New World Record! 100 Trillion digits of π.

Рет қаралды 283,572

Жыл бұрын

Check out Emma's blog post about the calculation:
cloud.google.com/blog/product...
Register for Emma's live seminar! It's on at 19:00 BST and different time zones are different.
cloudonair.withgoogle.com/eve...
Emma Haruka Iwao's records:
2019: 31,415,926,535,897 digits of π
2022: 100,000,000,000,000 digits of π
Chudnovsky algorithm
en.wikipedia.org/wiki/Chudnov...
And here is me Chudnovskying by hand: • Calculating π by hand:...
Bailey-Borwein-Plouffe formula
en.wikipedia.org/wiki/Bailey%...
y-cruncher - A Multi-Threaded Pi-Program
www.numberworld.org/y-cruncher/
Cheers to all of my Patreon supporters who mean I can jump on the ol' video machine whenever there is breaking maths news. You can also help support my videos. / standupmaths
CORRECTIONS:
- At 07:34 I say that the first column are the hex locations. They are not. Those are the base-10 locations in scientific notation. Sorry!
- A few people noticed that at 02:20 I say 128 when I mean 158. The on-screen number is correct.
- Let me know if you spot any other mistakes
Filming and editing by Alex Genn-Bash
Additional footage by Emma Haruka Iwao
Blah blah blah by Matt
Music by Howard Carter
Design by Simon Wright and Adam Robinson
MATT PARKER: Stand-up Mathematician
Website: standupmaths.com/
US book: www.penguinrandomhouse.com/bo...
UK book: mathsgear.co.uk/collections/b...

Пікірлер: 1 500

@legohead2731 Жыл бұрын

I’m so glad that mathematicians have finally figured out 0% of pi

@Ganpan14O Жыл бұрын

Here's to the next 0%!

@nosuchthing8 Жыл бұрын

Ha! Nice

@williamclay190 Жыл бұрын

It's technically a non-zero% but yeah

@legohead2731 Жыл бұрын

@@williamclay190 didn’t know! Can you elaborate?

@crikhard Жыл бұрын

@@legohead2731 it's infinitesimally small but not 0. effectively 0% the same way 0.9999... == 1

@thomasfrewer1328 Жыл бұрын

Google's automatic transcription is going to listen to Matt say "the last digit of Pi is zero" 0:27 and serve it up to at least one person who googles it.

@ethanjensen7967 Жыл бұрын

Lol "pi is exactly..."

@MikeRosoftJH Жыл бұрын

@@ethanjensen7967 Pi is exactly pi. :-)

@Nico_M. Жыл бұрын

So, it's acutally 6.

@Nate-bd8fg Жыл бұрын

@@Nico_M. 6.28310 (almost) exactly

@ziwuri Жыл бұрын

@@MikeRosoftJH π=π

@janmelantu7490 Жыл бұрын

“My personal best for calculating Pi is 14 digits and turns out Pi’s personal best is 14 digits” That’s a Parker Circle Constant if I’ve ever seen one

@toxicara Жыл бұрын

Yep, and the rational Pi that ends in 0 is now the Parker Pi!

@SKyrim190 Жыл бұрын

14 digits of pi is pretty accurate!

@ziwuri Жыл бұрын

@@toxicara that's rly funny lol

@adamplace1414 Жыл бұрын

This comment, as of 1:37 am central US time on June 16, has 314 likes. I'm not gonna be the jerk that adds one, so I'm liking it in spirit

@toxicara Жыл бұрын

@@ziwuri it's close enough to Pi to be good and useful, but not perfect... PARKER PI😁love you matt

@0utOfSkill Жыл бұрын

At 3:14 Matt says "classic π" and I refuse to believe that wasn't intentional.

@deepskyfrontier Жыл бұрын

There is a one in ten to the eightieth power chance that it was not.

@ps.2 Жыл бұрын

And by the way, I hope you noticed the upload date of the software Emma used? (3:35)

@davidhutchins8144 Жыл бұрын

Delightful ... 2x better than one person talking about PI. Now if you could only get 3.14 people obsessed with PI in one video...

@toxicara Жыл бұрын

so 3 mathematicians and an engineer then? 🤣

@archivist17 Жыл бұрын

@@toxicara or, as the engineer would say, five people (rounded up)

@supermanor Жыл бұрын

we could also get 22 people intrested in pi and 7 that doesn't

@TheDirge69 Жыл бұрын

@@toxicara ha ha!

@bertil0424 Жыл бұрын

I'm 14% obsessed with pi, so just throw me into the interview and another person

@ExtantThylacine Жыл бұрын

Can we just take a moment to appreciate Matt's brilliant editing by timing the moment he says: "Classic pi!" to be at exactly 3:14 ?

