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"The story of linear algebra begins with systems of equations, each line describing a constraint or boundary traced upon abstract space. These simplest mathemat
by pton_xd 2y ago
"The story of linear algebra begins with systems of equations,
each line describing a constraint or boundary traced upon abstract space.
These simplest mathematical models of limitation — each equation binding variables in measured proportion — conjoin to shape the realm of
possible solutions. When several such constraints act in concert, their collaboration yields three possible fates: no solution survives their collective
force; exactly one point satisfies all bounds; or infinite possibilities trace
curves and planes through the space of satisfaction. This trichotomy — of
emptiness, uniqueness, and infinity — echoes through all of linear algebra, appearing in increasingly sophisticated forms as our understanding
deepens."
Maybe I'm not the target audience, but... that really doesn't make me interested in continuing to read.
- jpc0 2y agoEven putting it here is annoying to me... Those are a lot of words saying nothing that I just spend time reading. I'm agreeing with you.
- wrs 2y agoIt's rather purple prose, but it's entirely meaningful. Maybe it doesn't seem to mean anything until after you know some linear algebra, though...
- dxbydt 2y agoits been a long time, but when i was taught this material, i was told there are only 3 cases - x+y=1, x+y=2 clearly has no solution since two numbers can’t simultaneously add to both one and two. x+y=1,2x+2y=2 clearly has infinitely many solutions. There’s only one equation here after canceling the 2, so you can plug in x’s and y’s all day long, no end to it. x+y=1, 2x+y=1 clearly has exactly one solution (0,1) after elimination. This example stuck with me so I use it even now. The author/Claude/Gemini/whatever could have just used this simple example instead of “trichotomy of curves through space conjoin through the realm of …” math, not Shakespeare.
- wrs 2y agoSure, but saying something in an ornate way is not the same as “saying nothing”.
- BlueTemplar 2y agoAlso, isn't this a great example of "when you have a hammer, everything looks like a nail" ? To explain this I would first and foremost use a picture, where the 3 cases : parallel, identical, intersection can be intuitively seen (using our visual system, rather than our language system), with merely a glance.
- sureglymop 2y agoI agree. Not what I would expect from a math book or script.
- jcranmer 2y agoThat is such supremely bad writing that it can only come from AI being told to spice up the original opening paragraph, and short of the original author being barely literate (and possibly even then), the original text would have been better writing. The overuse of the $15 synonyms is almost always a bad idea--you want to use them sparingly, where dropping them in for their subtly different meanings enhances the text. But what is extremely sloppy here is that the possibilities of "no solutions, one solution, infinite solutions" is now being described with a different metaphor for solution here. And by the end of the paragraph, I'm not actually sure what point I'm supposed to take away from this text. (As bad as this paragraph is, the next paragraph is actually far worse.) Mathematics already has a problem for the general audience with a heavy focus on abstraction that can be difficult to intuit on more concrete objects. Adding florid metaphors to spice up your writing makes that problem worse.