BBC Magic Numbers Mysterious World of Maths 2of3 720p HDTV x264 AAC MVGroup org

BBC Magic Numbers Mysterious World of Maths 2of3 720p HDTV x264 AAC MVGroup org

There is a mystery at the heart of our universe a Puzzle that so far no one has been able to solve it can be weird. Welcome to the world If we can solve this mystery, it will have profound consequences for all of us That mystery is why mathematical rules and patterns seem to infiltrate pretty much Everything in the world around us Many people have in fact described maths as the underlying language of the universe But how did it get there? Even after thousands of years this question causes controversy We still can’t agree on what maths actually is or where it comes from Is it something that’s invented like a language or is it something that we have merely discovered I think discovered Invented it’s both. I have no idea Why does any of this matter well maths underpins just about everything in our modern world From computers and mobile phones to our understanding of human biology and our place in the universe My name is Hanna Frey and I’m a mathematician In this series. I will explore how the greatest thinkers in history Have tried to explain the origins of maths extraordinary power Ephesian I’m going to look at how in ancient times our ancestors thought maths was a gift from the gods How in the 17th and 18th centuries we invented new? mathematical systems and used them to create the scientific and industrial revolutions and I’ll reveal how in the 20th and 21st centuries Radical new theories are forcing us to question once again Everything we thought we knew about maths and the universe The unexpected should be expected because why would reality down there bear any resemblance to reality up here? In this episode I discover how maths led Victorian scientists Into a world of invisible forces and particles we channeled teeth now this could be a coincidence and I reveal why the concept of infinity broke the rules about where maths comes from I’m very tormented by infinity is infinity real. I do not know the answer to that question Our world is governed by the rules of science But science wouldn’t work if it wasn’t for a far deeper set of rules those of mathematics It predicts the movement of the planets and the urban flow of the tides if you look hard enough at anything You’ll find mathematics hiding underneath If math is the language of the universe then where the numbers come from Before we learn that one plus one equals two the idea of one and two still existed the nature of Oneness and tunis has always been there The concept of numbers is something Universal all around the world and in every language we understand the idea of what 1 or 2 means This raises an intriguing question Is maths all in our heads is it something that we have invented a language that we use to describe the universe Or is it an? external physical Reality something that exists completely independently of us humans something that’s just out there Waiting to be discovered In ancient times we were in awe of the power of math seen as a gift from the gods It was considered pure and complete but through the centuries maths developed it wasn’t complete and after all new areas and Techniques have been invented and the more we explored science the more it became obvious that we couldn’t just rely on simple experiments we needed a theory and crucially a Mathematical description to be able to understand the world around us Things that seemed obvious at first often have a habit of melting away when exposed to the rigor of Experimentation. The problem for humans is overriding our instinct to trust our intuition our Senses aren’t always the best guide to the truth The Greek philosopher Aristotle Fell into this trap when he famously declared that something heavy will fall quicker than something that’s light For him, it seemed blindingly obvious and for centuries nobody disagreed with him On the face fear you might think they’re suggesting that heavier objects fall faster Than light objects was quite a sense of an idea after all he dropped them at the same height camera learns first But a 16th century scientist and mathematician called Galileo Galilei had a different explanation He believed Aristotle had failed to consider something crucial The incredible facts is not that Aristotle was wrong But that his law of motion stood unchallenged almost 2,000 years How could such a flawed ideas of mine for so long well to be fair there are a few reasons You can see a hammer hitting the ground earlier than the feather The reason for that of course is air resistance and Galileo argued that if you dropped them in a vacuum They would land exactly the same time To come up with this theory Galileo imagined the idea of a vacuum in which air resistance didn’t exist and created a series of laws that Describe the motion of falling objects They completely overturned Aristotle’s ideas Over 300 years after Galileo’s prediction Apollo 15 astronauts David Scott Gave the theory it’s most dramatic With no air resistance on the moon the hammer and feather hits the lunar surface at the same time a Physical description of the world on its own isn’t enough It has to go hand in hand with mathematics before you can truly discover the nature of reality Galilei was Incredibly impressed for good reason at the power of mathematics to give us insights to describe things that were happening to Articulate the patterns that the human brain is able to access it Almost seems miraculous that some symbols on a piece of paper can do that and in that sense it might lead you to think that math is the language of Reality DeLeo exclaimed that the world is a brand book written in the language of mathematics. I think the reason for this is that ultimately The world is completely mathematical and we’re just discovering that bit by bit He had this feeling that by using Mathematics he could get into these things which he wanted to be inevitable in mathematics Gave him that certainty the things are inevitable So he was the first to understand that in order to explain phenomena. He needs to use mathematics Galileo’s theories though ahead of their time raised as many questions as they answered There appeared to be some kind of a force that was pulling objects to the ground But exactly what that force was or how it worked Remained a mystery Solving this mystery would take the genius of a 17th century Englishman his name was Isaac Newton I’m heading to North Wales to do something. I’m not entirely happy about So my director was looking for a clever way to illustrate gravity And he came up with the bright idea to send me Down the fastest supply in the world at first as well I was in that meeting should have been in that meeting The same force that brought Newtons and Apple to the ground is the thing that’s gonna be propelling me Towards a quarry What do I let my love him but all this is nothing compared to how Newton performed experiments on himself Newton totally believed that the path to true knowledge lay in observation so rather than just read a book on optics a he decided to experiment by poking a blunt needle Into his own are we maybe don’t try that one at home? He wasn’t going to take someone else’s word for it He had to test these theories for himself as he began wrestling with bigger ideas such as gravity only Mathematics could help him find the answers When you think gravity is actually quite a strange beast This invisible force of attraction between me and everything around me, but one that’s weaker I can easily overcome it just by moving my own muscles Newton set out to find a way to describe this mysterious force Originally described in words his law of gravity was later written down in the form of an equation Don’t be fooled by a simplicity because this guy packs a real punch I’m using it to work out the force that will be acting on me as I head down the zip way To understand it you need to know what all the letters stand for. So let’s begin with if the force Newton says that between any two objects in the universe