Pi and Four Fingers - Numberphile 

I can remember every digit of 1/3 far beyond the 40,000th.

when i was a child i thought characters have 4 fingers so they have no middle fingers (it was a good theory at the time ._.)

"and then you draw an octagon" *scribbles everywhere*

This reminded me of the episode "Bye Bye Nerdie" where Frink was trying to make an audience of scientists to stay quiet, so the shouted "Pi is exactly three!"

3:07 - Me trying to solve math problems.

It's not about the fingers looking like a bunch of bananas, which can certainly happen. It's that in the early days of animation, they figured out that cutting down on the number of fingers cut down on the man-hours and money it took to tween them. For lovers of math, think about it as 2 fewer fingers to draw times 12 frames per second times 60 seconds times 10 minutes. That's 14,400 fingers you didn't have to draw, quite an economical difference.

I remember an episode where burns is talking about his grandpa, reminiscing about the past when they used to split atoms by hand. Showed an employee busting atoms with a hammer and his grandpa catches the employee stealing atoms by hiding them in his pocket. LOL

I love how Simon Singh goes into so much detail... It really makes maths so cool

3:06 octagon is an amazing shape

all I could concentrate on throughout this whole video was this guy's haircut

in the simpsons, Homer is actually the world's leading specialist in pie

i need that circle generator

The spigot formula that Simon refers to in the video is wrongly attributed to Bailey. It was actually discovered by Simon Plouffe (en.wikipedia.org/wiki/Simon_Plouffe), who has regretted sharing that discovery with Bailey and Borwein. Incidentally related to this video, Plouffe was a former world record holder for memorizing digits of pi to 4096 digits, which stood until 1977. Below are Simon's actual words on the topic of sharing credit of his discovery. It's a bit gut wrenching. It came from here: groups.google.com/forum/#!topic/sci.math.symbolic/a3kVKVYJhgc ---- This note explains the story of the so-called Bailey-Borwein-Plouffe algorithm and formula. The story began many years ago in 1974 when I wanted to find a formula for the n'th digit of Pi. I was studying rational and irrational numbers. With my calculator I was computing inverses of primes and could easily find a way to compute those inverses in base 10 to many digits using congruences and rapid exponentiation. Since it appeared impossible to do the same for Pi, I wanted then to find a simple formula f(n) that could compute the n'th digit of Pi. I had that idea for 20 years. Since the computation of Pi looks more complicated than the number E , i.e. exp(1), I studied a way to compute that number instead. At that time (around 1983), I had a simple Basic program that used a spigot algorithm to compute E, as expected that algorithm worked but of course but was taking an increasing amount of memory. My question was : why can't we do it for E or Pi or any irrational numbers like sqrt(2). It was during the year 1994 that I began to compute arctan series but I did not realized that this meant a lot. I was able to use an algorithm to compute arctan of 1/5 with fast exponentiation without realizing that it could compute arctan(1/5) in base 5 very fast since the rapid exponentiation was natural in that base. Later in 1995, around august 7 of that year I suddenly realized that log(2) was fast computable in base 2. Since I had a bit of experience with spigot algorithms and also my little Basic program to compute arctan, it was not difficult to adapt the algorithm to log(2). In the next few days I made my first program : A program to compute log(9/10) in base 10 using a very small amount of memory and very fast. The program had 432 characters long. That discovery was a shock to me. I realized that I had found it yes but it was not new to me since I could do arctan(1/5) easily too but it took me 2 years to realize it. This is where I began to use Pari-Gp, that program could find an integer relation among real numbers (up to a certain precision), very fast. During my stay at Bordeaux University in 1992-1993 I perfected that program I had that could interface Pari-Gp and Maple. That little Unix script had an enormous advantage of flexibility because I could set up a series of real numbers to test among 1 unknown. At that time I was beginning to find new results, the programs were able to find identities. That program was the one that found the formula for Pi in hexadecimal (or binary). I also used another one : PSLQ. It was a good program but a bit cumbursome to use since it is written in fortran. Nevertheless I made an interface to Maple too. Pari-Gp was by far easier to use and faster for small cases (up to 10 real numbers at the time with 100 digits precision was enough for those kind of problems). This is where I made the biggest mistake in my life : To accept the collaboration of Peter Borwein and David H. Bailey as co-founders of that algorithm and formula when they have found nothing at all. David Bailey was not even close to me when I found the formula. He was added to the group 2 months after the discovery. I was naively thinking that I could negociate a job as professor at Simon Fraser University, which failed. I am very poor at negociations. I remember that day when the Globe & Mail newspaper article went out in October 1995. I was at Jon borwein's house and he had a copy of the newspaper in hand. This is where I