So...what's the deal with probability?

And I am willing to collaborate with you or others and figure out potential contextual use of stats and probability in both universal and machine learning contexts, including how they are typically used. Anyone is welcome to contact me at http://linkedin.com/in/tekelsey

Todd Kelsey

Hi Grant, let’s say that in the name of Obi Wan Kenobi I implore you to make stats videos. Part of the reason being that there is a desperate need for more AI talent and also a desperate need for more jobs to be created because of all the ones being automated away. I do get and respect the notion of general applicability and I also think context can complement that understanding and ultimately draw more people in.

Todd Kelsey

Thanks, I do indeed have every intention of making these public. I want to clean them up a bit based on feedback from everyone here, but I think once I've finished what I have in mind for ODEs, I'll turn back to these.

3blue1brown

Hey Grant, I think a lot of the content in these videos are really great! I particularly enjoyed visualizing the posterior distribution in the Bayes videos. Selfishly, I do want to see what you had in mind with Bayesian networks. But, I fully respect your decision to not continue making more of these if they're not bringing you joy. What I would like to kindly request though is, do put up these videos you've already made. I'm able to access these just because I have the ability to support you monetarily. There are lots of people who might not be able to do the same. Having these videos out there has the power to inspire someone or deepen their understanding in whatever way. I feel it's a shame that such good content is restricted in this way is all.

Kaushik Mohan

You can ditch the idea of "essence of" series in probability if it doesn't fit. Just as a suggestion, my Uni arranges this topic in 3 courses: Intro probability, Mathematical statistics, then Stocastic processes. (All 500 level). I feel this serve the topic well.

Hey Grant, I think there's gotta be an interesting way to look at the relationship between: reality, the normal distribution, linear operations across the output of a function space, and why a low sample size with a t-distribution is statistically significant.

Good suggestion! If within the next year, there’s no CLT video, please chastise me profusely 😊

3blue1brown

I nearly finished a Ph. D. thesis in probability theory and it's obvious to me what's missing here. You want the glowing gemstone at the heart of probability? It's the Central Limit Theorem. I've heard mathematicians in many different fields say with complete earnestness that it is the most stunning and important theorem in all of mathematics. It's deep, it's pretty, it's incredibly relevant, and it's almost elementary. AND just about all calculus students had to find the normalizing constant for its density function at some point, and the fact that _that_ thing has pi in it when you think of it this way... Is a little nuts. Plus it has cousins like the Law of the Iterated Logarithm, whose wikipedia page has one of my favorite graphs ever ever ever. It's also not an exaggeration to say that, if at least _something_ like the Central Limit Theorem weren't true, our contemporary way of evaluating scientific certainty would have to be completely different

Suibeom

I'm also a fan of those books! While I agree that it's a very worthwhile thing to know about, I'm not sure that the philosophical foundations of probability are what people are necessarily looking for when they're struggling to understand the topic.

3blue1brown

I may be biased because I'm reading E.T. Jayne's Probability Theory, but about taking the "Essence of" that Cox or Jayne are taking, showing how bayesian probabilities are the ultimate logic?

Pierre Thierry

Grant, these videos are really good man, but I think I can understand why it's difficult to get into this. I think that's because probability and intuition tend to line up pretty well, especially for really basic cases. Contrast this with linear algebra, where students are just typically taught how to do things like matrix multiplication, etc (i.e. only how to use the machinery), without being given any background as to why the machinery is there. For linear algebra, it's exciting to do what you're doing! You get to tell people why the machinery is there, and what kind of cool stuff comes out of it. It's really hard to do that with probability. Maybe you can outdo yourself on these ones -- try turning the intuition into math, for a change, not the other way around! I found the 5 videos here really good, and you drew some really good parallels (ex. comparing all the different arrangements of 5 bits with 3 ones vs all the ways to choose 3 distinct things out of a set of 5 distinct things).