there is an attractive force and this force Depends on the mass of those objects. There’s capital M here. That’s the mass of the earth and then slightly smaller The little ember is me That little M is my mass and its measured in kilograms There’s also G. The gravitational constant which Newton knew had to exist Although he didn’t know exactly The size of it at the time and are there which is the distance between me and the center of the earth More generally what this equation is saying is that the bigger the mass of your objects like planets, for example The bigger your force between them is going to be and the greater the distance between objects the bigger This R is the weaker. The force of gravity is going to be So what does Newton say the force of gravity will be on me So if you plug in all of the numbers into this equation, you can calculate the force on me as I travel down the wire it works out to be 736 and the unit it’s Newtons Newton arrived at his now-famous Formula after studying centuries worth of measurements from astronomers that had gone before him His law of gravity not only explained why objects fall to the ground It predicted the positions of every moon planet or comet anywhere in the cosmos That is one devastatingly powerful equation This was Newton’s genius Once you’ve got a mathematical law you can use it to apply to anything apples Planets and people and if you can calculate exactly what their force will be It means it can predict all kinds of other things like my terminal velocity as I travel down to the bottom. So Let’s put it to the test As the force of gravity pulls an object to the ground it reaches a maximum speed this is called its terminal velocity Before you can calculate this figure there is a bunch of things. You need to consider such as the gravity drag and friction Along the cable Time to put my faith in mutant and the Fastest zip line in the world from my calculation. I recomment velocity is going to be about 90 miles an hour So, I think I’m gonna speak to this director again Well my day I Wasn’t used to check my speed prediction now disclaimer Just before I came down They added some flags to the back of me just to slow me down because the winds picked up as you can probably hear So I don’t think I’m going to quite hit 19 first, okay? there’s a big spike there on the bar and it says it’s 49 seconds for one mile, which is about what 75 miles an hour something like that Not bad not bad for a back-of-the-envelope calculation The power of Newton’s equation was that it could explain and predict so much about the universe It’s allowed us to think of nature as ordered not just on earth but throughout the cosmos She breakthrough of Newton was that he had the audacity to shatter this Idea that earth rules are different from heaven rules And Moon doesn’t fall down because it’s made of heaven stuff and say wait a minute, maybe all things Obey the same physical laws his laws a force and of motion We’re not meant to merely apply in say the heavenly realms or just on earth They were meant to apply everywhere and the idea was the whole of nature would really be captured by the single set of laws I mean a fact that we can write equations and know how to power a rocket and have it land on the moon and Come back Holy cow. I mean we take these things for granted but think about the power of equations to give us the trajectory and figure out how to Accomplish this incredible feat that is thrilling If evidence is needed to prove masses discovered part of the fabric of reality and surely this is is how Could something we invented in our brain have the power to reveal the workings of the universe? And the extraordinary power of mathematics wasn’t just confined to the stars By the end of the 18th century scientists and engineers were using it to drive innovation on a grand scale what became known as the Industrial Revolution This changed everything People didn’t just live and work in a fields anymore There was an explosion of growth in towns and cities as employment Switzer factories and driving this entire revolution with the invention of the steam engine The impact of this new technology was profound It opened up the country not just the people and goods, but two ideas New ways of doing things were propelling us into the age of the machine Behind all of this were the essential Calculations of the Machine age how strong the materials were how hot or cold something might get it was mathematics That was used to design faster and more efficient machines New skills were required and all of that So whereas before you would have craftsmen using hand tools now, you’ve had people in factories operating machinery But there’s also a sea change here in a way that we see it’s a belief that what a natural world might not be tamed at least The Industrial Revolution marked a major turning point in history From textiles to iron production and the spread of the railways almost every aspect of daily life was influenced in some way and at the heart of this revolution was mathematics Now this is a world that feels firmly rooted in reality We can trust the numbers and we know that they’re not going to let us down So forget all of your airy-fairy philosophical stuff here. This is maths in action It’s big its bold. And actually it’s pretty amazing Technological miracles were coming thick and fast Mathematics had given us a description of how the world works that was driving our understanding forward But also it could hint at how seemingly separate things could be connected By the 19th century Mathematicians and scientists began to wonder what else was out there. Just waiting to be discovered they soon turned their attention to the invisible link between electricity and magnetism Both had been known about for centuries from the raw power of lightning to navigation by means of a ship’s compass But they’d always been thought of as two very different things It was a working-class son of the Industrial Revolution Michael Faraday, it was the first person to see a connection between the two I’ve come to the Royal Institution to the place where Faraday had his laboratory To see if electricity and magnetism were linked to Faraday ran a series of experiments He took a warrior that had electricity passing through it and he watched as it moved the needle of a compass the Electric wire and the magnetic needle weren’t touching and yet one was having an effect on the other What was the connection? Faraday looked deeper What he did was to take a magnet like this one and a roll of Copper wire wrapped around a cylinder like this and then to pass one through the other very quickly like this The wire surrounds the outside of the cylinder so the magnet can’t come into contact with it and That’s really all there is to it Nothing more complicated than that the wire never touches the Magnus and yes As you can see from these LEDs probably not the originals that is enough to generate electricity Faraday realized there had to be some kind of invisible force working behind the scenes and He had a clever idea of how to make it visible We do is you take a permanent magnet and you place Some paper on top of it and then take some iron filings and sprinkle them on top now This I think is one of the most memorable experiments that you do at school, and I can remember that moment Where you see? The invisible force field that’s created by the magnet As the iron filings fall onto the paper they line up with the magnets field lines Now this is just two-dimensional here But actually these lines are three-dimensional they come out and they walk and curve and wrap around the entire make That’s pretty : it’s pretty cool Faraday’s iron filings experiment reveal the existence of an invisible field stretching hours into space he could see the lines of the force, but it was an Experimentalist and lacked a complete mathematical description of what was going on as a result many of his contemporaries Dismissed his ideas as fanciful It was the Scottish scientist James Clerk Maxwell Who took Faraday’s ideas and came up with a mathematical way