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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

#381

Post by copperx »

muzani wrote: post #294
ben_w wrote: post #166

Earlier quoted context omitted.

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.

Page rank is probably one of the more clever names out there. I didn't realize at first it was named after the founder, as it's a good description to how it works.

I can't believe I just realized it's named after Larry Page.

Re: Mathematicians should stop naming things after each other

#382

Post by kergonath »

mehrdadn wrote: post #304
kergonath wrote: post #244

Earlier quoted context omitted.

I have seen 'reciprocal space' used for 'Fourier space'. It is quite descriptive, and has the advantage of also working with Legendre transforms. 'Horizontal integrals' does not work. It refers to one way of visualising functions (and even then, only of 1 or 2 variables, and only with specific conventions), and not to the integral itself.

> 'Horizontal integrals' does not work. It refers to one way of visualising functions (and even then, only of 1 or 2 variables, and only with specific conventions), and not to the integral itself. We already have "left" and "right" Riemann sums...

Right, but left and right Riemann sums apply only to functions of a single variable; it breaks down in 2D spaces.

It’s not a general concept like Riemann (or Lebesgue) integrals.

Re: Mathematicians should stop naming things after each other

#383

Post by mehrdadn »

kergonath wrote: post #382
mehrdadn wrote: post #304

Earlier quoted context omitted.

> 'Horizontal integrals' does not work. It refers to one way of visualising functions (and even then, only of 1 or 2 variables, and only with specific conventions), and not to the integral itself. We already have "left" and "right" Riemann sums...

Right, but left and right Riemann sums apply only to functions of a single variable; it breaks down in 2D spaces. It’s not a general concept like Riemann (or Lebesgue) integrals.

One of your complaints was "It refers to one way of visualising function" right? Which is exactly what left and right sums do too.

Re: Mathematicians should stop naming things after each other

#384

Post by bikenaga »

I recall Paul Halmos (https://en.wikipedia.org/wiki/Paul_Halmos) once advocated for naming things in mathematics descriptively rather than honorifically. I recall his argument was that it aids in recall and understanding to name descriptively, and that there are better ways to honor discoverers.

I found this statement in "How to Write Mathematics" (https://bookstore.ams.org/hwm):

"... surely I cannot stop without a discourse on the proper naming of concepts (why 'commutator' is good and 'set of the first category' is bad) and the proper way to baptize theorems (why 'the closed graph theorem' is good and 'the Cauchy-Buniakowksy-Schwarz theorem' is bad)."

I thought he'd said more in "I Want to be a Mathematician" (https://www.springer.com/gp/book/9780387960784), but I just looked through the book and couldn't find anything. (Halmos was a particularist, and thought very highly of examples, and "I Want to be a Mathematician" has examples/opinions of how to do nearly everything in the profession, from teaching to writing to being a department chair to giving talks to doing research ... He was very opinionated, but also specific and absolutely clear, so at least if you disagree with him you know what you're disagreeing about.)

Re: Mathematicians should stop naming things after each other

#385

Post by Phrenzy »

DonHopkins wrote: post #180
kevingadd wrote: post #132

Earlier quoted context omitted.

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…

I'd call my sorting technique "AAAAAAAAAAAAAAA Sort" so it gets listed first in the algorithm directory.

!my sort is better.... sort.

Re: Mathematicians should stop naming things after each other

#386

Post by atq2119 »

Grustaf wrote: post #377
chongli wrote: post #254

Earlier quoted context omitted.

Working computer scientists (academics) are definitely not terrible at math. There are a great deal of complicated proofs involved in areas such as complexity theory, algorithms, and data structures. Their jobs are not altogether different from those of mathematicians.

It might be complicated, but as far as I’ve seen, not in a mathematical sense. Perhaps you have some examples?

The tight performance bounds for Union-Find data structures are ridiculously complicated to prove given how simple the algorithm is, even in a mathematical sense.

There isn't a lot of theory-building in algorithms, compared to the more traditional fields of maths, but the combinatorics are formidable.

Re: Mathematicians should stop naming things after each other

#387

Post by kergonath »

mehrdadn wrote: post #383
kergonath wrote: post #382

Earlier quoted context omitted.

Right, but left and right Riemann sums apply only to functions of a single variable; it breaks down in 2D spaces. It’s not a general concept like Riemann (or Lebesgue) integrals.

One of your complaints was "It refers to one way of visualising function" right? Which is exactly what left and right sums do too.

Well, yes, it’s bad, I am not defending it (and I have never seen it in the wild, even in class when I was taught Riemann integration). I am not sure how the supposed popularity of ‘right Riemann sum’ means that ‘horizontal integral’ would be any good.

Re: Mathematicians should stop naming things after each other

#388

Post by mehrdadn »

kergonath wrote: post #387
mehrdadn wrote: post #383

Earlier quoted context omitted.

One of your complaints was "It refers to one way of visualising function" right? Which is exactly what left and right sums do too.

Well, yes, it’s bad, I am not defending it (and I have never seen it in the wild, even in class when I was taught Riemann integration). I am not sure how the supposed popularity of ‘right Riemann sum’ means that ‘horizontal integral’ would be any good.

I guess I'm saying it's not bad; you're just declaring it as such. People find them quite intuitive. I don't know about you but I've literally never seen someone get confused over silly things like "why is it called a left sum if I can plot the function in the other direction".

Re: Mathematicians should stop naming things after each other

#389

Post by DreamScatter »

lambdatronics wrote: post #344
8note wrote: post #183

An important thing for name sis that you want them to be immutable because it's hard to refactor both all the writing using that name, and everyone's memory to change the concept of a spheroid from one definition to another. This makes it hard to choose generic names from the get-go since the first person to use name might not attach it to the best concept for it, making it unavailable for the best concept for the na…

Yeah, arguably geometric algebra and algebraic geometry should switch labels. Algebraic geometry is geometric techniques for solving polynomials (algebra) so it should really be geometric algebra. OTOH, geometric algebra is an algebraic formulation of geometry -- so that should be algebraic geometry. shrugs

I work with geometric algebra (I'm the developer of Grassmann.jl) and I disagree, I don't think it matters whether the two topics change their name.

Re: Mathematicians should stop naming things after each other

#390

Post by DreamScatter »

lambdatronics wrote: post #339
firebaze wrote: post #159

Complex things cannot be explained easily. As such, from this perspective, it doesn't matter if a complex topic is named by a person or by some abstract, ridiculously compressed word describing an aspect of it. But on the other hand, names are simply irrelevant. Anything is better than a name of a person, even if that person was brilliant. The person may be remembered as an aspect of some discovery (say, Einstein), b…

We've got at least one physicist in our corner: "Hestenes is adamant about calling this mathematical approach “geometric algebra” and its extension “geometric calculus,” rather than referring to it as “Clifford algebra”." https://en.wikipedia.org/wiki/David_Hestenes#Geometric_algeb... Unfortunately, this should really be called algebraic geometry, but that name is already taken by another field...

Come on, switching geometric algebra and algebraic geometry makes no difference.
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