Grant, it only fits into the spirit of this channel you do something about probability and statistics. Maybe part of your tension is you're struggling with the "Essence" part when the truth is there are many specialized subdomains and applications where the real value is. Maybe you should simply break up the topic and do separate series/videos, such as "Intro to Probability", "Essence of Statistics", "Random Variable Generation", "Applications of Bayes", etc.

I think you should consider making supplemental probability videos to already existing videos. For example, a video on soft-max distributions specifically to give more intuition on gradient descent. This might motivate to you explore a more fundamental idea in probability, enough so where you have an "essence" collection. I think the same can be said for linear algebra, although the first part was so good, extending straight into a second without supplementation would work too.

As for other free resources, I have a series of probability animations at <a href="https://goo.gl/4KeMeB" rel="nofollow noopener" target="_blank">https://goo.gl/4KeMeB</a> created as part of my free edX probability course, available via <a href="http://stat110.net." rel="nofollow noopener" target="_blank">http://stat110.net</a> (this site also has various other free probability materials). Topics of the animations include combinatorial identities and story proofs, conditional probability, discrete random variables and their distributions, continuous random variables (and the interplay between discrete and continuous), expectation (especially linearity), conditional expectation (including two of the most useful identities in all of statistics), and Markov chains. Of course, the style is very different from 3blue1brown videos, and I would love to see more 3blue1brown probability videos if Grant feels inspired to make more.

Hi Grant, I think it would be great if you could cover Geometric Algebra! I suspect it would be right up your alley.

He's got to put up something he can be proud of w/o pressure from us. I came to support the channel, not micromanage it. I don't want him to cheapen the product just because he made a promise to us.

Hi Grant Great work! Assuming you "advertised" that you'll deliver the probability series - I'm not sure if you actually "advertised" it, but I know I decided to support you because of it (as I felt/feel that the existing online material is not as good), and I must have seen some sort of “ad” - it would be best if you could find some motivation to finish up (soon), at lest the remaining topics in the comment section of ”The independence assumption” video. Otherwise, how are people who support you to believe that you’ll finish announced future videos/series. Our prior relevant belief would have to be updated towards disbelief. Cheers and keep up the good work!

Good suggestions, Emil, I think you're 100% correct that seeing the applications of abstract vector spaces is when the idea really hits the ground running. I was already planning on a Gram-Schmidt video, so perhaps doing two, where the second shows it in a more abstract setting, would be a nice way to go.

3blue1brown

On the topic of expanding the Essence of Linear Algebra series: I think it could be worthwhile to point out some concrete examples of other things enabled by the concept of abstract vector spaces and bases, like Taylor and Fourier series. I remember these concepts being much easier to internalise when I saw the connections between them and, say, the Gram-Schmidt method (and my view on Taylor series changed dramatically when I learned in complex analysis that they're not just an approximation tool, but in fact one way to _define_ whether a function is analytic), and how that concept extends very naturally to the Fourier transform. It might not be worth diving into for a full episode, but I think mentioning some concrete examples like that could really help expand the viewer's perspective. Either way, you're doing a wonderful job with all your videos, and in my opinion, one of the core qualities in them that keeps me coming back (and that made me a patron) is your clear passion for the subjects. I'd say don't be afraid to put down projects you don't feel passionate about - but on the other hand, as Hank Green put it: even if you're only achieving 80% of your 100% vision, don't be afraid to settle for 80% - because soon enough your 80% will be better than your 100% was before. :) <a href="https://www.youtube.com/watch?v=1LAhHDEtTD0" rel="nofollow noopener" target="_blank">https://www.youtube.com/watch?v=1LAhHDEtTD0</a>

Grant, you did an awesome job on the Essence of Linear Algebra -- the result is a real gift to today's students. If there is anything else you feel needs to be said on the topic, that seems like an awesome use of your time and patrons' dollars. More generally, I trust your intuition about these videos. If you just aren't feeling it on a topic, I don't mind at all if you drop the topic or just set it aside for a while. I take it for granted that breathing your particular brand of magic into videos on a topic is artistic expression, subject to all of the accompanying uncertainties. Go where your heart takes you.

