String Theorists Have Calculated the Value of Pi

String theorists have calculated the value of pi. Didn’t we already know the value of pi? At least the first one hundred trillion digits or so. Yes, but this is an interesting story about the relation between maths and physics. Let’s have a look.

Clarification to what I said at 4:20 -- There are many ways to calculate pi and indeed many converge much faster than that sum. I didn't mean to raise the impression that this is the only way we know to calculate pi!

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#science #sciencenews #physics #maths

[skunclep]

That image reminded me of Terry Pratchett’s “best mathematician on the Disc”, a camel who’s genius allowed him to perfectly calculate the trajectory required to knock-out any sandfly mid-air with its spit, and make that shot repeatedly!

[fretzT_T]

I didn't know you can make Pie from noodles

[peep]

"String theory emerged in the 1960s, ironically right around the same time that LSD did"

[shishirbhat]

The physicists are from IISC Bengaluru - Professor Aninda Sinha and post-doctoral researcher Arnab Saha from the Centre for High Energy Physics (CHEP) @ IISC

[eddieutube]

“And I’m complaining about everything and everyone so subscribe!”

Too funny. Love that sense of humor.

[jagatiello]

4:45 Ramanujan's series for Pi from c.1914 already adds roughly the same amount of correct digits with each additional term.

[olivierbegassat]

"A very technical form of art" is an interesting characterization of mathematics.

[aaronjennings]

Yes, pi is related to fractals. The Mandelbrot set, a well-known fractal, has a surprising connection to pi. In 1991, Dave Boll discovered that the number of iterations required for the sequence to diverge at certain points in the Mandelbrot set is directly related to pi. Specifically, the product of the number of iterations and the value of epsilon (a small number) approaches pi. This phenomenon has been extensively explored and visualized, revealing the intricate relationship between pi and fractal geometry.

[Gorilla_Jones]

String theory just pops an image of physicists playing with yarn balls like cats.

[sanate_sanghming]

1:31 "already familiar with building cases on nothing"... damn!! Never knew Sabine would be such a thuglife savage 😎 !!! 😂

[AmorLucisPhotography]

I wrote my master's thesis on "The Relationships Between Mathematics and Science", so I find this a very Interesting topic. We should not confuse "Nature is at the core, mathematical" with "Our most effective physical theories describe the world mathematically." Our theories, and the language through which we express those theories, are not "nature". They are descriptions of nature and we shouldn't confuse the description with what it describes. My own view is that the claim that "Nature is at core, mathematical" is an entirely trivial one. Mathematics is essentially an a priori investigation into logically possible structures. So long as the universe has an expressible structure, then there will be a mathamatical description of it. (This answers Wigner's problem, btw.) A deeper question would be *why* mathematics and physics intersect, but that's not the sort of question I can answer adequately in a comment here.

[anindyaguria]

The guy who did this work, taught me math methods of physics last autumn 😂
I'm kinda proud!

[ispamforfood]

Oh dear... She's got Albert Bobblestein out! Look out man, she's coming for you head! 🤣

[hamishfox]

4:44 with zero terms the answer is exactly 4. Pi=4 confirmed!

[davidjohnston]

Wow. I read the paper before I saw Sabine's video on it. As someone who writes successive approximation algorithms for mathematics libraries on computers, this is quite a useful result. In practice you use these things to refine a pre-computed start point out to whatever the required accuracy is.

[TranscendentBen]

I remember about age 12 looking in my father's "CRC Mathematical Tables" book at several formulas for Pi that converge much faster than the one shown art 4:24, and I wondered where they came from. Okay, I didn't even know algebra at age 12, but still I wondered a lot of things. Many decades later I read the book "Journey Through Genius" which told of many mathematicians, and more importantly, described their discoveries and how they did them. The chapter on Isaac Newton is of course the largest, and even then it explains how it's incomplete, but it had those Pi formulas and described how Newton derived them! The rest of the book is also very good, and had I read such a book as a teen (it wasn't even published until my late 20s), I probably would have majored in mathematics.

[johnburnside]

Is that camel a Discworld reference?
Ah, I checked down the comments and it is! Good job, Sabine!

[nrdgrrrl]

"String theorists have calculated the value of pi" sounds like the start of joke.
"And it's 42 in the 11th dimension, and it's impossible to prove it's right".

[richardboland]

Over integers k,
For all real, non-negative w,
And where B[a, b] is the beta function:

Sum_{k, -inf, inf} 1/( 2^(2w) B[ (2k+1)/2+w, -(2k+1)/2 + w ] ) = 1
(or 1/2 over either positive or negative k)

And when w is an integer, every term, thus every partial sum over a finite set of k in Z, is a rational number divided by pi. Obviously then, the rational numbers so given rapidly approach pi for sums over finite -k to +k as k goes to infinity. When w is a half-integer, the sum is a rational number that approaches 1, seemingly even more rapidly.

I am fairly certain this is equivalent to the method of computing pi presented by Arnab Priya Saha and Aninda Sinha in their recent paper: Field Theory Expansions of String Theory Amplitudes.


But string theory is not at all necessary. It is essentially a property of generalized binomial coefficients expressed using the gamma function in lieu of the factorial. Perhaps a better question is how string theory might be simplified by this observation rather than contemplating what string theory says about math.

[WewasAtamans]

Congratulations everone! That's the most practical application of the String Theory so far.