to link electricity and magnetism Drawing from the observations of previous scientists Maxwell distilled Electricity and magnetism down into four equations that worked for nearly every situation The symbols themselves aren’t important to the story. The key point is that Maxwell spotted a gap? The mathematics was telling him there was something missing in this last equation You realize there has to be another term in this equation one that looks like this and essentially what it’s saying is that if an Electric field is moving Then a magnetic field will wrap itself around it and it’s mirrored by this equation up here which says that if a magnetic field is moving an Electric field will wrap itself around it with this missing piece in place suddenly everything fitted together Mathematics had led Maxwell to see the bigger picture These equations are linking the two things together Electricity to magnetism magnetism to electricity back and forth from one to the other Using only mathematical ideas Maxwell had found the evidence to prove the electricity and magnetism were inextricably linked Together electricity and magnetism formed what he called an electromagnetic field This helped explain so much the equations Perfectly described what Faraday had seen with his experiments But Maxwell didn’t stop there. He showed how these field lines could move in time with each other creating electromagnetic waves By playing around with these equations Maxwell could calculate the speed of this way and it came out to be about 300,000 kilometers a second and I want a random number That was a number that Maxwell knew very well because it was the same as the speed of light in a vacuum Now this could be a coincidence You don’t really get quit since it’s like that in the universe There was only one possible explanation Lies had to be an electromagnetic wave Maxwell’s discoveries were genuinely revolutionary He’d given us a unified theory for electricity and magnetism and as an added bonus an explanation of light itself For the first time an electric field a magnetic field and light Could only explained using a single theory The elegance and simplicity of this solution was breathtaking Surely nothing the human mind could conceive of would ever be capable of thinking up something so sublime equations that reveal new truths about the universe It feels very much as if this answer was always out there It just needed someone who thought differently to discover it It’s quite uncanny how mathematics has Again, and again predicted new things in the physical world that we weren’t even looking for it You come up with novel predictions you come up with Ideas that there should be structures in the world That you haven’t yet discovered and then on inquiry you discover those to be real. That’s really extraordinary. I Can tell you from my personal experience it is Shocking not just surprising but shocking that mathematics makes predictions about the world around us The ancient Greeks found intriguing patterns in nature who seemed to follow the rules of maths Then Newton showed us how mathematical equations had the power to predict the movement of the planets revealing an ordered universe By the 19th century the formidable power of maths allowed Maxwell to unify electricity and magnetism It seemed inconceivable that mass could be anything other than something we discover But then something happened that turned this worldview on it head There was a new way to look at maths Someone had invented a different way of doing things Since the days of the Greek mathematician Euclid more than 2,000 years ago Right angles and parallel lines the kind we learned at school Have been the bedrock upon which all of geometry and our understanding of space is built But in the 19th century mathematicians started to wonder whether everything really was as it seemed or Whether there was the possibility of something a bit weird going on behind the scenes You can see it with games like pac-man What kind of a shape is the pac-man universe your instinctive answer might be a square and you’d be right sort of For instance if this little pink character exits to the left, it will re-enter on the right Which actually makes this universe More of a cylinder What’s more in other similar games you can exit out of the top and re-enter at the bottom Which means that the two loose ends have to bend around and connect up to one another It’s a bit of a strange idea to get your head around but these kind of computer games are not played on a square They are played on a doughnut Once you move from a flat square to another shape You can’t take it for granted that geometry will follow the rules. You’ve always expected it to Behind the scenes there can be something else going on entirely But hold on to your hats because this is all about to get much weirder Consider for a moment a traditional geometric view of the world imagine there are four colored courtyards What would happen when I leave one of the courtyards? If the world was as Euclid says it is and everything works. Normally if I turned left for time I would eventually get back to where I started I’ve left the yellow courtyard. I’ve gone through orange red and blue and I back in yellow again Nothing controversial here But who says there has to be four courtyards next to each other What if you got back to where you started after turning left only three times? But hang on I hear you cry as impossible except it’s not if you’re living on a cube Again on this side turn once turn twice turn three times and you’re back where you started No longer was there only one description of space by changing the rules You could now choose a different type of geometry It turns out there’s many different ways to think about space it would be very much like somebody discovered Piccadilly Circus by taking a left turn where they had always taken a right turn before people hadn’t even thought that there could be a distinction between the physical space and the mathematical space that Euclid had Star Wars studied with his axioms because the one of a sudden Euclidean geometry just earth. It’s like one way of describing a space and in fact, you know It happens to be a good one for describing space. We’re sitting in right now Not such a good one for describing space on astronomical scales. It turns out so it’s a little bit like a game namely I teach you the rule of chess and we play chess I Change the rules and we play a different game, but we still can play a game. So that was the feeling that maybe It is all you know, depending on which set of axioms you choose you can get a new type of mathematics But hang on a minute is when you just make up a new type of geometry then perhaps I’ve got this wrong Maybe math is something we invent after all With this newfound freedom mathematicians began exploring ever more abstract ideas the most intriguing of which was the notion of infinity And everybody show me this sign that we are going to be using to solve this problem off you go From an early age we all have an idea of what infinity is, but it’s hard to pin down Our minds aren’t built to wrap themselves around the concept of something. That is completely Endless and boundless and that makes describing exactly what to infinity is pretty tricky That keeps all going never stops The biggest one I could think of is ninety nine billion four hundred Googleplex There’s nothing bigger than infinity. This is that’s the biggest number that you could That you could possibly need I’m very tormented by Infinity. I have a love-hate relationship with infinity I love using me when I teach courses at MIT because it makes things so easy to derive and prove but In my gut I know there is no actually infinity. It’s just a convenient Approximation is infinity real it says about as real as the number one or the numbers zero It’s a concept. It’s a useful concept in describing a certain set of elements and In that sense is it’s it’s real. I think it’s fair to say That nobody in the laboratory is ever gonna have a dial that registers infinity that measures infinity We’re