Partial new video preview + Update
Added 2018-03-15 00:34:21 +0000 UTCHey everyone,
I thought I'd share a little about what is in the pipeline. Here's the first 2/3 of an upcoming video on winding numbers. Specifically, it's all the parts *not yet* about winding numbers :). This is the first project by the other new 3b1b team member, Sridhar Ramesh. In the background, he's also had some good ideas for how we could cover the Laplace transform (among other things), which we'll likely begin on after this project. So once those are out, you'll have Sridhar to thank!
"Grant!", I hear some of you yelling, "where's probability!?!". I've handed off primary ownership of that series to Ben (whom you'll remember from the Basel problem video), though I'll still be very attentive as an editor and animator there. For whatever reason, every time I'd sit down to sketch out ideas for that series, I'd find it hard to land on a central theme of what I wanted to say and how the whole thing should be framed. Ben, with more experience teaching this material in the classroom, has a pretty clear (and I think quite good) vision for what the full series should look like, which visuals should drive each episode, etc. Look out for the next episodes there in the coming weeks.
Personally, I'm also going to start thinking about a sequel series to the existing "Essence of linear algebra", since there's quite bit more I'd like to include. So now and then in the coming months you may see some videos drop in for that.
And of course, we have a long (very long) list of good one-off topics we'd like to hit soon. In no particular order, some towards the top include finding the circle in the Wallis product, some of the basics of quantum computing, how to think about extending factorials beyond natural numbers, and various bits of math applied to cryptography.
I'm not saying this will all come immediately (things take time as always), but there are many exciting things to come!
-Grant
Comments
The precise formula is a bit tricky to write down, but it's basically a polynomial with the zeros where you see them (and multiplicities where you see them), except that the zero on the lower right has a conjugation term to give it a negative winding. The cloverleaf effect comes because I rescaled the outputs so that the hopping dots would fit nicely on the square I allocated for the output space.
3blue1brown
2018-03-29 20:10:27 +0000 UTCwhat formula is that cloverleaf looking equation by the way?? the one with the 3 zeros?
Tomás Tomcat
2018-03-28 12:35:36 +0000 UTCGood idea, thanks!
3blue1brown
2018-03-25 05:52:51 +0000 UTCMy favorite (okay, the only one I knew, actually) proof of the Fundamental Theorem of Algebra! Nice!
Jacob Mirra
2018-03-24 23:58:16 +0000 UTCIt would have been good to run the RGB color brightness through a gamma function of about 2.2 in value. This will map better to how the human eye perceives brightness. If you take the halfway point of 128 and compare it to 256, nobody would say that the former is 1/2 the brightness, yet numerically it is. By running the RGB through the gamma function, viewers will perceive the halfway point as being closer to half as bright as the fully bright point. This might help color discrimination as you move around the graph space. Great video by the way!
2018-03-24 22:59:24 +0000 UTCI don't understand how you find the initial bounding region that you know to contain the zeros in the first place. Do you just pick an arbitrary large region with a winding number of n and start there?
2018-03-24 21:30:36 +0000 UTCYou're binomial terms video has a misplaced three in the numerator at 1:47. just thought you should know. :)
2018-03-22 05:52:17 +0000 UTCI think finding numerical solutions to 2d equations is extremely practical, don’t you?
3blue1brown
2018-03-20 01:19:02 +0000 UTCI think this is a great implementation of what you talked about on the podcast! And regarding linear algebra, I think this is a great idea, maybe even dip your toe into module theory or multi-linear algebra? How about the algebra of Hilbert-spaces, I know a lot of physics undergrads who would kill for that 3b1b video :P
ChalkyChalkson
2018-03-19 17:26:28 +0000 UTCKind of mirroring what Nitai said above, I think the inclusion of an error in the process of finding the algorithm is very rewarding - I feel that it's healthy to include exposure of how to get past issues in solving problems. Great video!
2018-03-18 20:33:42 +0000 UTCI'm a bit late, just wanted to say I love the fact that you showed a mistake in the video. You rarely do that, and I'm not saying you should do it more (please don't) but to occasionally do it to catch us off-guard, that's awesome.
2018-03-18 19:25:56 +0000 UTCGahhhh! Cliffhanger! Nooooooo!