@MathsMuallim Жыл бұрын

🤯🤯🤯

@achtsekundenfurz7876 Жыл бұрын

OTOH, 07:32 is a pain. Calling the first column the "hexadecimal" location, _really_ ? That's not pi, that's not even Parker Pie. More like Pewdie Pi...

@pelicanoe Жыл бұрын

And “wrong” at 6:28. That better be a coincidence...

@profdaniel1787 Жыл бұрын

@@pelicanoe Is that a swipe at tau? 😂

@ps.2 Жыл бұрын

Also, the same point in _Dark Side of the Moon_ is the words "rabbit, run" switching from tonic (I) to subdominant (IV). Oh. I thought I knew how this worked, but I guess that one's pretty meaningless.

@Jupiterninja95 Жыл бұрын

100 trillion is 10^14, and if π is a normal number there's a 1 in 10^14 chance of a particular string of 14 digits, so I think finding a 14 digit string of meta π makes perfect sense!

@rmsgrey Жыл бұрын

Yeah, and they mentioned that there are roughly 100 12-digit matches (98, though I believe that's not including the 13+ matches)

@n0ame1u1 Жыл бұрын

And also interesting, there's about 10 places with 13 digits, and about 100 places with 12 digits

@QuantumHistorian Жыл бұрын

And 10 matches of length 13+. This is all pretty much _exactly_ what you would expect. The weirdness, if anything, is that it matches so well to the expected value!

@yehudadavis9462 Жыл бұрын

Went hunting for this comment just to upvote. I was hoping Matt would add it in post, especially after expressing his surprise...

@reilandeubank Жыл бұрын

@@QuantumHistorian i guess when your number sets are this absolutely huge the probability seems to work out

@AmaroqStarwind Жыл бұрын

Scientists: “We can probably stop now.” Engineers: “We should have stopped at ten digits.” Mathematicians: “We need to keep going.”

@weedmilk Жыл бұрын

Engineers: “We should have stopped at 3.”

@solemnwaltz Жыл бұрын

3 digits? Or just 3?

@gasdive Жыл бұрын

@@solemnwaltz the Bible sets pi at 3.0

@stevenvanhulle7242 Жыл бұрын

@@solemnwaltz In a back-of-the-envelope calculation I sometimes use 3.

@quartzofcourse Жыл бұрын

As professor frink brilliantly claimed “pi is exactly 3”

@ClostridiumChampion Жыл бұрын

I like the poster in the background with "Education works best when all the parts are working." Featuring 3 gears that physically cannot turn, because they're interlocked.

@genericgamer2003 Жыл бұрын

He talks about that poster in his book 'Humble Pi' so I think he just keeps it up to see if anyone notices :p

@nowonmetube Жыл бұрын

Yeah he mentioned it in a video, in I think a stand up performance where he mentions his book.

@twiceineverymoment Жыл бұрын

Check out his talk "What happens when math goes wrong" at the RI, he mentions this and a lot of similar mistakes.

@ClostridiumChampion Жыл бұрын

Yeah, it would've surprised me if Matt wasn't aware. I was thinking maybe it could be some elaborate joke about teachers and students working well together, only for parents to come clog it up, but I wasn't sure. Thanks for directing me to his talk at the Royal Institute; I will definitely be watching that. He talks about the cogs already around 5 minutes in, if anyone else wants to see it. kzfaq.info/get/bejne/bLCneLyS0tC8oHU.html&ab_channel=TheRoyalInstitution

@josephurbanich7344 Жыл бұрын

It’s actually a really informative picture. The teachers and students are almost able to work together, but the parents are clogging everything up.

@Vini-BR Жыл бұрын

If a person could somehow memorize 10 thousand digits per second, it would still take them 316 years to reach 100 trillion digits

@Saka_Mulia Жыл бұрын

That's the scale magnitude I was looking for!

@Parax77 Жыл бұрын

This is not a Fact unless it's 314 years...

@daffa_fm4583 Жыл бұрын

three sixteen

@koharaisevo3666 Жыл бұрын

That is supprisingly fast.

@efhiii Жыл бұрын

That's a real Parker Fact.

@GrayBlood1331 Жыл бұрын

It's actually not too surprising that there's only 14 digits of mini-pi. Each successive correct digit of pi would be another order of magnitude less likely and would require another order of magnitude of regular pi to look through. 100 trillion is 10^14, so it makes perfect sense.

@solsystem1342 Жыл бұрын

Not quite. You get repeats which doesn't affect you much at low probabilities but once you hit like 1% you start getting significant error if you assume the next value will be 10 times the last. Since some of the numbers come up multiple times. This is most obvious for shorter chains where it's quite likely most 13 digit numbers are in their multiple times it's almost certain some of them won't be in there at all.

@gredangeo Жыл бұрын

So how many digits worth of pie would there need to be in order to have a meta Pi of 100 Trillion Digits? Because the magnitude doesn't seem to suggest that 10^100 Trillion is enough.

