Hello, @bleujay. Thank you for your kind and comprehensive response to my inquiry. This is a general topic that for me extends considerably beyond mere curiosity, although of that I have been blessed with plenty.
The instant "problem" I'm exercised with is that of my granddaughter's high school geometry/trigonometry course. She is struggling in it, and based on what I have observed, I believe that her problems are at least in part language based. There is an entire vocabulary that has grown up around this mathematical domain which (in my opinion) obscures rather than communicates.
What I believe has happened is that, over the course of centuries, mathematicians have made many interesting observations - in this realm of math, predominantly about lines and angles - and have created a bewilderingly rich vocabulary that perhaps goes to excess. In other words, at this point in my analysis, it seems to me that they have taken something quite conceptually simple and made it overly complex.
I will now attempt to reflect back a better understanding of what you are saying. Please do correct me if I've missed the point? I think your principle means something like this:
Language is the symbolic representation of ideas. The vocabulary of any language is the unique set of symbols associated with discrete ideas. Our minds are symbol processing computers. "Thinking" is a process whereby we store, organize, re-arrange, and communicate ideas, both to ourselves and others. Therefore, the richer our vocabulary, wherever it may come from, the more effective we can be at the process of "thinking."
In the case of geometry/trigonometry, my present intuition is that the language could use a top-to-bottom re-vamping. I strongly suspect that there could be a very helpful simplification, but I haven't proven that to myself yet. I will continue to struggle through this, partly for my own entertainment and growth, and of course for the sake of my granddaughter.
I thank you, dear @bleujay, for raising this interesting notion. :) 😄😇😄
Thank you for your reply @creatr.
Yes...lovely explanation....agree....thinking and therefore communicating; which is so important because The God communicates with mankind through His word.
Have you seen the movie...The Book Thief.....reminding one that letters become words, words become sentences, sentences become paragraphs, paragraphs become chapters, chapters become books.
Thank you for the reminder.....letters are symbols.
Regarding the topic of maths: Saxon Math is particurlary helpful with respect to the study of maths. Have a look...every mathematician bleujay has encountered respects it immensely.
Saxon Math consists of several volumes.... also available at Amazon. Robinson Curriculum has an explanation of it on his website as well. Perhaps one could extract the material needed to progress in geometry.
...a fun fact....Thieme did ten math problems a day to keep his grey cells active in that department.
Your thoughtful reply is appreciated.
Wishing you and yours all the best.
Thank you for the Saxon recommendation; I encountered Saxon years ago when we were almost entirely home-schooling, and appreciate being reminded of them. I have also heard of The Book Thief, but not yet seen it. I look forward to doing so.
On language; according to some, DNA itself fits the rigorous definition of a language, thus testifying to a wise Creator. A gentleman by the name of Perry Marshall has developed a fascinating presentation based on this thesis.
Thank you again for your thought-provoking interaction, friend @bleujay!