String Theorists Have Calculated the Value of Pi
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- เผยแพร่เมื่อ 27 ก.ย. 2024
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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.
Paper: journals.aps.o...
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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
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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
The guy Italy uncharged of covid policy got millions people ☠️
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...
5:44
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!
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.
I finished the book only recently. For this reference here alone it was worth to get to know _You B._
Came to see if anyone else noticed. I wonder if Sabine read him in the original German?
I showed the video to my wife who also immediately spotted the reference.
now it doesnt work with the African Blue sandfly
"String theory emerged in the 1960s, ironically right around the same time that LSD did"
Totally unrelated to Unix too
Absolutely one of the most hilarious comments, ever.
@@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...
Lsd was "necessary" for new age baalsht.
Nor ironic, it's called a coincidence
I didn't know you can make Pie from noodles
Oddly enough you can, sort of :) Do a TH-cam search for spaghetti pie recipes.
Some noodles make pie...😅
Strings may be 2d planes rolled up, so thats lasagne pasta
@@multivitamin425 ... not forgetting the famous cannelloni of Mars.
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
the lawyer joke 😂
yes
🔥
🔥
I love her deadpan / sarcastic humour.
Meh
“And I’m complaining about everything and everyone so subscribe!”
Too funny. Love that sense of humor.
Same!! xD
"A very technical form of art" is an interesting characterization of mathematics.
One of my university professors used to say that "math without physics is just philosophy with numbers".
And accurate too
@@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.
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.
@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.
String theory just pops an image of physicists playing with yarn balls like cats.
I assure you that is what is happening...
the results are pretty identical.
And the cat's name is Schrodinger.
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 "
That quickly gives rise to entanglement theory.
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.
The number of iterations is related to pi? That is so counterintuitive! Thanks for pointing it out.
@@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.
Now that is cool
@@aaronjennings8385 It would have been much more interesting if it was related to the fine structure constant.
this reads like it was written by chatGPT.
The guy who did this work, taught me math methods of physics last autumn 😂
I'm kinda proud!
Lucky guy
The physicists are from IISC Bengaluru - Professor Aninda Sinha and post-doctoral researcher Arnab Saha from the Centre for High Energy Physics (CHEP) @ IISC
1:31 "already familiar with building cases on nothing"... damn!! Never knew Sabine would be such a thuglife savage 😎 !!! 😂
Funny. But also quite shallow.
Its called denial
I'm here for her complaints! 💙
Oh dear... She's got Albert Bobblestein out! Look out man, she's coming for you head! 🤣
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.
"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".
4:44 with zero terms the answer is exactly 4. Pi=4 confirmed!
I'm glad someone else noticed this.
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
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.
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.
@@jimmyriba Gell-Man Amnesia
@@KbN132I'm glad somebody mentioned gell Mann amnesia. I love Michael Crichton's talk on this.
@@jimmyribayou really used this comment pointing out a minor criticism to fully jump down her throat
"...building cases on nothing..." I love your humour.
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
4:45 Ramanujan's series for Pi from c.1914 already adds roughly the same amount of correct digits with each additional term.
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..
The new paper is better.
@@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.
@@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.
@@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.
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.
I'm curious if the mathematics has some accessible job market roles (not professors, not top tier researchers etc)... 🤔
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? 😮
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.
Does the grand unified field theory have to be supersymmetric or have they decided that that was no longer necessary?
String theory doesn't properly work without supersymmetry, so they can't just kick it out.
@@SabineHossenfelderThanks for this video Sabine. I really hope you can respond to my other comment whenever you can. Thanks very much.
@@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?
Oh, the benefits of the string theory. Who knows, maybe one day they will even calculate the precise value of 1 (one)
Don’t you first have to define what is 1? Let’s not get ahead of ourselves. ;)
They probably are among those freaks who say that 2+2=5.
@@Walter-Montalvo Fortunately that is pretty much axiomatic, but to get to 1+1=2 takes a few hundred pages of work!
Got this covered, it's exactly 1
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.
First useful thing to come from String Theory since...forever.
