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I don’t see this article argument for a “lowest common denominator” approach. For example, how is replacing “Let M be a complete Riemannian manifold, G a compa

I don’t see this article argument for a “lowest common denominator” approach. For example, how is replacing “Let M be a complete Riemannian manifold, G a compact Lie group and P → M a principal G-bundle.” by “One of the main problems in gauge theory is understanding the geometry of the space of solutions of the Yang–Mills equations on a Riemannian manifold.” doing that? It gets rid of “Lie group” and “G-bundle”, but adds “gauge theory” and “Yang-Mills equations” Also, “Of course, one should not give a detailed blow-by-blow account of every pitfall and wrong turn”, IMO, is an argument against doing that. It more or less says: “assume that there are steps your readers can make on their own”.

sethhochberg 3y ago
As someone who never took much advanced math or physics in school and really doesn't understand what either representation of that material is staying, personally I find the second example far, far more approachable because it is far more googleable! If Gauge Theory is a concept required to relate to the other content in that sentence I've got no shot of knowing gauge theory is involved in the first example. I don't know what the arrow between P and M means. I'd have to look up what a G-bundle is. Its basically not clear to me which parts are syntax and which are proper nouns. The example which reads more like prose than an equation expressed in terms of English words gives me much, much more context for where to begin reading about what I don't know.
gumby 3y ago
One important element for me is that the framing should be as specific as possible. The article's example, regrettably isn't the best example of this, but: by saying "one of the main problems..." the author (quite reasonably, not click-baiting) is trying to say "this paper is about something important and is worth reading, or at least reading the abstract". Unfortunately for me (not necessarily others) these kinds of context act as framing, so I am less likely to match to a similar case in a different domain. Here's a CS example: let's just say you might have found a way to, say, compress the TLB or use fewer instructions to use it which speeds things up in most cases but slows them down in a few corner cases. You could start by talking about the problem of paging systems under high load or large RAM or something -- great! But if you described a novel hashing architecture, later in the paper pointing out that it's "..useful, for example in a pager", I might read the paper and say "holy cow this would work well for this thing I'm working on". That's why I prefer just the dry bones. I can hang whatever flesh I want onto them. But I know not everybody is like that, and that's OK. The world isn't supposed to pander just to my need (though it should, dammit!)

sethhochberg 3y ago

As someone who never took much advanced math or physics in school and really doesn't understand what either representation of that material is staying, personally I find the second example far, far more approachable because it is far more googleable! If Gauge Theory is a concept required to relate to the other content in that sentence I've got no shot of knowing gauge theory is involved in the first example. I don't know what the arrow between P and M means. I'd have to look up what a G-bundle is. Its basically not clear to me which parts are syntax and which are proper nouns. The example which reads more like prose than an equation expressed in terms of English words gives me much, much more context for where to begin reading about what I don't know.

gumby 3y ago

One important element for me is that the framing should be as specific as possible. The article's example, regrettably isn't the best example of this, but: by saying "one of the main problems..." the author (quite reasonably, not click-baiting) is trying to say "this paper is about something important and is worth reading, or at least reading the abstract". Unfortunately for me (not necessarily others) these kinds of context act as framing, so I am less likely to match to a similar case in a different domain. Here's a CS example: let's just say you might have found a way to, say, compress the TLB or use fewer instructions to use it which speeds things up in most cases but slows them down in a few corner cases. You could start by talking about the problem of paging systems under high load or large RAM or something -- great! But if you described a novel hashing architecture, later in the paper pointing out that it's "..useful, for example in a pager", I might read the paper and say "holy cow this would work well for this thing I'm working on". That's why I prefer just the dry bones. I can hang whatever flesh I want onto them. But I know not everybody is like that, and that's OK. The world isn't supposed to pander just to my need (though it should, dammit!)