Gilbert Strang: Linear Algebra vs Calculus

00:00:00.000 | - So planes in these multi-dimensional spaces,

00:00:05.000 | how difficult of an idea is that to come to, do you think?

00:00:10.220 | If you look back in time, I think mathematically

00:00:15.220 | it makes sense, but I don't know if it's intuitive

00:00:18.060 | for us to imagine, just as we were talking about.

00:00:21.220 | Feels like calculus is easier to intuit.

00:00:24.900 | - Well, I have to admit, calculus came earlier,

00:00:28.500 | earlier than linear algebra, so Newton and Leibniz

00:00:31.420 | were the great men to understand the key ideas of calculus.

00:00:35.920 | But linear algebra to me is like, okay,

00:00:40.200 | it's the starting point, 'cause it's all about flat things.

00:00:44.280 | Calculus has got, all the complications of calculus

00:00:47.260 | come from the curves, the bending, the curved surfaces.

00:00:52.260 | Linear algebra, the surfaces are all flat.

00:00:56.000 | Nothing bends in linear algebra.

00:00:58.140 | So it should have come first, but it didn't.

00:01:01.760 | And calculus also comes first in high school classes,

00:01:06.760 | in college class, it'll be freshman math,

00:01:10.960 | it'll be calculus, and then I say, enough of it.

00:01:14.440 | Like, okay, get to the good stuff.

00:01:17.620 | - Do you think linear algebra should come first?

00:01:21.000 | - Well, it really, I'm okay with it not coming first,

00:01:24.800 | but it should, yeah, it should.

00:01:27.200 | It's simpler.

00:01:28.140 | - 'Cause everything's flat.

00:01:30.280 | - Yeah, everything's flat.

00:01:31.760 | Well, of course, for that reason,

00:01:33.680 | calculus sort of sticks to one dimension,

00:01:36.720 | or eventually you do multivariate,

00:01:39.600 | but that basically means two dimensions.

00:01:42.360 | Linear algebra, you take off into 10 dimensions,

00:01:44.720 | no problem.

00:01:45.640 | - It just feels scary and dangerous

00:01:47.720 | to go beyond two dimensions, that's all.

00:01:49.920 | - If everything's flat, you can't go wrong.

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