Does the number Pi actually exist?

Whether or not pi exists has some very deep implications about circles, matter, computing, space-time, gravity, and quantum physics. Let's see if we can tackle some of them in honor of pi day!
________________________________
VIDEO ANNOTATIONS/CARDS
Does Electricity REALLY Flow?
• Does Electricity REALL...
SOL and S'mores:
• Can we Measure the Spe...
________________________________
RELATED KZbin VIDEOS
Physics Girl's Pi Day Video:
• Calculating Pi with Darts
3blue1brown's Channel:
/ 3blue1brown
Crash Course Computer Science:
• Representing Numbers a...
________________________________
SUPPORT THE SCIENCE ASYLUM
Patreon:
/ scienceasylum
Advanced Theoretical Physics (eBook):
gumroad.com/l/ubSc
Merchandise:
shop.spreadshirt.com/scienceas...
________________________________
HUGE THANK YOU TO THESE PATRONS
Einsteinium Crazies:
Albert B. Cannon, Tim Ruffles, LT Marshall Faulds, Ilya Yashin, Rick Finn
Plutonium Crazies:
Anamnesia, JKLMN Anderson, Timothy Blahout, Kevin MacLean
Platinum Crazies:
Vittorio Monaco, Neil.L.Steven, Al Davis, Stephen Blinn, Mikayla Eckel Cifrese, Evgeny Ivanov
________________________________
OTHER SOURCES
mathworld.wolfram.com/PiFormul...
www.geom.uiuc.edu/~huberty/mat...
www.exploringbinary.com/pi-an...
www.rapidtables.com/convert/n...
apod.nasa.gov/htmltest/gifcit...
www.etymonline.com/word/irrat...
en.wikipedia.org/wiki/Double-...
www.preposterousuniverse.com/b...
________________________________
LINKS TO COMMENTS
• Black Holes can SPIN?!?
________________________________
IMAGE CREDITS
World Map:
commons.wikimedia.org/wiki/Fi...

[@ScienceAsylum]

*Correction:* Several people (who clearly know more about computers than me) have informed me there is more than one type of transistor: Field Effect Transistors (FETs) and Bipolar Junction Transistors (BJTs). The ones I showed in this video are BJTs, whereas computers use FETs. Whoops! I stand corrected.

[@RavenAmetr]

Another thing, you can simulate huge registers (as big as memory (including HDD) allows) with byte arrays. Of course, it has an overhead of additional computations (to process an array as a number) and the slower type of memory you use, the slower the calculations will go.

[@RavenAmetr]

But overall it doesn't make any difference since we are talking about infinities.

[@angeldelvax7219]

The computers currently on the market mostly use FETs. But is is absolutely possible to build a computer using BJTs. After all, there are still some examples of computers that used solenoid relais as switches. So the example isn't necessarily wrong, it's just a bit uncommon ;) O, if you want to know why I think that I'm correct: I'm an electronics engineer. My specialization is technical computer science (building computers, processors, peripherals and writing the software needed to make it work).

[@steefant]

There were a number of computer architecture problems in the video. Additionally, to what was mentioned already (as far as I read) the notion of letting "the point float around the 64-bit register" is nonsense in the context of floating point numbers (that were explained correctly afterwards). Instead, that's actually called fixed-point arithmetic (because the exponent is not saved dynamically within the number). None of the errors were important to the question at hand... but it hurts nevertheless to see them in this pedantic channel ;)

[@tinldw]

Also, 1 and 0 are flows in opposite directions (or flows of electrons and "holes"), "no flow" (or disconnected, "High-Z", etc.) state is not normally used to transfer data.

[@Awokenify]

I came for the fun math, I stayed for the existential crisis.

[@DavidSexton77]

Lol !

[@joecraven2712]

I came for the existential crisis, I stayed for the fun math.

[@willtipton100]

I knew the video was gonna be good when this was the first comment I saw

[@JordonPatrickMears11211988]

Every-fucking-time

[@theanaesthetist1]

Swap the words "fun math" with Jack Daniel's, and you have an accurate description of my 40th birthday and the following day

[@Soupy_loopy]

Pi used to exist, but then I got hungry

[@99bits46]

@@kellyjackson7889 that's a typical american pie

[@extracheese5284]

Nah it's still in your poop but I know it's a joke

[@marccolten9801]

Old joke. First kid in a mountain family to go to school is asked what he learned. Boy: Pi R square. Father: That's stupid. Pie are round. CORNBREAD are square.

[@absurdist5938]

Fuck 😂

[@OneFingerYT]

He really milked those puns.

