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>>IN my experience, mathematical objects and concepts are simple, at the same level of difficulty as, say, quicksort or an AVL tree. All of math is that way. Wh

>>IN my experience, mathematical objects and concepts are simple, at the same level of difficulty as, say, quicksort or an AVL tree. All of math is that way. What's hard about math is the notation, not the concepts or mathematical objects that are presented. Okay. So can you give some examples of better notation for an operad or a quasitriangular quasi-hopf algebra? Or even tracking the indices on tensors as in Riemannian geometry? I'm not saying your wrong, the book Structure and Intepretation of Classical Mechanics makes some minor notation changes for greater clarity, or instance. But I don't think it terribly helpful to state that "math notation is horrible; no one can understand it but mathematicians".

erichocean 14y ago
can you give some examples of better notation for an operad Not really, no (although I don't think this proves anything one way or the other). Obviously there's a difference between mathematics and computer science, as well as a lot of overlap. My intuitive sense of things is that math "appears" to be more complex/novel/difficult than it actually is precisely because of the notation. More specifically, because math adopts notations that are useless without the accompanying text (see [0] for an example). In CS, this would be like code that only "worked" if you also parsed and executed the comments! My point is more or less that in math, this CS idea: List<List>, would be given a special name, it's own notation, along with a bunch of properties that, when presented as List<List>, clearly apply. In the List<List> example, for instance, it's obvious I can iterate on each inner list -- I don't need to define a special "property" on this "object" telling me that. In math, you would, along with special notation you invented just for your paper (yay!). When you define obvious properties of things, your mind starts to break down: the reason he's saying this is, presumably, because somewhere else some other obvious property doesn't hold. I need to pay attention. Except...you don't. It's just an artifact of how math is done. Of course, it's worse than that, because we wouldn't be content to refer to it as a List<List>. No, we'd need to give it a name, probably a random person's name, which you'd then have to learn. So much of mathematics, to me, is like this. Pointless complexity, invented notation, and random names for mathematical "objects" that are no more interesting than List<List>. Wow, a group of groups. Here's your PhD. Despite the snark, I do like math results, but I just really feel like they are needlessly unusable due to the notation. When you make something different, it feels different to people. They lose that concrete connection in their mind. If, instead of List<List>, I called that a Domanixly torus (note: not the geometric torus[1]), and then I went ahead and defined a bunch of "properties" of this exotic object I've created, people would (rightly) assume this was some new and exotic object. Except it's not, but the math-notation approach, and really, the whole way the field is conducted, makes it impossible to see that. Complexity is introduced where none was needed. Anyway, that's my intuitive sense of things: that math-notation obscures what is actually there, and in the process, makes its own results very difficult to apply and use, while also scaring away people who don't want to clutter their mind with "Domanixly torus" when List<List> would have worked just as well, and required far less mental gymnastics, but sadly, won't get you a PhD. [0] http://www.mtm.ufsc.br/~cmdoria/Notices/what-is-column/16-operad-htpy.pdf http://www.mtm.ufsc.br/~cmdoria/Notices/what-is-column/16-op... [1] http://en.wikipedia.org/wiki/Elliptic_curve http://en.wikipedia.org/wiki/Elliptic_curve , last paragraph of intro for an example

erichocean 14y ago

can you give some examples of better notation for an operad Not really, no (although I don't think this proves anything one way or the other). Obviously there's a difference between mathematics and computer science, as well as a lot of overlap. My intuitive sense of things is that math "appears" to be more complex/novel/difficult than it actually is precisely because of the notation. More specifically, because math adopts notations that are useless without the accompanying text (see [0] for an example). In CS, this would be like code that only "worked" if you also parsed and executed the comments! My point is more or less that in math, this CS idea: List<List>, would be given a special name, it's own notation, along with a bunch of properties that, when presented as List<List>, clearly apply. In the List<List> example, for instance, it's obvious I can iterate on each inner list -- I don't need to define a special "property" on this "object" telling me that. In math, you would, along with special notation you invented just for your paper (yay!). When you define obvious properties of things, your mind starts to break down: the reason he's saying this is, presumably, because somewhere else some other obvious property doesn't hold. I need to pay attention. Except...you don't. It's just an artifact of how math is done. Of course, it's worse than that, because we wouldn't be content to refer to it as a List<List>. No, we'd need to give it a name, probably a random person's name, which you'd then have to learn. So much of mathematics, to me, is like this. Pointless complexity, invented notation, and random names for mathematical "objects" that are no more interesting than List<List>. Wow, a group of groups. Here's your PhD. Despite the snark, I do like math results, but I just really feel like they are needlessly unusable due to the notation. When you make something different, it feels different to people. They lose that concrete connection in their mind. If, instead of List<List>, I called that a Domanixly torus (note: not the geometric torus[1]), and then I went ahead and defined a bunch of "properties" of this exotic object I've created, people would (rightly) assume this was some new and exotic object. Except it's not, but the math-notation approach, and really, the whole way the field is conducted, makes it impossible to see that. Complexity is introduced where none was needed. Anyway, that's my intuitive sense of things: that math-notation obscures what is actually there, and in the process, makes its own results very difficult to apply and use, while also scaring away people who don't want to clutter their mind with "Domanixly torus" when List<List> would have worked just as well, and required far less mental gymnastics, but sadly, won't get you a PhD. [0] http://www.mtm.ufsc.br/~cmdoria/Notices/what-is-column/16-operad-htpy.pdf http://www.mtm.ufsc.br/~cmdoria/Notices/what-is-column/16-op... [1] http://en.wikipedia.org/wiki/Elliptic_curve http://en.wikipedia.org/wiki/Elliptic_curve , last paragraph of intro for an example