asked him to become a professor at SFU. He simply replied right away < don't even think about it >. I thought, this is the best chance I will ever have to become a professor there, since it failed, I decided that I had to leave that place. I was very frustrated at that time, in late 1995 after the discovery. I realized that many small details where terribly wrong. They were getting a lot of credit for the discovery and I had the impression of not getting anything in return. My strategy failed. One of those details was the article of the Globe and Mail, I asked Peter Borwein : why did they putted the photo of you and your brother on the article ? Your brother has nothing to do with this!. He simply replied that the Public Relations at the University made a mistake. Later that year, I was invited to a ceremony in Vancouver for the CUFA (faculty of the year Award). This is a prize with plaque and mention that those 2 brothers received for the discovery of the formula. They simply mentioned my name at the ceremony and I received nothing at all. They made a toast to the queen of England, I did not stand up. In late 1995, there was that Canadian Math Soc. congress in Vancouver, I was not invited to talk about the discovery. There was even a guy (Stan Wagon) that said to me, I don't know if you have anything to do with this but in all case, this is good for you isn't ? Then in 1996, I realized that if I get up at night to hate them it is a very bad sign, it means that I have to leave that place (Simon Fraser university). I was convinced I had no future at all with those 2 guys around. I was making serious plans to leave. The story of the formula (my formula), was not the only one. The same thing happened with the ISC (the Inverse Symbolic Calculator). The story is even more ridiculous. I opened the site with my constants in July 1995 and it was an immediate success. The 2 Borweins had nothing to do with that thing, I had made the tables and all of the Unix programs to run it. The precious help I had was from Adam Van Tuyl, a graduate student, he made most of the code behind the web pages, later Paul Irvine made some additional code. At that time the local administrator of the lab. tried to convince me to stay even to pay me for maintaining the ISC, I refused. I wanted to leave with what I had : my tables of real numbers and sequences I worked for years (since 1986). This is why I opened the Plouffe Inverter with my name in 1998, to keep what was mine. When I realized that I was about to loose the paternity of the ISC, I left in march 1997. I went to Champaign Illinois to work for Wolfram and Mathematica. (this time it took me less time), that one was worst than the 2 brothers combined. I simply left as soon as I could, 5 months later. Peter Borwein wanted very much that I do a Ph. D. on the ISC but he wanted also to publish (with his name of course) an article before I deposit the thesis. Again the same story was going on, these 2 guys are so greedy I can't believe it. The behavior they had with me was not exclusive, especially Peter Borwein he was the same with most of his students, especially the good ones, sucking the maximum. Jon is the same but he has more talent in politics (more money too). He is good but has a tendency to site himself a lot. He thinks that if he had the idea of the sum of 2 numbers at one point in his life then all formulas in mathematics are his own discovery. About David H. Bailey. He came after the discovery of the formula and my small basic program , I had also a fortran version. This is where Peter Borwein suggested to add him as a collaborator to the discovery since he contributed to it (as he said), this is my second big mistake. Of course he accepted to co-write the article, who wouldn't ?! David H. Bailey (and Ferguson) are the authors of the PSLQ program. That program is the version of the Pari-Gp program. I used it a little it is true, but what made the discovery was pari-Gp and Maple interface program I had. So actually, that person has nothing to do with the discovery of that algorithm and very little to do with the finding of the formula. The mistake was mine. Saying that Bailey found the formula is like saying that the formula was found by the Maple and Basic program. I tried very hard to correct the situation avoiding the subject of the actual discovery of the algorithm and the formula, I made an article in 1996 for the base 10. I thought naively again that this would re-establish the situation, it did not. I almost accepted to do a film at one point in 1999 when a certain guy from England that wanted to make a movie on Pi and the discovery of the formula. he asked me if I would accept to talk about my with the Borweins. I did not wanted to go in that direction, I should had. There was that book of Jean-Paul Delahaye (le fascinant nombre pi) that mentioned the Plouffe algorithm and formula because I told him part of the story. In some way I was afraid of revealing that enormous story. Why was I so naive ? I had a previous collaboration with Neil Sloane and the Encyclopedia of Integer Sequences and the web site, this was really a big success and Neil is the person I respect the most in mathematics so this is why I thought (wrongly ) that my collaboration with the Borweins had to go well, a big mistake. Why do I write this ? To tell the truth and also the arrogance of those people makes me sick. Will I gain something from this ? I don't care, I have nothing to loose. Simon Plouffe Montréal, le 22 juin 2003.

