On the Need to Name After Scientists and Mathematicians

[inflector]

[RANT ON]

Warning: the following is partly tongue-in-cheek.

One of the things I find most difficult about learning advanced science and mathematics is the constant use of the names of scientists to describe concepts they invented, discovered or were somehow associated with. This makes it really hard to understand a concept because there is no tie to English words in the name, so you have to remember long lists of names that have nothing to do with the concepts that they embody.

Is this some sort of twisted right of passage? A Holy Grail-esque Bridgekeeper to ask us about the speed of unladen swallows? so that only the worthy may pass?

I mean, the Stress Energy Tensor is a name I can use. Ricci Tensor? not so much. I have to remember what it means. Like the difference between Riemann, Ricci and Weyl. More memorization.

God forbid (apologies to the atheists and agnostics, it's just an expression I grew up with, I claim no theological position hereby) that two or three scientists discover something! Then you have Bose Einstein Condensates, and the like. Couldn't this have been Quantum Coherent Condensate or something more descriptive? And the Einstein–Podolsky–Rosen paradox couldn't have been the Nonlocality Paradox?

The other problem is when you have a particular scientist/mathematician who has done broad work. This gives you terms like: Hausdorff. Is it a space, a measure or a dimension?

Oh, all three? Great. That's really helpful.

Are scientists and mathematicians so in need of praise that they prefer to have something named after them rather than have a concept referred to by the name they used when they came up with it?

I doubt that Einstein called his equations the Einstein Equations, I suspect he called them the General Relativity Equations or something descriptive. Why can't we do the same as he did? Wouldn't that honor him better?

[/RANT OFF]

 

[Rasalhague]

I often rant likewise! Yes, yes and yes: it would be a better tribute to all those scientists to express their ideas in the most accessible way we can, with names chosen to make their meaning and interrelationships as transparent as possible. It will cut down on the trivia and help us concentrate on the concepts themselves. And now is the time for it, in our every more interdisciplinary world.

Abelian group --> commutative group
Galois field --> finite field
(Bolyai-)Lobachevskian plane --> hyperbolic plane
generalised Stokes' theorem --> boundary theorem
Gauss' theorem etc. --> divergence theorem etc. (or better still, boundary theorem "3 in 3", to save having to learn all those names that disguise the underlying connection)

No need to puzzle over whether it's Minkowski space with a Lorentz frame, or Lorentz space with a Minkowski frame: let it be flat spacetime with inertial coordinates.

Boundary theorem was proposed by David Hestenes. Irrelevant historical aside: apparently Stokes didn't even discover the special Stokes theorem, so it's ironic that his name should be attached to its most general statement. A not uncommon situation in the cult of naming ideas after people.

We're not the only ones to object:

Other more exotic algebras that have been investigated and found to be of interest are usually named after one or more of their investigators. This practice unfortunately leads to entirely unenlightening names which are commonly used by algebraists without further explanation or elaboration. [ http://mathworld.wolfram.com/Algebra.html ]

Sometimes the concept is abstract and has no obvious name. Picturesque figurative terms can help make these memorable and at least obliquely or poetically suggest something of the idea: halo, galaxy (in nonstandard analysis), blade (in geometric algebra). They're preferable to ambiguously recycling the same small bunch of overworked Latinate expressions.

With already established concepts, where there's a choice between a bland, ambiguous or misleading term and one containing a proper name, I'd favour the proper name, at least as a stopgap. It's tempting to say power series, but Taylor series is more specific. Surely no need for a special name for a Taylor series at zero though. That's like calling addition after one mathematition except when we add the number 27, when we name it after someone else!

I've been saying geometric algebra in preference to Clifford algebra, although it might be argued that the latter is more specific. I gather Grassmann's actual work concerned something more general, more akin to geometric/Clifford algebra, than what his name is traditionally attached to. I hesitate at exterior algebra, as exterior is a mistranslation of Grassmann's term Ausdehnung "extension, expansion", which I guess has led to the figurative contrast: inner/outer product--but that's another story...

