Divergence intuition, part 1
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- เผยแพร่เมื่อ 2 ต.ค. 2024
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Vector fields can be thought of as representing fluid flow, and divergence is all about studying the change in fluid density during that flow.
I love how he teaches things visually first! It makes the math so much more interesting.
3Blue1Brown + Khan Academy = Every student's dream. In other words, a deadly combination
Actually he worked at Khan Academy til 2015. Then he left and started 3b1b
@@m.qasimkhan1485 okay, i got you👍
This series is amazing. I can't even imagine learning calculus without computer graphs, animations etc. What a time to be alive!
Well Newton and many past mathematician after him does lol
Haha. That makes Maxwell a computer!
Agreed 😂😂
Vectors are not so much an ancient concept, it's actually from the later part of the nineteenth century. People drew diagrams.
I took calculus about 17-18 years ago. We did not have these animations. I scored very well in the courses but a lot of it was procedural, now I can really understand the concepts.
Masterpiece of math explanation. Mr. Grant + Khan Academy = MAGIC
King of intuition
his animation is so satisfying to watch
Like our souls ❤️
Great video. Thank you for your life-long service. God bless you sir.
The animation is right to visualize divergence
I watched this so I can understand the logic behind some attack techniques in anime.
Gojo certainly uses these divergence convergence techniques a lot 😂
Same
He actually uses calculus and soldier turtle paradox
Imagine there's a soldier who is trying to catch a turtle, it doesn't matter what's the velocity of soldier is and what's the velocity of turtle is, but only thing that's important is soldier have a larger velocity than turtle... Ok now let's say I gave the turtle a headstart, let's say of 100m and I asked soldier to catch the turtle,
In theory, the soldier first have to travel 100m, but in that amount of time turtle moves away with some distance x, now soldier have to travel x and it that amount of time turtle moves y, and so on
This implies a soldier no matter how fast he is, can never reach the turtle, it was a great problem in its days cuz we know something like that never happens
Calculus solved this problem, it proved that all the point, even if they tends to infinity can converge and add up to a finite value, like 1/2 + 1/2² + 1/2³....
Adds up to 1
Now what gojo do is to use this calculus and paradox to it's advantage
He distort space and time, such that the space becomes quantised in packets which continues till infinity, but each packet is 2 times smaller than the other
Similar to the 1/2 + 1/2² ... Series
But wait, that's not all, he also distort space so that to travel every quantised space u will need the same amount of time, so the time taken to travel 1/2 = to the time taken to travel 1/2² = to the time taken to travel 1/2³ and so on
This revoked the turtle paradox and hence no one can reach gojo in finite amount of time
@@Sorya-gf7qw
just one Dislike.. might be a wrong click... that tells the worth ... thank you.
whoa source and sink flow. aero makes sense now atleast a little
You are magnificent
Excellent!!! 😍😍😍🇧🇩
thanks
hahahaa! I was able to follow that dot (water molecule). thank you, as always
This is great, congrats! One point is that the sink (4:37) cannot be related to a magnetic field... I guess you realize that just when talking about it...
Uhm...I know this voice
Khan if you werent here there would be no maths for me.
awesome😉
What animation are you using sir ?
What animation are you using sir ?
Thank you so much!
Is this 3 Blue 1 Brown?
Thank you, man!
I got it!
What great animations! Thank you!
this is inaccurate though. Divergence is the rate of CHANGE of the vector field along its respective directions, not just the vector field itself. A field could be pointing inwards and still have positive divergence if it the vectors get longer as they approach the origin. Whereas water would clearly increase in density inside that region. So this example makes no sense.
what would the field at the origin look like? which direction would it point in for the case described?
One of my major problems with this subject is trying to understand why the divergence of a magnetic field is zero. If I have a bar magnet, the magnetic field emanates from the north pole, and terminates on the south pole. Why then, is the north pole not considered to be a source of the magnetic field and the south pole a sink? Clearly, magnetic field lines are diverging away from the North Pole and converging on the South Pole. If the north pole of the magnate was enclosed in a gaussian surface, but the South Pole remained outside the surface, surely there would be a net flux of magnetic field across the surface wouldn't there?
Nope. There are no such things as magnetic charges. Magnetic field lines diverge from North pole OUTSIDE the magnet. But Gaussian surface is closed, so if you dont want to include South pole, you have to cross the magnet at some point. INSIDE the magnet field lines return from South pole to North pole in such amount, that divergence of magnetic field is EVERYWHERE zero.
I hope i said it clearly
The thing is: the magnet doesn't produce magnetic field. Magnetic field is everywhere, but has value 0.
If you put there A MOVING ELECTRIC CHARGE, and only then, you change value of this field to non-zero. Even bar magnet is essentially a huge bunch of electrons moving in such a way that their influence on the magnetic field add.
Therefore there is no such thing as magnetic charge. The source of changes in magnetic field is MOTION of electric charges, not particles themselfs.
...3Blue1Brown?
yeah, it's Grant Sanderson.
thank you
Are you the same guy from 3blue1brown?
Yeah, he is.
@@vojtechvotruba1979 i knew it!
:) :) :)
Bliss