4 ms·

Maybe, but a notation arrived at by an accretion of historical accident is not the way to introduce this stuff to beginners, inertia be damned. Edit: Notation

by thunk 17y ago

WilliamLP 17y ago
So raise your kids in Esperanto? Or does it really matter that much in the end?
- thunk 17y ago
  I thought someone might try that tack. Math is completely decoupled from its representation, so you can use whatever notation you want and not lose anything. I'm not gonna guess to what extent linguistic communication is bound up with its representation, but it's certainly more than math, meaning meaning can be lost. So your analogy doesn't work. Also, since mathematical notation is a tool primarily to facilitate mechanical transformations, and only secondarily for communication, you should use whatever lets you think biggest.
  - timwiseman 17y ago
    An excellent point as long as you do not need to actually communicate your results to anyone. As soon as you do, it becomes precisely as bound as language is.
    - deleted 17y ago
      [deleted]
- tokenadult 17y ago
  So raise your kids in Esperanto? I hope not. http://www.xibalba.demon.co.uk/jbr/ranto/ http://www.xibalba.demon.co.uk/jbr/ranto/ A Nobel laureate in physics who grew up in a non-English-speaking country recommends learning English as a key to physics research. http://www.phys.uu.nl/~thooft/theorist.html http://www.phys.uu.nl/~thooft/theorist.html
  - eiriarte 17y ago
    The author of that article is well known in the Esperanto world for being the author of that article... and nothing more ;) A true expert in Esperanto, the linguist and psychologist Claude Piron, debunked that article years ago: http://claudepiron.free.fr/articlesenanglais/why.htm http://claudepiron.free.fr/articlesenanglais/why.htm
onedognight 17y ago
Good teachers do try to use consistent notation, but they also understand the need to communicate with the rest of the world and so end up having to teach historical accidents. Here's a fun one: pi is wrong! http://www.math.utah.edu/~palais/pi.pdf http://www.math.utah.edu/~palais/pi.pdf
davidmathers 17y ago
"At school Feynman approached mathematics in a highly unconventional way. Basically he enjoyed recreational mathematics from which he derived a large amount of pleasure. He studied a lot of mathematics in his own time including trigonometry, differential and integral calculus, and complex numbers long before he met these topics in his formal education. Realizing the importance of mathematical notation, he invented his own notation for sin, cos, tan, f (x) etc. which he thought was much better than the standard notation. However, when a friend asked him to explain a piece of mathematics, he suddenly realized that notation could not be a personal matter since one needed it to communicate." The story is either in "Surely You're Joking, Mr. Feynman" or "What Do You Care What Other People Think?". I forget which stories are in which book. Both are great though.
- christopherolah 17y ago
  I thought my symbols were just as good, if not better, than the regular symbols -- it doesn't make any difference what symbols you use -- but I discovered later that it does make a difference. Once when I was explaining something to another kid in high school, without thinking I started to make these symbols, and he said, "What the hell are those?" I realized then that if I'm going to talk to anybody else, I'll have to use the standard symbols, so I eventually gave up my own symbols. -- Surely You're Joking, Mr Feynman (http://www.gorgorat.com/ http://www.gorgorat.com/) That said, I'm inclined to say that at some point it makes sense to break backwards compatibility in favour of a better system.

Maybe, but a notation arrived at by an accretion of historical accident is not the way to introduce this stuff to beginners, inertia be damned. Edit: Notation

by thunk 17y ago

Maybe, but a notation arrived at by an accretion of historical accident is not the way to introduce this stuff to beginners, inertia be damned. Edit: Notation

WilliamLP 17y ago

So raise your kids in Esperanto? Or does it really matter that much in the end?

thunk 17y ago
I thought someone might try that tack. Math is completely decoupled from its representation, so you can use whatever notation you want and not lose anything. I'm not gonna guess to what extent linguistic communication is bound up with its representation, but it's certainly more than math, meaning meaning can be lost. So your analogy doesn't work. Also, since mathematical notation is a tool primarily to facilitate mechanical transformations, and only secondarily for communication, you should use whatever lets you think biggest.
- timwiseman 17y ago
  An excellent point as long as you do not need to actually communicate your results to anyone. As soon as you do, it becomes precisely as bound as language is.
  - deleted 17y ago
    [deleted]
tokenadult 17y ago
So raise your kids in Esperanto? I hope not. http://www.xibalba.demon.co.uk/jbr/ranto/ http://www.xibalba.demon.co.uk/jbr/ranto/ A Nobel laureate in physics who grew up in a non-English-speaking country recommends learning English as a key to physics research. http://www.phys.uu.nl/~thooft/theorist.html http://www.phys.uu.nl/~thooft/theorist.html
- eiriarte 17y ago
  The author of that article is well known in the Esperanto world for being the author of that article... and nothing more ;) A true expert in Esperanto, the linguist and psychologist Claude Piron, debunked that article years ago: http://claudepiron.free.fr/articlesenanglais/why.htm http://claudepiron.free.fr/articlesenanglais/why.htm

onedognight 17y ago

Good teachers do try to use consistent notation, but they also understand the need to communicate with the rest of the world and so end up having to teach historical accidents. Here's a fun one: pi is wrong! http://www.math.utah.edu/~palais/pi.pdf http://www.math.utah.edu/~palais/pi.pdf

davidmathers 17y ago

"At school Feynman approached mathematics in a highly unconventional way. Basically he enjoyed recreational mathematics from which he derived a large amount of pleasure. He studied a lot of mathematics in his own time including trigonometry, differential and integral calculus, and complex numbers long before he met these topics in his formal education. Realizing the importance of mathematical notation, he invented his own notation for sin, cos, tan, f (x) etc. which he thought was much better than the standard notation. However, when a friend asked him to explain a piece of mathematics, he suddenly realized that notation could not be a personal matter since one needed it to communicate." The story is either in "Surely You're Joking, Mr. Feynman" or "What Do You Care What Other People Think?". I forget which stories are in which book. Both are great though.

christopherolah 17y ago
I thought my symbols were just as good, if not better, than the regular symbols -- it doesn't make any difference what symbols you use -- but I discovered later that it does make a difference. Once when I was explaining something to another kid in high school, without thinking I started to make these symbols, and he said, "What the hell are those?" I realized then that if I'm going to talk to anybody else, I'll have to use the standard symbols, so I eventually gave up my own symbols. -- Surely You're Joking, Mr Feynman (http://www.gorgorat.com/ http://www.gorgorat.com/) That said, I'm inclined to say that at some point it makes sense to break backwards compatibility in favour of a better system.