@solsystem1342 Жыл бұрын

@@gredangeo 10^10^14 digits is theballpark. You might want to multiply the whole thing by 1 million and then you can say it's pretty much gureenteed. Edit: this is a large number by the way. in the sense that multiplying it by a small number doesn't change its value all that much (obviously if you multiply it by 1 billion it's a billion times bigger but, in a physics context we start to talk about significant figures of the exponent here and multiplying by 10^9 just really doesn't change the number meaningfully it at this point)).

@Anonymous-df8it Жыл бұрын

Wouldn't it be 100 trillion digits with starting point 1?

@gmalivuk Жыл бұрын

@@solsystem1342 Yes, it's very unlikely that all sequences of length 13 are present and impossible that all of length 14 are there. However, a given 14-sequence has about a 60% chance of appearing at least once in 10^14 random digits, so we should not be surprised to find 14 digits of pi in 100T digits of pi. We shouldn't even be terribly surprised to find 15, since the probability for that is about 8%.

@kayodesalandy Жыл бұрын

*Matt at 13% error rate*: "Not too bad!" Emma: "I have a duty to precision."

@marasmusine Жыл бұрын

Parker Precision.

@Hallgrenoid Жыл бұрын

0:27 "The last digit of pi is 0" - Matt Parker, 2022

@johnacetable7201 Жыл бұрын

It's impossible for it to be 0.

@Hallgrenoid Жыл бұрын

@@johnacetable7201 implying there IS a last digit in the first place, it just isn't 0?

@johnacetable7201 Жыл бұрын

@@Hallgrenoid either of ways. Because of the way we write 'em down. 0.254=0.254000000

@Hallgrenoid Жыл бұрын

@@johnacetable7201 it's a joke. There is no last digit of pi, and so i quoted Mark out of context for the humor in it.

@johnacetable7201 Жыл бұрын

@@Hallgrenoid proof yourself. And mathematical jokes, same as any specific humour, imply either knowledge or ability to think.

@thomashirsch4302 Жыл бұрын

an excellent achievement! Minor correction: at 2:20, the voiceover says the calculation took almost 128 days, when you should have said "almost 158 days". Very understandable - it would have been pretty cool to do this in 2^7 days

@ObjectsInMotion Жыл бұрын

128 days is almost 158 days though

@AnEnderNon Жыл бұрын

@@ObjectsInMotion 158 days is more almost 158 days

@averyredpandy Жыл бұрын

Regarding the recursive pi it actually lines up almost perfectly with the probability. Since any given digit has a 1/10 chance of being the correct one, the chance of finding a 14 length recursive pi is 1 in a hundred trillion. Also there's 10 13-length ones(including the 14-length) and 98 12-length, all of which are pretty spot on.

@98009200 Жыл бұрын

Teacher: Is π rational? Student: YES! Teacher: wrong! Where did you hear that? Student: shows resources. 0:14 "This is the last 100 digit of PI"

@toxicara Жыл бұрын

yeah that annoyed me too. The last known digit Mr Parker!

@normanstevens4924 Жыл бұрын

@@toxicara On a previous Parker video google interpreted what he said as giving the exact value of pi. I assume he's trying to repeat that feat.

@MichaelOnines Жыл бұрын

@@toxicara If you couldn't detect the tongue firmly planted in cheek you are too innocent to be on the internet unaccompanied.

@3c3k Жыл бұрын

Teachers resigned🤣🤣

@Exeedo. Жыл бұрын

It will still be too much headache to convert 100 trillion digit number into a ratio of two integers

@macdofglasgow772 Жыл бұрын

BBP still blows my mind. Just seems counter-intuitive that you can pull out specific digits like that. Fun video as typical by Matt.

@mralistair737 Жыл бұрын

does that mean I could just work out the next digit and now I hold the record?

@vigilantcosmicpenguin8721 Жыл бұрын

@@mralistair737 No, because as soon as you'll do that, I'll work out the digit after that.

@ziwuri Жыл бұрын

Imagine your dream job as a kid was to calculate decimals of pi and you actually ended up in that job. Well, Emma doesn't have to imagine it.

@RTDelete Жыл бұрын

My favorite math joke of all time is still : "Pi is... about three"

@YodaWhat Жыл бұрын

Or take the 16th root of these 8 digits: 90032221 and get Pi to 10 digits.

@hughcaldwell1034 Жыл бұрын

I still like "That's a triple integral! That alone speaks volumes!"

@b.lakshmiganesh865 Жыл бұрын

@@YodaWhat 🤝

@FF_Fanatic Жыл бұрын

I'm loving the interviews. It might be cool to have Alexander Yee (the creator of y-cruncher and former record holder) on here sometime to go into some nerd talk about the program. I've had the pleasure of being able to chat with him outside of his legendary StackOverflow Q&A presence, and it's probably worth a shot if you're interested in having him on.

