4 ms·

I appreciate you taking the time to help people understand higher level concepts. From a different perspective... I have no traditional background in mathemati

by bradly 2y ago

I appreciate you taking the time to help people understand higher level concepts. From a different perspective... I have no traditional background in mathematics or physics. I do not understand the first line of the pdf you posted nor do I understand the process for obtaining the context to understand it. But I have intellectual curiosity. So the best path forward for me understanding is a path that can maintain that curiosity while making progress on understanding. I can reread the The Six (Not So ) Easy Pieces and not understand any of it and still find value in it. I can play with Arnold's cat and, slowly, through no scientific rigor other than the curiosity of the naked ape, I can experience these concepts that have traditionally been behind gates of context I do not possess keys to. http://gerdbreitenbach.de/arnold_cat/cat.html http://gerdbreitenbach.de/arnold_cat/cat.html

keithalewis 2y ago
[flagged]
- bradly 2y ago
  > Just stop whining about it in public. I'm curious if this is how my reply came across?
  - vo2maxer 2y ago
    Not at all. I share your sentiment. Many topics are beyond my intellectual grasp at this time, but I’m always hopeful that my curiosity will lessen their obscurity given time and persistence.
  - airstrike 2y ago
    Not at all. Your comment was perfectly fine! And that reply was way out of line...
  - keithalewis 2y ago
    Your statement "the best path forward for me understanding is a path that can maintain that curiosity" comes off as entitled. Only you owe yourself that. "I can play with Arnold's cat and, slowly, through no scientific rigor..." You are fooling yourself into believing you understand if you leave out rigor. If your post has the words "I" and "me" in every other sentence, maybe you should consider whether or not you are adding value for others in the online discussion. I doesn't cost you anything to ask other people to do things for you, and you will no doubt find other thoughtless people chiming in about your right to do that. If everything you need is not at your fingertips already, maybe no amount of handholding will help.
mnky9800n 2y ago
You aren’t supposed to understand things if you don’t know about them. That’s how it works.
mtizim 2y ago
With no mathematical rigor there is no mathematical understanding. You are robbing yourself, as the concepts are meaningless without the context. Truly appreciate the power of linear approximations by going through algebra, appreciate the tricks of calculus, marvel at the inherent tradeoffs of knowledge with estimator theory, and see the joy of the central limit theorem being true. All of this knowledge is free, and much more interesting than a formal restatement of "it was not supposed to rain, but I see clouds outside, I guess I'll expect light rain instead of a big thunderstorm".
- bradly 2y ago
  > With no mathematical rigor there is no mathematical understanding. You are robbing yourself, as the concepts are meaningless without the context. I will think more about this, but I'm not sure I agree. I have enjoyed reading Feynman talk about twins and one going on a supersonic vacation without understanding the math. Verisimilitude allows a modeling of understanding with a scalar representation of scientific knowledge, so why not? Of course I would like to understand the math in its purest forms–just the same as I wanted to read 1Q84 in Japanese to be able to fully experience it in its purest form, but my life isn't structured in a way were that is realistic even if the knowledge of the Japanese language is free. > Truly appreciate the power of linear approximations by going through algebra, appreciate the tricks of calculus, marvel at the inherent tradeoffs of knowledge with estimator theory, and see the joy of the central limit theorem being true. I can't even foil so the journey toward understanding can feel unattainable in the time resources I have. This absolutely may be a limiting belief, but the concept of knowledge being free ignores the time cost for some exploring these outside of academia or professional setting.
  - RossBencina 2y ago
    Indeed everything has an opportunity cost, and every life has its own priorities. Since you mention Feynman, I would like to observe that many expositors who target the lay audience have the skill of making the audience believe that they have comprehended(1) something of an intellectual world that they have no technical grounding to truly comprehend(2). In my view these are two distinct types of comprehension/understanding. So long as the audience is clear on which type of understanding they are getting, and is not wasting time unwittingly pursuing one type at the expense of the other then I see no harm. There is a risk however, that the pop expositors will put you in a headspace where even if you are faced with accessible, but type 2, material you will not be familiar with what really constitutes understanding. As a mature age student it took me quite a few years of maths exams to switch from 1 to 2. Nowadays I am more comfortable with admitting that I don't understand some piece of math (for that is the first step on the path to learning) than being satisfied with a pop-expository gist.
deleted 2y ago
[deleted]