[@mr88cet]

Pi clearly exists, as an abstraction, regardless of whether we can represent it perfectly in the physical world. I _think_ it was 3 Blue 1 Brown who pointed out, much to my surprise, that, unlike a circle, there is no simple analytical expression for the circumference of a general ellipse. However, that’s not really surprising at all in hindsight, because the only reason why a simple, analytical expression for the circumference of a circle exists, is that pi has been _defined_ largely just for that purpose!

[@BerryTheBnnuy]

I mean, ultimately, if we're talking about physical existence, then no number exists because all numbers are abstract concepts.

[@mr88cet]

@@BerryTheBnnuy, absolutely true. However, the “5” in “5 rocks” is a little easier to visualize than pi.

[@DendrocnideMoroides]

@@mr88cet -1 rocks?, 1/2 rocks to the exact atom? what even is a rock? if we had 5 rocks they are anyways not going to be identical so if we cut 1 rock in half 5=6? to solve these problems we cant use rocks we have to use abstract rocks, might as well use abstract circles

[@mr88cet]

@@DendrocnideMoroides, 0 rocks is more abstract a concept than 5, -1 rocks is more abstract still, and “i” rocks even more abstract still. However, I’d say that half a rock is still just rock, just smaller rock.

[@DendrocnideMoroides]

@@mr88cet for your last point that is why I said "we can't use rocks we have to use abstract rocks" if we had an abstract rock where all of them are identical then half of it would be different than the full.

[@InstantGiblets]

-1/12 ...I see what you did there.

[@aadityavicramsaraf6]

Hmm!! Yup I didn't notice but now I realize.. smart

[@saatviksingh]

What did he do exactly? Im stupid

[@randomdude9135]

@@saatviksingh -1/12 comes in Ramanujan summation of natural numbers. To be exact, the Riemann function of -1 is -1/12

[@aadityavicramsaraf6]

Okay let me make it clearer, 1+2+3+4+5+6+7...∞= -1/12. You can check for sum of all natural numbers, on the net

[@ncedwards1234]

Just to make sure everyone is on the same page of the "infinity=-1/2" thing, it's wrong. Well obviously it's intuitively wrong, but that doesn't mean much in math, I'd recommend looking up the debunks of it if you're crazy enough for some infinite sums.

[@prschuster]

This is where Plato's perfect forms comes in. He recognized that drawing a circle will always give an imperfect representation of this perfect form. So, if you accept Plato's idealism, and theory of perfect forms, pi does exist as an idea, if not manifested in the material world.

[@TheRosyCodex]

Actually no, even in a world of pure math, the ratio between a circle's area/circumference and it's radius is an incommensurable proportion

[@prschuster]

@@TheRosyCodex Of course pi can never be measure accurately in the material world because it's not a rational number. That's why it only exists as an ideal.

[@mrpedrobraga]

@@prschuster so you shifted the conversation from talking about pi to talking about what it means to exist itself... perfect!!!

[@MGSchmahl]

It all depends on what it means to "exist".

[@prschuster]

@@MGSchmahl If circles exist, then radius and circumference exist. Pi is just a relationship between radius and circumference, so it exists regardless of whether you can actually measure it exactly. Then we have to ask ourselves, "does geometry and math exist?".

[@k.lamareyev4418]

This guy is amazing. He dont tell you what to think or how to think but but makes you think.

[@neilbedwell7763]

Perfect timing. I love that this one vid clears up a million computational concepts and with complete nomenclature/vocabularly . You are up there for me, a modern day carl sagan / neil degrasse tyson for the community of us so inclined ones

[@mickmickymick6927]

Neil deGrasse Tyson exists in the modern day.

[@alainborgrave6772]

What is your definition of "exist" ?

[@arvidsalle2979]

Something that is

[@fritt_wastaken]

@@arvidsalle2979 everything is when we say it is

[@sebastianlukito6686]

This question works the same way: what's your definition of definition? Language is able to work with abstract truth and physical truth. When physics asks you about existence, ofc it asks if it physically exists or not and not the otherwise.

[@foxpup]

The answer is so simple that we often fail to automatically grasp it. If something exists, it must participate in causation with other things in the universe and vice versa.

[@fritt_wastaken]

@@foxpup It is not simple at all, It's quite the opposite. For any definition of existence, if you search hard enough, you can find counterexample. There is actually no objective line between existence and nonexistence, so either we draw a subjective line, or stop thinking "black and white".

[@vukbrankovic1339]

If you go to the atomic scale then there is not something like line in maths or any "perfect" shape at all, so if ideal cicrcle doesnt exist than line,cube,etc.. doesnt exist. Interesting how its all depends on your side of view, your glases... Thank you Nick for spending your time to help us learn something new, again!