@dantrizz Жыл бұрын

From what I remember there are 10^80 particles in the observable universe so, the probability of an error in the calculation being 1 in 10^80 is equivalent to Matt choosing a random particle in the observable universe, Emma also choosing a random particle in the observable universe, and those both happen to be the same particle.

@DavidBeddard Жыл бұрын

Wouldn't that be (1 x 10⁸⁰)²? I've always struggled with understanding probability.

@fullfungo4476 Жыл бұрын

@@DavidBeddard no, it would not. If you don’t understand why, try the following. Calculate by hand the chance of two 6-sided dice showing the same number. Hint: it’s not (1/6)^2, it’s just 1/6.

@DavidBeddard Жыл бұрын

@@fullfungo4476 Aha, right, gotcha. Thanks 🙂👍 I mean, I accept the truth of what you say, and can follow the calculation, but it runs counter to my intuition, always has, and my brain has struggled to overcome that.

@tim40gabby25 Жыл бұрын

That's gotta be unlikely, surely?

@vinicus508 Жыл бұрын

You can’t say that “there are” as if we knew the exact number cus we dont lol

@zechariahkitzhaber6625 Жыл бұрын

When I saw the news a few days ago, I was hoping you would make a video on this. You never disappoint with your content!

@SimonDonkers Жыл бұрын

Have they stopped the algorithm at exactly 100 trillion, or have they overshot and secretly already know the 100 trillion +1th digit? How far did they get past the nice round headline?

@ikjadoon Жыл бұрын

That'd be quite interesting to know. I imagine it probably did stop precisely at 100 trillion to save money (she notes needing to keep costs in the blog post). The official API also caps out at 100 trillion digits; it won't return any digits if you ask for the 100 trillion +1th digit. :( The incremental cost, however, wouldn't have been much.

@miriamrosemary9110 Жыл бұрын

I wondered that too

@lifthras11r Жыл бұрын

Pi computation algorithms at that scale don't continually emit digits; you give the number of fractional digits to compute in advance and the algorithm gives you all the digits at once after months of number crunching.

@jared5941 Жыл бұрын

on y-cruncher you enter the number of digits you want to compute, the software tells you in-advance how much RAM and Disk space are required to calculate the number you specified. Once you click start, the software begins computing Pi to that specified number of digits.

@esphilee Жыл бұрын

Can you even beat the temptation to keep it running for few more digit…

@johneckelkamp9655 Жыл бұрын

An interesting number to create would be a "decimal reduction" of pi, where the first digit of the new number is the first digit of pi (3), the second digit of the number is the 10th digit of pi (3), the third digit is the 100th digit of pi (7), and so on: 3378745... Each new digit catapulting you ten times deeper into pi.

@lucashowell8689 Жыл бұрын

Sounds like a fun start toward making a pi-based hashing algorithm … we can use the first few digits of the decimally reduced function to define the block size for the source, then use the contents of that block to define the next location and size of the decimally reduced pi function, which in turn defines the size of the source block once again, rinse and repeat… end of the day you get a unique location on the decimal reduction function that corresponds to the source file.

@Rampart.X Жыл бұрын

Why?

@Anonymous-df8it Жыл бұрын

Even more interesting, what number would be decimally reduced to pi??

@MoempfLP Жыл бұрын

@@Rampart.X You could check if new algorithms work correctly

@Xormac2 Жыл бұрын

Binary reduction should be interesting too

@seas0 Жыл бұрын

7:32 That is the scientific notation of the number, not hexadecimal.

@vaxjoaberg Жыл бұрын

100 trillion digits of pi? That's incredible! We now know 0% of all the digits of pi.

@keep-ukraine-free528 Жыл бұрын

I love witicisms!

@SuperPseudonymous Жыл бұрын

I am always excited to hear about the latest in PI news!

@billysoy7383 Жыл бұрын

Already looking forward to this!

@CrispyGFX Жыл бұрын

"I do pi for a living" That's a flex

@radadadadee Жыл бұрын

Just like any other baker in Walmart

@lewismassie Жыл бұрын

Emma's comment about using Pi calculations as a way to measure computing power over time is a really interesting one, as it takes into account not only computer strength but algorithmic strength.

@JackMott Жыл бұрын

lately the algorithm has been fairly constant, but it is nice for stressing distributed cluster arrangements as it is an algorithm that can leverage them well

@rafbambam Жыл бұрын

Hi Matt, I don't know if it's a long time you've posted something, but for me it was a long time that I got a message that a new video was out. But still a nice video, and it's even nicer to see that even Pi itself can't produce more Pi than you can. Greetings from Belgium.

@porkins1802 Жыл бұрын

The Nerd-love in this video is wonderful, keep up the good work and congratulations to Emma.

@justfellover Жыл бұрын

What is the statistical likelihood that Matt messed up his calculation and instead of getting the first 14 digits of π, he got the 43,420,162,171,515th thru 43,420,162,171,528th digits?