String theory has managed to not only overcomplicate physics, but also overcomplicate calculating Pi
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.
Not really. The conventional methods take a vast amount of supercomputer time and resources. This enables it in my iPhone.
@@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.
@@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
She says in the video that it makes calculating pi easier. She said she even attempted it herself
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.
Sabine, ich liebe einfach deinen Humor, auch dann, wenn du nur die Wahrheit ganz unverblümt sagst!😂 Danke, und bleib einfach, wie du bist! 😄
except... get a new dress
@@NoName-zn1sb Yes, the gradient colors look a bit odd given that she can look more beautiful in other dresses and/or colours.
no wonder they were making very slow progress, they didn't know about pi
Sabine, I love your sense of humor especially when you are feeling good. Remember, we love you.
The Pochhammer symbol is much much simpler than evaluating a raw Gamma-function integral. The Pochhammer symbol (also called "rising powers") is just a simple product of n terms (I'm surprised Sabine has this confusion, since she even wrote the definition in terms of a simple n-way product on the slide, and could also just have asked any mathematically inclined colleague). So the time complexity of the series is simple: Each term costs O(n) multiplications and additions, so evaluating m terms costs O(m^2) arithmetic operations. In summary: that is very very fast.
And taking a second look: the (n+1)st Pochhammer can be produced from the nth with a single multiplication, same with n!, so each term takes O(1) arithmetic operations, and the whole procedure becomes O(m).
But looking up the existing state of the art, the existing methods were also O(m) and just as fast. Sabines discussion of slow convergent series turns out to be simply due to her 1) being uninformed, and 2) not bothering to spend 5 minutes on Wikipedia instead of making a misleading video. This is so disappointing. :’-(
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.
The venn diagram at 5:39 is priceless
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 TH-cam. 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.
Math is just a language. That's why it is able to do as it does. Just like how we invented the word "star," we invented the word "infinity" and a symbol for both. And how we invented the word, "join," and also the symbol for addition, meaning to join. And a language can describe anything, once that thing is identified. Why are people so surprised? It's not that amazing. It's amazing how they divided it from the other two portions and dumbified everyone just by teaching a sliver of the language. Amazing how they put people in circular reasoning using linear thinking. Absolutely amazing. Had to have used pi for that.
1:30 that was saaaaavage
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.
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?
I do think that obscure math is often helpful for computer science. There are incredible feats of graphics rendering and cybersecurity/hacking that are born from weird math theories that aren't helpful for describing reality
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.
This group is from IISc, Bangalore. Feeling proud to be an IIScan.
You did nothing to contribute, so there is nothing for you to be proud of.
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?
5:45 You forgot to add Sabine “I complain about everything“ to the Venn diagram
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
𝜆 is an arbitrary complex number
@@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.
Nature is not mathematical, Mathematics is our way to explain nature to ourselves. Nature just is. You dond define Nature by Math, Math is defined by observing nature.
I liked it ...I also have same view ..n it's true
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?
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.
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.
Regarding psychology, I disagree. We stil do not know what consciousness is nor if it can be described mathematically.
@@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.
@@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.
@@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.
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.
Your tone and expression at the start of the video was very predicatable based on the title of the video 😂
My view on Mathematics is that it maps the boarder between the possible and the impossible. Just because it is mathematically "possible" doesn't mean that it's possible in reality, but if something is mathematically proved to be impossible then it really is impossible in reality.
I say this as someone with a degree (that I can remember some parts of) in Joint Math And Theoretical Physics.
Mathematics is a model. Expecting reality to be subject to it is using it as a sort of Voodoo doll.
Do you have math or programming TH-camr friends to go in together with on a video on this topic?
It would be interesting to hear about algorithm applications.
Thank you for "complaining about everything and everyone." 🤣🤣🤣
Pi isnt a constant of nature, its is a direct extension of the laws of logic and a couple of basic axioms. Thats like saying string theorist calculated 2 to be the smallest prime! That's not something we can find out there in nature, and to whatever extent maths describes the world, it is bevause we have tailored our axioms to suut the universe.
