String Theorists Have Calculated the Value of Pi

[@SabineHossenfelder]

This video comes with a quiz which you can take here: quizwithit.com/start_thequiz/1719206089323x869815540334730500

[@Thomas-gk42]

Thank you for these quizzes, they are a pleasure too.🌻

[@osmosisjones4912]

Calling people who question look at data testable verifiable data over sources are anti science. Your anti science. Only real scientist today are conspiracy theorist

[@osmosisjones4912]

The guy Italy uncharged of covid policy got millions people ☠️

[@AquarianSoulTimeTraveler]

I would say setting S1 and S2= -1/2 is like fixing the problem of volumetric calculation of like units... if we just make 0units×1units=1units or 1units×1units=2units... it is achieving the fundamental -1...

[@AquarianSoulTimeTraveler]

5:44

[@skunclep1938]

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!

[@mertanos]

Exactly my first reaction - I had to pause the video until I stopped laughing. I'm not really surprised that Sabine would pay her respects to sir Terry, though. Great minds and so on.

[@DuskyJoe]

I finished the book only recently. For this reference here alone it was worth to get to know _You B._

[@robertgoff6479]

Came to see if anyone else noticed. I wonder if Sabine read him in the original German?

[@erasmusvenport8830]

I showed the video to my wife who also immediately spotted the reference.

[@davesabra4320]

now it doesnt work with the African Blue sandfly

[@fretzT_T]

I didn't know you can make Pie from noodles

[@ftumschk]

Oddly enough you can, sort of :) Do a KZbin search for spaghetti pie recipes.

[@Karlheinze12356]

Some noodles make pie...😅

[@multivitamin425]

Strings may be 2d planes rolled up, so thats lasagne pasta

[@ftumschk]

@@multivitamin425 ... not forgetting the famous cannelloni of Mars.

[@jamiewalker329]

There's literally way of throwing noodles at tiles on a kitchen wall to approximate pi. It's called Buffon's noodle. Look it up....en.wikipedia.org/wiki/Buffon%27s_noodle

[@eddie1975utube]

“And I’m complaining about everything and everyone so subscribe!” Too funny. Love that sense of humor.

[@itsrachelfish]

Same!! xD

[@peep39]

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

[@anttikangasvieri1361]

Totally unrelated to Unix too

[@JosephLMcCord]

Absolutely one of the most hilarious comments, ever.

[@JosephLMcCord]

@@anttikangasvieri1361 Back when programmers were thinking in such a way as to want to even minimize the number of keys that they had to press, to do anything...

[@v2ike6udik]

Lsd was "necessary" for new age baalsht.

[@AlphaLionTrillionaire]

Nor ironic, it's called a coincidence

[@shishirbhat3463]

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

[@sapwho]

the lawyer joke 😂

[@tescOne]

yes

[@Limrasson]

🔥

[@lorn4867]

🔥

[@markxxx21]

I love her deadpan / sarcastic humour.

[@sylvainbougie7269]

Meh

[@jagatiello6900]

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

[@Techmagus76]

Sure but that one is already well studied with a lot of papers existing. So have you ever tried to get a new paper published on that one, see we have a new approach that made it much easier to publish a paper. Ok to be fair it is still interesting to study a new approach, why it converges against pi, how fast, what is the computational complexity, did we have a criteria to know/calculate how closed to pi we are etc..

[@melgross]

The new paper is better.

[@DeathSugar]

@@Techmagus76 > why it converges against pi look at gamma function and you will notice e out there and complex argument as input. the rest is easy to deduce, hail to euler.

[@matthiasklein9608]

@@melgrossI haven’t analyzed the new series yet but Ramanujan’s series gives you 8 digits of Pi per term. That’s 240 digits for 30 terms. And it doesn’t use a gamma function.

[@BarderBetterFasterStronger]

​​@@Techmagus76 Just so you hear it from an Internet pedant and not in real life - it's "close to". "Closed to" is never grammatically correct in the context of measuring accuracy - or possibly ever.

[@olivierbegassat851]

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

[@executor893]

One of my university professors used to say that "math without physics is just philosophy with numbers".

[@davidespinosa1910]

And accurate too

[@jimmyriba]

@@executor893 Not quite. Math without physics can be math with computer science, math with biology, math with economics, etc. Math is about understanding patterns, and transfers to all sciences. Sabine's arrogance doesn't suit her on this point. On the other hand, physics without math is just trying out random stuff.

[@JM-us3fr]

As a mathematician, I agree with that description. It also gets into the philosophy of knowledge and language a bit, so it’s difficult to really pin down what it is.

[@aYoutubeuserwhoisanonymous]

@JM-us3fr Math just seems to me to be study of methods of deduction to preserve the initial truth condition. if you find that somewhere 2=3 under the same definitions of the terms then you know you have gone wrong , the truth condition of RHS=LHS isn't preserved.

[@aaronjennings8385]

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.

