How on Earth are all of us go through the school and college and all other learning and no one ever does say: do the learning this way, spend hour on a page, ask so many questions, go back and forth, etc. Or, even if some one says this in passing, they never _show_ this process like that.
For that example problem at the end, they do a kind of confusing (and unnecessary) change of variables to get the PDF of distance traveled from the PDF of time. The PDF of distance traveled is not uniformly distributed - the object is moving faster as it falls. However, the PDF of time *is* uniformly distributed - the object is equally likely to be sampled at any time once it starts falling. So, since distance traveled is a function of time, you can calculate expected value of distance like this: E[distance] = integral of distance as a function of time * PDF of time (The bounds on the integral are zero and the maximum height the object can fall) To do it the way they do it, you can do a change of variables with the CDF for time into the CDF for distance then differentiate the CDF for distance to get the PDF, but this is an extra and not very intuitive step. Not sure if this makes any sense in a UA-cam comment but...
Kinetic energy is not a type of potential energy. You can think that potential energy is related to position and by position we think of interaction. This formula is related to the Calculus in 3 variables (conservative vector fields). The magnetic force is not conservative, so you cannot derive it as minus the gradient of a potential. Equivalent to kinetic energy is the first term of the Schrodinger equation. You can rewrite the kinetic energy of a particle as K = p^{2}/2m, where p is the momentum (note that there is 2m divided into the Schrodinger equation in the first term). So later in the book you will see the moment operator (which explains why there is a Laplacian).
wow this is gold mine. Thanks so much Andy you are lifting humanity.There are people like me who want to learn but always get overwhelmed and don't achieve much
This is fascinating, both in the new mnemonic Andy is demonstrating and the background quantum mechanics stuff. I'm following about 50% level (rusty in calculus) but am super curious and really dig the method of learning you guys are showing off. Good stuff!
@@julesjacobs1 the note thing is a custom tool he is working on, apparently. He says it at some point in the video. He seems to be actively developing it because he says he introduced a bug before this video.
a little bit surprised how much of this i already do. when doing a tutorial, i make a google doc and write lots of questions in it, anytime i feel i don't 100% understand something - which is a lot. and then try to answer those questions, if it's answered later.
Thanks so much! I can't wait to see more 😊 Andy, have you/would you ever made your memory system available? (If you have I must be a dunce because I can't find it 😄)
Regarding the discussion of Orthodox position around 50:00, I read this in a book “The Making of Atomic Bomb”, which made perfect intuitive sense to me: “But it led Heisenberg immediately to a stunning conclusion: that on the extremely small scale of the atom, there must be inherent limits to how precisely events could be known. If you identified the position of a particle-by allowing it to impact on a zinc-sulfide screen, for example, as Rutherford did-you changed its velocity and so lost that information. If you measured its velocity-by scattering gamma rays from it, perhaps-your energetic gamma-ray photons battered it into a different path and you could not then locate precisely where it was. One measurement always made the other measurement uncertain.”
The LaTeX tool is MathPix. For handwriting, I'm drawing on my iPad Pro in Notability. I display its screen on my laptop with QuickTime for the purposes of the video, but I don't when I'm on my own.
Does anyone know of a good revision app where you can input your questions and answers then have them asked back in a similar way to what Andy uses here?
My true education began after I graduated university and discovered Andy's work.
😂
Insanely informative video. This is a “how I do it” video, as opposed to “how you should do it video”. Worlds of difference appart.
The software used in the video looks amazing, I'm truly hoping it'll be released at some point
How on Earth are all of us go through the school and college and all other learning and no one ever does say: do the learning this way, spend hour on a page, ask so many questions, go back and forth, etc. Or, even if some one says this in passing, they never _show_ this process like that.
Because universities don't give you time to spend an hour on a page. At least mine doesn't. It's all quantity over quality/depth.
we spend too much time consuming information in school, and too less on evaluation and deeper processing… digesting
This is super cool. I like when people share their more-tacit knowledge over a live video like this. Thanks taking the time to do this!
Dwarkesh and Andy are the learning GOATS!
For that example problem at the end, they do a kind of confusing (and unnecessary) change of variables to get the PDF of distance traveled from the PDF of time.