Burt Humburg
2018-03-17 19:47:04 +0000 UTCAbsolutely love it and the effect at the end of stumbling upon an error in our thought chain
Lionel Pöffel
2018-03-15 23:55:21 +0000 UTCAaaaagh! Cliffhanger! I am very frustrated that this video is not yet available in its entirety.
jason black
2018-03-15 19:31:56 +0000 UTCBEST VIDEO YET! I love it when we find mistakes and you show us how to think about deconstructing our assumptions and rebuilding our mindset. THAT IS MATH!
2018-03-15 16:44:20 +0000 UTCYour videos are way over my head, but they make me appreciate math like nothing else. Thanks Grant
2018-03-15 16:22:49 +0000 UTCThe algorithm stopped when a circle is mapped to an annulus?
2018-03-15 13:17:43 +0000 UTCvery nice. but in the last animation, it seems like you used a "fake" function. well, there isn't such a thing as a fake function, but the green value is constant and it doesn't look as vivid as the regular functions. and it shouldn't be too hard to find a more natural counterexample.
Noam Ta Shma
2018-03-15 12:12:45 +0000 UTCOh, also, LOVE the fake but sort of real got-it-wrong part of the video.
2018-03-15 10:55:10 +0000 UTCThis is really interesting! If I may offer a humble suggestion-- well, more like questions than suggestions really. What are the practical applications of these winding numbers in the real world?
2018-03-15 10:53:36 +0000 UTCVery interesting teaser video, looking forward to the full thing. And *really* looking forward to the part 2 of Linear Algebra!
Edan Maor
2018-03-15 09:49:41 +0000 UTCWhen do you plan to continue the Neural Network series? I was really looking forward to the RNN part!
Ricardo
2018-03-15 07:57:22 +0000 UTCDefinitely very interested in the quantum computing and cryptography videos :)
2018-03-15 07:34:55 +0000 UTCAll sounds very exciting! Is there a public version of the complete list of one-off topics? Also, have you considered branches of mathematics such as category and type theory-would be interesting especially as you cover some aspects of discrete maths .
Robert Lamacraft
2018-03-15 06:10:30 +0000 UTCHow about the double factorial, it comes out pretty often when taking derivatives of infinite series.
2018-03-15 05:06:11 +0000 UTCMy dream is an Essence of Complex Analysis series!
Ben Goldsmith
2018-03-15 02:57:35 +0000 UTCGreate video as always! I probably have to "unlearn" what I have learned because the only way I can "re-visualize" this in my head is thinking about a surface in 3D with the vectors being gradients and what we want is an extremum point! :D In this sense covering "all" colors usually translates to going "around" a peak or valley. But if your path is just on the slope, then all you get is a single general direction all around. Although then there are saddle points to behold...
Alipasha Sadri
2018-03-15 02:17:33 +0000 UTCYes, I know Stephen, his stuff is really phenomenal!
3blue1brown
2018-03-15 01:07:12 +0000 UTCAwesome one!! Can't wait for the rest of this video and all of the magic you've for us in the coming months. Also, I'm pretty sure you might have come across another great YouTuber -- Welch Labs -- who made a similar series, although in a slightly different light. Here's the playlist: <a href="https://www.youtube.com/watch?v=T647CGsuOVU&list=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF" rel="nofollow noopener" target="_blank">https://www.youtube.com/watch?v=T647CGsuOVU&list=PLiaHhY2iBX9g6KIvZ_703G3KJXapKkNaF</a> The transform that Stephen (Welch) applies on videos to visualize "input" (complex) domain to the "output" (complex) domain mapping is a really nice idea, just as you are using colors.
2018-03-15 01:02:57 +0000 UTCI also came here to suggest an SVD video. No worries about the prob videos Grant, we want to see things that you're excited to put out! My sensitivity analysis teacher showed us your high-dimensions video in class and it is frequently referenced in class discussions. Something else I'd be excited to see is flushing out the connection between vectors and functions. I've found it challenging to relate orthogonal polynomials to orthogonal vectors in my journey.
Julian
2018-03-15 01:00:42 +0000 UTCThat is one of the big motivations for doing a sequel. That, along with PCA, tensors, how LA looks in quantum mechanics, as well as some odds and ends like thinking about transposes, etc.
3blue1brown
2018-03-15 00:51:25 +0000 UTCA sequel to "Essence of linear algebra"? NICE! I really hope you will cover the SVD at some point. You were so close in the original series! And the SVD is such a useful tool in real-life modeling and data analysis, it deserves a better intuitive understanding.
Vincent Zalzal
2018-03-15 00:44:44 +0000 UTC
