Dude, you’re the voice of Bob Ross for math and science. We’ve got a happy little “differential equation” over here 🎨 and some excited molecules over here 🖼.
"by the time we actually start doing something meaningful and physical with it we just turn it right back into a discrete one". Very insightful, thanks!
Very nice. As always you could be the greatest math divulgator of our time. This remembers me of my Stochastic Processes exam. From a symmetrical random walk (in 1D means same probability to go left or right) one can derive the diffusion equation, and from the asymmetrical version you can derive the Fokker-Planck equation, aka the diffusion-with-wind-equation :)
Man your explanations cant stop surprising me! I can keep thanking you for explaining in such an intuitive way. You feel the passion and the love for what you are doing.
That's what Grant, the dude in the video, does. 3Blue1Brown is his RUclips channel. One of the best math education/visualization channels on this whole site.
@@gileee Oh I know. I've played around with manim (the software library he uses to make the animations) myself, but Grant is still by far the king of making visualizations like these.
15:00 - It's a nice way to look at the diffusion equation! The rate of change of the variable (partial derivative) is directly proportional to the curvature of the curve (as a function of the space), with Diffusion Coefficient being the proportionality constant. The parts of the curve where the magnitudes of the curvatures are high experience higher time rate of change. This explains why the curve smoothens out, or in other words 'straightens out' as time goes by.
The "statistical noise" of 4:52 is not such, it isn't because the "random statistics" ( 4:38 ). It's actually because the implementation of the random walk explained at 3:52 : 50% hop to the left, 50% hop to the right The resulting curve would be smoother: - if we interpolate the values between steps - if we add a third option: 33% hop to the left, 33% stay, 33% hop to the right - Even better if it had 3 options with a discrete normal distribution, ie: 25% hop to the left, 50% stay, 25% hop to the right - The best would be a continuous normal distribution
Inspiring video. It made me to think about generalized Pythagorean theorem coming from duality in linear spaces. The divergence is another result of the duality that is coming from linearity it is keeping invariant and doesn't change with unitary transformations.
When you start talking about the brownian motion and then later appears de squared of the delta_x I was waiting for you to start talking about how this thing are managed to be constant allowing the solution truly exist, introducing in this way you viewers into Ito's Calculus.... hope you can extend the video with this modern view of Brownian motions analysis. Thanks you beforehand!
Hi! Why did you define the number of particles in the boxes as densities rather than concentrations? Are you assuming that the particles occupy all the volume of the boxes?
Anyone have any good resources (books/simple papers) for doing this kind of thing on a finite grid? I've been trying this with random walks on 8-neighbors and it keeps drifting and settling in the center and I'm not sure why that is.
Dear Grant, What software do you use to create the interactive graphical animations for your videos? Is this commercial software? Perhaps, did you write the software? If so are you able to opensource for those interested in the code? Thanks as always from a keen learner from your work. Regards, Joshua
0:06 guess i now know why his channel is named "3blue1brown. and i got the same eyes as him, just the 3 blue is grey for me and i also have a smaller brown dot in my other eye
Why would (delta x)^2/(delta t) be constant? (delta x)/(delta t) is molecules velocity and may be considered a constant value. But what about another delta x left?
Great question! If each particle is moving according to a random walk, then after many steps the distance traveled will not be proportional to the time. However, the *square* of the distance traveled will, in expectation, grow linearly with time. It's a fun little exercise to work out.
@@3blue1brown Please correct me if I'm wrong. Square of drift is proportional to time in the case of, strictly speaking, delta t (hence delta x) -> Inf. Here, though, we are dealing with small increments. Notwithstanding all this minutia, I am a big fun of your brilliant channel. Keep up your excellent work!
@@maharajxx also consider that as dx->0, the number of cells in a given volume of space goes to ∞. It's the granularity of x and t, not their magnitudes, that makes the random walk statistically a normal distribution, which has the squared relationship in the expectation that's at issue here.
