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That's really excellent writing. It explains the gist of it really well. I suspect the proof details are very complex though. It's also not clear if this method

That's really excellent writing. It explains the gist of it really well. I suspect the proof details are very complex though. It's also not clear if this method will practically be a speed up, or just asymptotically. It's still a very cool result though: I love how my intuition would tell me that solving matrix multiplication is surely the fastest way, and then someone comes along and explains this method and my brain goes "oh yeah, that does make sense it could be faster". That's the beauty of certain results and explanations.

toolslive 6y ago
My feeling was just the opposite. I was constantly thinking "stop acting like I'm 12 and have 0 knowledge about linear algebra." As usual, it just depends what your context is, and the author will be happy to know there's an audience that finds it excellent.
- Moodles 6y ago
  I have a master's degree in math and a PhD in STEM so I know how linear algebra works. So when I say it's excellent writing, I don't mean perfectly calibrated for me or you. I mean it's excellent writing for a wide audience to get the gist of it. I think that's very difficult to do for math. An average 12 year old would not understand matrices without a very clear explanation. Having taught math to both children and undergrads, I think it's very easy to underestimate how easy it is once you already understand it. A sentence like: > for any ε > 0 and 0 < δ < 1, using poly(dimension, #nonzeros, condition, 1/ε, 1/δ) floating-point operations, our algorithm finds a solution having less than ε error with probability 1 - δ. Would confuse the shit out of most people. This video explains really beautifully what I mean: https://www.youtube.com/watch?v=M64HUIJFTZM https://www.youtube.com/watch?v=M64HUIJFTZM
vendiddy 6y ago
It seems like there's a lot of potential for domain specific optimization if we can improve the guessing algorithms.

toolslive 6y ago

My feeling was just the opposite. I was constantly thinking "stop acting like I'm 12 and have 0 knowledge about linear algebra." As usual, it just depends what your context is, and the author will be happy to know there's an audience that finds it excellent.

Moodles 6y ago
I have a master's degree in math and a PhD in STEM so I know how linear algebra works. So when I say it's excellent writing, I don't mean perfectly calibrated for me or you. I mean it's excellent writing for a wide audience to get the gist of it. I think that's very difficult to do for math. An average 12 year old would not understand matrices without a very clear explanation. Having taught math to both children and undergrads, I think it's very easy to underestimate how easy it is once you already understand it. A sentence like: > for any ε > 0 and 0 < δ < 1, using poly(dimension, #nonzeros, condition, 1/ε, 1/δ) floating-point operations, our algorithm finds a solution having less than ε error with probability 1 - δ. Would confuse the shit out of most people. This video explains really beautifully what I mean: https://www.youtube.com/watch?v=M64HUIJFTZM https://www.youtube.com/watch?v=M64HUIJFTZM

vendiddy 6y ago

It seems like there's a lot of potential for domain specific optimization if we can improve the guessing algorithms.