Pi and Four Fingers - Numberphile

it's weird because the Simpsons only have four fingers on each hand The Simpsons should occupy a base eight world the one thing I can tell you is that there is one character in The Simpsons who has five fingers and this is why they live in a decimal world a while ago I began to realize that the Simpsons writers are very mathematical they drop in bits of maths in the series over the last 25 years and maybe the most common bit of maths it pops up in the symptoms is pie my favorite mention of pie is in an episode called Marge in Chains and the episode revolves around the fact that Marge is accused of stealing something from up whose kwik-e-mart and she's put on trial and up who is the main witness and he's in the witness box and Marge's attorney tries to discredit him by saying that his memory is not very good now up who responds by saying that in fact his memory is so good that he can memorize PI to forty thousand decimal places and the forty thousand decimal place is one when I met the writers I said all we know so how did all of this happen how did it how did it work out and one of them I think it was our gene said that he'd been aware of people's ability to memorize PI and the record at the time in 1993 was forty thousand decimal places as the roots of the reason why up who claimed forty thousand was because that matched the record at the time and I said well hat and who figured out that the forty thousand decimal place was one because this is kind of going back to before Google and and having things on tap and he explained that what they did was they contacted a mathematician who works in this area Chatwal David Bailey who is a world expert in PI and and David baby is actually invented a completely new way of calculating PI but before we do that maybe it's worth looking at some of the old ways first let's do it what did you got that bucket for to avoid my embarrassment drawing circles here is a circle generator whoops there we go right so if you want to measure PI you need to know the diameter and you need to know the circumference now the diameter is kind of easy to measure but the circumference is much harder and I think it was oh I think it was Archimedes who said well one way to begin to get a handle on the perimeter is to draw squares so you draw a square around the circle and you draw a square inside the circle now it's quite easy to measure the perimeters of a square a small square and a large square and you know that the perimeter of the circle must be trapped between those two numbers and it's a very very rough in Rayleigh calculation it's really not a clever way to measure pi but then imagine instead of using a square you'd use an octagon okay and the same thing you would do here you put an octagon inside like that and so the more edges that the polygon has the more accurate you can begin to home in on pi and I think Archimedes used 96 sided polygons in order to home in on his value of pi but that still doesn't get us very far and so eventually people begin to develop formula for working out pi Leonard Euler the 18th century mathematician came up with PI to the fourth power over 90 equals 1 over 1 to the power 4 plus 1 over 2 to the power 4 plus 1 over 3 to the power 4 plus 1 over 4 to the power 4 and so on and with this kind of formula and there are lots of of them the more terms you calculate the more accurate your value of pi now that's fine if you only need some of the early digits but if you want the 40,000 digit which is what up who wanted it's a lot of work and what David Bailey invented which is really clever is what's called a spigot algorithm and a spigot algorithm a spigot is a kind of a tap an old-fashioned word for a tap a taps drip drip drip drip drip drip and a spigot algorithm will drip you whichever decimal place you want so if you say well I want the nine hundred and ninety fifth decimal place of Pi you tune the spigot algorithm and the 99 nine hundred and ninety fifth decimal place of Pi drops out and so they called the right guy you know the Simpsons team we're talking to David Bailey the real expert you want the false ad digit David Bailey will give it to you except his spigot algorithm only works in hexadecimal so only works in base 16 so if you want pie written in base 16 to the 40,000 decimal place and David Bailey can can give you the answer so so in the end what they had to do was what David Bailey did was he just printed out 40,000 digits of pi and sent them in the post to the Simpsons office and they referred to that too for in order to check that the 40,000 digit was indeed one spigot of algorithm sounds like a work of genius is it very useful though what what person ever wants a specific digit of pi um that's a good question I mean pi is I mean there are two reasons for doing mathematics one one reason is to is to solve problems you know you might call that applied mathematics and engineers and scientists use it everybody uses it in order to get something done but the other half of mathematics is what we might call pure mathematics and it's purely there for the love of mathematics for the enrichment of mathematics and I suspect that a spigot algorithm is is really done for the love of it for trying to understand this wonderful number we call pi to other things worth mentioning about about up Pope's or up who's in the witness box he's saying that he can remember 40,000 digits of pi and that the the 40,000 digit is 1 and the Simpsons writers had got all this information from a David Bailey at NASA I tried to contact the writers of that particular episode a guy called Josh Weinstein and Bill Oakley and I I didn't talk to Bill but I did speak to Josh and I said to Josh just it's only you must be really interested in maths to put this in and he's not a mathematician and it turns out that when he wrote the script there was nothing about pile the attorney says to up ooh you don't have a very good memory and up whose response was nothing to do with pie Apple's response was oh yes when I was in India I was known as mr. memory and I've been over 400 films are made about my fantastic memory and so the original script did not mention PI but what happens in the Simpsons is that once you've done a draft script you sit down around a large table with eight or nine other writers and they pitch in and at that stage there were one or two mathematicians who said well why don't we make up whose memory why don't we define his memory by his ability to remember PI so it's the mathematicians who then crowbar that bit of Pi mania into the script the other interesting thing is that the 40,000 digit of pi is 114 thousand decimal place of Pi is one but that's only in decimal if you have other bases you will have other digits popping up in that place so by this stage we're thinking well okay the Simpsons world is a decimal world and there's nothing wrong with that my world is decimal your world as decimal the world seems to be decimal in the Simpsons however it's weird because the Simpsons only have four fingers on each hand and if you have four fingers or three fingers and a thumb on each hand let's do that that's eight digits The Simpsons should occupy a base eight world so why are they messing around with Pi in decimal when they should be messing around with pi in base eight in octal so when I was over in Lausanne geez thinking about this and talking to the rioters you know why or why is it that the characters got eight fingers why is this decimal and you know I soon realize it eight fingers in the cartoon world is a given Mickey Mouse had eight fingers Felix the Cat I think at eight fingers they all have eight fingers because if you have five it looks like a bunch of bananas apparently the one thing I can tell you is that there is one character in the Simpsons who has five fingers and this is why they live in a decimal world because the one character in the Simpson who has five fingers on both hands is God and God determines how numbers work and therefore the numbers in the Simpsons are decimal not octal in case you don't know but you probably do if you watch numberphile Simon has a book out all about the Simpsons and their mathematical secrets it has not one but two chapters about pi so why not check it out and I'll put a link in the video description if you want to have a peruse of some reviews and maybe make a purchase I've already got my signed copy and of course here at numberphile we've done loads of videos about Pi in the past and I'm sure we'll be doing more on the future I'll put a link on the screen for anyone that wants to check some of them out

Channel: Numberphile

Views: 1,308,430

Rating: 4.8935266 out of 5

Keywords: Pi (Number), Simon SIngh, The Simpsons (TV Program), digits, numberphile

Id: K305Vu7hFg0

Length: 9min 39sec (579 seconds)

Published: Thu Oct 31 2013