wait... life of pie was really about Apu?

Soo if i calculate π on a mac, does it make it an apple π?

Now... actually the interesting question is... what is pi's 40.000th digit in base 8?

Now I'm very curious if the 40,000th number of pi in octal base is also 1. Can someone run it?

I love how he's using a colourful kid's bucket to avoid embarrassment :)

I'm Cambodian, my early life was in base 5. when I was younger I was able to easily go from base 5 when talking with my parents and base 10 at school. Now a days I have to count if i want to remember what the Khmer equivalent of an English number after 15 lol.

I heard a rumor though, that in the episode "22 Short Films About Springfield", there aren't 22 shorts, but only 18 which is written as 22 in base 8. Is there any truth to that, indicating that they do sometimes use base 8 in The Simpsons?

3:06 for rage quit! XD

I bought this guy's book. Awesome read.

Keep on "splitting atoms" for the fun of it!

I like the circle generator. Where can you buy such a device? 2:12

They've done a base 12 video explaining how old societies used base 12 and how they counted with just 10 fingers. It's actually one of my favorite videos they've done.

Why is Simpsons not octal? I dunno, why are there myriad number systems throughout history not based on 10? 12, 20, 60, 27, etc. have been used at one time or another. I mean really, if number bases were based solely on digits then I feel sorry for the poor Sumerian that came up with base-60.

Interesting, but are we really a base 10 civilization because of our fingers. Haven't we used various bases throughout history? en.wikipedia.org/wiki/List_of_numeral_systems I'd argue that god has 5 fingers per hand because that would represent a human being the god of the cartoon.

i think that the Simpsons live in a base 10 world because the writers have 10 fingers

i tried to post the first 100,000 digits of pi, youtube responded "there was a problem saving your comment" XD

"There are two reasons for doing Mathematics. One reason is to solve problems. We might call that Applied Mathematics, and engineers use it, and scientists use it, and everybody uses it -- in order to get something done. But the other half of Mathematics is what we might call Pure Mathematics. It is purely there, for the love of Mathematics, for the enrichment to Mathematics. I suspect that the Spigot Algorithm is really done for the love of it, for trying to understand this wonderful number we call Pi." Well said. Well said.

"Circle generator". Awesome.

This guy's hair. It's so awesome.

Well I'm not fuckin Einstein...and I never went to any school.. (we don't have them worth the name in eastern europe) but I allways for some reason dream...that I knew math. But...then again...after 4 years of"education"..we were all suposed to work in some factory...girls in childcare or as nurses at the best Now I am to old..but still..the stuff fascinated me for all of my life. So go on..make kids think for themselves. .to..dream.. You do a good job:-)! Ceep on doing it right:-)!