never going to literally count to infinity we can approach it. But from that point of view. I don’t think we’re ever going to Embrace it the way that we embrace tables and chairs and finite objects inserted by definition. We can’t go there You can’t get there try and get closer to infinity. You know, it stays just as far away You might imagine that something is abstract as infinity is not very useful but in reality Infinity offers a way to solve problems that previously would have seemed impossible If you wanted to know the distance between the UK and New York you could try and use a ruler on a globe like this You’d have some trouble because of course the world is round and curves Unlike straight lines are quite tricky to measure Good luck in geography class where the globe and a measuring stick But what if rather than just using one ruler you use too much smaller rulers and use How they overlap to wrap around the curve of the earth Not by doing that. You’re not gonna get the exact distance between London and New York. You’re gonna get a much better approximation For it and you can imagine the more and more rulers that you use the better They’ll wrap around the curve of the globe and the better and approximation. You’ll end up with So here’s the key idea if you zoom in enough on any curve It will start to look straight and if you have an infinite number of teeny tiny rulers You can perfectly measure the length of any curve just by adding up all of those straight lines It’s only by harnessing the power of infinity that any of this is possible Okay, so why did you care? well It’s not just the earth that it’s got curves Because everything from the movement of satellite in the sky to the rise and fall of the stock market To understanding how our human behavior changes over time all of them rely on this idea of infinity Relying on an idea we don’t really understand isn’t something that sits comfortably with mathematicians In 1924 the renowned German mathematician David Hilbert Created a famous thought experiment to try and help explain infinity You did it by imagining a large hotel But this was no ordinary hotel, it had an infinite number of rooms Oh Yeah, can I have a room for tonight sorry Zambia fill er up tonight? Oh You ain’t got any rooms at all. Unfortunately. No, I’m sorry Hilbert wondered what would happen if all the rooms were full and a guest like me turned up Would there be room for one more in the infinite hotel? So today I’ve turned up and the place is fully booked they’re saying how many rooms actual whatsoever I’ve tried ask them if they know who I am But apparently they’re not familiar with my back catalogue of extremely niche online math videos if you can believe it Even in a hotel with an infinite number of rooms There’s a problem the manager can’t just put me in the last room because in an infinite hotel, there is no last room So if the hotel is full, how do I find a bed for the night? All you have to do is politely ask the person staying in room 1 to move along into the person in room 2 to move to room 3 3 to 4 4 to 5 and So on and so on and so on As there’s no last room if you move everyone along by one room number Every guest has somewhere to sleep Alas these room one Even if the hotel is full a room can always be found That’s because infinity plus one is still infinity so there’s always room in the infinity hotel because you can always add on an extra room at the beginning to make Infinity just that little bit bigger and if my friend wants to come as day two well Infinity plus two is still infinity, which is perfect that girl’s weekend away I Told you it was weird That’s the thing about infinity it’s a very slippery Beast There was one mathematician who set out to tame the infinite beast His name was Gyo contour and the question he wanted answer sounded deceptively simple how big is infinity with that one simple question Contour would start a revolution One that would have a profound effect on the foundations of mathematics I’ve come to holla in Germany. It was here that Kant or taught in the city the University For him infinity was the key that opened the door to a new mathematical landscape I Talk about you but I find it quite hard to picture in my head the size of something like our solar system or our galaxy the Milky Way These distances are so big that they defy our imagination But each of these things scales into insignificance They are infinitesimally small when compared to the vastness of infinity While the idea of infinity was known to the ancient Greeks some of Cantor’s contemporaries saw it as an offshoot of maths Rather than anything worth understanding in its own, right? This wasn’t good enough for Kant or if our knowledge of the world is built on infinity He said we can’t just accept it. We have to understand it To get a handle on infinity take a look at these two sets of numbers Let’s imagine that along here you’ve got all of the natural numbers the counting numbers So one two, three, four, five six, seven eight and so on now There’s gonna be an infinite number of these Now next to it. Let’s push the even numbers so 2 4 6 8 and so on on the surface of it It looks like this infinity will be bigger than that one As both of these lines will go on forever It seems obvious that the infinity of 1 2 3 4 will be bigger than the infinity of the even numbers 2 4 6 8 After all, there’s only half as many of those But actually if you shuffle all of these along they actually match up rather nicely So one goes with 2 2 goes with 4 3 goes with 6 and so on and so on Neither of these lists are ever going to run out As each list of numbers never stops Every counting number can always find an even number to pair up with As a result both infinite lists of numbers have to be the same size We know this is true because we can count them then that seems like a bit of a strange idea but just go with me on this for a second because you can start at The beginning and work your way up Counting as you go the first number the second number the third number and so on and so on now It’s true that you would have to carry on counting forever But you could be sure that you wouldn’t miss any of the numbers as he went Even though the infinity of the counting numbers looks bigger than the infinity of the even numbers. They’re actually the same size Next contour tried something different he set out to count all the numbers between zero and one Where is the most sensible place to begin is it naught point one? well No Because naught point naught 1 is smaller And it can’t be naught point naught 1 either because naught point naught naught 1 is smaller still and no point No, no, no, no, no, no, no naught 1 is smaller still wherever you try and start I can always find another number to squish in and that means There is no sensible place to start However hard you try you can’t count up. The number of numbers between naught and 1 This infinity is uncountable Contours disturbing conclusion was that some infinities are bigger than others The sheer audacity of his work set off a quiet revolution in the world of mathematics If Cantor or thought his work was going to be welcomed with open arms, then he was to be sorely disappointed He was attacked on all sides by his academic colleagues they called him a scientific charlatan and a Corrupter of the youth and Some even tried to sabotage the publication of his works Could it be that Cantor’s idea is on infinity were merely a product of his own imagination Something he invented His work on infinity consumed every waking minute in May of 1884 he suffered a nervous breakdown Eventually, he was brought here to the Nerf and center in Halle a psychiatric hospital How did Cantor’s desire to tame the infinite impact on his illness I’m meeting the hospital’s director Dr. Frank Pillman this for example is a note case note from 1907 mania an acute episode of a reality circular psychosis This is what we would today call Bipolar disorder there are some people who suggested that it’s flipped you know the the Struggle that he was having with his mental health was