 

[disregardthat]

I think it's cute. The pedagogical difficulties are minimal, and to implement names in the field itself provides a good way to honor great achievements in mathematics and the sciences. It is also often a historical reminder, and it's good to be able to put what you learn in a historical context, and that itself might in many cases be pedagogically positive.

Consider the Riemann integral and the Lebesgue integral. This is a good example of where the names give an historical context, and a good way of differentiate between the two. Descriptive names are not always easier to remember nor less ambiguous.

I consider rants about the difficulties of learning the material based on what the material is called symptomatic for someone who has difficulties learning the material regardless of what it is called!

I don't think anyone calls their creations after themselves, that would be excessively arrogant, but that's certainly not a counter-argument for honoring them.

 

[Rasalhague]

Descriptive names are not always easier to remember nor less ambiguous.

Where there's a choice between an ambiguous or unmemorably bland descriptive name and a distinctive, albeit arbitrary, personal name, I would prefer the latter.

I consider rants about the difficulties of learning the material based on what the material is called symptomatic for someone who has difficulties learning the material regardless of what it is called!

Even if this is true in my case, it's no excuse for adding to people's difficulties in general. Have you never felt the exhilaration of coming across that perfect explanation that cut through the tangle of names at a stroke, or, on the other hand, watched threads on here stumble on for ages with apparent disagreements that turn out to be due mainly to unfortunate terminology? I think that's a big motivation (behind my rants): those memories of a really stark contrast between a clear way of presenting an idea that made it easy to grasp, and less ideal ways that left me puzzled for months. So many times, the biggest hurdle I've found in learning something is working out how many concepts go by the same name, and finding some way to label them while trying to understand them--or spotting the concepts that are really the same but go by different names.

 

[inflector]

I think it's cute.

Well, that's a really big point in its favor.

The pedagogical difficulties are minimal

Seriously? When you have to read a paper on a new topic in an area of science of math that you haven't yet studied deeply or rigorously, you can't just read and understand the jist of the concepts when the papers are filled with lots of terms that give no clue to their meaning unless you know the vernacular. This is categorically more difficult and not in a trivial way.

You can't just use references like Wikipedia to learn the new terms either as Wikipedia is intentionally for reference. Some of the concepts are explained in terms that are easy to understand but most of the obscure ones are not. They are explained in terms of jargon and vernacular that themselves may not be known unless you happen to have studied that particular area of math or science.

I consider rants about the difficulties of learning the material based on what the material is called symptomatic for someone who has difficulties learning the material regardless of what it is called!.

Languages have words that mean specific things already. Proper names are generally meaningless. Using words that have no meaning to describe new concepts necessarily adds to the cognitive load required to understand any particular concept.

Contrast two concepts: multiverse and Minkowski space.

One can read an article about the multiverse and generally intuit the meaning of the word from context without having any prior knowledge of the meaning because the word reuses parts of words we already know that themselves have a common base in Latin. Our brains know these parts so there is little cognitive load for guessing the word in context. Once we learn the word, we can easily remember it.

The term Minkowski space tells us that it was probably invented by someone named Minkowski. As far as what it means? Well, there is no clue in the name whatsoever. None. So when someone encounters the word for the first time, they have to guess without any hints as to the meaning. Then they have to remember it. They might remember it if they are studying an area of science or math where it is common but if they only encounter it once or twice and then not again for several years, they will probably forget.

Another example: nucleus and neutron versus fermion and boson.

One can read about the nucleus and immediately understand what it is because the word means something in English already. Likewise a neutron gives a clue as to the electrically neutral nature of the particle, which in the context of the three major subatomic building blocks is its distinguishing relevant characteristic, same goes for electron.

A fermion? No clue what it is unless you already know. Boson? Same problem. You have to know. This requires memorization of new information.

