3Blue1Brown

Pop quiz time! Try to answer without looking it up.

Suppose I have a mystery function, and I tell you that there’s some secret value among all the numbers from 1 to N, where if you plug that value into my function, it returns True, otherwise, it returns false. For example, maybe it simply looks something like "f(n): return (n == 123)". But you can't see the inside of the function; it's a black box.

How long does it take to find this secret value? For a classical computer, there's no better method than to guess and check all N possibilities. Sometimes you're lucky and get it early; sometimes you're unlucky, and it takes closer to N; on average, it's N / 2. In CS, we call that an O(N) run time, disregarding the constant because we just care about how things scale as N grows.

Here's your quiz: How long would it take a quantum computer to do the same task?

2 days ago | [YT] | 3,375

3Blue1Brown

I've been spending most of this week writing/rewriting the script for Grover's algorithm video, which aims to highlight a connection between quantum computing and block collisions. Man, I thought this would be relatively simple, but it turns out to be very hard to explain quantum computing if you don't want to assume any background (shocking, I know!). It's one of those topics where once you know all the setup and premises, the result itself is swift and satisfying, but all the effort goes into wrapping your mind around the premises!

It's a fun challenge, but the turnaround time may be a bit longer than what I initially anticipated.

2 weeks ago | [YT] | 19,454

3Blue1Brown

In the recent videos I made with Terence Tao about the cosmic distance ladder, we necessarily had to move past some of the added details on each topic. Somewhat coincidentally, around the same time, Ben Syversen put up a video with the mathematician Alex Kontorovich all about the contributions Aristarchus made, involving the deductions of how far away the moon and sun were. If you liked the cosmic distance ladder piece, you'll definitely enjoy this one, and it answers many questions I saw people ask in the comments.

3 weeks ago | [YT] | 1,185

3Blue1Brown

I have a pi-day challenge for all the physics students among you (or anyone willing to set up an experiment). If you share your results with me by March 10th, I may feature them in a video, depending on how good the results are and how many I get.

Many years ago I made this video about how two colliding blocks on a frictionless plane can compute pi. The challenge is to implement this, physically, in practice. The original puzzle assumes zero friction and zero energy loss in collisions, so obviously there are limits to how far you can get. I can tell you the real limiting factor is energy lost in collisions, more so than friction.

Also, it's a wildly inefficient way to compute pi, to even get "3.14" you'd need this to work with a 10,000-to-1 mass ratio and have a way to count all 314 collisions. Matt Parker and I actually gave this a go, and the results were...okay, but could definitely have been improved :)

Note, there's no reason to restrict yourself to powers of 10. For example, you could use powers of 4 to compute pi in binary. A mass ratio of 64-to-1 should give 25 collisions, which is 11001 in binary, and pi looks like 11.001...

More generally, with a mass ratio of N-to-1, the number of collisions is around π / arctan(1 / sqrt(N)). So any big mass ratio gives you an approximation of pi by multiplying the number of collisions by arctan(1/sqrt(N))

If you do this, you can reach out to the channel via this page. 3blue1brown.com/contact

Be sure to have a link to footage of the experiment. If anyone can get it to work with 100-to-1, I'd be happy, and if anyone can do it for 10,000-to-1, I'd be both delighted and amazed.

1 month ago (edited) | [YT] | 753

3Blue1Brown

Final linear algebra quiz, on abstract vector spaces: beta.retainit.app/game/6655afcaa53b4eea9912a26f

1 month ago | [YT] | 752

3Blue1Brown

Still hungry for more linear algebra quizzes? Eigenvalues are arguably the most important topic in the whole batch.

Eigenvalues: beta.retainit.app/game/665599dfa53b4eea99129f06
A quick trick for 2x2 matrix eigenvalues: beta.retainit.app/game/6655a3f0a53b4eea9912a1fd

Full series: www.youtube.com/playlist?list...

1 month ago | [YT] | 781

3Blue1Brown

More linear algebra quizzes. Cramer's rule is a neat trick for solving equations, and for understanding inverse matrices. Understanding the geometry behind it is a great workout for testing your geometric intuitions of L.A.

Cramer's rule: beta.retainit.app/game/6645eb942b199800456d7518
Changes of basis: beta.retainit.app/game/6645f4302b199800456d7763

Full series: www.youtube.com/playlist?list...

1 month ago | [YT] | 544

3Blue1Brown

Next two linear algebra quizzes. These are from the part of the series that connected the geometric interpretation of dot/cross products to their formulas.

Dot products and duality: beta.retainit.app/game/66018d19802671038f34d0a2
Cross products: beta.retainit.app/game/6626a075555b85d7c3a75a5b
Cross products in the light of linear transformations: beta.retainit.app/game/6627db48ef110d1bc1c114ca

Full series: www.youtube.com/playlist?list...

1 month ago | [YT] | 513

3Blue1Brown

Next two linear algebra quizzes:
Inverse matrices: beta.retainit.app/game/65fc26f8f00f7bd6dc608a82
Non-square matrices: beta.retainit.app/game/65fc7f79df1259ad1fc379fe

1 month ago | [YT] | 501

3Blue1Brown

Two more linear algebra quizzes. Enjoy!

Matrix multiplication: beta.retainit.app/game/65f9b6e8df1259ad1fc1ea4b
Determinants: beta.retainit.app/game/65fa04f989ee6cb4079f7b34

Full series: www.youtube.com/playlist?list...

1 month ago | [YT] | 920