[@Walter-Montalvo]

The number of iterations is related to pi? That is so counterintuitive! Thanks for pointing it out.

[@aaronjennings8385]

@@Walter-Montalvo The number of iterations required for the sequence to diverge in the Mandelbrot set is directly proportional to pi, with the product of iterations and epsilon approaching pi. Lol.

[@RalphReagan]

Now that is cool

[@stopthephilosophicalzombie9017]

@@aaronjennings8385 It would have been much more interesting if it was related to the fine structure constant.

[@lucca3113]

this reads like it was written by chatGPT.

[@sanate_sanghming]

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

[@TheDigger76]

Funny. But also quite shallow.

[@zicadibrove4119]

Its called denial

[@TheSkystrider]

I'm here for her complaints! 💙

[@anindyaguria6615]

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

[@adityakulkarni4549]

Lucky guy

[@Gorilla_Jones]

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

[@believeroflight9888]

I assure you that is what is happening...

[@--ART3MIS--]

the results are pretty identical.

[@awakening5967]

And the cat's name is Schrodinger.

[@martineldritch]

Cats have taught me that "unravel" and "ravel" both mean the same thing ; " to cause to come apart by or as if by separating the threads of "

[@ginnyjollykidd]

That quickly gives rise to entanglement theory.

[@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.

[@davesabra4320]

I wrote my mistress' thesis and she graduated.

[@anonsurfer]

I think the relationship between physics and mathematics is sort of like the relationship between energy and matter, both being interchangeable. I also think that attempts to define "nothingness" and the notion of an absolute nothing not existing may have to do with this relationship. It's like asking if the number 0 is a true void/nothing with no activity going on inside it, or if 0 is both NOTHING and EVERYTHING (infinity) simultaneously. 0 being the underlying energy (E) manifested as infinite numbers - the matter (M) - expressed as all things and their opposites/contradictions - matter, anti-matter, universes, entities both living and non-living, tangible and intangible attributes (including thoughts, feelings, emotions, etc.).

[@alan5506]

Mathematics is nothing more than formal description with rules that are unambiguous. If nature can be described, then it is mathematical in nature. And the ONLY way to describe ANYTHING is mathematically BY DEFINITION. Because any unambiguous definition/description is part of what we call mathematics. That is why computer science is a branch of mathematics. Edit: I realize that "So long as the universe has an expressible structure, then there will be a mathamatical description of it." is exactly the same as "If nature can be described, then it is mathematical in nature.". I just hold the assumption that everything must be describable. So "why mathematics and physics intersect" is kinda silly to ask when you hold that assumption. Because to describe anything, it must be mathematical. If it isn't, then other people will interpret it a different way and your description is more inspiration/guidelines than a description.

[@coolcat23]

I maintain that nature is more closely related to computer science (computational processes) than it is to mathematics. Mathematics uses an extensional approach (input is mapped to output by just defining the relationship), i.e., typically lacks a constructive description of how exactly the relationship is established. Computer science is concerned with how to get from A to B, not just what the relationship between A and B is. Nature progresses from A to B, not by looking up how B relates to A, but by using concrete processes. Therefore, nature is not "at the core mathematical"; it can only be described phenomenologically by mathematics.

[@cowlinator]

The question is, why do relatively simple mathematics describe a world of indeterminate complexity so well? That's really fucking weird.

[@davidjohnston4240]

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.

[@WewasAtamans]

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

[@leogama3422]

😂

[@jimliu2560]

So ~50 years of String-Theory study really hasn’t paid off….

[@martiendejong8857]

And its not practical at all 😅

[@soosh9852]

Hi Sabine, first off, love your videos! My one criticism of this particular one is that you gave one example of a very slowly-converging series to pi and made it sound like no other fast-converging series have been known before this one, when there are plenty of other examples

[@johnburnside7828]

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

[@dw620]

It was indeed a circular reference.

[@Thomas-gk42]

Yes!

[@mark.J6708]

Brilliant.

[@hamishfox]

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

[@benjamindees]

I'm glad someone else noticed this.

[@fredrik3685]

I know all the digits in pi. I just don't know the exact order.

[@axle.student]

Thanks Sabine. You scratched my life long itch by bringing circles into the conversation :) Circles are the alpha and the omega :P The number of ways to calculate Pi is an irrational number approaching infinity lol > I was looking at the converging precision estimation algos to see if it could be improved, but everyone has had a a go at it already. I am still tempted to give it a shot when I get some time. > I did look for a more direct method by looking for a circle with a known radius and circumference. Still looking at that one. > Digital/logical math in nature is an illusion IMHO. Pi is just one of many illustrations of this.

[@arte.marcelo.castro]

wait, was that a Discworld reference at 5:23 with the camel stock footage? Brilliant! As if I didn't have enough reasons for loving this channel.

[@andybaldman]

“If pi emerges, a circle is involved somewhere.”

[@alphabasic1759]

"...building cases on nothing..." I love your humour.