Which concepts are easier to learn and remember? Clearly nucleus, neutron and electron because they tie into other concepts that someone learning already knows.

Finally, remember Einstein was famous for not remembering anything unnecessary. There was a reason for this.

Scientists and mathematicians like to rant about how most of the population is scientifically illiterate but these sorts of unnecessary extra complications do not help.

 

[Hurkyl]

Languages have words that mean specific things already.

Yes, the great feature of natural language!

Unfortunately, that is also the great drawback of natural language.

One can read an article about the multiverse and generally intuit the meaning of the word from context without having any prior knowledge of the meaning because the word reuses parts of words we already know that themselves have a common base in Latin.

Which is a deadly trap -- this implants an idea in your head which is very likely slightly wrong, and occasionally very wrong. It can be very difficult to get those errors out of your head as you go on to learn what the word is supposed to mean!


Also, natural language was designed for things we naturally encountered, and was mostly formed long long ago. There simply aren't words for many things, until we invent them!

 

[inflector]

Which is a deadly trap -- this implants an idea in your head which is very likely slightly wrong, and occasionally very wrong. It can be very difficult to get those errors out of your head as you go on to learn what the word is supposed to mean!

If someone coins a word that doesn't describe the concept properly, that's a bad idea clearly but not an argument in favor of picking names that have no prior meaning (or worse many other meanings because of common inventions/discoveries of a particular scientist/mathematician).

Also, natural language was designed for things we naturally encountered, and was mostly formed long long ago. There simply aren't words for many things, until we invent them!

Of course, one needs to invent new words (or combinations) for new concepts. No one is arguing that. But clearly there is a difference between a word like nucleus, neutron and nucleon and Poincaré group.

All I'm arguing for is not inventing words when not necessary and for thinking about what the words mean when inventing new ones. I'm also advocating that we stop using the more arcane terms when a more obvious example is available and just as accurate in the context. A good example being given by Rasalhague with flat spacetime and inertial coordinates instead of Minkowski space and Lorentz frame. In some contexts, the more specific terms might carry an extra level of necessary precision but in most uses I have seen they do not.

 

[apeiron]

Scientists and mathematicians like to rant about how most of the population is scientifically illiterate but these sorts of unnecessary extra complications do not help.

I completely agree with you and Rasalhague. Using the names of discoverers so as to preserve a historical context might make sense in the early days when knowledge is new and a community is small enough for the names of people to be highly relevant information. But 20 or 50 years later, it is just anachronistic and a huge source of cognitive drag.

Which is a deadly trap -- this implants an idea in your head which is very likely slightly wrong, and occasionally very wrong. It can be very difficult to get those errors out of your head as you go on to learn what the word is supposed to mean!
Also, natural language was designed for things we naturally encountered, and was mostly formed long long ago. There simply aren't words for many things, until we invent them!

This reveals a particular attitude that indeed seems prevalent within mathematical circles.

"We are dealing with pure abstractions that have no connection to the real world of the senses."

It is the ancient "reason pure/reality impure" prejudice that goes back to Plato. The senses can be mistaken, only reason can deliver truth.

It is the same intellectual snobbery that you see in the Bourbaki group or the refusal to sully maths papers with illustrative diagrams. See by contrast Roger Penrose's book, The Road to Reality, where he makes an unusual effort to convey his intuitive visual understanding of topological arguments.

Michael Atiyah has a lot to say about this attitude. For instance:

Broadly speaking I want to suggest that geometry is that part of
mathematics in which visual thought is dominant whereas algebra is that
part in which sequential thought is dominant. This dichotomy is perhaps
better conveyed by the words "insight" versus "rigour" and both play an
essential role in real mathematical problems.
The educational implications of this are clear. We should aim to cultivate
and develop both modes of thought. It is a mistake to overemphasise one at
the expense of the other and I suspect that geometry has been suffering in
recent years.

http://www.ime.usp.br/~pleite/pub/artigos/atiyah/what-is-geometry.pdf

How the brain thinks "abstractly" is something I have actually studied, so the anti-concrete imagery attitude is one that I know is based on shaky intellectual foundations.