exacerbated by his fight to try and find these answers around infinity And what’s your opinion on them? I won’t feel that the flexural occupation with mathematical theories. –is Nothing that makes you prone to get a psychiatric illness as far as we know About his personalities is almost been described as a very ambitious Person Certainly creative, of course. He tried to solve some unsolvable problems, but I think that’s the life of every mathematician The struggle to struggle with very difficult problems This is a memorial to cantle He was feared by his critics because he dared to question their assumptions of conventional mathematics His work on infinity was crucial for building more complex mathematical ideas that we rely on today This is where mathematic does stray much more into the realms of the abstract infinities bigger infinities countable and uncountable Infinities these are not things that you tend to find in the physical world So is it all just a product of our intellect and imagination is this mathematics? invented Certainly, when you just take the basic concept of infinity. It’s meant to be the biggest possible thing Right and then someone tells you that there’s lots of infinities so it’s certainly very puzzling concepts, but it’s an essential one It’s an essential feature of huge numbers of mathematical systems in so far that mathematics arises as an interaction between reality and Conscious rational minds and that’s what creates mathematics I would say infinity is real in that sense If you ask me, is it real in? Actual reality. I do not know the answer to that question nor do I know how to find the answer to that question? some people find that emotionally disturbing this idea of iterative reality is bigger than we thought I Actually find it kind of liberating. I think you’d be rather claustrophobic if a reality were really small Maths has taken us from a time when we could spot patterns in nature To being able to describe the invisible forces that form the structure of the cosmos To prove this hidden world we’ve invented mathematical tools and equations Maths has quietly almost invisibly Revolutionized the way we understand our place in the universe Today the argument about whether maths is invented or discovered is much more than a philosophical debate This is where it gets real this jumble of pipes and wires looks chaotic But it’s at the cutting edge of science if the researchers here succeed in their goal They’ll have found the answer to the world’s energy needs a form of power that’s clean renewable and free I’ve come here today to the Cullum Center for fusion energy where a group of people are trying to do something rather remarkable They’re taking a mathematical description of reality and trying to bend it to their will Harnessing the power of a star and using it to change humanity’s future Controlling the power of a star such as our Sun is as you might imagine incredibly difficult The Sun is one giant hot ball of gas called a plasma It’s heat is generated when atoms of hydrogen inside this plasma collide with each other very quickly releasing vast amounts of energy The challenge is to recreate that Reaction down here on earth and the first step is to form the plasma within this shape They’re trying to recreate the conditions that you find in the inside of the Sun and hold that plasma in place while it reaches temperatures up to 200 million degrees Celsius This doughnut shaped space is called a tokamak The most difficult part of this whole process is ensuring the plasma remains stable if Part of it touches the walls the plasma cools and the reaction stops Trying to prevent that from happening is the job of dr. Antony short the difficulty is that at 200 million degrees you get quite a lot of extra effects coming in it gets Turbulent like the churning sea there are various currents and turbulences and tides and all these things that make the behavior of it very tricky to understand and If you don’t account for the right things at the right time, it’ll do what it wants instead of what we want Driving this behavior are lots of subatomic reactions that no one has ever seen The only reason we believe they exist is down to MERS Anthony and his colleagues are using math to try and predict how these invisible particles will behave inside the plasma So here we have a photograph that was taken Inside the tokamak. You can see the hydrogen plasma here just glowing around the edges and they’ve overlaid photograph of the structure just seeking see roughly where a sitting for comparison there is also a Simulation of this a mathematical simulation and on this one. You can see very clearly these these little lines there called filaments This is where wisps of plasma go out and touch the side Now this one is purely mathematical But what the physicists do is make comparisons between the two to see how well their mathematical version? matches up to what really happened and if you put these two side-by-side you can see how well the mathematical version Matches up with what’s really happened By comparing the simulation of how the plasma is predicted to behave To what actually happens it becomes clear that the mathematical model accurately predicted where the plasma would break down Now the reason why this is important is because there’s no limit really to the number of mathematical simulations you can run but once you get them matching up to reality once you know that your Mathematical version is an accurate reflection of what’s happening inside that Is the first step to being able to control your plasma? nuclear fusion holds out the promise of almost unlimited supplies of clean energy If they can ever solve this problem the answer will lie in mathematics and its ability to describe an invisible world of subatomic particles and forces The only way you know, what’s happening inside that plasma is by using mathematics It’s the math that tells you how all of this works in trying to replicate what’s happening inside a star we’re pushing the boundaries of what science and Maths is capable of but we’ve been doing research in this area for decades We’ve had the equations for even longer and yet we’re still not quite getting perfectly neatly to the answer If there are these gaps around the edges if there are limits to how far the math can take us Then how can it be discovered? Maybe it is just an invention after all So where have we got to with our investigation of mathematics so far? Well Newton came along with his fundamental laws of gravity that led to these Incredibly powerful equations that can precisely predict the movement of planets in the universe But they’re not quite perfect but then you have cantor and his amazing ideas about different sizes of Infinities and mainly math starts to go down a slightly different path and the more you go down that road the more it’s to feel like Mathematics is in the Benedick Next time things get even weirder as the logic of math starts to break down There’s big paradox here Who shaves the bar? And we take another giant leap forward As mathematics redefines the nature of space and time Einstein completely upended our understanding of space time matter energy and kind of what else is there to the nature of reality? I mean, how did you think of that? our world is becoming stranger than we realize and There may even be multiple versions of it In an infinite If we trust the mass then where it’s taking us is somewhere truly bizarre What makes our world work the way that it does? Explore more about the magic and mystery of mathematics and how it impacts our everyday life Just go to BBC code at UK forward slash maths and follow the links to the Open University Halla joins Adam Rutherford investigating mysteries from pain thresholds to deja vu the curious cases of Rutherford and Frey on IPlayer radio tomorrow Brian Cox asks the big questions. Who are we and why are we here? human universe is at 8:00 here on BBC four and Causing a thousand tons of snow to hurtle down a mountainside in the name of science Avalanche making a deadly snowstorm on BBC 2 at 9:00 You

