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Couldn't agree more. One of the problems I always had with math textbooks was that you had to read them as a narrative rather than using them as a reference to

by vilya 17y ago

Couldn't agree more. One of the problems I always had with math textbooks was that you had to read them as a narrative rather than using them as a reference to dip in and out of. The reason being that most examples or formulas would use symbols defined earlier in the text without bothering to restate their meaning. So looking up a simple formula would turn into a multi-hour trawl back through the textbook trying to find definitions of all the symbols they were using. If only mathematicians - and textbook authors, especially - were taught to use meaningful variable names! On a related note, if anyone does know of a good math reference (esp. for calculus!) which makes an effort to keep it's formulas self-contained, I'd love to hear about it!

hackerblues 17y ago
I think there are two aspects to this that you might not have considered. 1) If your contact with maths is simply reading a formula out of a book and implementing it then long variable names might be fine. If you are actually trying to do a calculation then long variable names are terrible on two fronts: firstly because they take so much longer to write out, secondly because the additional characters obscure the 'moving parts' of an equation. I'd much prefer looking at "a(b+c) = ab + ac" vs "first_variable * (second_variable + third_variable) = first_variable * second_variable + first_variable * third_variable" 2) I don't really understand what you mean by meaningful variable names. Perhaps if you are using mathematics to model a specific thing then they make sense: eg number_of_people = number_of_males + number_of_females. However, mathematics as a discipline isn't about modeling specific situations, there is no "mathematics for groups of people" for instance. Instead mathematics deals with manipulating abstract ideas - do abstract ideas really have meaningful names? If you do have some idea then perhaps you could explain how you would define a derivative with meaningful names? The best I can come up with is: derivative(some_function(variable)) = limit small_change approaches 0 (some_function(variable + small_change) - some_function(variable)) / small_change Does that really assist cognition more than the standard: f'(t) = lim h->0 (f(t+h)-f(t))/h ? btw, can you see from this example what I mean about the extra wordiness hiding the parts? (Maybe I've just used the standard notation for so long the words mess up my pattern matching.)

by vilya 17y ago

hackerblues 17y ago

I think there are two aspects to this that you might not have considered. 1) If your contact with maths is simply reading a formula out of a book and implementing it then long variable names might be fine. If you are actually trying to do a calculation then long variable names are terrible on two fronts: firstly because they take so much longer to write out, secondly because the additional characters obscure the 'moving parts' of an equation. I'd much prefer looking at "a(b+c) = ab + ac" vs "first_variable * (second_variable + third_variable) = first_variable * second_variable + first_variable * third_variable" 2) I don't really understand what you mean by meaningful variable names. Perhaps if you are using mathematics to model a specific thing then they make sense: eg number_of_people = number_of_males + number_of_females. However, mathematics as a discipline isn't about modeling specific situations, there is no "mathematics for groups of people" for instance. Instead mathematics deals with manipulating abstract ideas - do abstract ideas really have meaningful names? If you do have some idea then perhaps you could explain how you would define a derivative with meaningful names? The best I can come up with is: derivative(some_function(variable)) = limit small_change approaches 0 (some_function(variable + small_change) - some_function(variable)) / small_change Does that really assist cognition more than the standard: f'(t) = lim h->0 (f(t+h)-f(t))/h ? btw, can you see from this example what I mean about the extra wordiness hiding the parts? (Maybe I've just used the standard notation for so long the words mess up my pattern matching.)