How to pronounce “pythagorean” in English

reason I’m educating you yourself. Do you understand?' 'I think so.' 'Do you know the famous poem by Frost about the two paths that "diverged in a yellow wood"?The Pythagoreans called it the Furca Pythagorica, the Pythagorean Fork. They represented it by the letter upsilon. Upsilon resembles our capital letter Y, right? It’s forked. Youwill face the Furca Pythagorica many times in your life, Ambrose. I’ve led you down a different branch of the fork than nearly anyone else will follow.'

We know that calculus is useful, but they asked themselves, "What possible use could there be for things like prime numbers?"Well Pythagorean ideas about numbers and their supremacy; all this numerological gobblygook seems little silly at first blush, but Pythagoreans were even writing prayers to numbers liketheir Tetraktys. But the earth shook under the feet of those number theorists a few decades ago. Prime numbers suddenly found a use; protecting secrets, cryptology.

of fourness. Anyway you see it's a pyramid of ten dots aligned in four rows. This one symbol forthe Pythagoreans embodied the foundations of the universe.So let's start with music, for instance. We number the rows as here. And now look at the ratios that those numberings define; the three different ratios defined by the Tetraktys.

It doesn't affect us.Learn your Pythagorean theorem.So let's not be bored.

So if you practice that, you can save literally ones of seconds of your life on a daily basis.And using the Pythagorean's System of Triangles you can show that.

So it's always wisdom text regarding hearing well.So this so-called Pythagorean theorem has no basis in fact, so let's get rid of it.

And 6 is equal to 1 plus 2 plus 3, which are its divisors.And the Pythagoreans especially were interested in number theory from that point of view.But as a real theoretical subject in mathematics, the only really important number theorist in the ancient world

our periodic chart in chemistry or perhaps even a little like string theory, only much cruder and, and much more powerful.So the Pythagoreans are the villains in our story, if they really are villains, which isn't at all clear. Now of course the National Security Agency isn't accustomed to dealingwith incarnations of the god Apollo, so they bring in an un, unusual young man named Ambrose Jerusalem.

'So do you think the feelings are lies? Are they bad?' 'No, not bad, Ambrose. Quite the opposite. They're too important to be badly handled.The successors to the Pythagoreans went wrong. They tried to reduce them to a superstitious system, to explain these poetic and highly individual experiences in terms of a simplisticuniversal, like reincarnation or numbers. I can’t prove it, but the original Pythagoreans to my mind clearly believed in living in the world. Memory—historical, personal—of

like e=mc2, right? It's got the same sort of simplicity and, and elegance.Now the Pythagoreans believed in the power of a very particular type of mathematics, based on integers. And closest in spirit to what we would call number theory today. Mathematicianswho specialized in this area used to pride themselves on studying the most useless form of math. They believed that their discipline enjoyed a kind of peerless intellectual purity.

to try to hunt down and destroy a group that may be older and wiser than we are and could bring a certain order and moral force to the world.So who are these Pythagoreans and how do they break the RSA algorithm? And what does ancient Greece tell us about our own evolving digital world and authenticity?These, these are the questions at the heart of 'Tetraktys'.

Yeah but that was the thing that was quoted to us so frequently.Why do I have to learn the Pythagorean theorem.What is it good for anyways.

And he couldn't fit in his Platonic model.So he returned back to the Pythagorean thinking, after realizing that Plato was a Pythagorean.So then he started assigning-- this is own handwriting-- he started to assign to the velocity-- here we're looking at the sun and a planet

In other words, why is Ambrose at the right intersection of ideas?The NSA believes that the cult of Pythagoreans has used its mathematical prowess to break a cryptographic algorithm known as RSA; many of you are probably familiar with it. Namedafter its inventors at MIT in 1977, Rivest, Shamir and Adleman. Here's a picture dating

So let me read a last bit from the book. This, this bit needs a little bit of explanation.The messages left by the Pythagoreans like the one left for Secretary Abel have been essentially flawless, but Ambrose and the NSA noticed a typo in one of them. In onemessage the word "Syracuse," like the name of the town in upstate New York, which is also the name of an, a city in the ancient world, Greek city, is misspelled. Somehow

Syracuse, Syracus. Is it really such a big deal? Couldn't it just be a spelling error or a typo?' 'It could be a typo. In that case it may not mean much, but every other piece of writingwe've seen from the neo-Pythagoreans or that I have at least, has been more or less flawless.' 'True. But a typo?' 'That doesn't answer your question, does it?''Can a single letter be important?' 'Yes, absolutely.' 'There's a town in northern Italy called Cortona. Ancient tradition asserts that the tomb of

seems to be coming to a head.But it's not clear whether the Pythagoreans are a malevolent or benign force. After all these are the people who tried to establish Utopia many years ago; the bringing a certainbeauty to the world and reviving classical ideals.

grew into stars and galaxies, that grew into the structure.So the idea here is to sort of take the Pythagorean idea of music of the spheres and bring it into this modern context.Except the question is that the music that we're going to get is not necessarily only harmonic.

But the fact that someone-- there are people who are smart who think these.Pythagoras who's the beginning of Greek mathematics had this Pythagorean brotherhood.

And this mysticism that we really can sort of date back to Pythagoras as influential as his sort of mathematical legacy. So and also sort of Gematria which came afterwards,the Masons all kind of has this sort of Pythagorean basis. In fact the Masons is essentially modeled on the Pythagorean Brotherhood which was this sort of cult like group where Pythagoras lived.So the reason why went to see Jerome is that he is a numerologist. You go to him, you pay lots of, thousands of dollars and you tell him what you're called, you give him your

be alone.'Now where does the mathematical view of the Pythagoreans come together with modern cryptology?In other words, why is Ambrose at the right intersection of ideas?

So this is the cornerstone of the RSA algorithm; this problem of factoring as it's called.And this is the problem that the NSA thinks that the Pythagoreans have solved in order to crack the RSA algorithm.As the story gathers pace, messages like the one that Secretary Abel came across multiplied.

The NSA ends up plunging into various types of computer forensics to figure all of this out and actually a remarkable thing happened while I was writing this story. I was makingup certain forensic techniques in Tetraktys to track down the Pythagoreans as it were, when this patent suddenly surfaced describing exactly the techniques I was developing inthis fictional context. Only I hadn't filed that patent; it was the NSA. So it's just one of these wonderful coincidences I guess I, I happened to, to divine what the, what

to how you use it in real life, in the world, jobs, whatever it may be.Apparently, every kid in America hates the Pythagorean theorem.Maybe you guys, I think this might be the one place that doesn't hate the Pythagorean theorem.

That could be your new HR hiring test.Dude, did you hate the Pythagorean theorem as a child.If not, you're hired at Google.

So if you practice that, you can save literally ones of seconds of your life on a daily basis.And you can prove that for two main locations using nothing more complicated than Pythagorean's System of Triangles.

He was studying an ancient Greek text one day, the Arithmetica by Diophantus.And Diophantus talked about the fact that there are lots of solutions to the Pythagorean equation, x squared plus y squared equals z squared.3 squared plus 4 squared equals 5 squared.

They trace the attacks to what seems to be a cult of followers of the ancient philosopher Pythagoras who was active in the sixth century B.C. So you see a, a bust of him here.Now we tend to think of Pythagoras as the fellow who discovered the Pythagorean theorem which, which in fact he probably didn't, but you'll remember we learn about this theoremin school; it's a theorem about right triangles. You see it here; a2 + b2 = c2.

'Reminds me of Xenophanes' story about Pythagoras and the dog. Have I ever told it to you?' 'I don't think so,' Ambrose said seriously. 'Pythagoras was the ancient philosopher whocoined the word "philosophy." He also invented—or at least popularized—the Pythagorean Theorem.Yes, I know you know that already. Well, the Pythagoreans thought of numbers a little like we might think of gods. Pythagoras himself was a bit of a loon.'

the NSA was up to as I was writing this story.As the story evolves, the Pythagoreans gradually infiltrate many parts of the world online and off. Lottery numbers get changed; airline schedules are modified; and some great eventseems to be coming to a head.

Apparently, every kid in America hates the Pythagorean theorem.Maybe you guys, I think this might be the one place that doesn't hate the Pythagorean theorem.That could be your new HR hiring test.

from them. And I don't know, I guess, philosophically, wehave Plato and Aristotle and for Plato knowledge was almost mathematical, Pythagorean, geometric,everything that was real knowledge had to be universal and necessary and constant.

at the very birth of what we call a Western science, music and astronomy and mathematics and what became physics were all unified.And it begins actually with Pythagoras, who was the one that came up with the Pythagorean scale by basically looking at this thing called a mono chord, onestring instrument and actually moving a bridge in these integer relations of the length of the string and generating the scale.

He traveled widely. Very importantly for the development of his own point of view as distinct from Socrates,he traveled to Italy, which was the center of the Pythagorean community.So this view that mathematics presents the key to understanding the world.

leader who didn't run anything himself but over the following centuries had lots and lots of people write about them and kind of raise them to this sort almost divine figure.And that's essentially why several hundred years after he died he was sort of most attributed the Pythagorean Theorem because he was the guy who kind of made maths mystical.And that's what I find fascinating when I was researching Pythagoras is that he's both the earliest name in maths and responsible for maths, but really what he did was he invented

that numbers were the fabric of the universe and they believed this in a way that resonates particularly well in our digital world.So this idea about the supremacy of number was encapsulated in a sacred symbol for the Pythagoreans called the Tetraktys; you see it up here.The tetra part as you may have guessed means four. There's really no good translation for the full word 'Tetraktys', perhaps the best translation is something like the essence

He held up two fingers as though in a sign of victory.'What happened to them?' he asked. 'To the Pythagoreans? They chose the wrong branch?' 'The Pythagoreans were the original utopians, Ambrose. Bringers of the gods’ fire to Earth,if you will. The first aristocrats in the true sense of the word. I don’t mean lazy snobs from privileged families with a ‘de’ or ‘von’ in their names. Just the opposite.