[@ozbloke9781]

Hey Dr Sabine! You’re marvelous. Let me explain. I am a lawyer, linguist, and artist. I never studied sciences. Your videos have activated me to spend some of my free time exploring science. I’m now at a state whereby I see physics concepts in daily life. I love your dry and ironic sense of humour. I appreciate everything you do and I think you’re amazing. Thank you.

[@GrahamChristie-jg8sw]

"nature is at the core mathematical" - I would go even further to suggest that both nature and mathematics are fundamentally about relationships and so is pi.

[@markdowning7959]

Well Pi is a ratio. But "nature and mathematics are fundamentally about relationships" between what?

[@GrahamChristie-jg8sw]

@@markdowning7959Wouldn't Pi be a relationship between the circumference of a circle and its diameter? Relationships describe how different entities interact and relate to one another. Nature demonstrates many relationships in biological systems, ecosystems, and physical laws. In mathematics, there are geometric relationships, relationships in statistics and probability, and equations and functions. Mathematics has the advantage of quantifying how different entities are interconnected. This is why I personally believe that mathematics can describe nature very accurately, though this is qualified within certain realms.

[@markdowning7959]

@@GrahamChristie-jg8sw Yes, I was agreeing about Pi. And certainly the world would be pretty boring if there weren't relationships/interactions/borders/surfaces or whatever between things. But I thought you were suggesting the relationships (verbs?) were more fundamental than the objects (nouns). Maybe they are, it's an interesting perspective.

[@GrahamChristie-jg8sw]

@@markdowning7959 Lets play see where that idea takes us: Assume that the most fundamental element in nature is a relationship, which itself constitutes information. Could we then build increasingly complex relationships between these relationship (basic units of information) and observe the emergence of intricate systems? Furthermore, could these emergent systems form relationships with other emergent systems, ultimately resulting in the manifestation of a field conjured from nothing?

[@markdowning7959]

@@GrahamChristie-jg8sw I'll have to reflect on all this for a while. Might relate to consciousness.

[@karldavis7392]

My favorite series for calculating pi is Newton's. He used the calculus he had developed on a slice of a circle, 60 degrees of arc. He made it into an infinite series of terms, each about 7 or 8 times smaller than the one before. You need to estimate the square root of 3 to a sufficient level of precision based on how accurate you want your estimate of pi. It converges down from above, not oscillating. There are some good videos on that method on KZbin. Because each term is so easy to calculate, and we all learn the building blocks of it in calculus class, I like it more than any of the newer methods.

[@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.

[@LindenAshbyMK]

I'm curious if the mathematics has some accessible job market roles (not professors, not top tier researchers etc)... 🤔

[@egoreremeev9969]

Pochhammer symbol is not defined by it's relation to gamma function, and it's better to call it falling(rising) factorial. Even though you can calculate it via factorials, but it does not need to be. It's just repeated multiplication, (a)_k = a * (a-1) * ... * (a-k+1). Which is true FOR ALL a and natural k, which it is for the formula in question (the argument is rational, but the k=n-1 is an integer). The problem with this sum is of different origin. Each term needs ~n multiplications, in the end you need to calculate ~N^2 multiplications for N terms. So effectively you need to compare it to other sums with N^2 of their terms if they do not need such amounts of multiplications.

[@Dr.M.VincentCurley]

Does the grand unified field theory have to be supersymmetric or have they decided that that was no longer necessary?

[@SabineHossenfelder]

String theory doesn't properly work without supersymmetry, so they can't just kick it out.

[@leif1075]

​@@SabineHossenfelderThanks for this video Sabine. I really hope you can respond to my other comment whenever you can. Thanks very much.

[@Dr.M.VincentCurley]

@@SabineHossenfelder but they only found one Higgs. To satisfy the string theorists wouldn't they have to find at least one other one with opposite charge and or spin?

[@dennisclapp7527]

Sabine, I love your sense of humor especially when you are feeling good. Remember, we love you.

[@gregcoyle8121]

I'd really like to hear your thoughts on GUTs. My specific issue is that everyone seems to realize that gravity is not a force, it's an effect of matter in spacetime. But everyone seems quite happy to completely forget that when attempting to reconcile and combine fundamental forces. I'm reasonably sure that not everyone is completely stupid, so what am I missing?

[@iyziejane]

The universe is quantum mechanical, and no sensible way to combine QM with the curvature of spacetime story has been found. Since we know that gravity can also be described as a force (the curvature story is optional), like a more nonlinear version of the electromagnetic field, it makes sense to seek a quantum field theory to describe gravity. But it was discovered 40 years ago that relativvistic quantum field theory isn't compatible with the kind of spin 2 graviton particles that would appear in a quantized version of general relativity (a theory based on tensors with 2 indices, rather than vectors with one index). The next simplest thing to consider after a QFT with point particles is a QFT with 1D strings, this motivates string theory, which does allow for spin 2 particles representing gravitons. But string theory has other problems too of course.