Nicholas Sterling

Good suggestions, would you mind throwing it on this reddit thread where I keep track of community requests? <a href="https://www.reddit.com/r/3Blue1Brown/comments/8u46tt/3blue1brown_video_suggestions/" rel="nofollow noopener" target="_blank">https://www.reddit.com/r/3Blue1Brown/comments/8u46tt/3blue1brown_video_suggestions/</a>

3blue1brown

While I feel guilty for all the poeple who waited and hoped for statistics, especially the patreons, I really can't hide how much I love this. One question tough: considering you want to talk about the transpose, are you also going to go into more detail with orthogonal matrices? As those are geometric objects per definition, they seem to be the first candidate for you to talk about and a lot easier to give intuition/animate, while also being insanely important.

Zairaner

Grant, You are great at explaining things in a usable way. So how about Geometric (Clifford) Algebra, which seems to be much superior to and more efficient than Linear Algebra. And what is Verlinde Algebra and why was it developed?

Tom LaFleur

would you be interested in the concept of bootstrapping?

bummer.

seerpea

Hi Grant. It makes sense to stick with topics that excite and inspire you. Those are the topics that you'll really rock and that energy will be passed on to your viewers.

Programmable Spacecraft

Hmmm, maybe, but I think there are those in the field of Statistics who would push back against the premise of it being 'unelegant'. I'll emphasize that me not tending more to the series has much more to do with an internal doubt about whether I have anything pedagogically new to offer here than it does with the prettiness of the field itself.

3blue1brown

Ah, I definitely hear you, and genuinely feel bad not meeting the core audience where they want to be met. I'll put together a list of other resources I'd recommend.

3blue1brown

Certainly, at some point, somewhere, somehow, these videos will be published to the broader public. It's just a matter of whether I choose to change them a little (for the relevant error corrections) or a lot (for more structural improvements).

3blue1brown

That's a good idea, I'll start putting something together. Right off the top of my head I can say one of my top recommendations for people going into machine learning is to take a look at Chris Olah's blog posts on the subject. And for college students (especially in a scientific field) who want an unabashedly Bayesian-manifesto of a book, Jaynes' "Probability theory" is rich with good material.

3blue1brown

Why not do a video explaining the difference between frequentist and Bayesian statistics ? I understand that there are a number of proofs that the two approaches are mathematically equivalent but I have never seen a good explanation of this.

I wonder if your aversion to statistics signifies a deeper underlying mathematical "inelegantness" (and difficulty to explain to us, because of this) in the field of statistics itself compared to, say, linear algebra or your other videos Keep the great work up, though!

Sad to hear about probability, but, these things happen. Two things: 1. I'm not sure about the other videos, but the "Thoughts on the classic Baye's rule example" was incredibly inspiring to me. Not even because of probaiblity, just because it drove home to me a point I've meditated on a lot since then - lots of times, when describing a scenario, people don't really buy it, which is why so much "abstract philosophy" discussions become derailed. That's totally besides the mathematical point of the video, but I'd urge you to find a way to publish it anyway! 2. As you might know, I've been waiting for some time for an intuition around the matrix transform, so I'm really excited to see what you come up with! Having now learned a fair bit more Linear Algebra, including recently tacking the concept of the dual map (which is equivalent to the transform) and the concept of an adjoint (which is relateda s well), I'm still looking for that Grant-style "here's how to picture this" intuition. So I'm really excited about you going in that direction!

Edan Maor

Hello, keep going, you make excellent choices.

Jorge Sinde

I'd be interested too!

I'll run contrary to the other opinions expressed here. I am about to have Statistics this fall and having the Essence of Probability would have been really timely, just as the Essence of Linear Algebra has been... I'd be able and willing to pay some extra on Patreon to finish these series, if it would help, as I'm upset for it to have ended this way, to be honest.