@@3blue1brown Is the constant of proportion just an arbitrary choice of the person creating the mathematical model or is there any connection to the real material that is diffusing? It seems like this is the only link missing between mathematics and physics in your presentation. I wonder if it can be filled in a mathematically rigorous way.
hello,I am very happy that I found you, I am doing distant course in DSML in collaboration with MIT , I wish if i too had a teacher like you , any suggestion for me , i am very much interested in deep learning and ai , and i know your lectures will be very useful for me and thanks for making them available for free ....
i see grant in the thumbnail, i watch. simple man and such...
yeahhh ! haha
we all do.!!
Likewise. He has that soothing voice.
@@jesselybianto8650 kinda like math asmr
Yes, no idea about diffusion, just wanted to watch him explaining it
fun fact: Grant’s voice is more famous than his face
I disagree. Everyone recognizes that plushy pie expressive face
I had never seen his face before, I literally kept thinking "This guy sounds like 3 blue 1 brown" lmao
@@vikranttyagiRN lol
@@greenstatic9294 +++++
Khan academy as well?
Dude, you’re the voice of Bob Ross for math and science.
We’ve got a happy little “differential equation” over here 🎨 and some excited molecules over here 🖼.
Check out his channel, 3Blue1Brown. Lots more of this.
There's another channel who does Bob Ross styled math explanations. Check out Tibees
And a sad calculus student over there.
Grant you NEED to do a series on PDEs. You are the best teacher I have ever encountered.
"by the time we actually start doing something meaningful and physical with it we just turn it right back into a discrete one". Very insightful, thanks!
Me: procrastinates studying heat and mass transfer all day
also me: oh look a grant sanderson video *click*
Excellent. I feel less dense already.
The intuition and derivation for the heat equation was superb! It felt very natural
Waaaait a minute! Isn't that the 3blue1brown guy?
Clicked for Grant, was surprised by intuitive explanation of stochastic calculus...this man is the gift that keeps on giving.
Very nice. As always you could be the greatest math divulgator of our time. This remembers me of my Stochastic Processes exam. From a symmetrical random walk (in 1D means same probability to go left or right) one can derive the diffusion equation, and from the asymmetrical version you can derive the Fokker-Planck equation, aka the diffusion-with-wind-equation :)
This is the most intuitive explanation of the diffusion equation. I finally get a rough idea of it this time. Thanks, Grant
Once you've seen this derivation, you'll always remember the unit of the diffusivity coefficient. Very cool stuff!
Man your explanations cant stop surprising me! I can keep thanking you for explaining in such an intuitive way. You feel the passion and the love for what you are doing.
Oh boy did I not continue deep enough into Calculus. I learned a lot, and will save this to my favorites for rewatching. Give this man some bongos.
Probably the best 20 minutes I've spent on RUclips. I could just rant on the insight and intellectual value. Cheers! 👏👏👏
Me as a high school student: I can understand this equation.
Me after university: Let me open my calculator app and check again if 6+7=13.
damn multi-variable cal in high school lol
I think Grant is the feynman of 21st century when it comes to teaching.
+
Nah, he's the Grant Sanderson of 21st century teaching
Jawad this
agree
Wow, that 3D graph of the surface was incredibly well visualized.
That's what Grant, the dude in the video, does. 3Blue1Brown is his RUclips channel. One of the best math education/visualization channels on this whole site.
@@gileee Oh I know. I've played around with manim (the software library he uses to make the animations) myself, but Grant is still by far the king of making visualizations like these.
Very high quality material. Just a small remark from a physicist after listening the first minute: heat is the one that flows, not the temperature.
for the 1st time in my life i see the hope of understanding laplacian... it freaked me out every time when i try to understand graph convolution
loved watching the smooth transition from a simple idea to an equation
So beautifully and lucidly illustrated! I thank the RUclips algorithm for bringing me to this channel.
