61–70 of 104 posts
“Before I learned the art, a punch was just a punch, and a kick, just a kick. After I learned the art, a punch was no longer a punch, a kick, no longer a kick. Now that I understand the art, a punch is just a punch and a kick is just a kick.” - Bruce Lee
I wish people had more exposure to building mathematical models of things. I am fairly convinced that the only real exposure I was given was to models that we knew worked. So much so, that we didn't even execute many. Specifically, parabolic motion is something you can obviously do by throwing something. You can, similarly, plot over a time variable where things are observed. You can then see that we can write an equ…
That's something you can verify by writing some simulation code, then drawing the curve, and then drawing the best matching parabola on top. It doesn't fit.
To model the issue mathematically you need some not-too-advanced calculus. On both the computer simulation and the mathematical model, you model the rope as being made of very small elements that are linked together (like a chain). In the simulation those elements are small, but finite. In the math you take the limit as the volume of the element tends to zero.
It's the same way of thinking but math gives some different tools, enabling you to solve the curve analytically
I wish people had more exposure to building mathematical models of things. I am fairly convinced that the only real exposure I was given was to models that we knew worked. So much so, that we didn't even execute many. Specifically, parabolic motion is something you can obviously do by throwing something. You can, similarly, plot over a time variable where things are observed. You can then see that we can write an equ…
Something I really like is that the curve that a rope or thread makes when fixed in two points but not under tension, it's not a parabola. It really looks like one though, but it isn't. It's a catenary. That's something you can verify by writing some simulation code, then drawing the curve, and then drawing the best matching parabola on top. It doesn't fit. To model the issue mathematically you need some not-too-adva…
Move this into modeling and then guessing stuff like bridge tensions, and you can easily show what many of the maths are good for.
We used to have this with the attempts at building tooth pick bridges and such. Which I still think is very illuminating. But, I think there are a lot of questions you can expose with models that were often only seen by the more advanced students. And again, I agree that getting people to mentally model these things is a good goal. Right now, people rarely ponder things on paper, it seems.
Earlier quoted context omitted.
People have pointed out similarities to a few things in this thread now. It's pretty much the bell curve meme: https://knowyourmeme.com/memes/iq-bell-curve-midwit
The bell curve meme is a static taxonomy of people, and if the link you posted is correct, its origins were explicitly political. The version described by Bruce Lee, and anybody who has achieved a high level of skill, is about the process of learning and mastery. In the bell curve version, the wisdom of grug brain and the wisdom of the monk are presented as equal, and the struggle of the midwit is framed as a pretent…
Is this a joke by mimicking someone on the mid-point of the 'bell curve meme' explaining the 'bell curve meme'?
I want to be Terrance Tao when I grow up
Looking at his success it's hard to not believe that some people are objectively better than others.
Well put! In empirical research, there is an analogy where intuition and systematic data collection from experiment are both important. Without good intuition, you won’t recognize when your experimental results are likely wrong or failing to pick up on a real effect (eg from bad design, insufficient statistical power, wrong context, wrong target outcome, dumb mistakes). And without experimental confirmation, your intuition is just untested hunches, and lacks the refinement and finessing that comes from contact with the detailed structure of the real world.
As Terry says, the feeling of stumbling around in the dark suggests you are missing one of the two.
I love how well-spoken Tao is. I've enjoyed lots of his lectures before; even if you're not an expert in whatever he's discussing he knows how to explain it just right to get you up to speed as best as he can. His communication and math skills are phenomenal.
> One can roughly divide mathematical education into three stages: Similarly with programming. 1. Write programs that you think are cool 2. Learn about data structures and algorithms and complexity and software organization. 3. Write programs that you think are cool. But since you know more, you can write more cool programs. If things are working as they should, the end stage of mathematics and programming should be…
> 2. Learn about data structures and algorithms and complexity and software organization.
> 3. Write programs that you think are cool. But since you know more, you can write more cool programs.
Hegel :-)
Earlier quoted context omitted.
People have pointed out similarities to a few things in this thread now. It's pretty much the bell curve meme: https://knowyourmeme.com/memes/iq-bell-curve-midwit
This is the best meme ever / So accurate in many ways
I want to be Terrance Tao when I grow up
Looking at his success it's hard to not believe that some people are objectively better than others.
(I don't know where you grew up; where I grew up we were always obliged to chant "with liberty and justice for all")