3blue1brown

Bertrand's paradox (with Numberphile)

In case the 40-minute video wasn't enough for you today, I also did a video with Numberphile about a fun conundrum from probability known as Bertrand's paradox. It was originally something I wanted to mention as a side comment in the cube shadows video, but it shaped up quite nicely to just make it a full separate video and have it posted as a sort of soft collaboration.

Linked above is the first part, but if you want more commentary going deeper into the problem, there is a second part...

Alice, Bob and the average shadow of a cube

New video! 

This is a long one, and took quite a bit of work in the end, but I hope you enjoy it. It's a story of problem solving, centered on one quite fun puzzle, which is to find the average area for the shadow of a cube, averaged over all its possible orientations. 

The artwork in here by Kurt Bruns, who happed to also be one of the interns this summer. Thanks for making it possible to hire out for something like that! It's a style I'll likely continue experimenting ...

Summer of Math Exposition results

In this video, I talk about the results of the Summer of Math Exposition, announcing the 5 winners, and mentioning many more of the entries I really enjoyed. Even then, there are countless others I think people will learn from which I didn't explicitly call out here.

The heart of the event was really the discord community associated with it, so many thanks to the moderators for helping to rein in the chaos there. I also wrote up a 2021-10-25 01:25:52 +0000 UTC View Post

Holomorphic Dynamics (early view)

This is the follow-on to the Newton's fractal video. I tried to frame it in such a way that it doesn't necessarily require watching the first as a prerequisite, so perhaps I should simply say here's the next lesson. In either case, let me know if you catch any errors or have any feedback!

Newton's Fractal, the finalized verison

Thank you for many helpful comments on the early teaser!

A draft for the follow-on should be in your inboxes shortly...

SIGGRAPH Talk + September update

Hey everyone,

Above is a recording for a remote talk I did for SIGGRAPH this year, for anyone who is curious. Apologies for the sound quality, something about the mixture of my mic's settings and Zoom seemed not to mesh well, but hopefully, it's not too terrible.

The finalized version of the video on Newton's fractal (teased in the last post) will be coming shortly. I ended up addi...

Root-finding fractals

Hey everyone,

While working on a video about the unsolvability of the quintic, I put together this kind of side plot about fractals that arise from root-finding algorithms.

In all likelihood, it's something I'll expand and put out as a separate follow-on video to the quintic one. Let me know if there's anything related to this topic you'd like to see or hear more about.

-Grant

Textbooks, pi creatures and problem solving | 3blue1brown Q&A for Bilibili

Last year, the page for 3blue1brown on Bilibili (a Chinese video platform) surpassed 1 million followers. Although this isn't exactly timely, I made a Q&A to mark the occasion, with questions drawn from the Bilibili audience in China.

Our plan is to first post it to the Bilibili page once the translation is done, then after a few days put it up on the new second channel on YouTube. In the meantime, enjoy an early view.

I have yet to add on the patron-thanks scroll at the end h...

More articles!

The new site is up! Here's some of what we've converted to written form, often with a some interactive elements sprinkled in where they seemed to fit:

- Calculus

   - Chapter 1: The essence of calculus
  &nbs...

New podcast episode: Beyond Khan Academy

Episode 2 of the 3b1b podcast is out now, featuring Sal Khan.

Since the podcast is a sort of a separate project from the main lessons that this Patreon is about, I'll spare your inbox and hold off on direct updates here as we continue putting out some weekly episodes (except perhaps in side-mentions within posts about the main projects). If you want to follow more actively, stay subscribed to "the 3b1b podcast" on whatever your favorite podcast app or platform is, or subscribe on YouTub...

First podcast episode is live!

The first episode of the 3b1b podcast is out now.  It's an interview with the mathematician Alex Kontorovich, covering all things math from education to research, outreach, the role of proof-checking software in modern math, and more.

The videos will live on a second channel, which is also probably a place where I'll put future things which are not necessarily animated math explainers.<...

New video: Why aren't you making math videos?

As mentioned in the previous update, we are doing a contest encouraging more people to get started with math exposition online.  Rather than simply posting an announcement video, I decided to put together some advice for anyone getting started with all this.

The great bloggification, SoME1, a podcast, and a promise that there are actual videos in the works

Hi everyone,

For anyone following closely, things might seem a little quiet on the 3blue1brown front, but under the hood, there's actually been quite a bit going on.

TL;DR:

- New website, which will include rich blog post versions of the videos.

- A contest encouraging people to make more math explanations online.

- A casual podcast about educational content creation.

- More videos on the way, I promise.

Bloggification

The main project this su...

A quick trick for computing eigenvalues

This is less of a visually focused video than the norm for the channel, but it covers something I wish I knew when I was in college.  Also, it involves a fun cameo from Tim Blais, from the (fantastic) channel Acapella science.

Back when I did the first episode of lockdown math about the "simpler quadratic formula", it occurred to me that the formula is useful in other contexts, eigenvalues being one of them.  Fast forward to these days, where I've been working on the next diff...

Final version of raising e to the power of a matrix

Hi everyone,

The final version is out!  For those of you who watched the draft, you'll find new content starting around 22:00, explaining the flow visualization and giving the main idea for why exp(Mt) solves the equations we are claiming it does.

The other big structural changes are to have aggressively cut down the section on real-number exponents and to reorder things so that the geometric solutions happens much earlier so that once we get to explicitly computing exp(90-de...