2:12 Students, get your compasses: Me:

Just a thought... if the spigot algorithm is designed for base 16, and someone wanted to find the forty thousandth digit of pi in base 8, it would not be hard to figure out which 3 bits would make up that octal digit in the binary representation, which can be derived from hexadecimal 4 digits at a time. So for example, if we wanted to find the 21st octal digit of pi, we could start with the 16th hexadecimal digit and simply remove the high order bit. That is to say, the 21st octal digit of pi would be the 20th octal digit after the octal fraction point, which would contain as its low order bit the 60th binary digit after the binary fraction point since there are exactly 3 binary digits to each octal digit and three times eight equals sixty. Likewise, that 60th binary digit after the binary fraction point would also be the low order bit of the 15th hexadecimal digit after the hexadecimal fraction point, since there are exactly 4 binary digits to each hexadecimal digit and sixty divided by four equals fifteen. So... Pi in hexadecimal to 16 digits, including 15 digits after the fraction point = 3.243F6A8885A308D Straight forward hexadecimal to binary conversion... ___3. 2 4 3 F 6 A 8 8 8 5 A 3 0 8 D 0011.0010 0100 0011 1111 0110 1010 1000 1000 1000 0101 1010 0011 0000 1000 1101 Pi in Binary to 62 digits, including 60 digits after the fraction point = 11.001001000011111101101010100010001000010110100011000010001101 Straight forward binary to octal conversion... 011.001 001 000 011 111 101 101 010 100 010 001 000 010 110 100 011 000 010 001 101 __3. 1 1 0 3 7 5 5 2 4 2 1 0 2 6 4 3 0 2 1 5 Pi in octal to 21 digits, including 20 digits after the fraction point = 3.11037552421026430215 ...so the 21st significant digit of pi in octal, or in other words, it's 20 digit past the fraction point, would be a 5. In hexadecimal, the high order bit of each digit is valued at 8, so since in this particular case the high order bit of the 15th digit after the hexadecimal fraction point is not part of the 20th octal digit past the octal fraction point, we get D-8=5. Sorry I couldn't find a way to format the conversions in a mono-spaced font as I had intended. If anyone wonders why I put the spaces in where I did, they can copy it to a monospaced text editor like Notepad to see.

Its also just a lot easier to animate and draw three fingers and a thumb, it still creates all the gestures you need them to make, still nice to know and cool they actually looked it up

7:59 I am tired of jokes about my giant hand. The first such incident occurred in 1956 when...

At 2:26 Archimedes chokes on his beer, overhearing someone explaining how you can measure volume by dipping in water and weighing what falls out.

Sooo... in 1993 there was no file that could have been searched to show the digit 40000 of Pi? surely they had calculated far more than that and computers where used a lot already at that time.

I don't think I could describe someone as a "...world expert in Pi..." and keep a straight face. 1:40

damn it i'm supposed to do my math homework but I can't seem to get of watching these videos xD

Actually, for an omnipotent entity, that would be pretty easy to do. The easiest way would be to redefine the values of the symbols. If that is cheating, another approach would be to violate the law of conservation of mass and energy, so that whenever a set of 2 elements is united with another set of two elements, an extra element appears in the union set.

The Doctor Who 50th anniversary is this month, so why not do an episode on numbers in DW? There was an episode entitled "42" (for many numerical reasons) in which happy numbers and primes figure.

I sow the video and I was like "wait, is this Simon sing? I love his books" and yes

3:03 nice octagon

I‘m currently studying to become a elementary school teacher. In my math class we repeated to whole curriculum for elementary school math WITH A BASE 8 SCENARIO. Our professor wanted us to realize how difficult it is for young children to start thinking in the 10-system by forcing us to imagine we only had simpson-like-hands with 4 fingers on each hand only.

lesson to be learnt: Mathematicians have too much free time.

Numberphile did a video about counting in base 12. Look for it, it was pretty interesting. Basically, count the count on the phalanges of your non-thumb fingers. 3 phalanges per finger, 4 fingers per hand, 12.

Actually There Are Two Characters That Have Five Fingers God And Jesus :P

I memorised Pi to 88 decimal places, as that was all I had available. And I couldn't even remember whether a thief was wearing gloves or not, or even the colour of his clothes.

