Hey everyone,
This is one video in a two-part collaboration with MinutePhysics. The video on his channel is about Bell's theorem, and our description there rested heavily on the quantum mechanical correlations that arise in looking at the probabilistic behavior of polarized light (thoug...
2017-09-13 14:27:41 +0000 UTC View Post
Hello $2+ Patrons,
Henry (from MinutePhysics) and I have been working on a pair of videos, one one Bell's inequalities, and one that's a primer on some of the wave math that underlies quantum. Here's a sneak peek of the first one for you guys.
As this is an early preview, please don't share it just yet. But once we make it public tomorrow, share like crazy!
-Grant
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2017-09-12 16:14:19 +0000 UTC View Post
Hello $4+ Patrons,
If you're curious to get a sneak peak on what I'm working on, here are a few animations for an upcoming video.
I just noticed in looking at this that some of the arrows in the photons seem a bit finicky, but I figure I'd show anyway to better reflect how bugs do inevitably come up now and then in doing this.
-Grant
2017-08-28 00:25:49 +0000 UTC View PostHey everyone,
You might have noticed that the probability series has been a little slow to develop, so I thought I'd give you all a little update for what I'm working on. Right now I'm in the middle of two projects which have a been more heavy on the research side, since each is a little out of my typical wheelhouse.
One is a pair of videos on a certain quantum mechanics topic...
2017-08-18 21:33:13 +0000 UTC View PostHey everyone,
As mentioned in the last video, I'm starting a podcast with two very smart and likable guys I met at Khan Academy, each named Ben. You can find it at https://www.benbenandblue.com/ .
Let me know if there's anything you'd like to hear us discuss!
-Grant
2017-08-15 01:03:53 +0000 UTC View Post
Hello all,
This is a fun one on trying to grapple with higher dimensional spheres. The puzzle that it centers on is a very famous example of where our intuition for higher dimensions breaks down, but the goal I set for myself here was to present it in such a way that the final 10-dimensional example doesn't actually feel that weird. I'm curious to hear what you think!
Per...
2017-08-11 22:50:26 +0000 UTC View PostHey everyone,
As some of you may have noticed, this Patreon page recently passed one of the goals I put out several months ago. Specifically, here's how it was described.
It's around this point that I'd start considering expanding beyond just me to help create more series in more topics.
Truth be told, you all caught me off guard a bit with how ...
2017-08-05 22:45:36 +0000 UTC View Post
Hey folks,
I have a new probability video for you. The plan is for this show up as chapter 3. Preceding it, but not yet made, there will be an introduction to basic combinatorics (e.g. n choose k stuffs) and a primer on probability basics, like conditionals and how to think about distributions. Here's a loose template for the videos I have planned so far:
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" pat...
2017-07-21 19:55:11 +0000 UTC View PostHey 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...
2017-07-13 00:17:02 +0000 UTC View Post
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/questio...
2017-07-08 14:33:34 +0000 UTC View Post
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 ...
2017-07-07 16:51:49 +0000 UTC View Post
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...
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 als...
2017-06-26 00:41:42 +0000 UTC View Post
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...
2017-06-15 06:22:16 +0000 UTC View Post
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, condit...
2017-06-15 06:05:24 +0000 UTC View Post
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, yo...
2017-05-26 17:58:22 +0000 UTC View Post
Hello +4's,
The upcoming video is on finding all possible pythagorean triples. Here are a few excerpts from animations I'm working on.
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 keep...
2017-05-19 15:55:18 +0000 UTC View Post
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 mat...
2017-05-18 21:09:45 +0000 UTC View Post
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:
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? ...
2017-05-08 16:16:24 +0000 UTC View Post
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
2017-05-04 04:38:54 +0000 UTC View Post
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...
2017-04-29 02:02:22 +0000 UTC View PostHey 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. 2017-04-23 18:10:44 +0000 UTC View Post
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...
2017-04-20 05:48:55 +0000 UTC View Post
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...
2017-04-15 06:04:00 +0000 UTC View Post
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 ...
2017-04-08 22:37:34 +0000 UTC View Post
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 e...
2017-03-29 21:10:53 +0000 UTC View Post
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 somethi...
2017-03-26 01:04:22 +0000 UTC View Post