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I wonder how much difficulty to "get" maths have to do with difficulty to grasp notation conventions. Probably not much in the big picture. But is there some bo

by mongol 5y ago

I wonder how much difficulty to "get" maths have to do with difficulty to grasp notation conventions. Probably not much in the big picture. But is there some book or dictionary that lays this out in a novel way that makes the reader feel they can understand it superficially?

Banana699 5y ago
Bad/Confusing/Complex notation can absolutely ruin a learner's attempt to grok a piece of math, it's not a trivial issue at all, and it comes up in all levels of math. But good notation doesn't necessarily mean easy understanding. It's just like language. If I speak a different language, forget about communication in any deep way. But even if I'm speaking the same language, it's still not guaranteed we can communicate well or at all. Absence of shared language guarantees the impossibility of communication, but it's presence guarantees nothing. The author is correct about one thing : Notation is incredibly under-appreciated and under-discussed by mathematicians, although it has immense power to shape thinking. Some visionaries like Charles Babbage, Kenneth Iverson or Stephan Wolfram might talk about it every 50 year or so, but that's it. It's mind boggling how the primary tool of communication is just developed ad-hoc on a whim with only minimal explanation and formalization. >But is there some book or dictionary that lays this out in a novel way What do you mean by "this"? is it specifically the overbars-and-underbars notation used in the article? as far as I know, that's the first time I encountered it. But the idea that exponentials, logarithms and roots all basically say the same thing and that notations should reflect that is discussed a lot, 3blue1brown has a very well known video that explains it in a visual way. https://youtu.be/sULa9Lc4pck https://youtu.be/sULa9Lc4pck
galaxyLogic 5y ago
Math notation, and there can be several is like a foreign language. You can only to learn it by using it a lot in practice. You can't just read a book that tells you how to speak a foreign language and that would be it. You have to learn and understand the symbols, and then you have to learn and understand what is being said using those symbols. You need to learn the letters and the words made with them and then sentences made out of words. It's a lot to learn. But practice makes perfect.
laichzeit0 5y ago
Don't think it has much to do with the notation. Take the integral sign for example. What are we talking about Riemann, Riemann–Stieltjes, Lebesgue, some weird stochastic integral? It's the same symbol. You won't "understand" it better by using a different symbol. Even the Riemann integral, to rigorously "understand" it requires lots of concepts from analysis like least upper bounds (infimum, supremum), partitions, etc. The notation is hardly the stumbling block here, there's no way of getting around understanding the details if you really truly want to "get" it. But again, in practise, when you're doing integration by hand, you've learned a few tricks that work and you hardly ever think about it at the level of analysis.

by mongol 5y ago

Banana699 5y ago

Bad/Confusing/Complex notation can absolutely ruin a learner's attempt to grok a piece of math, it's not a trivial issue at all, and it comes up in all levels of math. But good notation doesn't necessarily mean easy understanding. It's just like language. If I speak a different language, forget about communication in any deep way. But even if I'm speaking the same language, it's still not guaranteed we can communicate well or at all. Absence of shared language guarantees the impossibility of communication, but it's presence guarantees nothing. The author is correct about one thing : Notation is incredibly under-appreciated and under-discussed by mathematicians, although it has immense power to shape thinking. Some visionaries like Charles Babbage, Kenneth Iverson or Stephan Wolfram might talk about it every 50 year or so, but that's it. It's mind boggling how the primary tool of communication is just developed ad-hoc on a whim with only minimal explanation and formalization. >But is there some book or dictionary that lays this out in a novel way What do you mean by "this"? is it specifically the overbars-and-underbars notation used in the article? as far as I know, that's the first time I encountered it. But the idea that exponentials, logarithms and roots all basically say the same thing and that notations should reflect that is discussed a lot, 3blue1brown has a very well known video that explains it in a visual way. https://youtu.be/sULa9Lc4pck https://youtu.be/sULa9Lc4pck

galaxyLogic 5y ago

Math notation, and there can be several is like a foreign language. You can only to learn it by using it a lot in practice. You can't just read a book that tells you how to speak a foreign language and that would be it. You have to learn and understand the symbols, and then you have to learn and understand what is being said using those symbols. You need to learn the letters and the words made with them and then sentences made out of words. It's a lot to learn. But practice makes perfect.

laichzeit0 5y ago

Don't think it has much to do with the notation. Take the integral sign for example. What are we talking about Riemann, Riemann–Stieltjes, Lebesgue, some weird stochastic integral? It's the same symbol. You won't "understand" it better by using a different symbol. Even the Riemann integral, to rigorously "understand" it requires lots of concepts from analysis like least upper bounds (infimum, supremum), partitions, etc. The notation is hardly the stumbling block here, there's no way of getting around understanding the details if you really truly want to "get" it. But again, in practise, when you're doing integration by hand, you've learned a few tricks that work and you hardly ever think about it at the level of analysis.