[@kevindoom]

what about a circle carved from a sphere using inverse square law

[@l1mbo69]

Until you remember that even then this mathematics can describe reality so well

[@TheRealDescartes]

If you go down far enough then nothing exists, so to ask if something "exists" is already redundant in itself

[@walterbushell7029]

Do any of us exist as anything other than legends in our own minds?

[@thomasreedy4751]

Inorganic chemistry is pretty reliant on geometric shapes, so I feel quite certain tetrahedrons and hexagons exist.

[@brandonswan9247]

I feel like i finally found someone who actually knows what they're talking about.

[@John14-6...]

The concept of Pi transcending algebra sounds totally cool!

[@sphakamisozondi]

I'm a simple guy, when Nick uploads, I click, I like, I share

[@mandalamarcho8060]

I'm a simple guy, and I do same think I like you

[@k3mpy69er]

What’s really amazing is 314 spells PIE in a mirror.

[@AmitSingh-vt6ws]

illuminati confirmed

[@rodsims8471]

Ok .. that is Zen AF .. write it on paper and flip it around in the light .. LOL

[@justlikeyouful]

Whoah, trippendicular.

[@tobyinsley9010]

No it doesn't?

[@rodsims8471]

@@tobyinsley9010 " 4" looks like " P" .. "1" looks like "I" and "3" backwards looks like " E" . you need to use your imagination , a tiny bit

[@MiguelGarcia-zx1qj]

I love it. Exactly my point when (in the first class of a course on Numerical Methods and Statistics) I give my students an Oreo cookie (one to each, of course, that they can eat at the end) and a measuring tape, and tell them to determine Pi, experimentally. But there’s more. Even if space and time were to be continuous, and assuming General Relativity is true (or at least a good approximation to Reality), if you tried to measure a circle, you (or the lab, or space capsule, etc.) would be changing the curvature of spacetime, rendering the measure of Pi meaningless. Of course, I don’t go that far in the classroom, but tell them of a circle drawn on the surface of the Earth (or on a horse’s saddle) :D PS: I forgot that I'd already commented this video. Nevertheless, then I addressed other aspects of the "realness" of mathematical objects.

[@ScienceAsylum]

There's nothing wrong with commenting more than once, as long as you're not spamming my comment section 👍

[@fredbloggs8072]

I wouldn't mind betting space & time are in fact quantized, we just haven't figured it out yet.

[@red-baitingswine8816]

"2" is also an infinite sequence (unless it's a counting number). It's the ratio of the length of one side of a square to the length of two sides. Neither rational nor irrational numbers actually exist - they are limits. The "exactness" of the rational numbers is hypothetical (I.e. imagination) (but, of course, indispensibly useful).

[@srajanverma9064]

mann ! Now that is a pov!

[@ptrkmr]

Nah it’s an integer. I think a better way to get at your argument is to argue pi itself is a different number system entirely. One system is the integers, another the real numbers, and then the “irrationals”. The irrationals can just be seen as their own system with a different base system. Similarly these irrationals extend out perpendicular to the “xy” plane with its imaginary counterparts. Pi is an inherit part of imaginary numbers, so I’d argue it’s simply another base of another “number” system. I don’t think number is a great way to view it though. It’s a concept we use for math, which can be represented by a number. Other fundamental concepts we do real math on are zero and infinity. You can’t write the number of infinity. It just exists. Same for pi

[@red-baitingswine8816]

@@ptrkmr In plane geometry there are almost no numbers, and we assume that some exact shapes and relationships exist. Do they actually exist?

[@carriertaiyo2694]

The puns were crazy. I'm surprised he didn't put a picture of a pie on the screen every thyme he said pi. :D

[@RazorM97]

🥧🥧🥧🥧🥧

[@ffggddss]

I sea what you did their! (And don't forget the parsley, sage, & rosemary!) Fred

[@mondkalb9813]

Yeah, but then ... we all know, that pie exists. Until we eat it.

[@matthewe3813]

exist should be egg-sist 🥚🥚🥚

[@declanokeeffe5088]

Really interesting! Keep putting out these kind of vids👍

[@cosmotect]

Awesome video connecting a lot of things you don't see together very often

[@deant3980]

Glad i discovered your channel. Entertaining and informative in a strange way. Thanks mate. Keep it up.

[@napadave58]

That ‘strangeness’ you’re picking up is Nick, I think. I just found this channel a couple of days ago and he is (imo) one of the best in the business. I like John and Hank Green too ... but this dude is extra-hilarious, making for, I think, a better entertainment and learning experience.

[@algerianhanisaid]

Dear Nick, Its always a great pleasure to learn and watch your videos. You're really accurate within your explanations and you do not show off because of your knowledge. thanks for that !