Matrix exponentiation (early view)

Hi Everyone,

Here is a draft of an upcoming video about exponentiating matrices, which will be the first of multiple.  As always, kindly let me know if you find any errors.  I'm sharing this a little earlier in process than I usually do.  This is essentially right after the first pass of stitching everything together, so I'll likely make a few more changes between now and the final version, but any feedback you have offer as I do so would be welcome.

Currently I'm c...

Video bloggification and continuation of differential equations

Hi everyone,

First off, I wanted to thank you for the very kind response to last month's update.  It means a lot to me to know that so many of you are supportive not just of the videos themselves, but also of the time spent on the tooling behind them.

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As I mentioned in that post, I recently hired 2021-02-28 18:33:29 +0000 UTC View Post

Manim Community

In my last post, I mentioned a little bit about what I had been doing with manim, but one thing I neglected to talk about is that for a while now, there's been a lot of parallel development from an active community that forked an older version, which you can find at https://www.manim.community/ 

Essentially, in the past, I have often put manim more on the back burner, and as such was not always attentive to incomi...

January update, (manim upgrades, part-time hire, etc.)

Unfortunately, no new videos for January.  I've paused the Patreon billing for this month since in general content production has been slower recently, and you've all been very patient.

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A lot of my time this month went towards manim, the open-source python library I wrote to do the animations for the channel.  More and more, I've seen other people create math/CS explainers using manim; to name just ...

Medical test probabilities draft

Hey everyone,

Here is a draft for a video about medical test probabilities I plan to publish soon, let me know if you catch any errors or otherwise have feedback that can be incorporated.

I've talked a bit about plans I had for this topic in previous posts, and this video is one I sort of split out from an earlier draft.  The target here is a viewer who has either not come across Bayes rule yet, or who has a little but not enough to have become familiar with how it can be fra...

Discrete Fourier Transforms

Hi Everyone, just a quick post here to share a lecture I did on the basics of what a Discrete Fourier Transform is for MIT's 18.S191, hope you enjoy!

At the end I reference a really excellent breakdown and motivation for the FFT algorithm by a new channel I've found which uses my animation engine, Reducible.  Here's the link: https://youtu.be/h7apO7q16V0

Current video status + A couple lectures

Hey everyone,

I was really hoping to have a new video out to you by now, namely the one on medical tests and probability.  If all goes to plan, the projects in the coming month or two should make up for the recent dry spot.

This has taken much longer than most projects, especially considering the fact that if I do things right, the end result shouldn't be _that_ long or complicated.  The aim is for this to be digestible to as many people as possible with just a handful o...

Update

Hey everyone,

I wanted to share a bit about what videos have been brewing and what to expect in the hopefully-not-too-distant future.

The next video out will discuss how to reason about the probabilities surrounding medical tests.  At the base, I think it would be helpful to simply visualize what all the relevant jargon means, terms like sensitivity, specificity, PPV, etc.  But beyond that, it seems worth clarifying what exactly these tests tell us, what they don't, and ...

MIT Lectures

Hi Everyone,

I mentioned in a previous post that I'd be collaborating with an MIT group on a course they're running about "computational thinking" this semester.  Well, it's happening!  Linked above is the first live lecture I gave.  There was also an asynchronous lecture earlier in the week giving the basics of working with images in the language used for this class (Julia).

Course intro: https://yout...

Hamming codes part 2, early view

Following up on the last post, here’s a draft of part 2 to the error correction project.

(Edit: swapping out video link for the finalized version)

Hamming codes, part 1 (early view)

Hi Everyone,

Above is an early view of the next video.  I should get part 2 to you in the next couple of days, then the plan is to publish them both jointly.  Also, in conjunction, Ben Eater is making a video about implementing this algorithm on breadboards, and currently, I have blank spots in the video over the points where I'll reference his, so those will of course get filled in by the final version.

There are so many more interesting things to say on this topic, eve...

The monster (early view)

Hi everyone,

A few weeks ago some fellow math YouTubers (James Grime and Matt Parker) decided to put together a kind of mega-collaboration, where a number of us would each make a video on a common theme and invite the audience to do the same.  The theme they chose was "What's your favorite number over 1,000,000?"

At the time I was in the middle of animating the Hamming Code video (still coming, by the way), but I thought I'd at least draft up an outline to see how I felt abou...

Update

Hey everyone,

It's been a few weeks since the last video, and the one I'm working on now still looks like it might take a while, so I thought I'd pass along a little update.

The current project is on Hamming codes and error correction.  Originally I thought this would be a quick follow up to the chessboard puzzle, but I got sucked into reading a lot more about error correction in general.  All said and done, this particular video will still stay focussed on Hamming codes...

Solution to the chessboard puzzle

The two videos on the chessboard puzzle are now live!  Give that I've already shared the first with you, linked above is the other part done with Matt Parker on Stand-up Maths.

In it, we demonstrate what it looks like to actually carry out the solution, and then share the details of what we were doing.  More than that, though, it's a discussion of how each of us thought about it when we first heard it.  Simply showing the puzzle and solution would be a fairly short video,...

The impossible chessboard puzzle (early view)

Hi Everyone,

Here's a draft for half of a recent project done in collaboration with Matt Parker.  While the video on his channel will include the actual solution to this relevant puzzle, this video is all about a kind of meta-puzzle around it, analyzing whether or not it should even be possible, in a sense.  I hope you enjoy it!

Currently, I've left blank spots where I'll insert footage from the Stand-up Maths video once we have a final version there.  If there are ...