New video, the hyperdarts puzzle, done with Numberphile

I love it!

3blue1brown

Here's another good way to think about why adding up P(S>n) gives you the expectation of S: E[S]=P(S=1)+2P(S=2)+3P(S=3)+4P(S=4)+. . . =P(S=1)+P(S=2)+P(S=3)+P(S=4)+. . . +P(S=2)+P(S=3)+P(S=4)+. . . +P(S=3)+P(S=4)+. . . +P(S=4)+. . . The first line is P(S>0)=1. The second line is P(S>1). The third line is P(S>2), and so on.

Daniel and Rebekah Slonim

Thanks for another great video!

Daniel and Rebekah Slonim

That's a great way to think about it!

3blue1brown

Thanks! We had fun making this.

3blue1brown

I think I'll try to keep up some form of live action lessons more. Maybe that will just be as guest appearances elsewhere, or maybe as more of its own thing. Just so long as it doesn't distract from the main visuals-centered content.

3blue1brown

Yup! It's just like this puzzle, but with simplexes instead of spheres.

3blue1brown

Another way to think about how small a high dimensional ball is when compared to a high dimensional hypercube: In two dimensions there are four corners of the cube (square) outside the ball (disc). In three dimensions there are eight corners of the cube outside the ball. They take up a larger portion of the cube than they do in two dimensions. I guess the trend continues, so that there are more and more corners as you go into higher dimensions, eventually taking up most of the space. Actually if you think of one dimensional balls and spheres, they would be the same thing: segments; the same segment, actually; with no corners of the "square" going beyond the "ball"; i.e., with the same "volume".

Daniel Armesto

The answer to your little quizz is just e. Right?

Daniel Armesto

I finally get why my stomach gets more round when I eat more pi... it adds a dimention! :D Sorry I will leave now....

Aniket raj

I liked your enthusiasm in real life, which is a nice counterpoint to your calm and analytical animations. You should do this more often!

Boudewijn Redeker

After watching your first two shots, remind me to never play darts with you.

flashin' the new ring! awesome video, i like the comment at the end about how analytic and geometric thinking kind of have opposite intuitions

Great video!

Daniel Armesto

Well done! It was cool getting to see you talking alongside the animations, and very good exposition. Liked how you teased the simpler variation at the end, now I want to see you animate the volume for an n-dimensional unit simplex to illustrate that answer.

Eric Severson

Excellent... Liked the give-and-take discussion, intertwined with the summary graphics

Richard Hackathorn

I think so too! It made me wonder if on 3b1b, it might be beneficial to do more of the equation-presentation with handwriting. It feels a bit more friendly and approachable, like a one-on-one between a student and a tutor.

3blue1brown

A fantastic video, good job to all involved!

Vincent Zalzal

Great combination!! :D I think both your and Numberphile's styles/formats complement each other really well.

Janik

Maybe a little spoiler, but still... "You're not quite twice as good as somebody who has no skill whatsoever" *LOL*

Daniel Brahneborg