I just wanted to comment and say I support the plans and decisions you’ve described. I’m always excited for more linear algebra, and if you’ve got geometric understanding for the transpose and symmetric matrices to share I’d love that!

Hey Grant! I love all your videos though I am a patreon because of the probability series. In the meantime, can you recommend any references for concepts like Gaussian distribution, Poisson distribution, Entropy and information, etc ?

Roshni

Sorry to hear that, your videos are great content. I will keep supporting the channel, though I started supporting it specifically for Probability reasons. It somehow feels that the series will not be complete without it and it also somehow gives the idea that there is no essence to it.. Keep the good work!

Sergiu Coroi

You, Sir, have a problem being a perfectionist. I believe that's also why having a larger team didn't work out. Your videos are really good, keep going! As i stated previously, to teach probability is tough. I thinks it's because the subject needs a lot of intuition and humans have a lot of wrong intuition about it. Plus everyone is on a different level of mathematical intuition. Also, i am a patreon because of the promised probability videos, but also because of your great videos, which are publicly available. I recommend them to undergrad students all the time. The best part is, that you explain math visually, which creates that intuition for math.

Jan

Hey Grant. First off, your lineup of future videos looks AMAZING! I'm very, very excited to see what you do with all these topics, and thanks for all that content. That being said, I did originally become a Patreon to check out the probability videos (but let's be honest, I should have been a Pateron long before that). As a student taking probability, watching these videos actually did help me a ton. Your Bayes theorem video with the graphical interpretation of it was a lifesaver as my teacher loved to ask Bayes questions. Pretty much all of my class got at least a part of these questions wrong, but I speedran them by drawing weird rectangles and squares. At one point, my teacher even exclaimed that he didn't know what the hell I was doing with the squares, but it was amazing that it worked. My point is that your videos, while being incredibly entertaining (I know, who finds math videos fun?), can also be very helpful to a select number of viewers who are/will take something relevant to your topics. Therefore, I personally believe that the videos you made over probability should be somehow accessible to the general audience. I understand that you may not feel that they are as complete as they could be (though I thought they were very well fleshed out videos), so it could be nice to have these videos as a list somewhere where students like me can access them and learn about a small tidbit in probability. That's just my opinion, based on anecdote. Thanks for being a great creator, as always!

Thanks for the update, I'm very excited about moar linear algebra content! I'm eager for essence of probability too when / if the muse arrives.

As someone hopefully going off to grad school next year to study data science -- damn! I was excited to watch the probability videos to get some better statistical intuition. That being said, I love that you're adding to the linear algebra series! Totally loved the original series (I spent many hours pausing every few seconds while watching those to think and get intuition) and I know it's been really influential for linear algebra learners everywhere. Thanks as always - you'll always have my support!

Alex Loftus

If you need someone to bounce ideas off of for the quantum computing series I'm happy to help. It isn't my area of research (AMO) but it has been a hobby for quite a while

It seems to me that there could be a very nice series beginning with the high school program and evolving into the college program. If the other essence series are any indicator, there will be something in that series for everyone. Also, I think that it could help be a foundation for one offs on the other topics, much in the same way that the calculus series hinted at real analysis without relying on it. With all that said, I agree with the previous commenters - whatever you decide will be the best decision!

Could you put out a video on this and which resources you recommend as divided into the buckets you listed? I don't remember if you announced a probability series, but it would be nice to conclude this to non-patreons as well

I originally supported your channel on Patreon to see the Probability previews, and was very excited to see the remainder. That being said, I am not disappointed in the slightest at your choice(s) to do with running the channel. Your direction and content are both incredible and I look forward to seeing the future content. Whatever it may be. Keep doing you.

If you don’t love what you’re doing, then it’s not going to be good either way. Also, I really like your philosophy about this.