@francoistrempe Жыл бұрын

I loved that "keep going" after the "back to the interview". This is exactly the kind of things that make for great videos. Well done!

@midori4352 Жыл бұрын

Watching your channel restores my faith in the capacities of human intellect. Thank you for your content! This video made my day! :)

@SeniorPoteyto Жыл бұрын

Just in time for 1M subs! Congrats Matt.

@alasdairhurst Жыл бұрын

Now let's get ready to celebrate when he gets 100 trillion subscribers!

@SeniorPoteyto Жыл бұрын

@@alasdairhurst Well that's gonna take a while.

@bosch992 Жыл бұрын

Congratulations Matt!!

@cosmicjenny4508 Жыл бұрын

@@alasdairhurst The first KZfaq channel to reach a morbillion subscribers.

@John_C_J Жыл бұрын

@@cosmicjenny4508 What have you done?

@mikepictor Жыл бұрын

Matt: I can compute PI to 14 digits Emma: Hold my beer

@robhulluk Жыл бұрын

Matt: Ok, I'm holding your beer. Matt: I've been holding your beer for a month, how long is this going to take? Emma: Only 157 days

@JohnR31415 Жыл бұрын

Do we know what the longest series of zeros is in there?

@UncleKennysPlace Жыл бұрын

Yeah, 'cuz I'd quit at three zeros in a row!

@JohnR31415 Жыл бұрын

@@UncleKennysPlace clearly got the end at that point ;)

@elhartzer1639 Жыл бұрын

@@UncleKennysPlace am engineer, can confirm.

@quantumbanana Жыл бұрын

Since its 10^14 "normal" digits, you can expect to find 14 digit strings. So the answer is likely 14 0s, and if not it is almost certainly 13.

@Dreeev Жыл бұрын

Probably around 13-14 digits as well (the chance of getting the first 14 digits of pi should be the same as the chance of getting 14 digits which are all 0s)

@threeprongedfork7061 Жыл бұрын

I am so happy you had Emma on, so cool

@genericgamer2003 Жыл бұрын

Very cool! Thanks for sharing this with us

@alan2here Жыл бұрын

In positively curved space, PI is 0 to 4, and in negatively curved space, PI is at least PI. Makes everything much simpler.

@eroraf8637 Жыл бұрын

Why would they change pi? Pi is pi! PI IS PI!

@alan2here Жыл бұрын

@@eroraf8637the circle constant in these other spaces is a different value than it is in flat space, another difference is that it also changes in those spaces depending on the size of the circle

@eroraf8637 Жыл бұрын

@@alan2here I'm well aware. I was making an "Incredibles 2" reference.

@Smitology Жыл бұрын

@@alan2here Well the mathematical constant won't change, the circumference just isn't pi times the diameter in those geometries.

@thatchessguy7072 Жыл бұрын

Announcer: Good news everyone, we found 100 trillion digits of Pi! Interviewer: So how many digits of pi do you need to use at most in any real world problem? Announcer: About 30. Interviewer: 30… trillion? Announcer: No, just 30 digits. Interviewer: Oh… ok.

@gerenaleonray Жыл бұрын

Nasa uses 15 digits for rockets. An atom-precise measurement of the universe would only need around 40. lol

@Max_Griswald Жыл бұрын

Congrats on a million subs!

@MrPeterPanos Жыл бұрын

Great video, well done Emma!!!

@darrennew8211 Жыл бұрын

I liked Feynmann's take. He memorized it up to 700ish digits, until there were six nines in a row, so he could recite it and end with "four seven nine nine nine nine nine nine nine and so on." As if all the remaining digits were nine.

@feliciabarker9210 Жыл бұрын

The problem with this gag is it requires your audience to wait patiently whilst you recite 700 digits of pi

@ytkerfuffles6429 Жыл бұрын

its not 47999999 its 34999999

@BlokenArrow Жыл бұрын

You only need 83 digits to describe a sphere the size of the universe to the order of the Planck length

@TonyHammitt Жыл бұрын

355/113 is only off by 8 millionths of a percent. Close enough...

@billowen3285 Жыл бұрын

Woah

@Fallkhar Жыл бұрын

That's a cool gear poster Matt! I lover the reference

@exiledtobronze8694 Жыл бұрын

Gratz on 1Mil subs

@hingedelephant Жыл бұрын

Whew! Just in time, too. I was really missing this level of precision.

@angelainamarie9656 Жыл бұрын

No doubt right? My circles are going to be really *nice and round* now

@Frrk Жыл бұрын

Finally I can properly set up my bicycle speedometer!

@CarletonTorpin Жыл бұрын

This has been my favorite Stand Up Maths video. Good energy, just enough complexity for non-math-majors, and a nice editing style. :)

@airatvaliullin8420 Жыл бұрын

Fascinating! We're almost there to compute them all!!!

