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Grant Sanderson

@3blue1brown.com

18K followers 17 following 39 posts

Math videos

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Grant Sanderson @3blue1brown.com · 20d

In the fifth and final of a series of guest videos I've been posting, @BenSyversen delves into a question anybody who has had to do ruler and compass constructions in a geometry class may have wondered: What's the point?

Grant Sanderson @3blue1brown.com · 20d

Much of Euclid’s Elements is easily misunderstood. Some proofs seem to have logical gaps. Some constructions seem pointless, others seem needlessly convoluted.

Each of these provides a window into how the ancient Greeks thought about math and the philosophical role that geometry played.

Why ruler and compass? | Guest video by ⁨@bensyversen⁩

YouTube video by 3Blue1Brown

Grant Sanderson @3blue1brown.com · Sep 7

New video about a piece by the modern artist Sol LeWitt, and the group theory behind it.

youtu.be/_BrFKp-U8GI

Grant Sanderson @3blue1brown.com · Aug 28

Guest video 3/5 while I'm on leave is now up! It's by a former SoME winner, covering key ideas in statistical mechanics to create a simple and discrete model mirroring the behavior of a fluid transitioning between a liquid and gaseous state. Enjoy!

youtu.be/itRV2jEtV8Q

Simulating Phase Change | Guest video by Vilas Winstein

YouTube video by 3Blue1Brown

Grant Sanderson @3blue1brown.com · Aug 23

Hey, psst, you can find early views for two upcoming guest videos on Patreon, one about statistical mechanics and another covering a story of modern art and group theory.

Notes on early releases are always helpful before finalizing a video.

www.patreon.com/posts/explor...

Exploration & Epiphany (Early view) | 3Blue1Brown

Get more from 3Blue1Brown on Patreon

www.patreon.com

Grant Sanderson @3blue1brown.com · Jul 25

For context, I knew I'd want to take some time away this year (paternity leave!), so I reached out to a few other creators whose work I respect and asked if they'd be interested in me commissioning a guest video during my absence. It's a pretty good lineup coming!

Grant Sanderson @3blue1brown.com · Jul 25

New video on the details of diffusion models: youtu.be/iv-5mZ_9CPY

Produced by Welch Labs, this is the first in a short series of 3b1b this summer. I enjoyed providing editorial feedback throughout the last several months, and couldn't be happier with the result.

But how do AI videos actually work? | Guest video by @WelchLabsVideo

YouTube video by 3Blue1Brown

Grant Sanderson @3blue1brown.com · May 4

In the most recent video about quantum computing, I saw many comments expressing a similar point of confusion regarding Grover's algorithm.

I made a follow-up to (hopefully) clarify some of the issues and to address a few other under-emphasized points.

youtu.be/Dlsa9EBKDGI

Where my explanation of Grover’s algorithm failed

YouTube video by 3Blue1Brown

Grant Sanderson @3blue1brown.com · Apr 30

To get around the question P=NP, and whether some clever analysis of the gates could also reveal the answer, the framing here is to assume the only thing you can do with the function is try it out on inputs.

Grant Sanderson @3blue1brown.com · Apr 30

That part of the video could have been better phrased. For any problem you'd want to use this for, you would know the gates, so it's not a black-box in that sense. But to have a catch-all stand-in example, I want to presume there's no insight you gain about the answer by analyzing those gates.

Grant Sanderson @3blue1brown.com · Apr 30

It's known you cannot do better than O(√N), which is certainly not as earth-shattering as an exponential speed-up would be, and questionably useful given the enormous overheads of quantum computing. Nonetheless, it's thought-provoking that such a thing is possible!

Grant Sanderson @3blue1brown.com · Apr 30

If you translate this setup into a quantum computer (explained in the video), Grover's algorithm offers a "faster" way to do this, in that it's O(√N).

Grant Sanderson @3blue1brown.com · Apr 30

As a generic stand-in for the kind of problem it solves, suppose you have a function acting on {1, ..., N} which returns True on one and only one value in this set. If all you can do with this function is try it out on numbers, then it takes an average of (1/2)N steps to find the answer.

Grant Sanderson @3blue1brown.com · Apr 30

What do they do then? This video builds up to Grover’s algorithm, a general method in quantum computing for finding solutions to any NP problem, i.e., anything where you have a quick way to verify solutions, even if finding them in the first place may be hard.

Grant Sanderson @3blue1brown.com · Apr 30

A common misconception about quantum computers is that they would solve hard problems by trying all possible solutions in parallel. This vaguely gestures at something true, but the reality is more subtle.

Grant Sanderson @3blue1brown.com · Apr 30

New video! This covers the fundamentals of quantum computing and builds up to a step-by-step walk-through of an important algorithm in the field.

youtu.be/RQWpF2Gb-gU

But what is Quantum Computing? (Grover's Algorithm)

YouTube video by 3Blue1Brown

Grant Sanderson @3blue1brown.com · Mar 13

I hope so too, the thought of a high school teacher using this idea for a lesson was a key motivator in the back of my mind.

Grant Sanderson @3blue1brown.com · Mar 13

The most viewed thing I've ever made is a short about two colliding blocks computing π. I just made a new edition of the explanation for why π shows up there, setting things up for a (coming soon) follow-on connecting it to quantum computing.

youtu.be/6dTyOl1fmDo

There's more to those colliding blocks computing pi

YouTube video by 3Blue1Brown

Grant Sanderson @3blue1brown.com · Feb 26

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.

Grant Sanderson @3blue1brown.com · Feb 26

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))

Grant Sanderson @3blue1brown.com · Feb 26

Note, there's no reason to restrict yourself to powers of 100. 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...

Grant Sanderson @3blue1brown.com · Feb 26

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 :)

Grant Sanderson @3blue1brown.com · Feb 26

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. The hardest part is energy lost in collisions, more so than friction.

Grant Sanderson @3blue1brown.com · Feb 26

Many years ago I made this video about how two colliding blocks on a frictionless plane can compute pi.

My challenge to you is simple: Implement this in practice.

Grant Sanderson @3blue1brown.com · Feb 26

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.