3blue1brown

Re-recording of an old favorite (no charge of course)

Hey everyone,

I've been working on the next probability video, which involved sort of revamping my original plans and pulling out some content as a separate video.  Anyway, in part of the writer's block that ensued, I went back and re-recorded one of my favorite older videos which had some pretty bad audio.  This probably goes without saying, but this is not the kind of "new video" patrons would be charged for :)

Anyway, for those of you who never saw the original (or even for ...

How much counting to include in EoP?

Hey Patrons, 

So I'm putting together a video on the binomial distribution meant to go pretty early in the series (likely video #2 or #3).  The plan is for this to follow a video covering the basics of what a distribution is (along with joint distributions and conditionals), and for the binomial distribution to be the first testing grounds for practicing the modes of thought introduced in the previous, perhaps to be followed with one on the Poisson distribution.

Naturally, part...

Cryptocurrency supplement: How secure is 256-bit security

Hey everyone,

As promised, here is the supplement to yesterday's video.  No charge, of course, since this is an add-on to a different main project.  I had a lot of fun putting this together, let me know what you think!

Also, I'm going to do a Q&A session, where you can answer questions here: http://3b1b.co/questions.  For you, the patrons, I'm of course happy answer any questions anytime, but this will ...

New video! Ever wonder how Bitcoin (and other cryptocurrencies) actually work?

Hello all,

One thing I've enjoyed doing in past videos is putting together a narrative for how the viewer could reasonably have invented the relevant piece of math themselves.  Admittedly, there's always something a little contrived in doing this, since the actual process of discovery involves many more wrong turns than a ~20-minute video can allow, but it's a pattern among many expository works that I've personally found to be most helpful.

I thought it might be fun to do something...

Sneak peek for the 2's: Cryptocurrencies

Hello $2+ patrons,

Here's a draft for tomorrow's video about the protocol behind bitcoin and other cryptocurrencies.  The only part I haven't put in yet is a little preview for the supplement video, which I'm hoping to put out Saturday or Sunday. 

Comments welcome!  As you know, I am prone to typos in videos, so if you catch anything I'd love to know.

Thanks,
-Grant

Photo thanks for the $2+

Hey $2+/video Patrons,

Given that I had originally said I'd share with you some form of photographic thanks with a $2 bill, while taking some photos on my flight back from VidCon today I thought I'd dig through my wallet.  And sure enough, I had a two.

The flight is kind of a funny story.  A friend of mine from when I worked at Khan Academy who also has a YouTube channel* was also going to VidCon this last weekend.  When we met up, he mentioned that we should have flown do...

Thoughts on the classic Bayes' example

Hello again,

Following up on the last post, this video goes into one of the most famous examples of Bayes' theorem.  Part of why I wanted to include it in the series is to give my own take on the example, putting out the possibility that Bayes' rule may not be to blame for the counterintuitive nature of it.  But more than that, it's a good example of how something seemingly paradoxical becomes obvious once you clearly picture the sample space, which is a theme I hope to have througho...

Bayes' rule!

Hey everyone,

Although I have yet to decide on the  full table of contents for the probability series, the most obvious video to include is one covering Bayes' rule.  So I decided to start creating things out of order and begin with this one.  I expect this will show up as chapter 3 or 4 in series, and it will definitely be preceded by some discussion of probability basics, conditional probabilities, and likely something on counting.

In fact, I decided to include two video...

New video! All possible pythagorean triples, visualized

Hey everyone,

This is kind of a fun one.  The first time I ever learned about the formula for generating pythagorean triples, it was in the context of stereographically projecting rational points onto a circle.  The visual intuition of that is nice, but the actual algebra to work out a formula is quite a mess, and (at least for me) the actual result is easy to forget.

However, you can land on that same general formula just by squaring complex numbers with integer coordinates, w...

Animations for the fours

Hello +4's,

The upcoming video is on finding all possible pythagorean triples.  Here are a few excerpts from animations I'm working on.

https://youtu.be/Z6nsLuzUl0M

https://youtu.be/Jv_MaB1IKN8

https://youtu.be/KOv_cTozGkY

-Grant

New video! Pi hiding in prime regularities

Hello all,

You might notice that this is the longest video I've ever made, coming in a 30 minutes.  It's one of my favorite pieces of math, and exemplifies why I love number theory so much.  The progression here is a nice example of a problem which walks the delicate line between achievable, and intractably complicated, and it feels like the universe is really giving you a hand by keeping things on the "achievable" side of that line.