 

[epenguin]

https://www.physicsforums.com/showpost.php?p=2905404&postcount=7 :rofl:

 

[Hurkyl]

This reveals a particular attitude that indeed seems prevalent within mathematical circles.

Or, y'know, it could just be an observation borne from direct experience with people who take analogous too seriously, names too literally, or otherwise just get some error stuck in their head early that takes a long time before it's recognized and fixed.

Some people never get it fixed.


It is (IMO) naive to think that everything can be explained in simple terms. We see inflector condemning the use of meaningless names, without apparent regard that the alternative is very likely to be a misleading name, which is downright harmful to the student. That is a bad thing.


I know you have a soapbox you want to stand on, but it would be nice if you saved it for a time it was actually relevant to the discussion.

 

[apeiron]

Or, y'know, it could just be an observation borne from direct experience with people who take analogous too seriously, names too literally, or otherwise just get some error stuck in their head early that takes a long time before it's recognized and fixed.

Do you have much evidence to back up this opinion then? I can accept it as being a likely issue in a small way, but not a major one that is therefore a good reason for avoiding plain language terminology.

So we have two arguments. One that argues on the basis of cognitive load, the other that says we don't want to give people easy mental anchors because they will just misuse them.

To me, it seems the general utility argument easily outweighs the occasional potential abuse one.

If you don't get people started down the path to learning, they will never get far enough even to start making mistakes.

And I see nothing in what we know about human thought processes that means once people begin with an overly-concrete set of associations, that they cannot then go on to develop more refined understanding of what a concept "really means". Children do it all the time. It is how they learn "doggie" is not a word to use for cats or pigs, but could be used for Pluto or K-9.

So if you want to argue your view based on evidence about human concept learning, please continue.

Maybe it is as you say, in your experience, and backed by pedagogical research, that it is better to teach abstract knowledge using non-concrete terminology. This is the approach that is known to work best.

I just don't believe it from my own personal experience and knowledge of human thought processes.

 

[inflector]

It is (IMO) naive to think that everything can be explained in simple terms. We see inflector condemning the use of meaningless names, without apparent regard that the alternative is very likely to be a misleading name, which is downright harmful to the student. That is a bad thing.

First, it does not follow that the alternative to a meaningless name is one that will "very likely" be a misleading name.

I've provided several concrete examples of good and bad names. You have provided no misleading names in counterpoint. What is misleading about the term: "flat spacetime" or "inertial coordinates?"

Second, no one ever claimed that "everything can be explained in simple terms." I never used the word "simple." I am only arguing against UNNECESSARY complication.

I know you have a soapbox you want to stand on, but it would be nice if you saved it for a time it was actually relevant to the discussion.

Was this really called for? If you think a post is off topic then report it or PM the originator.

I happen to think the point from Michael Atiyah was very germane:

Broadly speaking I want to suggest that geometry is that part of
mathematics in which visual thought is dominant whereas algebra is that
part in which sequential thought is dominant. This dichotomy is perhaps
better conveyed by the words "insight" versus "rigour" and both play an
essential role in real mathematical problems.

This is exactly the problem I was pointing out in the OP. A concern for precision at the expense of understanding is misguided. As apeiron pointed out, a tendency to resort to math equations all the time, even when drawings and illustrations are better communication is illustrative of the same underlying tendency. This is another example of an unnecessary increase in the cognitive load. Exactly the point of my OP and very germane to the discussion.