Thanks Grant ! One take away for me : Directly-Unsolvable PDE, Numerical simulations to the rescue !
This video just made me less dense. Loving it, thanks Grant!
15:00 - It's a nice way to look at the diffusion equation! The rate of change of the variable (partial derivative) is directly proportional to the curvature of the curve (as a function of the space), with Diffusion Coefficient being the proportionality constant. The parts of the curve where the magnitudes of the curvatures are high experience higher time rate of change. This explains why the curve smoothens out, or in other words 'straightens out' as time goes by.
So beautiful! We also use this equation in population genetics to study how allele frequency changes along with time.
I'm new to the field. Could you recommend a reference with implementation?
It is a revolutionary little equation. Basically, what it states is - the higher the inequality, the higher the incentive for change.
19:00 oh wow, this really opened my eyes regarding why exactly the mean value formula for harmonic functions works!
The "statistical noise" of 4:52 is not such, it isn't because the "random statistics" ( 4:38 ).
It's actually because the implementation of the random walk explained at 3:52 :
50% hop to the left, 50% hop to the right
The resulting curve would be smoother:
- if we interpolate the values between steps
- if we add a third option: 33% hop to the left, 33% stay, 33% hop to the right
- Even better if it had 3 options with a discrete normal distribution, ie: 25% hop to the left, 50% stay, 25% hop to the right
- The best would be a continuous normal distribution
If I had his voice, I’d never stop talking! 😂
Inspiring video. It made me to think about generalized Pythagorean theorem coming from duality in linear spaces. The divergence is another result of the duality that is coming from linearity it is keeping invariant and doesn't change with unitary transformations.
Gorgeous way of teaching diffusion equation!
I like the approach (thinking about random walk) and the clarity of the explanation :)
When you start talking about the brownian motion and then later appears de squared of the delta_x I was waiting for you to start talking about how this thing are managed to be constant allowing the solution truly exist, introducing in this way you viewers into Ito's Calculus.... hope you can extend the video with this modern view of Brownian motions analysis. Thanks you beforehand!
HEY I KNOW THIS VOICE :O
I liked this video, but why the Schrodinger Equation is a diffusion equation ? Perhaps the Wave Function is diffusing in space, any idea ?
Frikkin wizard-man, this guy!
How does this man teach everything I learn?
i really like your style and appreciate it that you explain julia
Brilliant animations as always!
And I think that if you give the time dependent side an imaginary number, you get the schrodinger equation from quantum mechanics.
11111
x=x+1
Let ε < 0.
area over curve
AoE2?
Suppose 1=2
A bit unclear why we have dX^2 in denominator when we take difference of differences 😢
It already clicked when you increased to dots to 10,000. That's why you're a great teacher, Grant.
P.s. missed 3b1b.
The temperature do not just GENERALLY flow from the warm part to the cold part. It's the first law of thermodynamics.
Ohhhh nice. I'm in a semiconductor course and was wondering how ficks law came to be.
It was great. Your videos are amazing. I hope you continue to upload these kind of videos.
Is it a Blue Yeti microphone?
first time here and worth it, i see grant's handwriting
Ahhhh, so this is the '1brown'. Love your videos so much!
20:30 In some cases you can solve this equation exactly (Green functions, etc.). So you can kind of check your computer code against these solutions
No idea how this ended up in my Recommended at 01:15 am but I did like it.
Hi! Why did you define the number of particles in the boxes as densities rather than concentrations? Are you assuming that the particles occupy all the volume of the boxes?
Finite differences, it makes more to use finite volume schemes, specificly when D is not a constant
Wow, RUclips has never shown me these. And I never noticed them on Twitter I guess.
this makes a math nerd happy 😭
I'll be Happy If He writes a book on Mathematics.
Then we wouldn't be able to hear him talk...
when will you come back to 3blue1brown :(
He's producing lectures for MIT... obviously that's much more prestigious than a RUclips channel.
I took this class last semester wish i would have waited for this one!!!