@RC32Smiths01 Жыл бұрын

I am absolutely astonished right now. Pi is simply one of the most iconic numbers, and the commitment to unraveling it is commendable. Congratulations to her!

@radadadadee Жыл бұрын

"iconic" lol

@NimbusAlamaa Жыл бұрын

Small correction: at 2:20 you say the total time was just under 128 days, when the blog says it's just under 158 days

@joelsmith3473 Жыл бұрын

Alright, so now I know that it takes Pi over 43 trillion digits to "remember" pi to more digits than me.

@InviDoll Жыл бұрын

Emma is so cool. More Emma!

@djsyntic Жыл бұрын

I found a few digits of pi in my couch cushions. I know it's not many, but I know that people like more digits. The digits I found were 4, 7, and a 9... though that 9 could have been a 6 as it wasn't clear what way was up for the digit. Also, I'm not entirely sure where they belong within pi, but they were clearly labeled as "digits of pi - made in America" along the side.

@jellezwaag Жыл бұрын

Their match in Pi-obsession contrasts nicely with their miss-match in humor:D

@samharkness8861 Жыл бұрын

Great work! Thank you for explaining that great point in the importance of calculating Pi. Because there are people throughout humanity who have an innate want to discover more purely out of curiosity, we have a graph which shows the exponential increase in computing power throughout human history. Beautiful.

@stevenvanhulle7242 Жыл бұрын

The first appearance of "42" is at position 92. It baffles me that they even went further after that.

@MrNiceBanana Жыл бұрын

Love your work Matt, I've been a huge fan for a while now. I do want to point out the "Education works best when all the parts are working" poster in your background features three gears that can't actually rotate together... Not sure what that says about all the parts actually working.

@MorzakEV Жыл бұрын

🤣 yeah, if you read Matt’s book Humble Pi, it specifically mentions how that poster is bungled.

@VAXHeadroom Жыл бұрын

7:36 Matt says "This is the hexadecimal location in Pi" when it's actually a scientific notation decimal value...

@OnlyPenguian Жыл бұрын

The value may be in scientific notation but it refers to the location of a hex digit?

@webentwicklungmitrobinspan6935 Жыл бұрын

i love the passion for pi and i hope that i will be smart enough at one time to get existed about it as well and google cloud is truly amazing btw

@idjles Жыл бұрын

Awesome that Emma wants to join your hand pi calculations.

@AnInnocuousBlueCube Жыл бұрын

I hope that these efforts continue, and that during my lifetime they run into an absolute desert of sequential 0s that makes them question absolutely everything until it goes back to normal after the 600th zero or so.

@spudhead169 Жыл бұрын

In the TOS episode "Wolf in the fold". Spock orders the Enterprise computer, to the exclusion of all else, to calculate to the last digit the value of Pi in order to force jack the ripper out of the computer after he invaded it. Based on computer advancement trends we can see and measure today, what would you expect a computer in 2266, running flat-out over a period of about 5 minutes to manage with regard to the amount of digits?

@miriamrosemary9110 Жыл бұрын

I love this question

@zmaj12321 Жыл бұрын

wow

@phizc Жыл бұрын

1.40544760E+48 digits in 5 minutes tripling in 3 years is an increase of about 1.4422496 per year. It's 244 years to 2256. 1.442496²⁴⁴ × 10¹⁴ / (158*24*60) × 5 = 1.40544760E+48 Note: I used the calculator on my phone, so I may have messed something up. Edit: Oh, and in 244 years the computers will be about 6.39534875E+38 times faster than today.

@spudhead169 Жыл бұрын

@@phizc That might have issues seeing as that's about the amount of atoms in the Earth. The computer would have to have some crazy storage technology to even hold that much information in such a relatively small volume.

@phizc Жыл бұрын

@@spudhead169 true, but OP asked how many digits based on current trend..

@TranquillShot Жыл бұрын

Cutting it close for the webinar! Haha Woohoo for Pi!

@koshin_ Жыл бұрын

This is so cool!

@hens858 Жыл бұрын

I probably found the 100 trillion and one number of pi, it's a 3. (With around 10% chance of being corrected)

@karlneff Жыл бұрын

Good work lad!

@XenFPV Жыл бұрын

And then 14159265 etc and the pattern just repeats from there. Pi wasn't irrational this whole time! Just a very long sequence.

@ottolehikoinen6193 Жыл бұрын

Thanks for saying this, now I don't have to.

@QuantumHistorian Жыл бұрын

You could use the BBP algorithm and find out what it is exactly pretty easily (possibly even by hand).

@calvindang7291 Жыл бұрын

@@QuantumHistorian You definitely can't do it by hand - it's an O(n log n) algorithm to find the n'th digit. (The algorithm to find the digits of pi is O(n log^3 n log log n), in addition to just being slower in general.)