100 thoughts on “BBC Magic Numbers Mysterious World of Maths 2of3 720p HDTV x264 AAC MVGroup org”

  1. i have a mathematical challenge for you. What is infinity divided by infinity (so infinity/infinity=???)? Is it 1 or infinity? My guts says, it's 1 because any number divided by itself is usually 1, except for 0/0 (for some reason a division by 0 is not allowed).

  2. The one girl's description of infinity was so cute: "it's the biggest number that you could possibly need". I also liked how Hannah seemed relieved when the psychiatrist said that obsession with math wouldn't cause mental illness.

  3. About how many numbers there are between 0 and 1. If 0 doesn’t exist there are no numbers at all. Surely??? There was no year 0.

  4. Believe it can be argued that Mathematics is a man made tool that allows us to mimic nature and the world around us. Then it is clear Mathematics ability to mimic has its limitations when pushing it's use to the far limits of the macro and micro ends of the spectrum Then it can be said that we are left scratching our head where our mathematical tool went wrong and how we must improve the tool to make it work once again to meet the rigors of of the new demands we have placed on the tool.

  5. The Gallileo experiment on the moon??? Given there is no gravity in space and the astronauts themselves wore weighted boots to prevent them flying off into space, what on "moon" (see what I did there?) caused the hammer and FEATHER! to fall and not float off into space???

  6. It's easy to understand how math is an invention of the mind(i.e symbolic representations of forms of ideas of the human mind influenced by culture) once you've studied the Idealism of Berkeley, Hume, Kant, Hegel, Schelling, Schopenhauer, Nietzsche, and Cassirer.

  7. Doesn't need quite this much explanation. Your audience probably has an IQ of at least room temperature, so why not pick up the pace a little?

  8. Thanks, Hannah Fry for indirectly letting us know your weight.*+(mean+earth+radii+%2B+(elevation+Bethesda+UK)+%2B+100+meters)%5E2)+%2F+(Newtonian+gravitational+constant+*+mass+of+the+earth)&assumption=%22UnitClash%22+-%3E+%7B%22Newtonian+gravitational+constant%22,+%7B%22GravitationalConstant%22%7D%7D


  10. If all our young students would be taught by someone like Hannah Fry, they'd all be geniuses. Either that, or they'd all be reduced to whimpering piles of hormones.

  11. I just want to go on about her work on the stairs describing the numbers between 0 and 1. It's the worst TV presentation ever. She COMPLETELY misstates everything. First, the count of FRACTIONS between 0 and 1 is NOT greater than the count of positive integers. You can list the fractions in order by first listing all fractions made only with 0s, Next, all fractions made only with 0s and 1s. Next, all fractions made only with 0s, 1s, and 2s. And so on. Every time you contemplate adding to the list, you skip it if the denominator is "0". You leave out any number whose value is either 0 or 1 if your list excludes those. You leave out fractions such as 2/1 and 3/2 that are greater than 1. And you leave out any fraction that is equal to another fraction already added to the list. At some point your combining will take you to 2/4 but since 1/2 is already there you skip 2/4. I can  type the first numbers in the list here: 0, 1, 1/2, 1/3, 2/3, 1/4, 3/4 … Notice that "1/2" isn't the third-smallest value in the list so far, and yet it has been assigned the third slot in the list. Obviously then it's not impossible if you simply don't rank the fractions by order of their value. Since every fraction in such a list can be paired uniquely to an entry in the list of positive integers and vice versa, the members of my list (i.e. Cantor's list, of fractions) will NOT have a count greater than the positive integers. So, Hannah Fry has been wrong twice here: First, she says there is no way to find a FIRST member of the list because there's not way to find a SMALLEST member of the list. That's wrong as shown above. SECOND, she says that when a set of numbers has a property called "squishability" (the ability to put an additional number between any two existing numbers in the set), then it makes it impossible to list them. That's wrong too, because squishability IS a property of FRACTIONS and yet the fractions CAN be listed. Her third instance of being wrong is in failing to state that despite having the squishability property and despite having no least-valued member, the FRACTIONS between 0 and 1 do NOT have more members than the positive integers, but the set of ALL numbers (fractions and irrationals) DOES have more members than the positive integers. That is the crucial distinction. She should have made it clear that the impossibility of construction the list (the pairing of listed numbers to a list of positive integers) arises ONLY from throwing the irrationals into the pot along with the fractions. That crucial distinction is left out by her assertions that the squishability-property and the absence of a lowest-valued member are what make the listing impossible. They don't. You really do need to do a visual of Cantor's list for this, even though the producers will scream at her "We don't WANT to accurately present Cantor's work!!!   We want to make 'watchable televison'.  So we're going to shoot a hair-care commercial of a beautiful redhead model (you) hopping about on stairs instead."  Not really her fault she got stuck with that attitude, but it IS infuriating.

  12. Infinity is NOT an invented concept. (None of maths is invented. If it were, buildings would fall down and machines wouldn't work. These are physically observable facts. People who say that maths is invented have not framed the question "is maths invented?" in a way that makes it decidable.) It is impossible to take half the water out of a measuring-cup infinitely many times. It is impossible to take half the water out of a measuring cup finitely many times for all finite numbers and yet fail to empty the cup of water. (For one thing, water isn't infinitely divisible although we perceive it as such in many circumstances.) And yet our answer to the question "Is it true that if we COULD find an infinitely divisible substance, and remove half of it from a measuring-cup, and keep repeating that operation, we would never empty the cup?" is "Yes it is true", and that is NOT based on rules that humans invented. It is inferred from actually interacting with physical reality. Because of our interactions with physical reality, we are able IMAGINE removing half the content from a measuring-cup, doing that FOREVER, and never emptying the cup. We can't actually PERFORM that experiment, but we know what the result would be, and the reason we know what the result would be is that we have interacted with physical reality, NOT because we have made an agreement that certain rules apply. Since it is physical reality that dictates this notion of infinity, anyone who says that infinity is an invention rather than a discovery is a liar.