What would it even mean for the univer NOT to be mathematical? It'd mean that it doesnt follow any logical rules, which is incoherent for things to exist at all, they need to have definite behaviour, so the "why is the universe so mathematical?" question is just the "why us there something rather than nothing?" question in a trenchcoat, and im not sure its even a coherant thing to ask
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. ❤
I've been waiting for this. Saw you tweet about it on x
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.
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.
The Chudnovsky pi formula converges much faster at a rate of about 20 binary or 6.25 decimal digits per term.
As long as physicists describe nature by mathematical equations of course there is a relationship between nature and mathematics, thats not surprising at all. Also physicists only use mathematical models but none of these models truly describe the full reality, just certain aspects of it. Maybe we need to figure out new ways of formulating physics without mathematics, e.g. instead of simple mathematics, use complex probabilistic algorithms, if thats possible...maybe the universe is ran by such complex algorithm, mathematics can never put this in simple formulas so as long as physicist try to formulate nature in formulas they might fail.
But in the end, the quantitative relationships between measurable parameters will still exist. And therefore mathematics will always be used to model those relationships. I think it is inevitable that it be so, if we want to predict outcomes. Thus, like for you, I don't find it surprising at all that mathematics is the tool at the core of our physics understanding. But we still need the human insight to interpret what it is trying to tell us (like for example Dirac interpreting his model's results as suggesting existence of a particle, positron, not previously found experimentaly).
You don't need the gamma function to calculate the Pochhammer symbol; that's just an equivalent form. It's a product related to the factorial function: (x)_n = x(x+1)...(x+n-1). In particular, (1)_n = n!.
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.
Nice cameo there from You Bastard! 😁
I work with an engineer who one day was trying to estimate or figure out how much he needed to take out of a 24 inch diameter round section to reduce the diameter by 1 inch. I said take out one slice of Pie!😅 or roughly 3.14 inches. He looked at me like I had 3 heads, then he looked confused and slightly embarrassed. He simply said I'll have to look into that and went and hid on his office😅
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
we (you me and the strings) vibin
You and everything else lol
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.
I wouldn't say that nature at its core is "mathematical", but I'd say it's "computational". Love the vid!
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
Nature does a lot of non computational things. Like how pi is used exactly.
@@cherubin7th Things happen in nature, "it" doesn't "do" things. And humans have invented a convenient language to describe what is happening. hth
@@tbunreall Quantum mechanics is literally an algorithm to compute probabilities. It's been in search of an interpretation for 100 years for a reason.
@@cherubin7thWhat does it do with π that isn't computational?
All circles have their own value of pi determined by the ratio of the diameter to the circumference; thus, the length of the diameter must be determined first before the true ratio of the pi of a particular circle can be determined: The ratio of 3.14159265... is not a constant.
The 98th trillionth digit to pi is 3
How did you find this? I was looking for ages!
With a probability of 0.1 it really is 3
Fascinating! Thanks, Sabine! 😊
Stay safe there with your family! 🖖😊
Wake me up when they calculate the value of alpha.
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.
@@robmorgan1214 What is the 12th digit? Make a theoretical prediction and publish it, please. It hasn't been measured yet.
@@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.
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.
Many years ago I heard CS Wu give a talk. She said that there was a group of experiments to measure Plank's constant h, and a group that measured h-bar (i.e., h divided by 2 pi). So, from physics you could measure 2 pi! After the laughing calmed down she added, and if you know pi you can use physics to measure 2.
Rapidly converging series: en.wikipedia.org/wiki/Pi#Rapidly_convergent_series So it's not really that fast, but that's fine. Rather, what you said about it being interesting because it falls out of string theory is the cool part. Always fun to see things like that. I remember being blown away when I learned that spherical harmonics are not only used to compress spherical photos but also describe electron orbitals.
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
I bet it is close to 3.14.
Engineering approximation π=e=3 is fine enough.
@@piotrfelix Sin(x) = x
@@piotrfelix g = 10
It is totally pointless to regard only the number of terms at convergence, when the terms involves difficult computable gamma functions (to high precision).
😅👌Funny and intelligent mixture, only one point, that makes your place so unique!