[@Stadtpark90]

I get the same confusion: if we agree that gravity is emergent, why are we still looking for a theory that spits out a graviton exactly and naturally, when we already know, that it will only ever exist approximately, but not as a real thing? Shouldn’t the goalpost have moved? Isn’t an exact and natural graviton now a sign, that such a theory will involve infinities, and as such never describe reality as it is implemented? In a continuous universe infinities are ok. But in a discrete universe, where gravity and dimensions are only implemented approximately (- like pi), there should be no exact “force carrier” for gravity, because it is not a force? I probably drew some wrong conclusions from hanging around the wrong corners of the internet… 😂

[@MasterChakra7]

​@@Stadtpark90 Because of the wave-particle characteristic of particles. If an electron really is a probability density before it's observed, then how does its gravitational field operate, and where ? How does it change upon measurement, the very thing that "gives" the electron a precise position ? We (sort of) have no problem dealing with an electron's quantum behaviour, but general relativity doesn't show any sign of probabilistic behaviour or sudden change upon interaction with mass.

[@bobkoroua]

​@@MasterChakra7 It appears to change as it is measured.

[@stormtrooper9404]

@@iyziejaneWhat about the inertia? Still there aren’t solutions for that problem no matter how you treat gravity, much less with QM behavior.

[@ispamforfood]

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

[@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".

[@francescoferrante1791]

I like your honesty. 🙂

[@knofi7052]

Sabine, ich liebe einfach deinen Humor, auch dann, wenn du nur die Wahrheit ganz unverblümt sagst!😂 Danke, und bleib einfach, wie du bist! 😄

[@NoName-zn1sb]

except... get a new dress

[@softwarerevolutions]

@@NoName-zn1sb Yes, the gradient colors look a bit odd given that she can look more beautiful in other dresses and/or colours.

[@Mythhammer]

Great video. This is what I long ago subscribed for.

[@МихельКонстантин]

This video makes it sound like mathematicians used slow-converging Madhava-Leibniz series to approximate pi before string theorists came in to save them, but they identified the problem of slow convergence literally centuries ago and generated a ton of fast converging series for pi. So really, not a big deal that string theorists discovered this

[@jimmyriba]

Yes, this video is a really surprising low level for Sabine. This is elementary stuff. Also her confusion thinking that evaluating the Pochhammer symbol (simple rising powers) is as difficult as evaluating the Gamma function, when it’s literally just multiplying n numbers together. Her staff even wrote it on the screen for her! It makes me suspect that her videos on stuff I know nothing about are equally shoddy.

[@andrewhone3346]

As a mathematician who knows this stuff, I still think it's an entertaining video talking about things that most of the audience don't know much about, and discussing the boundary between mathematics and physics. The series given here doesn't look like it converges as rapidly as Ramanujan's formula for pi.

[@KbN132]

@@jimmyriba Gell-Man Amnesia

[@alphabetagamma12]

​@@KbN132I'm glad somebody mentioned gell Mann amnesia. I love Michael Crichton's talk on this.

[@roelin360]

​@@jimmyriba​you really used this comment pointing out a minor criticism to fully jump down her throat

[@ittaiklein8541]

Not only do I learn interesting things with you, Sabina, I am also treated to some of the best standup, out there! Please carry on. ❤

[@silveraxx]

The last part is a reference to discworld? You Bastard is the sole remaining camel in the Royal stables of Djelibeybi (lit. Child of the Djel). He also happens to be the greatest mathematician on the disc.

[@boopsnoop5469]

Loved the paper! It was honestly a lot of fun, it reminds me of random trains of thought I would have while studying QFT. Gamma and Zeta functions connect things like crazy!

[@ictoan5966]

String theory has managed to not only overcomplicate physics, but also overcomplicate calculating Pi

[@Michael-kp4bd]

It makes me wonder if they just stumbled across a formulation in one area that happens to coincide with (and overcomplicate) merely relating a circle to its radius, or a sphere, or whatever topology and corresponding dimension relates those two geometric features. But pi does pop up in many areas, so I couldn’t really tell you if that’s what’s happening. If it’s not just an equation that is isomorphic to known calculations of pi, then what they have may be meaningful and not just an overcompensated pi-calculation algorithm. And also I know your comment may have been fully made in just.

[@melgross]

Not really. The conventional methods take a vast amount of supercomputer time and resources. This enables it in my iPhone.

[@Michael-kp4bd]

@@melgross i don’t know if that’s true. It comes down to the Big O (computational demand with scaling). Any cheap ass computer can handle algorithms for the first 20 digits in less than a second. For the trillionth digit of pi, you’re running this for trillions of iterations. Hence supercomputer. If you know the Big O complexity for this algorithm over the existing ones, please share because it would yield the answer.