Cool episode. But the guy seems to erroneously think that finger number is _deterministically_ related to base systems - and that's not the case. After all, all humans have 10 fingers, but many cultures have base 20, base 5, or even base 60 systems...

3:06 when you give up drawing and just... explode

It's silly to say that the number of fingers on each hand is the reason we use base 10. It's purely cultural. Even looking at older English, you can see that numbers used to be base 12 (you don't say 2-teen, you say twelve). The Mayan culture used base 13, there are other cultures that use base 20, etc... The fact that the world uses base-10 today probably has more to do with the Arabic numerals being base 10, which is what has become the standard for representing numbers worldwide.

There are cultures where people use base 12 numbers - they count left-hand out, right hand out, for one and two, then extend a finger for 3 and so on, another finger for 4. If the Simpsons count like that with 8 fingers and two hands they would also live in a decimal world.

Can't you use a string to measure the circumference?

I once taught a math class that was aimed at elementary school teachers. One student asked why we learn to do math in base 12. Besides the real reason, which was to understand how the structure works, I said it will also come in handy in case we make contact with a species that has six fingers on each hand.

Jesus also has 5 fingers.

I have posted this reply on several pi-related sites, but this looked like another spot it might be applicable. I applied the modified series for the value of pi = 4/1 - 4/3 + 4/5 - 4/7 + . . . . I then programmed a 1-million-row EXCEL spreadsheet to calculate the running sum with the addition of each successive fraction. By the way, if presented all at once, at the size the digits appear on the screen, the spreadsheet would stretch for 5 miles, top to bottom. After 1-million fractions, I only found the first 6 decimal places of pi. It is well known that this series converges very slowly. I found that log10(no. of fractions)~=significant number of digits of pi. It would therefore, take the sum of approximately 10^14 of these fractions to generate pi to 14 decimal places. Upon averaging the subsequent pairs of fraction sums and creating a second column averaging each pair of sums in the initial column, you get a sum that more quickly converges on the published value for pi, although it is still very slow. I found that if you repeat the average of averages calculations, generating new columns of fraction sums, you can greatly increase the rate of convergence for the value of pi. After 16 columns of such average of averages, (this is optimum for determining the first 14 decimal places), you will arrive at 14 significant decimal places of pi requiring only the first 33 fractions, instead of the projected sum of 10^14 of these fractions. While this is a brute-force-and-ignorance approach, I have not seen this accelerated method presented anywhere else.

Did i ever tell you the definiton of insanity?

I like the way you call it "Circle Generator"

Simon always reminds me a bit of Earthworm Jim.

Watching this video again and wow that formula is amazing. Plugging in the first 3 terms, we get π > ~355 billion + 2.2 billion divided by 113 billion + 0.7 billion

Remembering that the 40,000th decimal place of pi is 1 doesn't require much of a memory. Did Apu claim he knew all of the preceding decimal places of pi? And was he tested on that?

There's a use for the spigot algorithm. You can verify the result of other algorithms that compute the whole sequence by only calculating the last digits and comparing them to the output. That's way faster than calculating the whole sequence with another algorithm.

Is Pi an infinite number?

I sort of "formulized" Archimedes' method: Pi = n*tan(360/2n) n = number of sides. This formula basically finds half the perimeter of a shape with a radius of 1, half the perimeter because it is the radius not the diameter. If you use say 1,000,000,000,000 for "n" the answer is very close to pi.

So what's the graham's numbers'th digit of pi?

He explains things so elegantly...

Surely the easiest way to find the area of a circle would be to use SIMPSONS rule. Boom boom

How can you memorize 40,000 decimal places, and still have place for knowing how to tie your shoes? That's insane

That moment when you are watching this at 3:14

As this video progressed, I was really, really hoping the producers of the Simpsons had buried an Easter egg in Apu's line, by determining that the 40,000th *octal* digit of pi *also* happened to be 1, so the line worked in either base and made it ambiguous as to which base the characters were really using.