[@MikeOxolong]

Congrats on your 2^7 * 10^3 subs

[@nnerik]

2^10*5^3

[@ffggddss]

50³ + 3·10³ Fred

[@realitycheck3363]

Out!! Just...get out, all of you!!!

[@SoI-]

AKA 128,000 subs

[@Dong_Harvey]

@@SoI- so ~ (1/2)e*10^5

[@johnmaclean2040]

Such a great video. So many great points!

[@sgvern1]

Nick, I have made a few comments on your vids, but have always forgot to mention how entertained and informed I am watching them. You are a Marvel. No not the comic book hero, a real hero of science education. Can’t get enough. My brain doesn’t turn to mush when watching, it gets strong and stronger. At my age, sixty-eight, that is a good thing. By the way, how many out there have ever used a slide rule to solve a problem. Yeah, I am that old. I missed the abacus though. Keep on Keeping on, man.

[@cosmoelbrujo7829]

Your channel is really good, cheers from France

[@p12psicop]

At 2:23 I almost had a myocardial infarction by laughing so hard that I was unable to inspire for several minutes.

[@marejov83]

Same here!

[@perspective500]

I had the same thought, thank you for making this video 🙏

[@rasanmar18]

Very good question. I think, first if all, we have to define what existing means. In the physical world there are many ideal concepts that really do not exist, not only pi, but I think the point is that they are useful for our purposes of abstraction and prediction.

[@NidusFormicarum]

Exactly! What is the difference between Pi and say number 1? Does number 1 exist in the physical world? Of course not! Four apples are of course real, but the number itself is an abstraction.

[@jenf2580]

I think THE pi is the ratio of circumference and diameter of an ideal circle. A perfect imaginary circle. Nothing is perfect in this world. That's why we get something like pi too as imperfect.

[@djkm9558]

If its the ratio of the diameter and the circumference of an imaginary circle, how did they compute a trillion digits of pi?

[@factnotfiction5915]

@@djkm9558 See the Wallis formulas basically they are series expansions of various transcendental functions then you can choose how far along the expansion you calculate

[@abhik294]

Wellllll.......Not So Faaast!!!😂😂😂

[@andrewpaulhart]

Yes. In summary PI is not a number. it is a ratio. Problem solved. The question was wrong

[@magicmulder]

Andrew Hart // Ratios aren’t numbers? What about 2/3?

[@tiger-ow8ks]

Wow its such a nice day ( night) both of my favorite youtubers nick and electroboob posted videos...

[@michaeledwardharris]

This is one of your best videos. You hit a lot of really crazy stuff here.

[@ScienceAsylum]

Really? I was just messin' around with this one.

[@GamerTime_2002]

"does pi actually exist?" Mr.crazy: quantum mechanics.

[@baksban74]

I liked the explanation of this on the numberphile, the Tree Gaps and Orchard Problems. Insanely simplified version is that if you point any one direct the actual chance of you hitting anything is basicaly zero, and yet all around you you have "trees"(all the real numbers). And of all the gaps in that plnatation we know so little of those directions that lead to 'numbers' like Pi, e, root 2 and so forth.

[@kylorenkardashian5518]

I really enjoyed this video. I work in water treatment & pie is utilized daily. this video helped answer abstract questions my professors could not. I would love to see you tackle some water math

[@tcwright7544]

Wow . Thank you so much!!

[@oris1766]

Good vid. Love you♥️

[@volbla]

The first lemma should obviously be: What does it mean for a number to exist?

[@phoule76]

cheers!

[@RazorM97]

they represent something, like a number on the number line,geometrical proportions and sizes, or logic itself.. objects, and they are just abstract it's also a language, but they are supposed to be this, and themselves whatever they might mean,positions from an undefined point namely 0 i guess which can be anywhere you go, so it's well defined,and there are the axioms and proofs(in real life too), this is what math is about and problem solving... however they are still abstract, and keep in mind that our brains do the math too so it would be a mental representation,but what isn't a mental representation actually?... anything is, and most of stuff around us is empty space and how our brain perceives it from it's huge scale. the ultimate question would be mind over matter.. is the circle actually valid even if it's just too perfect so that could be just an illusion of our brains?

[@mishagjata7374]

A=1, B=256, C=1.24, D=8.643586, Pi =3.14?????? Get it?

[@RazorM97]

@@mishagjata7374 C*D/2 would give you something close to pi

[@mishagjata7374]

@@RazorM97 Funny numbers :)

[@crouchingtigerhiddenadam1352]

One of my favourite videos! But my reply "It's a Squirrel! And how you can wire them up to make a running adder." on the community page? NAILED IT!!!

