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However, coming up with simple names is incredibly difficult. It's easy to write a 10,000 word on a complicated topic, but incredibly difficult to squish it into a few letters.
Some profiling would show that names increase the difficulty of math by 0.001%. I don’t see an issue here.
I'm curious if you feel the same way about programming -- do bad variable and function names only increase the difficult of understanding someone else's code or library by 0.001%?
Some profiling would show that names increase the difficulty of math by 0.001%. I don’t see an issue here.
All the examples given are of trivial things. Isoceles triangles and Fermat's last theorem. Both things you can explain in a sentence.
Let's look at something with "mnemonic names": groups, rings and fields. Quickly by just looking at the name which one is the most generic and which most specific.
Maths already involves a ludicrous amount of rote memorization, I'm not sure that using some guy's name is the hard problem. Internalizing all its nuance is.
Sounds reasonable. Let's call this new policy "Ball's Law".
It must be called the "mathematicians should stop naming things after each other" law!
Some profiling would show that names increase the difficulty of math by 0.001%. I don’t see an issue here.
How did you come up with this number? You took 100,000 samples and 99,999 of them agreed? I don't personally know 100,000 mathematicians.
Entropy
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.
Some profiling would show that names increase the difficulty of math by 0.001%. I don’t see an issue here.
It seems like the experimental procedure would require definitions at least several layers deep, the control based on real names and experimental group based another metric. Maybe the experimental groups names would be more closely tied to the structure of the math they were naming though that seems challenging.
Yep; check out how the programming community does it! We have descriptive names for things like "Apache", "React", "nginx", "Rust", and "Java"!
That's because "easy to google" is much more important in the short, medium, and long runs than "easy to guess what it does"