3 ms·

I recently used category theory to clarify my thinking on a difficult type-conversions problem I had in some C++ code that needed to generically handle many dif

I recently used category theory to clarify my thinking on a difficult type-conversions problem I had in some C++ code that needed to generically handle many different combinations of const/non-const and value/reference/pointer to another. It is useful for programming, and I don't see why you're so negative on introductory texts existing to teach just category theory. To use your example specifically: in fact I do not care about set theory, algebra, and topology, I just wanted to know whether it would be useful for my specific problem. So I read Pierce's Basic Category Theory for Computer Scientists, and found it useful. This insistence that if you want to learn W you must first spend N years learning X, Y, and Z is the kind of elitist bullshit that puts laymen off learning abstract math. If you can't explain a subject to someone outside the field, can't explain it without telling them to go spend a few years of study before they talk to you, then you simply do not understand your subject.

xyzzyz 15y ago
This insistence that if you want to learn W you must first spend N years learning X, Y, and Z is the kind of elitist bullshit that puts laymen off learning abstract math. If you can't explain a subject to someone outside the field, can't explain it without telling them to go spend a few years of study before they talk to you, then you simply do not understand your subject. It's a very romantic, but totally untrue point of view. Sure, you can say that topology is a study of shape, algebra is a study of structure, algebraic topology is a study of shape using algebraic or combinatoric means, and homological algebra is, well, abstract nonsense without any connection to real life problems, notions and intuitions, but yeah. Unfortunately, this does not give you any more insight into these subjects than say, describing solid-state physics as "theory of rigid matter" or neurobiology as "theory of brain". What's more, when you do s/abstract math/modern physics/ in the first sentence of the quotation, it sounds really silly: how can you, for instance, study solid-state physics, if you have no idea about electromagnetism, crystalography, or quantum mechanics? Sure, you can pick up a textbook on solid state physics and read it, but you won't understand anything without the background the author assumed you have. Seriously, if you think that you don't need to learn algebra or topology before algebraic topology, pick up a Hatcher's book[1], read first chapter as many times as you like, and, if you make it that far, which I seriously doubt, try to do any of the exercises at the end of it -- after reading first chapter, you're supposed to be able to do at least some, if not all of them. Mind you, Hatcher's book is considered to be a gentle one, and if you don't believe me, try May's lecture notes[2]. To sum up, most of the time you can explain laymen in vague terms what the field is about, more or less (but not always, as is the case with, for instance, homological algebra). However, you cannot explain what you actually do in these fields, because, well, your layman will just not speak language you'd need to use -- I have yet to hear how does one explain what is a derived functor to a layman, you seem to be interested in category theory, why don't you try? I'm happy with the fact that world and science is not simple as you describe -- if it was, all the smart minds from ages past would have already discovered everything, maybe leaving only fruits at the very top of the tree. Now, they only picked the low hanging fruits, and I have a chance to continue their work by standing on their shoulders. Actually, most of them were already standing on the shoulders of other scientists, and because of that, you have to spend more years climbing. [1] - http://www.math.cornell.edu/~hatcher/AT/AT.pdf http://www.math.cornell.edu/~hatcher/AT/AT.pdf [2] - http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf

xyzzyz 15y ago

This insistence that if you want to learn W you must first spend N years learning X, Y, and Z is the kind of elitist bullshit that puts laymen off learning abstract math. If you can't explain a subject to someone outside the field, can't explain it without telling them to go spend a few years of study before they talk to you, then you simply do not understand your subject. It's a very romantic, but totally untrue point of view. Sure, you can say that topology is a study of shape, algebra is a study of structure, algebraic topology is a study of shape using algebraic or combinatoric means, and homological algebra is, well, abstract nonsense without any connection to real life problems, notions and intuitions, but yeah. Unfortunately, this does not give you any more insight into these subjects than say, describing solid-state physics as "theory of rigid matter" or neurobiology as "theory of brain". What's more, when you do s/abstract math/modern physics/ in the first sentence of the quotation, it sounds really silly: how can you, for instance, study solid-state physics, if you have no idea about electromagnetism, crystalography, or quantum mechanics? Sure, you can pick up a textbook on solid state physics and read it, but you won't understand anything without the background the author assumed you have. Seriously, if you think that you don't need to learn algebra or topology before algebraic topology, pick up a Hatcher's book[1], read first chapter as many times as you like, and, if you make it that far, which I seriously doubt, try to do any of the exercises at the end of it -- after reading first chapter, you're supposed to be able to do at least some, if not all of them. Mind you, Hatcher's book is considered to be a gentle one, and if you don't believe me, try May's lecture notes[2]. To sum up, most of the time you can explain laymen in vague terms what the field is about, more or less (but not always, as is the case with, for instance, homological algebra). However, you cannot explain what you actually do in these fields, because, well, your layman will just not speak language you'd need to use -- I have yet to hear how does one explain what is a derived functor to a layman, you seem to be interested in category theory, why don't you try? I'm happy with the fact that world and science is not simple as you describe -- if it was, all the smart minds from ages past would have already discovered everything, maybe leaving only fruits at the very top of the tree. Now, they only picked the low hanging fruits, and I have a chance to continue their work by standing on their shoulders. Actually, most of them were already standing on the shoulders of other scientists, and because of that, you have to spend more years climbing. [1] - http://www.math.cornell.edu/~hatcher/AT/AT.pdf http://www.math.cornell.edu/~hatcher/AT/AT.pdf [2] - http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf