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  • Today we have our committees.

  • Cattle problem.

  • It waas for a time, probably the most famous unsolved problem in math.

  • But now no one has really ever heard of it.

  • But it's a great story, and I'm gonna tell it to Brady.

  • Wait, do we need to know who are comedians?

  • Is?

  • Yeah, I think everyone needs more communities is, like the most best, brilliantly, most brilliant of the ancient mathematicians.

  • And this problem was not known about until in 17 73 at the German Intellectual.

  • He was a play rides his famous intellectual got hold Efraim Lessing, who at that time was the librarian at Val from Bootle, which is the great North.

  • You're appear in library and discovered a manuscript written in Greek that no one had ever seen or picked up.

  • Will Commentated commented about before in this manuscript, it said it was a letter from our communities to era tossed Anees, who was his contemporary, actually, at the Library of Alexandria.

  • On it was a poem rift of 22 rhyming couplets in Greek, which said, This problem and I'm gonna my ancient Greek isn't very good, so I'm going to transcribe the problem into language off today.

  • So the sun God quite nicely do a graphic of the sun.

  • God had a herd of cattle.

  • Call the cattle problems wearing your the sun God, I have the wrong God.

  • I had a herd of cattle and our comedians from Syracuse.

  • Syracuse There it Sicily.

  • So the sun god had cattle and the cattle was on the Isle Island off Sicily.

  • There are bulls in there, a cows and they come in different colors.

  • And this is how we describe them.

  • The droid balls.

  • Ah, half plus 1/3 off the black balls plus the levels, the black holes 1/4 plus 1/5 off the Dapple balls.

  • Now, my first comment here is that this is an absolutely terrible problem.

  • It is so boring.

  • It's incredibly dull, and you're gonna have to speed it up.

  • But actually do carry on because we do get to why is actually really quite fascinating.

  • White bulls plus black pulls equals square number and the dappled bulls plus the bulls equals a triangular number, and we have it.

  • So just to point out a few things here, that might be interesting.

  • We've got bulls, male, cows, female.

  • We have only got unit fractions are square number, so that's the number that's a square of another number.

  • So 149 16 25 etcetera.

  • A triangle number you must have done many things are tracking numbers, but they are the ones that triangle off.

  • So that's one and then three and then six.

  • And then Ted, basically, when you doing dots together, makes a triangle and heard is cows and bulls together both genders.

  • So you have this.

  • I'm looking at it, and I get the school of dizzying effect that this is the world's most horrible simultaneous equation.

  • Question.

  • What we would do is that we would write it all out called White Bulls Ex Black Balls.

  • Why untapable something else there?

  • None.

  • None equations in, however many unknowns and we start working at.

  • So what happened back to the story when Lessing in 17 73 found it?

  • Hey wasn't mathematician and he went to his local mathematician and said, Can you solve this on Dhe?

  • It's true.

  • What you do is let's go because the first section is really straightforward.

  • This is something that we could probably do.

  • Many people really could probably do.

  • You would get an answer off.

  • It's just over 50 million cattle.

  • The herd has about 50 million, which means on Sicily, because I'm his son King and I want to know ham eggs.

  • My heard you've got one cattle, one piece of cattle, one animal for every about 500 square meters.

  • Okay, but this is a problem written as a poem and in this kind of commentary on the problem as we g o.

  • And he says, Um, don't get smart with and say that it says Even if you've got this far, thou cannot be regarded off high skill.

  • So there's some idea.

  • The president sentence puzzle is kind of taunting you.

  • Let's then try and include the White Bulls.

  • What's the black girls is a square number.

  • This is something that was also solved shortly after it was discovered.

  • And now the solution is 51 trillion.

  • So that number in the herd is 51 trillion.

  • In other words, if you're trying to put a ll these cattle on the Isle of Sicily, Sicily is completely covered in cattle.

  • You can't see one square sentence within a millimeter of Sicily on the cattle are stacked dozens if not hundreds of meters high.

  • So it's this massive mound off groaning moving cattle now on to the ninth line, because now is where things get really difficult.

  • In fact, if you include the line Dapple bulls, plus yellow balls is a trying the number.

  • This is now beyond the realms off 18th century mathematics.

  • No one can solve it on it becomes a celebrated problem.

  • It gets around.

  • Is the Arkham Edie's problem with so close, so close to solving it?

  • But no one can do it.

  • The beginning of the 19th century Gas is the great German mathematician.

  • The best off his age is rumored that he has a proof, but no one ever sees it.

  • And it's only 100 years after the puzzle was first discovered that the first person kind of gets the answer.

  • And this is August am Thel, a German on of a German mathematician, and he doesn't get the full of sir.

  • He just realizes that the answer begins with the digits 766 and continues for another 206,542 digits.

  • Okay, so how big is this number?

  • This number in terms of the herd on the Sun King on Sicily.

  • You're gonna start layering Sicily, put the bottom layer off cattle dappled yellow, whatever.

  • Start building them up.

  • You're gonna go.

  • You're gonna go out the atmosphere you're gonna then go beyond the moon.

  • You're actually going to go beyond the solar system at the galaxy and go to the end of the universe, and you're only just beginning is gonna blast through the end of the universe.

  • In fact, this number is so big that if every cattle waas an atom, they know enough atoms in the universe as we know it.

  • It is such an enormous bonkers number beyond all comprehension.

  • Okay, so why would we ever want to know this number?

  • Well, some people did so a couple of years after three friends in America decided they wanted to tackle this problem and they spent four years on this problem.

  • The only got another 44 digits.

  • Imagine that.

  • So this is something that people wanted to know.

  • It was this kind of kind of crazy Arkham Edie's number.

  • It was only in 1965 with the advent of soup supercomputers that the full number was actually drawn printed out in its entirety, and it took about seven hours on stretched to 42 sheets of a four.

  • So what can we say about the authorship off this problem?

  • Lots of people said, How do you know are comedians?

  • Well, we don't know.

  • All we have is the problem, and it states that it's from our communities to air.

  • It's Austin.

  • Some academics, some researchers think, Yeah, who know that probably isn't.

  • But a lot of them do on one reason why it might, because we know that our comedians is really, really interested in massive numbers.

  • In fact, in the Sand record or one of his most famous kind of treaties is he invents a whole system of numbers to try and describe, try and count the number of grains of sand there are in the universe.

  • So we already know he's into this area.

  • And maybe this problem wasn't something to be solved, but just a demonstration kind of the awesomeness of mathematics to show that with nine very simple statements, statements using nothing complicated, you can actually create a problem that describes a number utterly beyond comprehension on that is going to take 2000 years to solve.

  • I mean, surely that some kind of genius If you wish to please the sun God, Well, why not check out his latest book?

  • So you think you've got problems?

  • It's by Alex Belus.

  • It's full of puzzles and teasers like the one we just discussed.

  • It's the latest of Alex's mathematical books, and I'll include some links in the video description, along with more of our videos here on number five that we've made with Alex over the years.

  • Thanks for watching.

Today we have our committees.

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アルキメデス数 - Numberphile (The Archimedes Number - Numberphile)

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    林宜悉 に公開 2021 年 01 月 14 日
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