Another issue I find continuously which is the same sort of problem, is the need to show all the steps for mathematical rigour in the body of papers rather than putting the steps into an appendix. In general, unless the paper is about the steps as some sort of proof, there is no need to force the reader to follow the steps just to read the paper. If the math is good, then show the math separately in an appendix, curious readers can follow along later or in the event that the paper's conclusion is controversial then they can verify the steps. But if the point of the paper is not the math, then the math shouldn't take up 3/4 of the body of the paper.

 

[Rasalhague]

Killing field, the best/worst of both worlds!

 

[inflector]

Ah yes, quite right.

Named after a mathematician and also a misleading English word.

 

[disregardthat]

Seriously? When you have to read a paper on a new topic in an area of science of math that you haven't yet studied deeply or rigorously, you can't just read and understand the jist of the concepts when the papers are filled with lots of terms that give no clue to their meaning unless you know the vernacular. This is categorically more difficult and not in a trivial way.

You can't just use references like Wikipedia to learn the new terms either as Wikipedia is intentionally for reference. Some of the concepts are explained in terms that are easy to understand but most of the obscure ones are not. They are explained in terms of jargon and vernacular that themselves may not be known unless you happen to have studied that particular area of math or science.

And you suppose that if the names of the concepts alien to you were given "descriptive" names, it would be easier to find a reference from elsewhere? I reckon it would be harder! Jargon and conventions will be there regardless of how concepts are named. I imagine it would be even harder to orient oneself in a sea of descriptive names. Names after creators sometimes serves as milestones in this sea.


I have never had any problems with remembering names, and I personally know none who has, so let's flip the coin: do you have evidence for that naming conventions is a significant cognitive drag for students in science and mathematics?

I personally consider naming conventions a de-sterilization of the subject as a whole, and while having no non-trivial problems familiarizing me with the terms I appreciate the implicit historical and contextual references; which are certainly not anachronistic!

Do not lump the "intuition" vs "rigour" debate into all of this, that is a separate issue. It is not justified to say that this is an expression for "the same underlying tendencies".

 

[Hurkyl]

the other that says we don't want to give people easy mental anchors because they will just misuse them.

Or, y'know, I could have meant what I said and not this silly exaggeration. There are two issues:

• A good "mental anchor" is fine, if we don't naïvely assume that's all the student needs to gain intuition and understanding of something, and the student knows that he's expected to weigh anchor and progress beyond such superficial knowledge
• If we gratuitously seek to hand out mental anchors when we can't find good ones, we are likely to do more harm than good

I've provided several concrete examples of good and bad names. You have provided no misleading names in counterpoint. What is misleading about the term: "flat spacetime" or "inertial coordinates?"

Flat space-time is a wonderful example of a misleading name. In this context, you are clearly using it to refer to Minkowski 3+1 space -- however, flat space-time includes many other space-times, such as higher-dimensional analogues of cylinders and toruses.

 

[Jimmy Snyder]

Is it more evocative to use the name "field" rather than calling it "Snyder-Einstein space" after its originators?

 

[apeiron]

• A good "mental anchor" is fine, if we don't naïvely assume that's all the student needs to gain intuition and understanding of something, and the student knows that he's expected to weigh anchor and progress beyond such superficial knowledge
• If we gratuitously seek to hand out mental anchors when we can't find good ones, we are likely to do more harm than good

You complain about strawmen, but it is you who are offering them. Why would I suggest that we naively assume anything, or gratuitously hand out anything? How could that arise on my side of the argument?

If you can provide actual evidence that students actually do better with names rather than descriptions to label things, then please do.

In the meantime here is another little snippet that suggest views might differ...