Just by the nature of space and time, everything gets stretched and squeezed into an infinitely thin line.So you started with an explanation of how time dilation, it depends more on acceleration than actual velocity of the observer, but then when you got into the Pythagorean theorem

He was probably given the questions in advance, but they were tricky questions and he gives very brilliant answers.There was a book on number theory, elementary number theory, "The Book of Squares" about Pythagorean triples.And then there's a reference to another book that he wrote, which was supposed to be "Liber Abaci for Dummies," we might want to call it today.

So it's always wisdom text regarding hearing well.So we know that, in California, every 10th grader has to learn the so-called Pythagorean theorem, which

and also the history of probability really begins with gambling so it's interesting to go and speak to someone who is on the kind of cutting edge of gambling.And also I went to Scottsdale, Arizona to meet Jerome Carter. And the reason I went to meet him is that he is a modern day Pythagorean. And Pythagoras is the most famous name inmaths. Pythagoras is also the oldest real person, as in Adam and Eve didn't exist or just ideas that maybe they did, but the person who we learned at school who's the oldest

mused, 'I wonder whether I’d remember if I’d been a horse in another life.' 'Do you?' Dr. Jerusalem asked. 'What would you remember?''I don't know. Maybe my pasture. And people petting me. And how hay tastes.' 'I've raised a confirmed Pythagorean then. Do you know the Pythagoreans tried more orless just that?' 'What do you mean?' 'They used to perform exercises to improve their memories. Every evening, Ambrose, they would try to recall all of the events that had occurred over the course of the day. Imagine

So these number theorists found themselves whisked away from their ivory towers into the fortress of the NSA.Now Ambrose realizes that as computing gravitates toward the center of our universe and cryptography spreads, the whole Pythagorean idea of prowess in number theory, of secrecy and so forth,doesn't seem so far off base any longer. Pythagoras said famously that the universe is number and he meant it in a mystical way. Well cryptology directly links the knowledge of numbers with

coined the word "philosophy." He also invented—or at least popularized—the Pythagorean Theorem.Yes, I know you know that already. Well, the Pythagoreans thought of numbers a little like we might think of gods. Pythagoras himself was a bit of a loon.''How?' Ambrose asked in surprise. 'Well, one story goes like this: He was walking down the street in Kroton—in southern Italy—one day, when he saw a man kicking a dog. Normally,

The successors to the Pythagoreans went wrong. They tried to reduce them to a superstitious system, to explain these poetic and highly individual experiences in terms of a simplisticuniversal, like reincarnation or numbers. I can’t prove it, but the original Pythagoreans to my mind clearly believed in living in the world. Memory—historical, personal—ofcourse it's the substance of life. Without that depth of perception, we’re Cyclopes, one-eyed monsters. But today we replace our human memories with computer memories, with

As the story gathers pace, messages like the one that Secretary Abel came across multiplied.Other powerful people start to be menaced. So how do Ambrose and the NSA sleuth out the identities of the Pythagoreans? They use a number of techniques: there's classical scholarship;there's gumshoe sleuthing; and computer forensics also come into play.

Dr. Jerusalem laughed, 'Yes, so maybe this is some Russian empress who according to the great wheels of cosmic justice was reincarnated as a mare.' He chuckled at his private joke.'Reminds me of Xenophanes' story about Pythagoras and the dog. Have I ever told it to you?' 'I don't think so,' Ambrose said seriously. 'Pythagoras was the ancient philosopher whocoined the word "philosophy." He also invented—or at least popularized—the Pythagorean Theorem.

And also I went to Scottsdale, Arizona to meet Jerome Carter. And the reason I went to meet him is that he is a modern day Pythagorean. And Pythagoras is the most famous name inmaths. Pythagoras is also the oldest real person, as in Adam and Eve didn't exist or just ideas that maybe they did, but the person who we learned at school who's the oldestliving person we know definitely existed is Pythagoras. And this is kind of interesting because surely the oldest living person we should be studying maybe in history, but no.

And that's essentially why several hundred years after he died he was sort of most attributed the Pythagorean Theorem because he was the guy who kind of made maths mystical.And that's what I find fascinating when I was researching Pythagoras is that he's both the earliest name in maths and responsible for maths, but really what he did was he inventedanti-maths 'cause he thought that numbers were not just numbers, did not just represent quantifies but also represented qualities. So two was feminine, three was masculine,