[@jjtt]

​@@melgrossnah, you can run the chudnovsky brothers' series anywhere already, and that one lets you compute the nth digit of pi without computing all the previous digits

[@swiftycortex]

She says in the video that it makes calculating pi easier. She said she even attempted it herself

[@hanspetermarro4188]

The rhs of the Madhava-Leibniz series is Arctan(1) calculated from the Taylor series of Arctan. From tan(x+y) = (tan(x)+tan(y))/(1-tan(x)tan(y)) deduce that Arctan(1) = Arctan(1/2) + Arctan(1/3) and do the Taylor thing again. You'll now get Pi/4 = Sum_{k>=0} (-1)^k ( (1/2)^(2k+1) + (1/3)^(2k+1) ) / ( 2k+1 ). The first 20 terms of this series give you more than 10 correkt digits.

[@paulrite5358]

They have just used that a string with its ends connected maximizes its enclosed area when it forms a circle.

[@SpiritmanProductions]

I'm confused. I thought gravity was the bending of space by massive objects such that objects appearing to orbit them are just travelling in (what is for them) a straight line, on a curved part of space. Now they're still looking for gravitons? Which is it? 😮

[@stargazer7644]

Gravitons and space bending by mass are both just models. Models are just useful approximations to how the universe actually works. Gravity isn't really either one of these things. Are photons particles or waves? Those are both models. They're really something entirely different.

[@arctic_haze]

Oh, the benefits of the string theory. Who knows, maybe one day they will even calculate the precise value of 1 (one)

[@Walter-Montalvo]

Don’t you first have to define what is 1? Let’s not get ahead of ourselves. ;)

[@stopthephilosophicalzombie9017]

They probably are among those freaks who say that 2+2=5.

[@NoNameHere-pm6hw]

@@Walter-Montalvo Fortunately that is pretty much axiomatic, but to get to 1+1=2 takes a few hundred pages of work!

[@VFella]

Got this covered, it's exactly 1

[@DrDeuteron]

my (undergrad) standard model TA, a theorist, said 1 = pi = 2 = sqrt(2) = I = -1 (this was in case he had to evaluate a diagram) and no, it wasn't Terrence Howard.

[@MCsCreations]

Fascinating! Thanks, Sabine! 😊 Stay safe there with your family! 🖖😊

[@rgarbacz]

Thank you for the excellent science news. I have a question: as Pi would be different in not euclidean geometries - how does it relate to the other ways of calculating it?

[@Hyposonic]

First useful thing to come from String Theory since...forever.

[@deepaknanda1113]

1:29 😂😂😂 building cases on NOTHING

[@AdvantestInc]

The intersection of string theory and pi calculation is fascinating! Great content.

[@Walter-Montalvo]

5:45 You forgot to add Sabine “I complain about everything“ to the Venn diagram

[@ospididious]

I love you Sabine. You're always on point. Keep it up.

[@bedabyasbehera2058]

This group is from IISc, Bangalore. Feeling proud to be an IIScan.

[@martinrosol7719]

You did nothing to contribute, so there is nothing for you to be proud of.

[@a1productionllc]

Sabine, I do like your sense of humor, especially at about 6 minutes, where you speak about complaining that you do! Your segue into the ad for Brilliant, is quite good. Know where I can find a good Mathematician, to collaborate with me on a physics paper based upon the Bible? Have a good day.

[@michaelgreenberg6344]

The venn diagram at 5:39 is priceless

[@deafponi]

The use of the camel, mayhaps at Terry Pratchett reference? :) keep up the great work guys, I love your content

[@trinityy-7]

no wonder they were making very slow progress, they didn't know about pi

[@Aikman94]

LOOOL

[@ChristiaanCorthals]

how many decimals of Pi do you really need if you calculate distances, lengths etc... when there is the Planck length that limits the accuracy anyway.

[@Ian_Carolan]

+1 for the Terry Pratchett camel/maths reference 😉

[@REKlaus]

Thanks for another informational video. Maybe do a video on why scientists have to prove their theories using math and how do they know where to start their formula??

[@ecneicsPhD4554]

The day string theory discovers fire I would become a bit more interested.

[@ffggddss]

20 terms to get 10-place accuracy is good, but isn't that about the same level of efficiency as John Machin's famous series? You know, the one that goes: ¼π = 4tan⁻¹(⅕) - tan⁻¹(1/239) using Taylor series for arctan? Anyway, that's still really good. BTW, what exactly is λ? The sum can't be evaluated at all without knowing that. Fred

[@quhdshb]

𝜆 is an arbitrary complex number

[@ffggddss]

@@quhdshb How can that work when λ is arbitrary? If you change its value, won't that change the result, so that it won't always be π? Anyway, at 4m37s, she shows a calculation in which λ and k, [one less than] the number of terms being summed, are both set to 20. Not sure how she arrives at that identification.

[@adrianpalmer4983]

7. Its 7. The 98th trillion digit of Pi is 7

[@sleepingbee101]

I've been waiting for this. Saw you tweet about it on x

[@terryflopycow2231]

Your tone and expression at the start of the video was very predicatable based on the title of the video 😂

[@Foolish188]

Amazing! The first real finding from String Theory!

