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It took me a long time to realize math consisted of abstractions. I was never told, for example, that matrices are a useful abstraction (shorthand?) for repres
by vendiddy 1y ago
It took me a long time to realize math consisted of abstractions.
I was never told, for example, that matrices are a useful abstraction (shorthand?) for representing linear equations.
Or that imaginary numbers were an invented abstraction that made certain calculations easier.
It would have been nice to learn it from the perspective of how those abstractions came into being and why they're useful.
- Nevermark 1y agoEven if we narrow math to numbers, what many people thing of as "math", we quickly move from arithmetic to patterns. The patterns of repetitions of single things, repetitions over different things, repetitions between different things, repetitions over repetitions, ... Natural/counting numbers are just the simplest patterns of repetition.
- Jensson 1y agoNumbers are an abstraction, not just "imaginary" numbers, all numbers are imaginary they don't exist in reality.
- sieabahlpark 1y ago[dead]
- bee_rider 1y ago> I was never told, for example, that matrices are a useful abstraction (shorthand?) for representing linear equations. Congratulations on overcoming the (very weird) choice of whoever taught your intro to linear algebra class.
- godelski 1y agoI'm not sure how to interpret this comment, it could easily be read in multiple ways. (Depends on priors) Regardless, it's a shockingly common occurrence. I'd agree it's not the right way, but it is also a common way. That perspective might define those priors
- bee_rider 1y agoYeah, I was worried it might come off as sarcastic or something. Hopefully the original commenter doesn’t take it that way, or reads this follow up. Unfortunately, adding stuff like “honestly” often makes a comment look even more sarcastic. It is a real pain. But yes, I am expressing honest admiration—it was a bad move on the part of the teacher I think, which the poster seems to have overcome!
- godelski 1y agoWell I appreciate clarifying! I originally took it as sarcastic but second guessed myself. I figured math is pedantic, so maybe being a little pedantic here could help haha. I went through the same thing, it really isn't easy. But it is also why I don't blame others for not seeing it. It would be hypocritical to do so. I'm just not sure what's the best way to share, I'm open to ideas. Unfortunately we have to contend with priors that we see here, though I'm happy if my efforts even make one more person able to share in this beauty.
- vendiddy 1y agoNo worries I did not take it that way!
- thaumasiotes 1y agoNo, it is "very weird". Without knowing that a matrix represents a system of equations, Gaussian elimination would be pointless.
- rtkwe 1y agoOr just your regular 8/9th grade Algebra course where you should have learned systems of equations. That's where I first encountered using matrices for systems of equations at least. (maybe it was Algebra 2+ but it was definitely before taking Linear Algebra in college).