[@mjmulenga3]

Does π exist? Yes. My favourite definition of whether something exists this: it's real if it's necessary in order to describe observations. π is necessary in many fundamental calculations, so it exists. You cannot draw a line exactly π metres long or count out π dollars, but it exists.

[@dmitriy4708]

Why is it necessary? Some alien civilization could easily use something like ellipse close to a circle with specific alternative for pi as approximation of round objects and if it is close enough it would be pretty much the same, just some additional problems with formulas, maybe it is a part of their culture to not think about circles. We don't have circles in reality anyway. So, pi is not necessary, it is just easier to use. So, your criteria for existence is strange, limited by your imagination and nothing like colloquial meaning of the word.

[@mjmulenga3]

@@dmitriy4708 first of all, Pi isn't about circles. It pops up in areas of maths that have nothing to do with geometry and it's fundamental to maths itself. For example, Euler's Identity: (e to the iπ +1 +0). Second, it's not my criteria for existence. It' the criteria that physicists use.

[@dmitriy9053]

@@mjmulenga3 1) No, Euler's identity is such because of a circle in complex coordinates plane. And it is not only that, it is a periodic function, so you provided only one example of infinite amount of answers to this. Pi is always about circles even if it does not seem so. And physical existence is having coordinates in space-time, nothing more.

[@dmitriy9053]

@@mjmulenga3 So, Euler's identity would be e^(pi*i) = e^(-2pi^2*k)*(-1), where k is an integer. Not so pretty, right? If k is 0 we have simple solution of -1 that you presented. Such are periodic functions. Whatever, do not think that something is necessary just because we chose to use it or even if you do not have any idea how can we do it otherwise. Math is just a tool we use, it could be different potentially.

[@phandinhthanh2295]

Resorting to practical necessity is a very bad way to justify the existence of a pure mathematical object.

[@Infinitesap]

Pretty awesome :) you covered some ground here!

[@quahntasy]

The puns were crazy lol. Insta like and share coz of "pan out" joke.

[@andrewrivera4029]

Sick bro, thanks for the video it really clearly stated the problem of a GUT.

[@alphaprime1871]

Terrific video. Hats off

[@ajaygmysore]

Many thanks for linking the continuous-discrete problem with quantum mechanics-relativity.

[@user-vc5zt9ci12]

This is an excellent video! I would definitely say space is fundamentally discrete It follows on to another interesting point about mathematics and its relationship to the universe I think. We have many laws, fundamental constants etc, that would appear to be in place (by definition) before the big bang. This therefore gives the impression that they somehow 'exist' outside of the universe... which isn't a thing imo. The point I am trying to make (badly) is that if all the laws/constants/numbers are not emergent - then none exist! and if they are emergent, then they cannot be constant or unchanging because they rely on the state of the universe Nice puns btw!

[@davidshechtman4746]

@Tim Erskine; Rob Bryanton talks about the fine structure of the universe being essentially arbitrary and created at the moment of the big bang in some of his "Imagining the 10th Dimension" videos.

[@TheLupukapa]

Instant like on the video because "Pan out" joke

[@pascal6077]

But then you'd have to press like again for laughing at his own cheesy pun xD

[@sockman-pc3dm]

Same

[@muratigentijan8911]

the by information you give is in all your videos more intresting than the actual main quuestions themself...this is a compliment

[@nigelburkitt6365]

Absolutely love your work and the enthusiasm for these subjects. On several occasions now, I have sensed or felt that you could go even deeper on some aspects but have backed off. May I ask if you are aware of the "God Series" books by Mike Hockney ? Keep up the inspiring work .

[@seanspartan2023]

Pi exists as a concept, but like many concepts in pure mathematics, they cannot be realized physically in reality. Others include infinity, infinitessimals, transfinite numbers, ... Sometimes even mathematicians don't always agree. At one point in history negative numbers were considered controversial, but they are generally accepted now.

[@SamiJumppanen]

This is true. We're using numbers or math to describe things. Working fine to a certain degree.

[@Alexagrigorieff]

SNL: "Is it pizza?" "It's *almost* pizza"

[@Pedritox0953]

Great explanation!

[@ThecrackpotdadPlus]

Long time watcher, first time commenter - you broke my brain bro. Keep it up :)

[@TheRealReTox]

Okay. I mean, physics is one thing but when you combine that, maths, and my beloved computer technology I'm on geek overload. Too good!

[@tmdrake]

Nice to here someone talk about Floating Point Math.

[@patmat.]

Great video!

[@djplays2157]

Thank you for dong this im meaning so much. Thank you

[@erictaylor5462]

Oh my god, I just realized something. I was playing chess with an Australian friend of mine. He kept saying "Checkmate" even though I had an escape from check. I think he might have been saying "check, mate." not "checkmate."

