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Mathematicians should stop naming things after each other

nautil.us

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Re: Mathematicians should stop naming things after each other

#161

Post by Davidzheng »

kxyvr wrote: post #89
saithound wrote: post #50

This is one of those articles that might sound convincing to non-mathematicians (because it is annoying to learn names for difficult concepts, and many people can relate to that experience), but will not sound all that convincing to domain experts. It'd be hard to deny that descriptive terms are easier to memorize. Sometimes a piece of natural and/or physical intuition allows such terminology to arise. Scientist and…

As a counterpoint, I've a Ph.D in math and I largely agree with the article. Frankly, it's difficult enough to keep track of the names in my own field much less interact with people in other fields who would greatly benefit from these results if they were comprehensible. While I agree that precision is necessary, is it really that hard to say something like a complete inner product space vs a Hilbert space? Should we…

If you have to write complete inner product space a hundred times in an article that's pretty annoying tbh

Re: Mathematicians should stop naming things after each other

#162

Post by mattkrause »

kevingadd wrote: post #132
ardit33 wrote: post #93

Earlier quoted context omitted.

I Disagree with you, in Computer Science we have things like: "Quick Sort", "Merge Sort", "Map", "Hashtable", "LRU", etc... etc... They are much more descriptive and easy to remember, even though the Algorithms can be complex themselves. Event the name "Boolean", could be changed to "Conditional"... and be even more readable. Also, Dijkstra algorithm can be generalized to "Shortest Path Algorithm" (there can be more…

terms like "quick sort" and "map" are actively harmful because what they mean is VERY ambiguous, and in some cases becomes wrong over time. "quick sort" is no longer the quickest sort algorithm by any standard, it happens to just be quicker than some of the algorithms that came before it. "map" tells you nothing about the properties of the data structure other than that it 'maps' keys to values, but even the nuances…

> Calling this narcissism does everyone a significant disservice.

It’s not even really narcissism.

Here’s the original paper describing what is now called Dijkstra’s Algorithm: http://www-m3.ma.tum.de/foswiki/pub/MN0506/WebHome/dijkstra.... Note that the algorithm isn’t called that anywhere in the paper. In fact, it’s not even named.

When other people want to discuss that work, they need to call it something, and some natural solutions are “an algorithm proposed by Dijkstra” and, subsequently, “Dijkstra’s Algorithm”, as you can see in this contemporary paper. https://www.ams.org/journals/qam/1970-27-04/S0033-569X-1970-...)

As that second paper shows, you can’t really call it “the Shortest Path Algorithm” because others were developing other approaches for similar problems. “Shortest Path, Assuming All Edge Weights are Non-Negative and You Can Afford to Search Blindly Without a Heuristic, Algorithm” doesn’t really roll off the tongue either.

Re: Mathematicians should stop naming things after each other

#163

Post by davidivadavid »

gourlaysama wrote: post #106

This seems to misrepresent why people bother naming things. It's not like mathematicians are spending their time randomly naming every object/property/structure/... they encounter just for the sake of it. A "Kähler manifold" exists, as a name, because there is no way to fully describe what it is (and bring forward in the reader all the corresponding context) in two or three words. Using a long sentence (full of thing…

Uniqueness of names is definitely important — the question is can we do better?

If all we want is uniqueness, we could just number theorems and concepts using GUIDs.

Might as well abdicate and embrace the fact math is going to be automated, and all mathematical objects are just abstract constructs devoid of meaning that can be referred to by arbitrary labels.

But it seems like there's more to it.

The names of mathematicians are interesting for the genealogy of theorems... but they're also completely opaque about their semantics.

Is it not possible to think a system could make math more intuitive by relying on a more structured nomenclature?

Re: Mathematicians should stop naming things after each other

#164

Post by sdenton4 »

detaro wrote: post #147
chongli wrote: post #138

Earlier quoted context omitted.

for example: operating systems, programming languages, human computer interaction, etc. Those topics might seem to have nothing to do with math but all of their components have mathematical underpinnings. Algorithms, data structures, complexity theory, and even the physics of end-to-end latency, colour perception, etc. There probably are some people out there, working in these fields with only a high school math back…

Everyone who completed a physics degree has done at least as much math as a CS degree holder, is physics a subfield of math? (I think there is a discussion to be had about making the distinction "CS" vs "theoretical CS" as the GP comment does, or if it should be "CS" vs some other term ("computing"? feels a bit general))

I tried reading "the road to reality" and came to the conclusion that math is physics minus all the boring parts.

(Mostly joking. Mostly!)

Re: Mathematicians should stop naming things after each other

#165

Post by DonHopkins »

crazygringo wrote: post #55

Hard disagree. Once you get to the advanced levels of any field, terminology being "accessible" doesn't really matter, but being precise does . Areas like philosophy and law actually suffer in my opinion when they overload common words with uncommon meanings, or descend into weird disambiguations that depend on suffixes. For example, in philosophy there's "contractarianism" and "contractualism", and trying to remembe…

Even with people's names, you get bizarre confusions and mutations.

https://www.tek.com/blog/window-functions-spectrum-analyzers

>Hamming and Hanning

>These two similarly-named Hamming and Hanning (more properly referred to as Hann) window functions both have a sinusoidal shape. The difference between them is that the Hanning window touches zero at both ends, removing any discontinuity. The Hamming window stops just shy of zero, meaning that the signal will still have a slight discontinuity.