Thanks to those who caught a few errors on t...

Early view of tomorrow's video: Pi hiding in prime regularities

Hello $2+ Patrons!

I've decided to change the $2 reward from the photographic thanks to instead giving you all a little early view of stand-alone videos that I finish before the Friday that I plan to publish.  Given my propensity to make mistakes, this kind of early viewing can be helpful.

As you can see, tomorrow's video is a rather long one, but it's one of my favorite pieces of math, and I think the culmination is worth the time it takes to get there.

Let me know if you cat...

Sneak peek for the fours

Hello $4+ patrons,

Here are a few preview animations from the upcoming video, which will be entitled "Pi hiding in prime regularities".  As usual, these are just the animations themselves out of context, with no narration or anything, mean mostly as a sneak peek to let you guess at what the contents of next video might be.

Links:

https://www....

Share your thoughts on probability

Hello Patrons, 

Now that calculus is wrapped up, that means the next big "Essence of" project will be on probability.  Even though I won't start working on it for a few weeks, instead focussing on two upcoming stand-alone videos, I'd love to hear your thoughts on what you'd like to see in the probability series.

What topics do you want?  What perspectives made things click?  What do you think is not represented in other resources about probability?  What aspects ...

Higher order derivative footnote

Hello all!

I made a small footnote video on higher order derivatives to precede the Taylor series video.  No charge, as this is a purely supplemental and smaller video.

-Grant

Taylor series video!

Hey Everyone,

The last installment of "Essence of calculus" is on Taylor series.   I enjoyed reading through the comments on the previous post about what made the topic click for several people, and it helped to solidify what I wanted to say here.  At the moment, I'm marking this as chapter 10, but I'll see if I can make one more video for the series next week and squeeze it in as the second to last.

At the very least, since I have (somehow) not yet mention higher order de...

When did Taylor series click for you?

Hey everyone,

I'm putting together a video on Taylor series, and I don't know about you, but when I was a student first learning this topic I definitely did not appreciate how important they are.  It seems that only happens once you run into a situation where you actually need a polynomial approximation to turn a problem from hairy-to-the-point-of-impossible to something simpler to solve.

I'm curious to hear, what was your experience with Taylor series?  When did they first cli...

New video: Averages with integral, EoC Chapter 9

Hey everyone,

This is the follow-on discussion of integrals.  Originally I had intended for this to have a wider scope, but I chose to narrow in on the example of finding an average for a few reasons: It's good practice for the general idea of turning a finite approximation into an integral, it also is a nice example of how something that looks like a sum in a finite situation looks like an integral in a continuous one, and most importantly it offers a completely different view of why the...

New calc video! Integrals and the fundamental theorem of calculus

Hello Patrons,

After the desert of differentiation, we are finally at the oasis of integrals.  You may notice that much of this video overlaps with the (new) first chapter of the series.  Given that they are separated by 7 videos, it seems fair to have a little review, and the aim here is that similar statements/visuals might be seen in a different light with and without the context of derivative intuitions preceding.  I'm curious to hear what you think of this approach.

A...

New version of chapter 1 for Essence of calculus

Hey everyone,

I decided to create a different version for the video introducing the series.  There's no charge here, since it's a remake and not a new video.  As always I'm all ears to hear what you think.

The main motive here is to clarify with an example how the goal of the series is for the viewer to feel like the rules/constructs/formulas in calculus can come about naturally from your own explorations, rather than by prescription from a higher authority. 

I also ...

New calc video! Limits.

Hi Patrons,

The next installment of "Essence of calculus", about limits, is now ready.  I appreciated the comment thread about whether or not to include a discussion of the epsilon-delta definition, and ultimately decided to include it.  It's at once so visual and so commonly confusing that it would've been a shame to leave it out.

I don't know about you, but I'm getting pretty excited for the series launch.  It's been a huge help to have comment threads on previous videos...

Some early limit animations for the fours

Hey 4+ patrons,

Here's a couple animations from the upcoming limits video.  As you can tell, I ultimately did decide to go with including some talk about the epsilon-delta definition in this one.  I think it's one of those topics that has the potential to be made much more understandable with animation, so it would have felt like an opportunity lost not to at least say a little something.

-Grant