[@jycapuras]

Mother Nature continues to boggle our human curiosity... presenting us with a seemingly innocuous relation between the circumference and the diameter of a circle and then... revealing a surprisingly endless non-repeating pattern of decimal numbers for its numerical approximation. This is Mother Nature at its best - refusing to be pigeonholed by human understanding... Fundamental reality is much much more robust and magical than we can ever imagine... despite our blind faith in mathematical precision which at best is still just an approximation!!!

[@user-ex7yq6xq9s]

Him : OR DO I ??!!??? Michael from Vsauce : Now finally a worthy opponent

[@lennarthoekveen9339]

I LOVE the background music so much in these videos.

[@silatapeldoorn]

Hoi Nick, About the question you answered at the end about the spinning of black holes. To me the real question is: why did there rise forces if something accelerates? Are those forces still there in an empty universe? Can you accelerate in an empty universe. Is acceleration always with respect to other bodies? And why does one feel a force while the other doesn't? How do you know who is actually accelerating? Questions Ernst Mach asked long before. Thanks for your very fun and educating video's! I'm a physics teacher from the Netherlands and this is by far my favourite KZbin channel. Kees Stoop

[@wurttmapper2200]

Could you make a video about how binoculars and telescopes work?

[@FromJustJ]

I agree that we need to start with definitions. But you missed the most important definition of all: "What does it mean to say a number 'exists'?"

[@LuisAldamiz]

Numbers do not exist: they are adjectives to nouns, only what is named ("noun-ed") exists. Numbers have no names (nouns) because they are adjectives, so they only exist the same as pink, tall or much do.

[@danielsteel5251]

@@LuisAldamiz Yes. Exactly. *Numbers* are the names of the properties by which objects are distinguished. "Does '3' exist?" is as meaningless/ill-posed a question as "Does 'many' exist?" or "Does 'yellow' exist?"

[@guifdcanalli]

Physically exists*

[@JannPoo]

The way I understand it, this video is asking: "are there two lengths or distances of physical objects whose ratio is exactly and precisely to the infinitesimal decimal equal to pi?" For instance while the question of a number's existence is a philosophical matter, we know that we can have "2" quantities of a certain object. We know that if Paul has 1 apple and Mark has 2 apples, the ratio between these two quantities is exactly 2. But can we have something that is exactly "pi", or is anything that we calculate as being "pi" or a product of "pi" just an approximation? This is an interesting question, but unfortunately it's a question that is impossible to answer. You could make an argument that if two objects are four meters apart and they move to each others until they touch, there has to be a point in time when their distance is exactly "pi" meters. But how can you prove it? It all comes down, as the video concludes, to whether space is continuous or discrete.

[@hank1519]

Good point!

[@billpotter9716]

Nice explanations. The puns are painful, and what's with the seemingly random pictures? walnuts etc. I am now going in search of a few more pi related videos. I also just subscribed. :)

[@ScienceAsylum]

The clipart is just in case anyone was missing that particular pun. There's either clipart or a prop for every single pun (I think).

[@vedant2918]

By Mistake Discovered this channel.. Watched all videos for 2 hours straight..

[@SandeepChatterjee66]

my five one of the most favourite channels, 3Blue1Brown, VSauce , Science Asylum, Veratasium, The Physics Girl I find mention of them here 🙂🙂🙂

[@ScienceAsylum]

Looks like I'm in good company 🤓

[@sinom]

It just has the problem of "do numbers exist"

[@zachbattleman6138]

Yeah, like I'd argue 1 doesn't exist or not exist anymore than pi does. It's just a quantity we chose to define.

[@bobbing3778]

This guy is good. Very well reasoned.

[@BackYardScience2000]

I love how much you say "A Perfect Circle". One of my favorite bands.

[@iasked8240]

Clicked on the video to learn about Pi. Now I know everything about a CPU.

[@ScienceAsylum]

You're welcome 😉

[@An0nim0u5]

And the hunger drove him crazy & we got our video...

[@carlborgen]

Would love to hear your take on the wolfram physics model. It has descrete space as far as I know :)

[@CountSacke]

I've been curious. I've seen Sean Carroll's Core Theory equation at 7:24 quite a bit, but can you actually explain it in a way that doesn't just get reduced down to "This part represents Quantum Mechanics and this part is Gravity..." and so on.

[@olyvertwist07]

In England they say, you are a bloody brilliant man

[@nathanielgregg543]

Numbers are just names that we use to describe quantities relative to some standard and in some context. If you think the number 1 exists in physical reality, could you tell me how big it is?

[@RadioJonophone]

It's as big as it needs to be.

[@greatbriton8425]

and?