@Howtheheckarehandleswit Жыл бұрын

On the chances comparison, quantum weirdness I think isn’t a very good example, because it’s unintuitive and imprecise. However, 10 ^ 80 happens to be pretty close to the estimated number of particles in the observable universe (3.28 * 10 ^ 80). So, given that, we can say that if every single particle in the universe did this calculation and checked the error the same way, we would expect 3, maybe 4 of them to think that they are right but actually be wrong

@_Karlsson Жыл бұрын

I was waiting for this so I could calculate the area of my dining room table precisely enough.

@docshoe Жыл бұрын

After watching this video I remembered a friend of mine and me thinking about the "π-Packer". It was back in late 80ies when I was writing a compressor/decompressor for the Commodore 64. The main idea of the "π-Packer" is to find the program/data´s byte representation somewhere in the digits of π. So you can represent any block of data using an offset and length, the only difficulty is to find the sequence. That algorithm coud be improved by only searching smaller blocks and store multiple offset/length pairs. And if you fail at all you can always switch to the "e-Packer" ;) I bet Matt likes the silliness of the "π-Packer".

@QuantumHistorian Жыл бұрын

To anyone asking why google pays for something like this, this very video is the answer! Paying for a few months of super computer time is relatively cheap for all the publicity they'll get from it.

@IanSlothieRolfe Жыл бұрын

Also, Google is expanding its computing power on a continuous basis, so using it for this kind of thing costs them nothing in terms of hardware and gives it all a good exercise. As for the staffing costs... Google is into everything, and when you research "useless" things you can sometimes make profound discoveries on the way.

@lifthras11r Жыл бұрын

@@IanSlothieRolfe Not only that, but the current algorithm is bounded by I/O bottleneck which is unlikely to be fixed in the near future. So this computation actually ran in a single computer as it's impossible to efficiently distribute tasks without further I/O overhead. So it is not really a good way to use cloud computing, and yet Google can therefore basically throw another computation for months whenever a bigger instance is available and generate yet another publicity for free.

@cuddlyfoxgirl Жыл бұрын

"this is the hexadecimal location in pi" 7:35 … that looks like scientific notation to me, not hexadecimal

@malkomalkavian Жыл бұрын

You got the actual person! That's big :) well done

@Nobody_Special310 Жыл бұрын

Glad to know you found those digits. Hope you don't lose them again.

@overlisted Жыл бұрын

Now you can start looking for even rarer amongi!

@matthewbertrand4139 Жыл бұрын

well now the next logical barrier to smash is 1 quadrillion digits. maybe make a pit stop at 314,159,265,358,979 digits. edit: well damn, Parker beat me to the punch. i hadn't watched far enough yet lol

@claudioestevez1028 Жыл бұрын

It's nice that the 100 trillionth digit is zero, so we can round it up to 99,999,999,999,999 digits without feeling guilty.

@zka77 Жыл бұрын

0:10 I love that poster on the wall saying "all the parts are working". If you set up 3 gears like that, you can't rotate them as they will get stuck. So they are not working. Oh the irony.

@ps.2 Жыл бұрын

Yep. That's why he displays the poster. He wrote a whole book about real-world mathematical mistakes (some that actually matter, unlike the poster) called _Humble Pi,_ and has included this poster in talks about the book as well.

@JustSomeBloke1 Жыл бұрын

The question I would have asked, given the opportunity, would have been "what is the longest string of the same number in pi?". So at 34" the quoted sequence has 3 4s together, but what is the most number of repeated digits?

@yahccs1 Жыл бұрын

The 1st million places have some digits repeated up to 5 or 6 times. A string of 0's or 9's would make a good place to truncate it and be accurate for the next few decimal places.

@Benny_Blue Жыл бұрын

So, in your pi^pi^pi^pi video, you said we need a lot more pi to calculate the answer. If the current exponential rate of discovery holds, is there any hope for us?

@alexparadise6121 Жыл бұрын

I don't think so. It seems that even with exponential increase in computing power, the number of known digits of pi^pi would grow roughly linearly with time, and further powers sub linearly.

@timetraveller6643 Жыл бұрын

TOPIC REQUEST: Hello Matt, can you tell us about the various map projections that preserve certain properties of a sphere? eg. area, great circles as straight lines, circles as circles, shortest distances, etc.

@Sauromannen Жыл бұрын

Thanks, that made my day (already at 7 in the morning).

@ianburton5624 Жыл бұрын

This brings up a couple of questions in my mind. 1) What is the distribution of numbers in pi, not just single digits but also higher numbers. I would imagine that the single digit distribution would be uniform. 2) What size of circle would be necessary to see a measurable uncertainty in the circumference, of course dependent on the type of measurement.

