
Pi Connects Colliding Blocks to a Quantum Search Algorithm - rudrarch
http://abstractions.nautil.us/article/508/how-pi-connects-colliding-blocks-to-a-quantum-search-algorithm
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jknew
Here is the 3blue1brown video that is alluded to in the article:
[https://youtu.be/jsYwFizhncE](https://youtu.be/jsYwFizhncE)

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svat
The posted article is by 3blue1brown (Grant Sanderson) himself. Where the
article says _" Early in 2019, I published a set of three videos about
Galperin’s result..."_ the link is to the playlist
[https://www.youtube.com/playlist?list=PLZHQObOWTQDMalCO_AXOC...](https://www.youtube.com/playlist?list=PLZHQObOWTQDMalCO_AXOC5GWsuY8bOC_Y)
of which the video you posted is the second video. IMO, it's best to watch all
three (or at least the first two) together :-)

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kilovoltaire
If you want to learn more about the quantum search algorithm, I got a lot out
of this pretty in-depth essay on how it works-

[https://quantum.country/search](https://quantum.country/search)

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pfdietz
I got to the "mnemonic medium" part of that and promptly lost interest. No, I
don't want you to track me.

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dreamcompiler
Quantum Country is a fantastically useful learning resource. They're tracking
you so you don't have to digest it all in one gulp, and can pick up where you
leave off.

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sabujp
anything that is cyclical or periodic is going to have a Pi in the formula
that describes its behavior

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hansvm
Often this is the case, and pi crops up plenty of other unexpected places, but
counterexamples abound as well.

Pick any function defined on [0, 1], and replicate it along the real line at
unit intervals. You can force a description of it using pi, but the most
natural descriptions won't have any reference to it at all.

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throwlaplace
>replicate

you mean construct the periodic extension?

>You can force a description of it using pi

don't know what about the fourier series is forced...?

>but the most natural descriptions won't have any reference to it at all

can you give an example? when comparing piece-wise definitions and fourier
series definitions i think the fourier series _is_ the more natural.

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klyrs
> can you give an example?

How about a sawtooth; no pi needed, and the period is 1.

f(x) = x-floor(x)

The Gibbs phenomenon is my proof that Fourier series is not more natural.

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mhh__
Why? The Gibbs phenomenon is just an exhibit of a finite Fourier series, no?

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throwlaplace
fourier series converges pointwise but not uniformly. for many use cases you
would like uniform convergence (e.g. approximation in an entire neighborhood
of a point) and a fourier series won't give you that no matter how many terms
you add. but like i said above - gibbs only occurs at non-removable
discontinuities and so you shouldn't expect it to be well behaved at those
points regardless of the representation.

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bloopernova
This is fascinating to this very-much-a-math-beginner person.

It's like a glimpse into another dimension.

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hprotagonist
or, indeed, many dimensions.

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kragen
Grant Sanderson is doing such amazing work in divulgation of science and
mathematics, promoting, I think, real understanding rather than the mere
illusion of fluency. He's like the opposite extreme from WIRED Magazine, Chris
Anderson, Malcolm Gladwell, and Deepak Chopra.

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lostlogin
And here I was wondering if 3B would be powerful enough, or would I need to
get a 4.

