2 ms·

Well an equation is certainly the more precise way of describing something, but not really the simplest. My most vivid memory of this is my Automata class; the

by hahajk 9y ago

Well an equation is certainly the more precise way of describing something, but not really the simplest. My most vivid memory of this is my Automata class; the instructor led with the equations before describing in plain language. Take push down automata as an example [1]. The equations are found in the formal definition, but the informal definition is much clearer. [1] https://en.m.wikipedia.org/wiki/Pushdown_automaton https://en.m.wikipedia.org/wiki/Pushdown_automaton

Jach 9y ago
An equation is compressed, which helps give it its precision, and can create an illusion of simplicity. Just like "a witch did it" is compressed, but if you expand it all of the complexity is inside "witch" and "it", and as you expand "it" you might arrive at some true simplifications in the untwisting sense like physical laws that make you wonder about the need for "witch"... But even if you expand the math it's still all together one of the simplest ways to describe something. That's why I like programs more, there's less implicit compression and it's easier to expand things you aren't familiar with. And there's the formalization of Kolmogorov complexity you can use for things. As you say, informal explanations are great for understanding and bringing clarity, a lot of the time they're just used to help expand the unfamiliar math, but also a lot of the time they trade off precision, conciseness, or accuracy. At worst they complicate things with twists and relations in the informal explanation that don't exist in the real deal. Sometimes that might be helpful in the same way technically unrelated mnemonics are but it's important to point them out. The conflation of simple, easy, concise, precise, clear, intuitive.. is the root of the issue when discussing what makes a good explanation.

2 ms·

Well an equation is certainly the more precise way of describing something, but not really the simplest. My most vivid memory of this is my Automata class; the

by hahajk 9y ago

Jach 9y ago
An equation is compressed, which helps give it its precision, and can create an illusion of simplicity. Just like "a witch did it" is compressed, but if you expand it all of the complexity is inside "witch" and "it", and as you expand "it" you might arrive at some true simplifications in the untwisting sense like physical laws that make you wonder about the need for "witch"... But even if you expand the math it's still all together one of the simplest ways to describe something. That's why I like programs more, there's less implicit compression and it's easier to expand things you aren't familiar with. And there's the formalization of Kolmogorov complexity you can use for things. As you say, informal explanations are great for understanding and bringing clarity, a lot of the time they're just used to help expand the unfamiliar math, but also a lot of the time they trade off precision, conciseness, or accuracy. At worst they complicate things with twists and relations in the informal explanation that don't exist in the real deal. Sometimes that might be helpful in the same way technically unrelated mnemonics are but it's important to point them out. The conflation of simple, easy, concise, precise, clear, intuitive.. is the root of the issue when discussing what makes a good explanation.