The PDF of distance traveled is not uniformly distributed - the object is moving faster as it falls. However, the PDF of time *is* uniformly distributed - the object is equally likely to be sampled at any time once it starts falling.
So, since distance traveled is a function of time, you can calculate expected value of distance like this:
E[distance] = integral of distance as a function of time * PDF of time
(The bounds on the integral are zero and the maximum height the object can fall)
To do it the way they do it, you can do a change of variables with the CDF for time into the CDF for distance then differentiate the CDF for distance to get the PDF, but this is an extra and not very intuitive step. Not sure if this makes any sense in a UA-cam comment but...
Kinetic energy is not a type of potential energy. You can think that potential energy is related to position and by position we think of interaction. This formula is related to the Calculus in 3 variables (conservative vector fields). The magnetic force is not conservative, so you cannot derive it as minus the gradient of a potential. Equivalent to kinetic energy is the first term of the Schrodinger equation. You can rewrite the kinetic energy of a particle as K = p^{2}/2m, where p is the momentum (note that there is 2m divided into the Schrodinger equation in the first term). So later in the book you will see the moment operator (which explains why there is a Laplacian).
wow this is gold mine. Thanks so much Andy you are lifting humanity.There are people like me who want to learn but always get overwhelmed and don't achieve much
Thank you, Alita! 🙇♂
This is fascinating, both in the new mnemonic Andy is demonstrating and the background quantum mechanics stuff. I'm following about 50% level (rusty in calculus) but am super curious and really dig the method of learning you guys are showing off. Good stuff!
Would love to try that software! Thanks for the video
What is the software he uses?
@@julesjacobs1 I second that question!
@@julesjacobs1 the note thing is a custom tool he is working on, apparently. He says it at some point in the video. He seems to be actively developing it because he says he introduced a bug before this video.
Oh em gee, mathpix is super neat!
Thanks Andy! For the super helpful video
Now if only I had this pdfjs thing...
a little bit surprised how much of this i already do. when doing a tutorial, i make a google doc and write lots of questions in it, anytime i feel i don't 100% understand something - which is a lot. and then try to answer those questions, if it's answered later.
I’m still watching this and finding it absolutely fascinating. May I now what tool you’re using to annotate the pdf?
Thank you for this!
Hi Andy,
Is the software used in the video part of orbit project, if so could we expect it to be available?
Thanks so much! I can't wait to see more 😊 Andy, have you/would you ever made your memory system available? (If you have I must be a dunce because I can't find it 😄)
This particular prototype isn't available, no-sorry.
@@andy_matuschak Thanks for the reply! 😊
Regarding the discussion of Orthodox position around 50:00, I read this in a book “The Making of Atomic Bomb”, which made perfect intuitive sense to me:
“But it led Heisenberg immediately to a stunning conclusion: that on the extremely small scale of the atom, there must be inherent limits to how precisely events could be known. If you identified the position of a particle-by allowing it to impact on a zinc-sulfide screen, for example, as Rutherford did-you changed its velocity and so lost that information. If you measured its velocity-by scattering gamma rays from it, perhaps-your energetic gamma-ray photons battered it into a different path and you could not then locate precisely where it was. One measurement always made the other measurement uncertain.”
what is he using to identify the characters?
So cool
How do you feel about using an infinite canvas to take notes? Would it be better than writing flashcards for elaborative learning?
Andy, can you share links to the tools you use? The clipboard Latex black magic and the setup you use for handwriting. Many thanks
The LaTeX tool is MathPix. For handwriting, I'm drawing on my iPad Pro in Notability. I display its screen on my laptop with QuickTime for the purposes of the video, but I don't when I'm on my own.
what do you use for annotating PDF?
Does anyone know of a good revision app where you can input your questions and answers then have them asked back in a similar way to what Andy uses here?
The one I use is called Anki
I've been using RemNote for over a year. Works for me.
@@sakuragisukeluro2489 +1 for anki
what is the PDF reader they are using, its on localhost
It says pdfjs.
Aaaaaaaand im immediately lost. Cya!
Honestly, the high school students in india know more physics than these guys
does what you wrote strike you as particularly relevant, meaningful, or helpful?
@@ethanjkemp I get ur point. Apologies
Some high schoolers who prepare rigourously for JEE (main/advanced) perhaps. But how many of them remember that stuff years afterwards?