Grothendieck had a flair for choosing striking,
evocative names for new concepts; indeed, he saw
the act of naming mathematical objects as an integral
part of their discovery, as a way to grasp them
even before they have been entirely understood
(R&S, page P24). One such term is étale, which in
French is used to describe the sea at slack tide, that
is, when the tide is neither going in nor out. At slack
tide, the surface of the sea looks like a sheet, which
evokes the notion of a covering space. As Grothendieck
explained in Récoltes et Semailles, he chose
the word topos, which means “place” in Greek, to
suggest the idea of “the ‘object par excellence’ to
which topological intuition applies” (pages 40–41).
Matching the concept, the word topos suggests the
most fundamental, primordial notion of space. The
term motif (“motive” in English) is intended to
evoke both meanings of the word: a recurrent
theme and something that causes action.
Grothendieck’s attention to choosing names
meant that he loathed terminology that seemed unsuitable:
In Récoltes et Semailles, he said he felt an
“internal recoiling” upon hearing for the first time
the term perverse sheaf. “What an idea to give such
a name to a mathematical thing!” he wrote. “Or to
any other thing or living being, except in sternness
towards a person—for it is evident that of all the
‘things’ in the universe, we humans are the only
ones to whom this term could ever apply”

http://www.ams.org/notices/200410/fea-grothendieck-part2.pdf

 

[epenguin]

Killing field, the best/worst of both worlds!

And I have always wondered in what direction the Poynting vector points.

 

[Rasalhague]

And you suppose that if the names of the concepts alien to you were given "descriptive" names, it would be easier to find a reference from elsewhere? I reckon it would be harder! Jargon and conventions will be there regardless of how concepts are named. I imagine it would be even harder to orient oneself in a sea of descriptive names. Names after creators sometimes serves as milestones in this sea.

I wonder if personal names tend to make more distinctive search terms. Perhaps not such an issue these days, as google gets ever smarter. (Search Google video for "Jacobian" and see all the adverts for Hessian bags, Hessian upholstery etc.)

Do not lump the "intuition" vs "rigour" debate into all of this, that is a separate issue. It is not justified to say that this is an expression for "the same underlying tendencies".

Sometimes a straight definition is worth a thousand "well, it's a bit like this, and a bit like this"s! And depending on the context, a paper with lots of equations could well be more accessible to a beginner, while one pitched at advanced readers will naturally assume they can fill in the gaps for themselves.

Flat space-time is a wonderful example of a misleading name. In this context, you are clearly using it to refer to Minkowski 3+1 space -- however, flat space-time includes many other space-times, such as higher-dimensional analogues of cylinders and toruses.

Good point. A similar case might be Lobechevskian geometry versus hyperbolic geometry. How about commutative group, totally transparent if you already know what a group is and what commutative means, while Abelian group is half opaque, an extra word to look up; like putting the credits on in the middle of the film.

I also think there's something to be said for an arbitrary (too arbitrary to mislead) but picturesque name for an abstract concept.

Hmm, Minkowski space, Lorentz frame (sometimes also called a Cartesian frame), ah, so Minkowski and Euclid are the instrinsic ones, and Decartes and Lorentz the coordinate guys... but then there's the more general term Lorentzian manifold (now Lorentz has become instrinsic), and what would Lorentz-Minkowski space be, the same as Minkowski space, or something more general? Is Lorentz metric synonymous with Minkowski metric? Is it the canonical component expression of the Minkowski metric? Or is it named for its association with Lorentzian manifolds, and thus a general pseudo-Riemannian metric tensor, or are both Minkowski metric and Lorentz metric component expressions, the contrast being between Lorentz's all real components and Minkowski's use of an imaginary time component, or possibly any of the above, depending on the author? With nothing inherently Minkowskiish or Lorentz-like about these concepts apart from the fact that both men were associated with this whole area of research, its hard to guess, and easy for the meaning to drift. An aptly descriptive/suggestive name might not be immune to confusion, but it might stand more chance.

 

[inflector]

Flat space-time is a wonderful example of a misleading name. In this context, you are clearly using it to refer to Minkowski 3+1 space -- however, flat space-time includes many other space-times, such as higher-dimensional analogues of cylinders and toruses.

You illustrate by your very example another problem with a word like Minkowski. I say Minkowski space and you think 3 + 1 spacetime when that was not the distinction I was trying to illustrate.

