also in the scientific names of a couple others: Cryptochiton stelleri (a marine mollusc) and Atremisia stelleriana (a plant in the sunflower family). And a school: Steller Secondary School in Anchorage, Alaska. https://en.wikipedia.org/wiki/Georg_Wilhelm_Steller https://en.wikipedia.org/wiki/Georg_Wilhelm_Steller

JdeBP 6y ago

Part of the problem is the "Googling for concepts" idea. What did Google Scholar tell you? And did adding the word "barycentre" improve that?