Anyone have any good resources (books/simple papers) for doing this kind of thing on a finite grid? I've been trying this with random walks on 8-neighbors and it keeps drifting and settling in the center and I'm not sure why that is.
It'd be nice to see some Finite Volumes Method solving the diffusion problem...
your voice sounds like 3 blue 1 brown. good lecture but was surprised to hear that exact voice cadence.
Is there a course for differential equations
Excellent channel
Great ! Makes me feel mathematical young, but I’m not young I did these exams 30 years ago, I wish I had this fun at the time
Everyone is commenting about him, but no one is talking about the topic. Probably because it was explained clearly.
why did the uppercase D disappear
Bonus: the diffusion equation plays a central role in Grover's function inversion algorithm in quantum computing.
Brilliant content, thank you!
3blue1brown has a second channel? I had no idea.
you had me at "hot rod"
Very beautiful explanation video. Now you can blink
Awesome! Thanks Grant
Hi, I'd like to know how did you make the graph animation
thanks
it's his own library called Manim ("math animations"); it is open source
I prefer using conservation of mass in integral form and the divergence theorem tô deduce the equation
Amazing explanation. Thanks a lot.
How can I make such animation?
Dear Grant,
What software do you use to create the interactive graphical animations for your videos? Is this commercial software? Perhaps, did you write the software? If so are you able to opensource for those interested in the code? Thanks as always from a keen learner from your work.
Regards,
Joshua
He uses a library called Manim in Python. As far as I know, he is the one who founded this library.
You have good looking, good voice and good teaching!
Temperature does not flow. Its eat.
3 Blue 1 Brown is DIFFUSING!
2:54 if you are watching on phone and full screen and jiggle the phone a bit while looking at the dot It'll make a nice effect
What if the fraction of the density variation is not 1/2?
Rho, rho, rho your boat
Gently down the slope
Merrily, merrily, merrily, merrily
Life is but a delta
Great class, professor.
Absolutely perfect.
This is Pewdiepie if Pewdiepie is a mathematician.
0:06 guess i now know why his channel is named "3blue1brown. and i got the same eyes as him, just the 3 blue is grey for me and i also have a smaller brown dot in my other eye
Somebody buy this man a nice pen and squared paper!
Incredible!
Sir,please teach us also about advection..please😥
So that's why cityfolks where I live can't understand the keep your distance signs. Because they're too dense. Which means they don't keep distance...
Very well explained !!
This was helpful! Thank you!
amazing explanation !
Why would (delta x)^2/(delta t) be constant? (delta x)/(delta t) is molecules velocity and may be considered a constant value. But what about another delta x left?
Great question! If each particle is moving according to a random walk, then after many steps the distance traveled will not be proportional to the time. However, the *square* of the distance traveled will, in expectation, grow linearly with time. It's a fun little exercise to work out.
@@3blue1brown Please correct me if I'm wrong. Square of drift is proportional to time in the case of, strictly speaking, delta t (hence delta x) -> Inf. Here, though, we are dealing with small increments. Notwithstanding all this minutia, I am a big fun of your brilliant channel. Keep up your excellent work!
@@maharajxx also consider that as dx->0, the number of cells in a given volume of space goes to ∞. It's the granularity of x and t, not their magnitudes, that makes the random walk statistically a normal distribution, which has the squared relationship in the expectation that's at issue here.
@@3blue1brown Is the constant of proportion just an arbitrary choice of the person creating the mathematical model or is there any connection to the real material that is diffusing? It seems like this is the only link missing between mathematics and physics in your presentation. I wonder if it can be filled in a mathematically rigorous way.
AWESOME EXPLANATION!!!
3blue1Brown ?
hello,I am very happy that I found you, I am doing distant course in DSML in collaboration with MIT , I wish if i too had a teacher like you , any suggestion for me , i am very much interested in deep learning and ai , and i know your lectures will be very useful for me and thanks for making them available for free ....