[@yirehmiyahmagsayo361]

sir, your so funny and education and openminded in any subject in science sir

[@gayatri555]

I love the pan out joke

[@greatbriton8425]

Everything you said applies to the length of a straight line or to a simpler fraction like 1/2. You can measure them more and more accurately but you'll never be exactly right because the atoms won't be perfectly positioned with respect to the two ends, except in very unusual circumstances. Ultimately we come to subatomic particles and then on to quantum mechanics and the probability of a particular position which won't stay still. With Pi the calculation is complicated by the deviation of the line resulting in us needing to approximate it in ever more accurate assessments but still the real issue is that we can't measure reality perfectly. If we discovered a way to measure the circumference of a circle as easily and accurately as the diameter, we'd no longer have an endlessly more and more accurate measure of Pi, we'd come to a conclusion, but we'd still not ever be 100% accurate. So I don't see the problem. Even 1/3 doesn't quite exist expressed in decimal, because you can't stop writing the decimal 3s. It's no solution to say 'repeating'... No one can measure that far. So all in all the fact is that there's noting special about Pi. What we have is a roughness in our ability to measure the universe.

[@jorgecelis8459]

Wow, I swear just last days I was wondering about this. If space is discrete, the most "accurate" model of the universe should forbid the use of irrational numbers (accurate in the sense that is a better representation, probably not in the experimental results which by the order of magnitude will work as well as if the space was continuous, at least for the experimental capacity of the present)

[@user-kc7fv6ue4e]

graet! thank you!

[@phil3038]

I've always wondered this!! 🙂🙃🙂

[@jerry3790]

Still waiting for the third of Quattuordecember to celebrate the actual Pi day.

[@stevethecatcouch6532]

Or celebrate it on July 22. 22/7 is a closer approximation to pi than 3.14.

[@pedroff_1]

Or for the thirty first of April, which obviously is closer (/s)

[@ffggddss]

@@stevethecatcouch6532 Just barely! |π - 22/7| = .001264489... |π - 3.14| = .001592653...

[@pedroff_1]

@HaleyHalcyon - Gaming Channel no, what we do is say today is 2019/3/25, that's the way we do!

[@Cardgames4children]

This video is great since it explores an idea that I wish got more philosophical scrutiny. Like pointed out near the end, the quantization implied by QM means that any ideal notion of the real number line (i.e., that which is encountered in a course on analysis) cannot have a physical implementation, since something continuous cannot be embedded into a quantized structure (I think, seems like a reasonable inference). There would be gaps. In fact, in such a world as implied by QM, can anything even be continuous? Motion and temperature fluctuations only seem to be continuous, as they are just a many of very little quanta lumps of certain things. But anyway, in such a world, things like e and pi might not be physically real (since they are irrational), and so the equations that we have describing reality that use those constants would, in fact, be describing a reality that is not *exactly* like ours (one is an idealized continuous reality, the other discrete). Would that make anything in a discrete reality just approximations, albeit very good ones, to an idealized, continuous reality? I mean, who really cares practically, since the approximations are very good anyway, but don't you want to know what IS?

[@localverse]

Aren't all quantum things waves according to a recent Science Asylum video? Waves themselves are continuous even if we can measure them as discrete objects. Which means quantum is really about energy instead of objects. In that case maybe space is continuous but vacuum energy is discrete.

[@michaeljames5936]

Unless you believe in a real Platonic 'world of forms', it is not possible to even imagine a perfect circle, since that would be a product of a quantised brain.

[@anshumanagrawal346]

Even if everything is continuous, formulas of Physics ARE still approximations with very real errors

[@martinmuller3244]

This philosophy you are describing dates to the 1890's, when Mathematics started to be tied down accurately enough to allow detailed scrutiny. The debate fell effectively into the constuctivist camp (you should only ever use mathematical concepts that can be constructed; non-constructivist proofs such as reducto ad absurdum should be avoided) and the idealist camp, who felt that mathematics would be too constrained by this requirement. At the time we understood it as an ontological (existance) argument (along the lines you present it here). It is really with Goedel that we understand mathematics as a branch of logic. The problem nowadays is understood as a problem of epistemology (knowledge) rather than ontology. So perhaps a better way to look at it is that both classical mechanics and quantum mechanics are encoded in quite tight logic, with logical rules that allow experimental setup and experimental outcome to be related to each other. There is a beautiful book by Errett Bishop that derives all of calculus, all the way into the Hilbert Spaces you need to construct what we understand of quantum mechanics in a constructivist fashion. The upshot of this is that you can always represent the quantum mechanics of the experimental setup to the accuracy you need, as long as you have a big enough Turing machine (viz a vie Computer). So it is not the mathematical representation that stymies us, but our cleverness in crunching the numbers.