  13. Will somebody break it to these geniuses that the plural of MATH is MATH.
    One 2×4 is wood. When you have 100 2x4s it's STILL WOOD and NOT WOODS!!!

  14. way wouldn't infinity and zero be "same" their effects on math seem to be the same just that different amounts of infinity there's different amount of zero. if there's zero apples within a mile or zero apples within 10 miles. you could add those together to make a larger zero. if base 10 or base 2.thare zero and infinity.

  15. One of the most curious aspects of human nature is the need some have to negate what is most difficult to understand. Thus, the choice of thumbs-down reaction to videos and concepts such as this. What is this need to be so contrary?

  16. Universals has to be a question about focus, inclusion contra exclusion.
    —Is the electromagnetic field a coninuum of waves, or a set of quatum determined particles? I believe the sciences and mathematics has come to a specific point. Wether we're forced to make up our minds about wat we're trying to understand…

    The nature beyond our selves? Or nature within our selves?

    So, what nature is yours?

    As if there were any distinction between intrinsic and acquired nature? I seriously don't think so. The question remains. Do I want to understand the universe as a set of particles by zooming in on a particular phenomena? Or, do I want to zoom out to regard the whole of the universe as a web of entangeling fluctuations in fields – not indifferent from each other?

    You are the answer. Not YouTube…

  17. Fifty minutes in and I am sad that this video is almost over and that there is only one more episode in the series. I wish it could go on for ever. 🙁

  18. This Maths woman's explanation of infinity was best expressed by the poet Poe "There is no Exquisite beauty without some strangeness in the proportion" Thanx for allowing me to appreciate the beauty of this series and dream of everything and nothing at the same time.

  19. 5:28 I fell into a trap when my friend, who was a skydiver, told me that after he had spent a month in hospital, that he had lost so much weight that when he went skydiving with his team he had to put weights onto his belt to keep up. You need to read Aristotle's Meteorology to understand his physics.

  20. 45:27 The argument of the uncountability of reals is misrepresented. By the argument Hannah Fry presents here, the rational numbers would be uncountable, too. But they are countable.

  21. Maxwell did not summarize the laws of electricity and magnetism in those 4 equations. Maxwell wrote down something like 20 equations. It took many years for other scientist to understand what in the hell he published. But in the end it was Oliver Heaviside that wrote them in the form you see in Engineering and Physics texbooks. Now Maxwell came up with all the theory and was the genius that figure all this out but he did not write them in the form we know today because vector calculus wasn't invented unit Oliver Heaviside invented it. He is the one that recast the equations in vector form that all scientist and engineers learn about today.

  22. I wonder what my force will be on the zip wire? Um, your weight? in newtons of course because it looks cooler.

  23. Mathematics is a study of patterns by humans. The study is invention, the patterns are discovered. The patterns ‘exist’ whether humans discover them or not. Some, myself included, like MIT physicist Max Tegmark, suspect that these patterns are foundational, as in the foundations of the ‘physical’ world. Because (abstract) patterns exist independently of our physical world, e.g. pi is (IS!) precisely the same whether the world exists or not, patterns therefore provide a possible foundation for all of existence. Some worry that this contradicts religious principles, but it does so no more than other ideas about how the world works. Furthermore, since abstract pattern, our limited human studies not withstanding, is both ultimately infinitely infinite, and “perfect”, characteristics usually attributed to deity, perhaps it is no wonder the Pythagoreans saw it as a religion.

  24. its both objects and numbers in short id have to learn more to give you a better reason why

    ill try, number are just how many objects make up something and we use math to understand how.

    I think we would first have to understand why language was created to understand why maths makes sense

    or at least that's what id have to do

  25. i didnt like your infinity hotle it was ballshit to say the least, Infiniti is not a number it stands for goes on for ever even though you draw infinity with a start point and ends it at the start point at that point its starting over. leasts say 100 was that last number but was to high for you to know they say they dont have any rooms but ones always being made so if youre next it line you get room 101 now there full next person id like a room, sorry were full *but it is an infinite hotle * so one room should be instantly made into existence once the last one is taken anyway it doesnt just stop and start or push down the line, if you were pushing down the line your room would be zero and the guest that was in 1 and moved to 2 would still be in room 1 if they didnt have numbers youre just pushing numbers in the opposite direction if everbody did that youd be going into the negatives and thats my way of looking at it, probably take you more than a night to get to your room if you didnt take the 1st one but in saying that if there is a room for everybody to moved down in then there is a room for you 🙂

  26. "No energy system can produce sum useful energy in excess of the total energy put into constructing it" (The Fifth Law).

  27. Why is it that some men cannot separate sexuality from intelligence? It's a sad indictment of the male species.

  28. I get a gut feeling that the "gravity ride" is somewhere near Dinorwic, where my grandfather mined slate. This is after 13 minutes of watching from the start.

  29. 37:40 Use 1 ruler & you get X. Use 2 & you get a number slightly smaller. Using 3 or more do you get the same percentage smaller with each step? Can this be used in determining Pi? I think the word Mantissa as the numbers to the right of a decimal point becomes an approximation of the correct value as in 1/3 becomes 1.33333 & so on. This would go beyond, like headlights, that which you could see with any large numbers of rulers.

  30. 49:21 Not having the time I would still like to see a table where Infinity is added, subtracted (from & something subtracted from), multiplied, divided, & all other operations & permutations with normal, large, extremely large (infinity minus one which might be labeled with a backwards "L"), imaginary, another infinity & any other which I don't know of.

  31. I know you are not supposed to ask a lady her weight (Mass), but you did give it away with the answer. (Grin).

  32. The hamer and the feather fall with the same speed in a vacuum here on earth and on the moon. Or on Mars for that matter. Or on any planet or moon or even on a comet.

    If you have a cylindrical vacuum container big enough for that experiment and you place it in outer space, then what will the hammer and the feather do when you let go of them?