Jesus also has 5 fingers on each hand in the simpsons Alltime10s

Although I have never been a fan of the Simpsons, this is a fascinating video in which I enjoyed greatly- the promise of mathematics in the Simpsons is almost enough to convince me to now watch them. Thank you, Numberphile, for taking the time to create these videos for the love and understanding of math.

Mmmm.... Pie..... -_-

Our maths teacher played this video on the projector in the background while we worked!

also jesus i belive has 5 fingers

6:04 When you love maths so much that your forehead makes a π.

life of pi....stole this..... from the simpsons???

Stupid question here but is there any base system that would make pi not an irrational number?

Whoah... mind blown... why? Because I've never learnt about this 'base' stuff before. It's only just occured to me now, the link between the word 'decimal' and the number ten ('dec' and all that). I have actually wondered lately why it's the number 10 which has to be so special. Why it's 10 that is so significant. 1 - 10 - 100 - 1000 - etc. But why 1 and 0? Why is it 1 2 3 4 5 6 7 8 9 10... repeat in expanding pattern? Why 10 digits? Obviously, explaining my question is a bit difficult due to some kind of explanatory gap or something. I'm just trying to understand why maths works, and why it works with this numeric system. Specifically in reference to 1 and 0. Is this whole 1, 0 thing significant only because of the numerical language we formed to use in order to express an understanding of the world of mathematics? Or would this 1, 0 thing be significant regardless of the form of the numerical language we use to understand maths? Not to the mention the quetion of how it is significant at all if this significance isn't an illusion for some reason or other... Yes, too many questions and not enough understanding. But basically I'm just asking Why and How in terms of mathematics and the way in which we express understanding of mathematics.

Pi with Pie is the first numberphile video I watched.

God...

I´ve seen a show where the Simpson creators simply say that they have 4 fingers because it´s alot faster to draw/animate

lol wasted all the time for the cop out of "God" being the reason.

"bucket" == "circle generator" :D at 2:02

Tau is better!

Kind of a silly premise, fingers aren't the reason we use a decimal system. The first practitioners of advanced maths used base 60 (because it's relatively easy for fractions and calculations). Base 10 is also relatively easy to use but has the added bonus of being easier to write. It's interesting to note that humans have also used base 5, 12, and 20.

I love it when my worlds cross. The writer Josh Weinstein is the original Tom Servo from the first season of Mystery Science Theater 3000

Well, pi is an important number, indeed. That extreme precision is also important in important calculations, not only for pi but for many other measurements. Without this level of precision it should be impossible to spaceships land on the moon, per example, and they would deviate from correct routes by thousands of kilometers. Another example is the recent landing at the surface of a comet

The day Brady decides to make a video about the Euler's number, I'll die happy.

Great Video Numberphile, I love all of your videos

By far the funniest pi joke in the Simpsons is when Dr. Frink is trying to get everyone's attention so he yells out pi is exactly 3.

The guy, for some strange reason, reminds me of Vaas from Far Cry 3, giving a very much more sophisticated version of his speech about how he realized people all around him do the same thing over and over, expecting things to change :D

"D'zero!" Thanks for the Reply and Hab a great day! Mark

While not practical, I really enjoyed the info provided in the video.

We use a base 10 system. There are 10 basic numbers (0 through 9) that we put together to make all the other numbers we use. We just put those numbers in the different places (ones, tens, hundreds, etc.) So the number 12 in base 10 really means there is 1 ten and 2 ones. In base 8, that number would be 1 eight and 2 ones. In base 7 it would be 1 seven and 2 ones.

I've really enjoyed these video on The Simpsons and maths

In decimal (dec), "25" means 2x10 + 5, which is twenty-five. Octal (oct) is base-eight so, in octal, "31" means 3x8 + 1, which is also twenty-five.

This is awesome. There was a big article about Simon Singh's work on the Simpsons in a big German newspaper this week, which I really enjoyed reading. Although I knew it all from the channel already :D thank you for sharing your thoughts with us on YT and not only writing books (which, of course, is great as well)