[@SNixD]

My way of thinking is that Physics is a collection name for the laws of nature and that Mathematics is the language with which we describe them. Grossly simplified everything else is just abstraction layers used to hide the underlying complexity. For example, psychology is an application of how biochemistry interacts with external stimuli. That biochemistry is just a specific field of chemistry which in turn is a form of particle physics. If we understood it well enough, which we don't, we could describe all of psychology with math but for now we'll have to make do with explanations like stress, social anxiety, not getting enough sunlight or hormonal imbalances.

[@seanehle8323]

Physics is a model - a human construct - calling our results "Laws" sounds cool and all, but at the end of the day, the model is NOT the reality it describes. The model is an approximation limited by the human perspectives that create it.

[@procerusgigas]

Regarding psychology, I disagree. We stil do not know what consciousness is nor if it can be described mathematically.

[@dott8775]

​@@procerusgigas Was going to say that. It's interesting how one can think of themselves as a scientist just to find themselves engaging in scientism.

[@SNixD]

@@seanehle8323 I'm just working from the assumption that nature works in a set way, which would be the laws, and we call that physics. The fact that our understanding is flawed in places doesn't change the fact that our models are meant to describe how nature works.

[@SNixD]

@@procerusgigas I can understand that logic. Personally I'll continue with the assumption that until proven otherwise, consciousness, like all other phenomena that have been explained before it, will be of physical origin.

[@peterhall6656]

Friedmann and Hagen used the Schrodinger equation for the hydrogen atom to work out Wallis formula for Pi back in 2015. Basically if you do something that involves an integral which is a species of an n-dimensional ball you will get a Gamma function and hence Pi floating around.

[@Otsuguacor]

There's a lot of formulas that approximate to pi... String theory used them to describe the behavior of a curved string moving freely and randomly... Then Those geniuses used those "string theory formulas" to calculate pi... Is it not a circular logic?

[@editfarkas4503]

I've always wondered and never received a clear explanation of what a string (or an n dimensional brane for that matter) really is, what it is made up from. What is vibrating?

[@ColinJonesPonder]

Nice cameo there from You Bastard! 😁

[@aSphericalCow618]

I've watched a few dozen videos without subscribing to this channel but equation camel finally did it for me.

[@Thomas-gk42]

😅👌Funny and intelligent mixture, only one point, that makes your place so unique!

[@StanPope-ru4ox]

I watch Sabine because her wordplay makes me laugh, even when I've no idea what she is talking about. Sometimes I even start to understand. Thank you, Sabine! :)

[@diggernash1]

Math arose out of perception, was then used to perceive, and now it seems to halucinate. 😅

[@InbredCannibalNecropedophile]

Math is the language of exact description. We use it when we want to describe an idea exactly.

[@BKNeifert]

An easier way is to use a Sine Function. I saw a person use them and got several digits quickly. But, that would mean closed loops of strings are actually perfect circles. As pi is just a number that tells us a thing is a perfect circle. As everything, from area to circumference--even different pieces of it--ratio to pi if something's a circle. That's also how Sine functions intuit rates of change in calculus, is by telling you the difference off of pi a thing is from the slope on the curve. Which basically gets calculated from the curve of the parameter, but also works in Areas too. Which is neat, because when you have a piece of pie, it's actually equal to pi, but there's straight lines on the parameter, and actually the number pi is calculated from the parameter of the circle.

[@swistedfilms]

It occurs to me that the Planck length is (about) 1.61*10^-35 meters and yet pi has decimal places far beyond 35 decimal places. Once you get beyond a certain number of decimal places the fractions become almost meaningless and yet there they are in pi.

[@melgross]

It’s not the actual numbers that the concern is all about. It’s that it’s a non repeating fraction. It’s difficult to understand why a circle isn’t some even multiplication of the diameter or radius. The search has been about trying to see if at some point, it ends, or whether it just goes on for infinity. In a non flat universe, you could find a curvature that would allow an exact three times multiple, so this is also a way of trying to see if it could tell us anything about the possible curvature of the universe. So it’s actually interesting work for several reasons.

[@DinsDale-tx4br]

@@melgross Sorry but no coconut. Irrespective of the curvature of spacetime Pi is still Pi. If you want to bend or warp a circle then it is length is not the same as its projection on a flat plane. Of course you could create such a thing out of plastic but you'd have a hard job of making all the buildings around you bend in the same way. In a consistently warped manifold, Pi is still Pi.

[@DinsDale-tx4br]

If you lay a plank length cartesian grid across spacetime. then depending upon your origin only a subset of points may be traversed to. Light will follow up down left right but not diagonal hence will be equal upon all paths between two points. This is not factored into current theory of how things happen down there in the Plank world. But the point is, you could shift your origin, as an 'observer' by some epsilon and have a whole different grid. The Mathematics allows for that, but does the physical reality? Let our initial origin be the point at which the photon was instantiated. It will follow its path irrespective of our grid changes during observation. So, in a nutshell, the continuity of The Real Line has limits in observational Physics.