The intersection of string theory and pi calculation is fascinating! Great content.
Thank you for clearing this up. I’m much better now.
Oddly enough, at 4:00 when you set set s1 and s2 to -½ and the left side of the equation is equal to π, the right half is equal to 47.
Camel?🤔
It's alluding to the camels doing maths in Pratchett's flat world. With apologies...
World Camel Day is π days later on the Discworld.
@@SabineHossenfelder No need to apologize for a Terry Pratchett reference.
@@SabineHossenfelder Loved the reference :)
One of the few times it's acceptable to point at the screen and yell "You Bastard"
The use of the camel, mayhaps at Terry Pratchett reference? :) keep up the great work guys, I love your content
Im not sure your complaint about the Pochhammer symbol is valid. Yes, it's defined in terms of the Gamma symbol, but Gamma(x+n)/Gamma(x) has a very simple reduction to iterated multiplication. Nothing fancy at all.
To compute Gamma(1/2) directly, on the other hand, is a whole other game.
Keep Complaining Sabine 👏👍😋
Hear hear!
I think the idea of string theory would make it a lot more sense if it were wave theory. Particles have been shown to be both waves and particles at the same time.
What if there's a fine line, that some parts of our universe are so small that they can be both wave as well as particle at the same time due to superposition.
I think the closest we'll ever come to a theory of everything is therefore the idea that everything is made up of waves, and that these waves need the current of its surroundings to evolve. If there is no current, I'm not talking a vacuum, we're talking supervacuums, then that should in theory create an absence so great that it might cause a singularity to form.
well finally something that string theory CAN accomplish. String theory, the graviton, Super Symmetry all smoke and fluff. Sorry Brian G.!
😂😂😂😂
Great video. This is what I long ago subscribed for.
Math is like sex. It has practical applications, but that's not why we do it.
You can do maths for fun while having sex with a suitable partner. It is great.
I like your honesty. 🙂
Sabine is the best , simply the best person to listen to on You Tube. I just so wish , I had teachers like you.
She´s a teacher for all of us.
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.
Was that You Ba***** from Djelibeybi I saw in there? Greatest mathematician on the disc.
That equation is only half good as it gives Pi instead of Tau!
Oh, pi finally calculated? Finally
Value of Apple Pi is around $8.99 at the local bakery
Sounds like you have cosmic inflation where you are. : /
I would have subscribed just for your last sentence: “and I complain about everything so please subscribe” 😅
But I can’t: I have already subscribed.
At the very least string theory created 1000's of worthless jobs.
To be honest, even as a physicist, I don't think that nature is inherently mathematical. I started to realize this when I began doing research, in which for solving a problem we make an approximation, than another approximation, than another assumption, than other approximations. Now I think that math is one of the ways in which we are partially able to understand some recurrent patterns in nature. Many others, in fact, don't seem to have any relationship with mathematics. I'm not even thinking about social "sciences" here, but just about basic quantum mechanics, in which basically the majority of events are non predictable mathematically (only on average).
3:15 is much less incomprehensible with a few hours of calculus study. An Invitation to Mathematics is the best retainable study material I have found. Norman Gowar
Missed an opportunity to make the timestamp 3:14 smh
I'll stick with drawing my circle and triangle to just measure pi. Just need a bigger drawing and a higher resolution ruler, right?
Back in my school we had declared the 14th of March "pi-day" and did just that. Our group only had the trouble that we got a space assigned too small for our ambitions, and our endpoint lay somewhere behind the wall of the room. That did not stop us from working around that with some extra trigonometry and still getting the most accurate result of all groups.
All you need, is a big enough circle. And probably lasers. Back then, we didn't have lasers.
Equip recognized aspatio-temporal numbers with division to define universal minimum quantitative and hence scalable entity, Planck's constant equal to one divided by sixsixthreethirtysixzeros, establishing a standard when applied ideal-materialy is called measurement * ?
* Standard deviation is the average difference of numbers in an actual sample from their average, called mean equal to their sum divided by how many of them there are - sample size - minus one, specifying an historical event frequency distribution, but decay excludes this predictively.