by bradly 2y ago

keithalewis 2y ago

[flagged]

bradly 2y ago
> Just stop whining about it in public. I'm curious if this is how my reply came across?
- vo2maxer 2y ago
  Not at all. I share your sentiment. Many topics are beyond my intellectual grasp at this time, but I’m always hopeful that my curiosity will lessen their obscurity given time and persistence.
- airstrike 2y ago
  Not at all. Your comment was perfectly fine! And that reply was way out of line...
- keithalewis 2y ago
  Your statement "the best path forward for me understanding is a path that can maintain that curiosity" comes off as entitled. Only you owe yourself that. "I can play with Arnold's cat and, slowly, through no scientific rigor..." You are fooling yourself into believing you understand if you leave out rigor. If your post has the words "I" and "me" in every other sentence, maybe you should consider whether or not you are adding value for others in the online discussion. I doesn't cost you anything to ask other people to do things for you, and you will no doubt find other thoughtless people chiming in about your right to do that. If everything you need is not at your fingertips already, maybe no amount of handholding will help.

mnky9800n 2y ago

You aren’t supposed to understand things if you don’t know about them. That’s how it works.

mtizim 2y ago

With no mathematical rigor there is no mathematical understanding. You are robbing yourself, as the concepts are meaningless without the context. Truly appreciate the power of linear approximations by going through algebra, appreciate the tricks of calculus, marvel at the inherent tradeoffs of knowledge with estimator theory, and see the joy of the central limit theorem being true. All of this knowledge is free, and much more interesting than a formal restatement of "it was not supposed to rain, but I see clouds outside, I guess I'll expect light rain instead of a big thunderstorm".

bradly 2y ago
> With no mathematical rigor there is no mathematical understanding. You are robbing yourself, as the concepts are meaningless without the context. I will think more about this, but I'm not sure I agree. I have enjoyed reading Feynman talk about twins and one going on a supersonic vacation without understanding the math. Verisimilitude allows a modeling of understanding with a scalar representation of scientific knowledge, so why not? Of course I would like to understand the math in its purest forms–just the same as I wanted to read 1Q84 in Japanese to be able to fully experience it in its purest form, but my life isn't structured in a way were that is realistic even if the knowledge of the Japanese language is free. > Truly appreciate the power of linear approximations by going through algebra, appreciate the tricks of calculus, marvel at the inherent tradeoffs of knowledge with estimator theory, and see the joy of the central limit theorem being true. I can't even foil so the journey toward understanding can feel unattainable in the time resources I have. This absolutely may be a limiting belief, but the concept of knowledge being free ignores the time cost for some exploring these outside of academia or professional setting.
- RossBencina 2y ago
  Indeed everything has an opportunity cost, and every life has its own priorities. Since you mention Feynman, I would like to observe that many expositors who target the lay audience have the skill of making the audience believe that they have comprehended(1) something of an intellectual world that they have no technical grounding to truly comprehend(2). In my view these are two distinct types of comprehension/understanding. So long as the audience is clear on which type of understanding they are getting, and is not wasting time unwittingly pursuing one type at the expense of the other then I see no harm. There is a risk however, that the pop expositors will put you in a headspace where even if you are faced with accessible, but type 2, material you will not be familiar with what really constitutes understanding. As a mature age student it took me quite a few years of maths exams to switch from 1 to 2. Nowadays I am more comfortable with admitting that I don't understand some piece of math (for that is the first step on the path to learning) than being satisfied with a pop-expository gist.

deleted 2y ago

[deleted]