[@ProLogic-dr9vv]

Thank you . another video on the same intellectual level that I am on , I love this and I can't get enough , 57 years old been into science for about 50 years , yes I have been a scientist for a log time and I will never burnout on this. Acquired Savants I have .

[@standardoperationsop9467]

Thanks!

[@standardoperationsop9467]

Your videos are amazing. 😀 THANK YOU!!! I am glad KZbin added the contribute button. Creators like you deserve it.

[@sohee7597]

2:18 I love how red + green = orange to my brain

[@user-jt5ot4hy9q]

We deal with infinite series by (incomplete) approximations that serve our purposes. On the other hand, we can formulate numbers larger than the sum of all things in the universe. So there is certainly some disconnect between math and reality. Math seems like Plato's Ideal Forms, a generalized abstract of what really is.

[@walterbushell7029]

In fact, for every infinity, there is an infinity larger that it, so at least as many as there are positive integers or rational numbers, the smallest infinity. We have more infinities than we have things to usefully count..

[@Bestape]

How about "continuously discrete" like the squares in the golden spiral decaying into the vanishing point?

[@bondedcastaway3085]

Can you do a video on how a circuit board works? Id love to truly understand it

[@WakeUpUniverse66]

HAPPY 3.14 DAY!!!!!!!!!!!!!!!

[@damejelyas]

4:42 Just to add an information the binnary point is actually called a Floating point. ;@

[@dr.jamesolack8504]

damej elyas In this realm.....

[@DClairRobinson]

Can't you take the average of all possible measurements from center to edge? That would correct for the "not smooth" edges right?

[@raulcoronado6024]

👍Thank you😆

[@charliefrancis6438]

After 5 shots of vodka and a cigarette, I realized that a circle cannot be quantized , because pie seems to be a never ending number that doesn’t seem to exist, so I went looking for KZbin videos that explains this , this is the best one that I have found 👍🏻

[@holomurphy22]

It's not necessary to have infinitely small precision for pi to have physical meaning. Take a circle with a diameter of 10^1000000 meters. Its circumference uses 1000000 digits of pi if you measure up to a meter, so no need of quantum mechanics here

[@MiguelGarcia-zx1qj]

@@holomurphy22, get a copy of Maple (even a twenty years old version can do it), and you can ask for as many digits of Pi, as the computer memory (adjusted for internal representation of numbers in Maple) allows. This is the easy way. Alternatively, use a specialised program to compute as many as you want ...

[@holomurphy22]

@@MiguelGarcia-zx1qj Alright but how does this relate to my comment?

[@MiguelGarcia-zx1qj]

@@holomurphy22, you're right, I missed the part about "physical meaning". My fault. I interpreted your answer as pertaining to the video's first theme: calculating Pi experimentally by drawing a circle. Nevertheless, giving "physical meaning" to the first 1000000 digits of Pi is not the issue here; for that matter, it does not differ from giving "physical meaning" to the first 1 or 2 first digits of Pi

[@holomurphy22]

@@MiguelGarcia-zx1qj I answered to the comment above of Charlie. I dont see how its the same to give physical meaning to 2 digits and 10000... digits. There are measure limits.

[@zombieblood1675]

Pi: exists Science asylum:

[@somnathsaha4819]

Great sir

[@EvilSandwich]

3:48 That feeling when I've worked with logic circuits for so long that I could tell I was looking at an XOR Gate just from the transistor arrangement. :p

[@alexandertownsend3291]

People often ask if pi exists which is both a valid and interesting idea to ponder, but I think that people tend to pick this number instead of a number like 5 because the idea of "fiveness" has a different feeling than the idea of "pi-ness". The number 5 is more commonplace to every day experiences. Every day we count things. We encounter collections of 5 things all the time. The number pi on the other hand while still useful is not as common to every day experiences unless you happen to be a mathematician or do measurements of circlular objects and their geometric properties on a regular basis. There is also the question of what is meant by a number existing. So my question is this: Does any number, be it 5, pi, -17, 2+5i, etc exist?

[@ZumaZoom07]

I’ve thought about that and have am come to the conclusion that only 1 is real because although there can be five apples, they all represent different places in spacetime. It gets a lil sticky if we say that 0 is also a number because… there is either nothing or something… but then that’s “two” things which in turn makes three things and so on… what was the question?

[@davidprime6080]

I would have liked to have seen a discussion of Plato's theory of Forms included since some thinkers, including Roger Penrose, think that numbers might exist in that realm. Apart from that, I enjoyed the presentation

[@bummers]

The same can be said about triangles or squares?

[@kennylex]

Is it random if they toss the arrows in a general direction, how do we know if something is random?