[@melgross]

@@DinsDale-tx4br it may be Pi, but the numbers are different.

[@ray_ray_7112]

This is exactly the point I was about to bring up here. It's true but as Melgross said, it's more about the repetitive fraction. The plank length thought is still a good thought but then we would have to know the actual size of the universe, providing that it isn't infinite. If it is infinite, then we can create circles of infinite size and even if they were divided into plank lengths we wouldn't have the true dimension. I am not sure if I made sense of how I worded that., As Neil DeGrasse Tyson once said: You can't get the correct answers if you don't even know the right questions to ask.

[@EpicCamST]

Check Buffon's needle problem, it's much easier to understand, and the best part is that you can do the experiment at home - by throwing a needle many times, you can approximate pi

[@caesar_cider2777]

i like string theory, because at the absolute basic level it boils down to "the way the strings dance determines what something is" and i vibe with that

[@tamarinds]

we (you me and the strings) vibin

[@beautimous7347]

You and everything else lol

[@smugless191]

I liked having a quiz at the end. I got one wrong, which I'm pretty sure was the question about what closed strings model. I only remembered hearing that the closed strings model gravitons in the video, but when answering the question, I felt like it made sense that closed strings would model all bosons. However, I only answered with gravitons.

[@michaelwinter742]

In Soviet String Theory, strings close YOU

[@codeawareness]

Really good video Sabine, thank you. I am not familiar with the math software you're using, but I've always wondered how mathematicians can trust these digital tools, what with all the round-off errors compounding everywhere. I'm sure there are smart ways to program, but when I do a sum in Python my trust level in the answer decreases exponentially with the difference in magnitude of terms I'm working with. :)

[@stevercarter5317]

Thank you for clearing this up. I’m much better now.

[@johng.1703]

mathematics is not just a number system, it is also a language used to describe something. like you can describe the area of any given room by l*b so in that sense the universe is mathematical, but you can also describe things in English, so the universe is also English, or any other language you use to describe it.

[@DelfinoGarza77]

The 98th trillionth digit to pi is 3

[@hamishfox]

How did you find this? I was looking for ages!

[@melbar]

With a probability of 0.1 it really is 3

[@AntiNatalAtheist]

Sabine is the best , simply the best person to listen to on You Tube. I just so wish , I had teachers like you.

[@Thomas-gk42]

She´s a teacher for all of us.

[@wildphysicspianoboy97]

1:30 that was saaaaavage

[@CanadianSmitty]

Great vid. Side note, have you come across that article about there being 2 arrows of time? If you do, can you make a video on it?

[@dgo4490]

Actually, logic comes first, math and physics are sub-products of logic, one is used to quantify and estimate using abstract values, the other to describe the properties of physical objects.

[@roelin360]

Didn't they try to derive all of math from logic in the Principia Mathematica and it ultimately failed? More importantly, we can try to define science from a set of axioms but it's unclear whether that'll ever reconcile with all of our observations. The thing that makes science not entirely logic is the very requirement that we need to base and adjust our models on irl measurements of things that may defy our models' logical axioms.

[@reycolas7929]

I like the addition of the quiz, it's helping me to focus while watching the video !

[@reycolas7929]

However, you have to pay to see where you were wrong...

[@SweepAndZone]

Erm what the sigma

[@Amseldrossler]

Loved this episode. Short and sweet, interesting with tons of humor.

[@Zurpanik]

I wouldn't say that nature at its core is "mathematical", but I'd say it's "computational". Love the vid!

[@tbunreall]

It's only computational to a certain degree though. At the smallest level all we get is probabilities. I guess you can say we can compute the probabilities, but that kind of seems like a cop out

[@cherubin7th]

Nature does a lot of non computational things. Like how pi is used exactly.

[@TheDigger76]

@@cherubin7th Things happen in nature, "it" doesn't "do" things. And humans have invented a convenient language to describe what is happening. hth

[@jyjjy7]

@@tbunreall Quantum mechanics is literally an algorithm to compute probabilities. It's been in search of an interpretation for 100 years for a reason.

[@jyjjy7]

@@cherubin7thWhat does it do with π that isn't computational?

[@DrakiniteOfficial]

Hey Sabine, one of the quiz questions does not match what you said in the video, specifically the one about closed loops. You only said that closed loops describe gravitons, but the quiz also said that they describe electrons.

[@markdowning7959]

Thank you for "complaining about everything and everyone." 🤣🤣🤣

[@nunomaroco583]

Hi, always brilliant, very interesting and easy clarification, thanks 👍

[@ediakaran]

Wake me up when they calculate the value of alpha.

