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Math Intuition Cheatsheet

betterexplained.com

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Re: Math Intuition Cheatsheet

#2

Post by fenomas »

This is terrific. I'm mathy enough to know e to several places, and use it in programs occasionally, but if you'd asked me how it might be intuitively derived I'd have been at a loss. And that's just for something inside my comfort zone - the article on linear algebra is just as illuminating.

This looks like it will be my commute reading for the week. But more than that it just makes me happy that it exists.

Re: Math Intuition Cheatsheet

#3

Post by akrolsmir »

I'd read Yudkowsky's popular "An Intuitive Explanation of Bayes' Theorem" as well as a few others, but the article on this site made me feel like I actually understood it for the first time. The examples were clever, short, and simple, while still demonstrating how powerful Bayes' Theorem can be.

The concise explanations here seem more helpful than semester-long university courses I've taken. I definitely look forward to exploring his other articles on math and programming.

Re: Math Intuition Cheatsheet

#5

Post by bithive123 »

I am often saddened by how much easier it has been for me to acquire computer science versus mathematical literacy. Embarrassingly, years after a poorly-timed calculus course left me thinking I had to be able to prove the central limit theorem in order to use calculus, the biggest barriers have turned out to be things programming as a discipline has learned to avoid; encouraging varied and/or terse notations, opaque variable naming schemes, and arbitrary use of jargon where simpler terms would suffice.

A friend of mine who is a physicist once complained to me that every time he had to install some scientific software package on his computer, he had to deal with a litany of arbitrary things which seemed to have nothing to do with his task. I countered with my experience learning math and joked that at least programmers are willing to occasionally refresh our idioms and notations to better reflect our mutual understanding.

Re: Math Intuition Cheatsheet

#8

Post by kalid »

bithive123 wrote: post #5

I am often saddened by how much easier it has been for me to acquire computer science versus mathematical literacy. Embarrassingly, years after a poorly-timed calculus course left me thinking I had to be able to prove the central limit theorem in order to use calculus, the biggest barriers have turned out to be things programming as a discipline has learned to avoid; encouraging varied and/or terse notations, opaque…

(Kalid from BetterExplained here)

Thanks for the comment. There's this weird notion in Calculus education that we need to start from first principles. Limits were invented a century after Newton died, yet they're taught first. "Oh, students won't understand calculus unless they can build it from first principles. I don't care if Newton worked out gravitation with his understanding, it's not good enough."

My little candle in the darkness (http://betterexplained.com/calculus/lesson-1) is to start with intuitive notions (X-Raying a pattern into parts, Time-Lapsing parts into a whole) and then gradually introducing the terms. Eventually, if people are interested, we can get into the theory (which is like getting into the Peano axioms of arithmetic, if you care to go that deep.)

I think in math there's a tendency to express things in the lowest-level "machine code" we can. We need more comments and pseudocode outlines :).

Re: Math Intuition Cheatsheet

#9

Post by kalid »

fenomas wrote: post #2

This is terrific. I'm mathy enough to know e to several places, and use it in programs occasionally, but if you'd asked me how it might be intuitively derived I'd have been at a loss. And that's just for something inside my comfort zone - the article on linear algebra is just as illuminating. This looks like it will be my commute reading for the week. But more than that it just makes me happy that it exists.

Thanks, glad to hear you're enjoying it. I realized that until I could explain a concept intuitively, I didn't really understand it -- and it became a mission to find some analogy that really clicked for me. Hope it gives you some entertaining reading.

Re: Math Intuition Cheatsheet

#10

Post by kalid »

akrolsmir wrote: post #3

I'd read Yudkowsky's popular "An Intuitive Explanation of Bayes' Theorem" as well as a few others, but the article on this site made me feel like I actually understood it for the first time. The examples were clever, short, and simple, while still demonstrating how powerful Bayes' Theorem can be. The concise explanations here seem more helpful than semester-long university courses I've taken. I definitely look forwar…

Glad it was helpful!

There's a strange tendency in technical explanations to expand, expand, expand. A heuristic I have: Imagine you're writing a letter to yourself, before you started the course. There's no reason to waste your own time, just cover the key difficulties and how to overcome them, in simple language you would have understood.

(Oh, this letter also costs $5 a word, so let's make them count!)

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