5 ms·

i did not understand quaternions until I read Hamilton's original works. Maybe i just have a 19th century brain or something. but i found them delightfully free

i did not understand quaternions until I read Hamilton's original works. Maybe i just have a 19th century brain or something. but i found them delightfully free of modern gobbldeygook. https://www.maths.tcd.ie/pub/HistMath/People/Hamilton/ https://www.maths.tcd.ie/pub/HistMath/People/Hamilton/

romwell 8y ago
>Maybe i just have a 19th century brain or something. but i found them delightfully free of modern gobbldeygook. No, you can blame Bourbaki for that. People such as V. Arnold decried the way mathematics is now presented[1]. It was from Hamilton's book that I learned what the word vector means and why it's used. It simply means carrier (as in malaria vector that you might heard from biologists) - and carries the space, by a translation! Such lucidity is absent from all linear algebra books I've seen. We need to go back to the presentation style of 19th century, where not only the result, but the thought process is presented. Today's papers look like they are written for formal verification systems. [1]https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html
- crocal 8y ago
  This reasonates with me so much. Thanks for the tip.
- selimthegrim 8y ago
  If you liked Hamilton, you should try Lanczos' Varational Principle of Mechanics.
- swpdkfn 8y ago
  I share the same sentiment. The state of modern mathematics exposition is well summarised IMO by "they like the logically most efficient path; that rarely coincides with the pedagogically most efficient one", to paraphrase. I also have an anecdote similar to yours regarding Hamilton and vectors: I think it was in one of the "Analysis Infinitorum" (Euler) that I found the natural logarithm being called the "hyperbolic logarithm" (it was the English translation of course). When I was a kid I was perplexed by how everyone seemed to insist on using e as the base of their logarithms and exponentials -- why the hell? Reading Euler's treatment of the subject would have been very satisfying then.

romwell 8y ago

>Maybe i just have a 19th century brain or something. but i found them delightfully free of modern gobbldeygook. No, you can blame Bourbaki for that. People such as V. Arnold decried the way mathematics is now presented[1]. It was from Hamilton's book that I learned what the word vector means and why it's used. It simply means carrier (as in malaria vector that you might heard from biologists) - and carries the space, by a translation! Such lucidity is absent from all linear algebra books I've seen. We need to go back to the presentation style of 19th century, where not only the result, but the thought process is presented. Today's papers look like they are written for formal verification systems. [1]https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html

crocal 8y ago
This reasonates with me so much. Thanks for the tip.
selimthegrim 8y ago
If you liked Hamilton, you should try Lanczos' Varational Principle of Mechanics.
swpdkfn 8y ago
I share the same sentiment. The state of modern mathematics exposition is well summarised IMO by "they like the logically most efficient path; that rarely coincides with the pedagogically most efficient one", to paraphrase. I also have an anecdote similar to yours regarding Hamilton and vectors: I think it was in one of the "Analysis Infinitorum" (Euler) that I found the natural logarithm being called the "hyperbolic logarithm" (it was the English translation of course). When I was a kid I was perplexed by how everyone seemed to insist on using e as the base of their logarithms and exponentials -- why the hell? Reading Euler's treatment of the subject would have been very satisfying then.