I meant flat as distinct from curved when I used the term flat spacetime. In some specific contexts, say contrasting the coordinate systems of special relativity and general relativity, that is the important distinction, and it is only in those contexts that the term flat spacetime would be the proper term.

I did not mean Minkowski 3 spatial and 1 time as distinct from Euclidean 4 spatial dimensions.

Depending on the context, the relevant differentiators are either "flat" versus "curved" and/or "3+1 D" versus "4D."

If instead of saying "Minkowski space" depending on the context and required distinction, the terms were replaced with either "flat spacetime" or "3+1 spacetime" a reader who was not too familiar with the topic would be able to discern exactly the difference or contrast which was intended. If precision is the goal, the important distinction is the 3 + 1 aspect of Minkowski space in some instances and the flat versus curved aspect in others. If one wishes to specify both aspects, then "flat 3 + 1 spacetime" fits the bill just fine and would be easy for anyone to understand.

Just because Minkowski developed the idea of a spacetime that both happened to have 3 + 1 dimensions and to be flat, we need not necessarily tie the two together as if they are one concept. They are two different concepts.

They are wedded together only because of this historical accident that Minkowski happened to develop a spacetime that incorporated both concepts at the same time.

 

[inflector]

Hmm, Minkowski space, Lorentz frame (sometimes also called a Cartesian frame), ah, so Minkowski and Euclid are the instrinsic ones, and Decartes and Lorentz the coordinate guys... but then there's the more general term Lorentzian manifold (now Lorentz has become instrinsic), and what would Lorentz-Minkowski space be, the same as Minkowski space, or something more general? Is Lorentz metric synonymous with Minkowski metric? Is it the canonical component expression of the Minkowski metric? Or is it named for its association with Lorentzian manifolds, and thus a general pseudo-Riemannian metric tensor, or are both Minkowski metric and Lorentz metric component expressions, the contrast being between Lorentz's all real components and Minkowski's use of an imaginary time component, or possibly any of the above, depending on the author? With nothing inherently Minkowskiish or Lorentz-like about these concepts apart from the fact that both men were associated with this whole area of research, its hard to guess, and easy for the meaning to drift. An aptly descriptive/suggestive name might not be immune to confusion, but it might stand more chance.

Genius!

 

[Hurkyl]

I meant flat as distinct from curved when I used the term flat spacetime.

"Minkowski space" refers to a large collection of geometries -- just like "Euclidean space" does. I was adding precision.


The thing that "Minkowski" signifies that "flat" does not is that the underlying differentiable manifold is isomorphic to Rⁿ.

e.g. a cylinder is a flat surface, but it is clearly not a Euclidean plane or a Minkowski 2+0 plane.

 

[inflector]

"Minkowski space" refers to a large collection of geometries -- just like "Euclidean space" does. I was adding precision.

The thing that "Minkowski" signifies that "flat" does not is that the underlying differentiable manifold is isomorphic to Rⁿ.

You clearly know a lot more about the specifics of the mathematics and physics than I do at this point. I won't dispute that. I also don't dispute the idea that there is a lot of precision necessary to completely describe concepts and to differentiate them. At the advanced level this precision is important.

Nevertheless, the level of precision is very often unnecessary in order to convey the concept.

Further, I would argue that describing something as having an "underlying differentiable manifold isomorphic to Rⁿ", is a better way to introduce the concept, and if the concept is common enough to require it's own specific word, I'm with Rasalhague: use a word that does not have misleading prior meaning. I think he showed pretty clearly in his last post that overloaded names don't help clarity or precision if you don't already have a good grasp on the underlying issues and concepts. And overloaded names (like Minkowski or Lorentz) are just as likely, perhaps more likely, to lead to students coming to the wrong conclusions.

Again, as an example, positron is a great word. It was invented so it has no prior or dual meaning but the meaning that one can infer does in fact help with memorizing the term and its associated concept.