The Hamming Window is named after Richard Hamming.

https://en.wikipedia.org/wiki/Richard_Hamming

But the Hanning Window is named after Julius von Hann, and lots of people just throw in an extra "ing" to make them sound alike, but its excruciatingly correct name is Hann Window.

But it seems fitting that they're almost but not quite alike, and so is their spelling. Maybe for symmetry there should be a Halling Window that stops just below zero.

https://en.wikipedia.org/wiki/Julius_von_Hann

https://en.wikipedia.org/wiki/Window_function#Hamming_window

https://en.wikipedia.org/wiki/Hann_function

https://numpy.org/doc/stable/reference/generated/numpy.hanni...

https://numpy.org/doc/stable/reference/generated/numpy.hammi...

Re: Mathematicians should stop naming things after each other

#166

Post by ben_w »

knome wrote: post #124
ardit33 wrote: post #93

Earlier quoted context omitted.

I Disagree with you, in Computer Science we have things like: "Quick Sort", "Merge Sort", "Map", "Hashtable", "LRU", etc... etc... They are much more descriptive and easy to remember, even though the Algorithms can be complex themselves. Event the name "Boolean", could be changed to "Conditional"... and be even more readable. Also, Dijkstra algorithm can be generalized to "Shortest Path Algorithm" (there can be more…

Tim Sort, Hamming Codes, Huffman Coding, RSA keys, LZW encoding, Duff's Device, Bloom Filter, Carmack's Reverse, awk, linux, git. We have a lot of things named after those that discovered, invented or popularized a structure or technique. Certainly nowhere near as commonly as does mathematics, I will agree. In CS, no doubt, we often end up on the other end, where a single term means different things in different cont…

Page rank. I thought git was named by Linus, and to the extent that it is named after him, it was self awareness of his reputation?

I remember when Duff's Device was a neat trick; does anyone still use it these days?

Edit: a neat trick, not a bear trick.

Re: Mathematicians should stop naming things after each other

#167

Post by thaumasiotes »

xrisk wrote: post #122
chongli wrote: post #114

Earlier quoted context omitted.

in Computer Science we have things like: "Quick Sort", "Merge Sort", "Map", "Hashtable", "LRU", etc... Those are trivial concepts though. The article brings up "perfectoid spaces", as if to suggest their superiority to "Scholze spaces", yet neither name gives any clue as to what they are: In mathematics, perfectoid spaces are adic spaces of special kind, which occur in the study of problems of "mixed characteristic",…

> You won’t get anywhere at all if you try to enter the field without a mathematical background. Unnecessary gatekeeping. There’s a lot of engineering-oriented research that has nothing to do with math.

There is no research anywhere, in any field, that has nothing to do with math.

Re: Mathematicians should stop naming things after each other

#168

Post by thaumasiotes »

Godel_unicode wrote: post #145
crazygringo wrote: post #55

Hard disagree. Once you get to the advanced levels of any field, terminology being "accessible" doesn't really matter, but being precise does . Areas like philosophy and law actually suffer in my opinion when they overload common words with uncommon meanings, or descend into weird disambiguations that depend on suffixes. For example, in philosophy there's "contractarianism" and "contractualism", and trying to remembe…

I've always thought there was a nice breakdown here in math; name things after what they are if they can be stated concisely, name them after discoverers as a short hand for here-there-be-dragons.

There's no system. Abelian groups are a concept that is simple, intuitive, and easy to describe concisely.

Re: Mathematicians should stop naming things after each other

#169

Post by dmurray »

Godel_unicode wrote: post #145
crazygringo wrote: post #55

Hard disagree. Once you get to the advanced levels of any field, terminology being "accessible" doesn't really matter, but being precise does . Areas like philosophy and law actually suffer in my opinion when they overload common words with uncommon meanings, or descend into weird disambiguations that depend on suffixes. For example, in philosophy there's "contractarianism" and "contractualism", and trying to remembe…

I've always thought there was a nice breakdown here in math; name things after what they are if they can be stated concisely, name them after discoverers as a short hand for here-there-be-dragons.

Is that the breakdown? Euclid's Algorithm, Pythagoras' Theorem, Fermat's Little Theorem are all elementary, but the example upthread of a "perfectoid field" which is a "complete topological field K whose topology is induced by a nondiscrete valuation of rank 1..." is much more abstruse.

Re: Mathematicians should stop naming things after each other

#170

Post by ben_w »

bumby wrote: post #157
jfoutz wrote: post #117

Earlier quoted context omitted.

Meanings of words drift over time, like, litterally.

Isn’t this why science deliberately chose Latin for naming? Being a dead language it won’t change meanings over time

I think that’s because when science started to get serious, Latin happened to be the lingua-Franca of those in Europe who could afford to be part of it. Equivalent deal for why we use Arabic numbers.
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