[@robmorgan1214]

I did that a few months ago. It's pretty straightforward, but you have to take Wojciech Zurek's work on Born's rule pretty literally... most physicists are not willing to do this.

[@ediakaran]

@@robmorgan1214 What is the 12th digit? Make a theoretical prediction and publish it, please. It hasn't been measured yet.

[@robmorgan1214]

@@ediakaran Unfortunately, these kinds of calculations are not that simple. These measurements and calculations are very subtle things even if they're relatively straightforward. I'll publish eventually, but even though it's painfully straightforward and rests on a solid foundation in fundamentals, this is the kind of thing that needs to be done with care and deliberation because the actual calculation not just the analytical toy needs to be both easy to follow and accessible to your average physicist, ie not just someone who's spent the past 30 yrs of their life up to their eyeballs in the fundamentals literature... silos and the plague of "expertizm" are destroying the ability of physicists to communicate about pretty basic stuff. Just predicting, publishing, waiting 30 years for an experiment, and then for someone to remember a d3ad guy made this prediction decades ago that got ignored (because the math was strange and unfamiliar or the paper was obtuse), or shot down out of hand due to a sloppy or casual but ultimately irrelevant error is not prudent. The more important issue isn't the prediction or even the calculation. It's the WHY. Turns out there's a lot of first principles reason for alpha and not some other random number so I'll tell you this much: it's an epiphenomenon directly rooted in the Quantization of the electric field so you don't need to know much about anything beyond the concept of the action you just need to be meticulous with your assumptions and make sure you don't overlook trivial solutions to equations such as: Born's rule isn't an afterthought it's the direct consequence of the assumptions of Unitarity and the qualitative concept of "repeatability" in a Hilbert space. This has profound implications on the interpretation of probability as a physical, not mathematical concept, which directly informs the "derivation" of alpha... at least it did for me. Following Wojciech Zurek (responsible for the famous cloning theorem) down that rabbit hole is how I got here (you can get the gist from a few talks he gave on Born's rule a couple of years ago they're on YT). Just play around with the math as he lays it out, and you can work it out on your own and get within 1 part in 10^6 in a couple of hours using mathematica ... it really doesn't require much more knowledge than undergraduate QM and familiarity with some of the basic bread n butter mathematical techniques in common use by condensed matter theorists for the past 30 yrs, but for my "alpha paper" you're gonna need to wait several years while I nail down the details with colleagues and collaborators. Hell, at this rate it's highly probable that someone else will beat me to the punch as there are a number of people that I know of who are obviously thinking along similar paths and have more time and resources for this kind of work. Like Wojciech's Born's rule thing, once you see it, you're like... well, that's stupid and kinda obvious. Why didn't someone do this earlier... turns out Gleason beat Zurek to the Born's rule thing by decades! But no one noticed because the paper was IMPOSSIBLE to read. This is an exercise in careful detail oriented work, not a massive string theory Einstein level eureka moment. It's CONSEQUENCES are significant from the perspective of the humans who overlooked it, but it changes very little about our understanding of fundamental physics other than to help build physical intuition about how to interpret quantum mechanics without resolving some of the larger outstanding questions in the field (Gleason's/Zurek's Born's rule thing is more important). Alpha is neat, but it seems to be a realization of medium importance unless I've overlooked a forest sneaking up on me while staring at this particular tree... the temperament necessary to look under rocks for irrelevant trivial solutions to well characterized equations that everyone smarter than you KNOWS don't matter is fundamentally at odds with the romantic grandiose "math is beautiful" crowd looking for answers to conform to their ironic attraction to symmetry (ironic since symmetries in theories generate charges which manifest as forces...that attract other particles as well as the theorists who love them... but we only have evidence for 3 fundamental forces... right now, there's no convincing evidence i can think of that gravity is a force... adding or expecting more symmetry in your math is just wearing a hat on a hat). I just responded because I saw your comment and thought it was funny. Everyone thinks this is important because Feynman said so... but I cut my teeth and was raised and mentored by more nobel laureates and top tier talent than you can shake a stick at (before fleeing the petty toxic and sad world of academia for industry... one of those prize winners was even a Feynman guy)... all of whom possessed disparate contradictory opinions about all this stuff, so I have no problem saying Feynman was wrong and that this isn't an objectively crucial question PRIOR to figuring it out. It's just an odd corner piece missing from the puzzle and something Feynman THOUGHT was important and might turn out to actually BE important, just probably not in the way he expected... when he was working on the theory, no one had the edge or much else nailed down, so that corner probably would have been a huge help but we made do without it... bottom line, I'm no Feynman, and this probably isn't that big of a deal.

[@RyanW1019]

It’s interesting that an equation from string theory spat out a way to calculate pi, but we already had plenty of faster-converging sums than the one you mentioned. The new equation isn’t a new best one either, so it’s more just another “look, another place pi showed up” curiosity.

[@gracebromfield9070]

Keep Complaining Sabine 👏👍😋

[@Walter-Montalvo]

Hear hear!