@eroraf8637 Жыл бұрын

The distribution of single decimal digits is indeed basically uniform, and there are no currently known correlations of consecutive digits. As for precision, 37 digits is sufficient to calculate the circumference of the observable universe to within the diameter of a single hydrogen atom. Anything beyond 100 digits is literally meaningless for anything physical.

@Patmorgan235Us Жыл бұрын

@@eroraf8637 yeah each digi increases the precision by x10 so you really only need a handful for most day to day stuff.

@cara-setun Жыл бұрын

You’d need a circle with a radius of 10^1400 lightyears to see the uncertainty with your eyes

@cara-setun Жыл бұрын

@@micahmeneyerji eh, close enough

@Smitology Жыл бұрын

@@cara-setun Yeah you were about 10^(100,000,000,000,000) lightyears off

@Vini-BR Жыл бұрын

(If I'm calculating this correctly,) this number of digits is so big that: - Let's have a random sequence of any 13 digits - Considering that the digits of pi are all random, you have the chance of finding that exact sequence of digits 10 times on average within that pi calculation!

@XCC23 Жыл бұрын

"Considering that the digits of pi are all random" 1. the digits of pi aren't *actually* random, they're the same every time we go look. 2. The property you're looking for is normality - for any positive integer n, all sequences of length n have a density of 1/(b^n), but we don't actually know if pi has that property. We *think* so.

@Vini-BR Жыл бұрын

@@XCC23 You're right! I should probably have said "if the digits of pi are evenly distributed"

@XCC23 Жыл бұрын

@@Vini-BR that's *better* but still not strong enough. The sequence that just goes 1234567890... has the digits evenly distributed, but it clearly doesn't have all possible sequences in there. You really need every string of every length to be evenly distributed as well.

@JohnSmith-gu6hf Жыл бұрын

The poster on your wall of gears is hilarious.

@wcsxwcsx Жыл бұрын

I'm always up for infinite pi. Keep it coming.

@ExplainedThroughRap Жыл бұрын

Awesome stuff! We just dropped a rap to help memorise the 1st 100 digits of PI! 🔥🔥🔥🔥🔥🔥🔥

@ZetaGirlPower Жыл бұрын

Matt and Emma share a job description: calculating pi for a living.

@archivist17 Жыл бұрын

Pi Makers. Like Fray Bentos.

@vigilantcosmicpenguin8721 Жыл бұрын

Well, Emma calculates pi, and Matt just Parker-calculates pi.

@arandomdiamond2 Жыл бұрын

Exciting!

@justarandomdood Жыл бұрын

Wow this happened a week ago :O Congrats!

@ajay_constantine Жыл бұрын

A 100 trillion!? Damn that's insane....

@JellyMonster1 Жыл бұрын

Are there other sequences (not just the first 14 digits of Pi) of say 13 or more digits that repeat somewhere else? Also, what is the name of that hyperbolic image on your wall? - I don't think I have seen that before.

@patrickskelly8517 Жыл бұрын

You'd expect any given 13-digit sequence to appear about 10 times, since the chance of it appearing at any given digit is 1/10^13, and has 10^14 "tries". If something has a 1/n chance of happening and you try n times, the chance that it won't happen any of those times is 1/e. Since we have 10n tries, the chance is (1/e)^10. So for any given 13-digit sequence, the chance that it *doesn't* appear even once is (1/e)^10, or 0.005%. The chance that it doesn't appear at least twice is the square root of that, so about 0.7%. The picture is Angels and Devils by Escher

@Moonless_Future Жыл бұрын

Of course this channel is the one that would establish itself as the go-to source for breaking pi news. Makes perfect sense.

@davidf2281 Жыл бұрын

0:27 "And the last digit of pi is zero." -- that is quite the bold statement.

@landsgevaer Жыл бұрын

In base pi it is 10.0. #qed

@davidf2281 Жыл бұрын

@@landsgevaer Touché!

@Mutual_Information Жыл бұрын

We must be careful! We'll run out of digits soon!

@MmmVomit Жыл бұрын

Interesting that as you remove a digit from meta-pi, the frequency goes up by roughly 10 times. That seems to support the idea that pi is normal. This is not proof, and math really works on proof, not evidence, but it's still a nice result.

@warrengibson7898 Жыл бұрын

If my memory is correct, pi was calculated over a weekend to a record 10,000 digits in 1948 on the ENIAC. A few years later I stumbled on a printout that only filled two pages, and have been fascinated with pi ever since.

@johnchessant3012 Жыл бұрын

Very cool, but it's that education poster behind Matt that made my day :D

@matthewdee6023 Жыл бұрын

Pi video idea: how did the change in mathematical tools/abstractions impact on the "people who like to calculate Pi" community? I'm guessing that the introduction of calculus had a big impact :-)

@Hallgrenoid Жыл бұрын

Ooh I'd like this.

@JdeBP Жыл бұрын

As I understand it, there's now a colloquial term for Derek Muller having already done a video on a subject idea for Matt Parker. (-: