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I think it's also strategical. Math is an area of science that most of the time is not worth as much as it costs to continue. But sometimes, one of these little
by erikb 9y ago
I think it's also strategical. Math is an area of science that most of the time is not worth as much as it costs to continue. But sometimes, one of these little things turn out so huge that they change all our lives. So we really need math, but most of the time there is no logical reason to invest in it (knowledge, time, money). What to do about it?
One way that seems to have begun common in Math is to make it magical. The entry burden is hard as hell, and most reasonable things in math are expressed in a way that as best sounds mystical to common people.
This gives math some kind of credibility. Nobody wants to be the one to say how little they actually understand about it, so they continue to support the crazy magicians instead of losing face. And in the end humanity is better off for it.
PS: You can see that it is not necessary to be so cryptic but still math continues to do so, when you compare it to programming. For instance math continues to use a greek letter ∑ (sigma) to express it. In programming it's mostly a "for loop" or a "sum() function". Most people can understand "sum([1,2,3])" or "for <something> do <something> done", but they don't know the greek alphabet. So it's possible to encode math more readable, but math continues not to do so, and as argued before, probably also has good reason to do so.
- mathperson 9y agosigma is one character versus at least 3 for "sum() function". it literally takes 20 seconds to figure out what the symbol is...
- abecedarius 9y agoBut the plus sign is also one character. Why not use a big plus sign instead? That would not only be clearer, it generalizes systematically: use a big multiply sign instead of a capital pi, etc. When I was a kid I was a little intimidated by those higher math books with the "Greek E's" in them. Years passed before I learned in my early teens what they actually meant (and that it was simple, and they weren't even E's).
- mathperson 9y agoTHE BIG PLUS SIGN IS USED IN MATHEMATICS! It has an entirely DISJOINT meaning from simple summation... https://en.wikipedia.org/wiki/Direct_sum https://en.wikipedia.org/wiki/Direct_sum
- abecedarius 9y agoThat's a plus inside a circle. This logical tweak to the notation was proposed by someone I forget, maybe 3blue1brown.
- mathperson 9y agono its the direct sum notation. you have no right to tell mathematicians what notation they should or should not use. what you are entitled to is to write a mathematical paper and use some notation and try to market it. but that requires getting a phd, learning mathematics, publishing on the arxiv, going to conferences, going to talks, talking to mathematicians,......... its much easier to say "BUT MUH PLUS OH SCARY GREEK!"
- abecedarius 9y agoMy point was that the direct-sum sign you brought up was different from the plus sign that I brought up. There's no conflict.
- mathperson 9y agoI am sorry if I seem frustrated. its just I can tell you are a thoughtful, curious person, who seems like you want to enjoy mathematics. but instead i feel like you are lapsing into a math phobia and a concern with trivialities. the fact you seem genuinely interested makes it more frustrating. mathematics is not notation. notation is just arbitrary historical nonsense. an OLD professor I know complains about using fraktur (annoying german script used in abstract algebra for ideals-german mathematicians in the 1880s developed the heart of modern algebra) because "we won the war". don't let it blind you to the beauty and depth and complexity of mathematics. yes sometimes its annoying AF. (god don't even get me started on what physicists call things). but the struggle is worth it and there are things that can be improved but there is no magic bullet
- erikb 9y agoMost people are scared of things they don't know, not because there are logical reasons, but because they don't know. Human nature. If you walk on the street and you show random people a simple sum, they won't get it with sigma in the middle because their brain just wants to avoid it. But if you use english words to describe it people will get it instantly.