    I theorize that they will stay where you let go of them … if you can let go of them without giving them the slightest push?

  33. Legend has it, when Hannah was in 4th Grade, her mathematics teacher
    once asked: Which numbers between 1 and 10 can be divided by 2?

    All, replied the little Hannah.

  34. According to the HolyScripture, there are mysteries between miracle numbers and magic numbers. So, General Relativity has two aspects___Divine Relativity and Carnal Relativity. The concept of a right balance between the the two is important. Otherwise, mathematics goes awry. ______.

  35. Our place in the univuss.
    My hand stinging her face a second later with a reverberating slap. Now. How shall we go about mathematically describing the exact trajectories of this motion?

  36. 13:23 : About infinity and that there's no real actual infinity: – except for universe, which is physical, and might very well be infinite…

  37. 2:14 Because that reality created this reality out of the same Mass and the same laws of physics that control Mass oscillation and associated illusions of sensory perception caused by having one foot stuck to an initial (true) inertial frame of reference and the other one in a state of oscillation creating 3 observed moment arms connected to time dilation. All a center of gravity cares about is what's in the middle. Every major mystery in physics and astronomy from anti-matter asymmetry to "missing" dark matter is screaming out the answer… but if you don't let go of false complex assumptions that hide simple answers in this information frame you will never see the real picture hidden in a pile of illusions.

    Einstein was correct in holding on to logic connected to cause and effect… but the most difficult aspect of physics is putting on the straight jacket as cause and effect only supports one correct assumption. The most important pattern in Nature connected to time and space is being ignored because of false assumptions hiding it's raw logic and relative simplicity.

    27:17 Maybe it was caused by a loose cable like this "coincidence"….
    In 2011 OPERA announced it had done apox 1500 measurements of the muon neutrino traveling 453.6 miles @ (v-c)/c=2.48e-5 sec. over a period of 3 years. That appears to show the muon neutrino created at the speed of light was exceeding the speed of light by 2.48e-5 sec. Now here's the incredible coincidence caused by the "loose cable" that resulted in the mistake being announced worldwide… after the E158 ratio reduction calculations were posted on Nature's Forum.

    SLAC's E158 weak force asymmetry ratio {a} is created by adding the EXACT distance light travels in one hour to the EXACT distance light travels in one thousand years… and basic math reducing the E158 WF Asy gain down to 453.6 miles shows that is an EXACT match @ 2.48e-5 sec by creating an asymmetry in time of 0.20e-5 sec. just as predicted in the reverse oscillation phase. You don't have to use imaginary time to get the two measurements to match because (relative to our frame of reference) neutrinos oscillate in space connected to time and the mathematics added the 4th oscillation phase of the graviton better known as the electron hole shown opposite the electron… and that's where things get heavy due to the subtrahend of the EM wave created.

    SLAC confirmed time has asymmetry (adding a 2nd reverse arrow to time tailoring entropy to support Life's evolution) a year later in November 2012 adding yet another amazing coincidence. Then just a few months ago Monica Olvera de la Cruz at Northwestern University doing computer simulations working with nanoparticles engineered with DNA in colloidal crystals made a startling discovery that "rocks the current understanding of matter" and "upended the current accepted notion of matter" when she used a 1.4 nanometer nanoparticle 3/4 the size of DNA which exposed the electron oscillation phase of DNA. They had been using nanoparticles far bigger where the resulting structures appear static fixed in place, but when missing the space connected to time needed to support the reverse atomic oscillation phase of DNA the smaller nanoparticle appeared to turn into an electron and "this is where the magic happened" they said. 

    Monica's discovery has been confirmed and supports the mathematics that show Life has Mass, and Mass oscillation creates the atomic structure of matter that in turn creates a filter for sensory perception connected to time.

  38. Hannah Fry is a good example for how much the attractiveness of a person can be shaped by her personality. At first sight I would say that, to my personal taste, she's not a particularly pretty woman. But once you start watching her she's transformed by her charm and intelligence and seems much more enchanting to me than any catalog beauty.

  39. She gets on my nerves: talks too fast and pronounces words in an unexpected way. By the time I decipher and connect the sound of the word with its meaning, she has progressed with her thought/sentence – and that part is lost to me, I do not/ can not follow her. If she is so smart, she should talk much slower and pronounce things like an educated person, not like a sales lady at some London vegetables' market.

  40. OMG, This can't be serious? Are we to praise a man for his genius, (Sir Issac Newton) who actually poked a "blunt" needle into his eye, rather than read a book? ("on OPTICS")? Great, now I suppose 'astronaut" David Scott "drops the hammer, on logic?" We've all heard the expressionism: Great Scott!" according to Oxford Dictionary (Great Scott) is an arbitrary euphemism for "Great God!" We can decode the criminal minds who deceive us by ciphering their narrative's via Latin Scotia = Scoti or Scott? Ancient Greek (skotía = “dark, shadowy”). David in Hebrew "Dāwîḏ" = “beloved?"

    Maths in "INACTION" (2500°F − 32) × 5/9 1371.111 is the proper formula, and your the Mathematician?

    So in essence she wants us to verify a visual experiment conducted by a "FAKE SPACE" Astro-NOT?" conveniently named Beloved "DARK" god? Adding more salt to our wounds, she just warmed us minutes earlier that we shouldn't trust our senses? So how does confirming something via the illusion of "TV" somehow doesn't violate that principle?

    BTW, ("NASA, means Beguiler")?

    Other words that form (MAGICAL SPELLS): Astro = light, Naut = not? (Not Light)? aka "fleecing us in fake space?"

    Who can forget (Jason and the Argonauts)? The Greek term Naut = sailor BTW. …by now, you are surely getting the feeling we're getting FLEECED? ("NASA's" budget for 2019 is $21.5 billion. or 5.9 million a day?)

    The Golden rule of fleecing: ("to cheat, swindle, strip of money.")

    e.g. Didn't the Lame "Lunar Excursion Module" (LEM) aka ("Lemon") after all it ("Lem – ON", the Moon?) Remember, porr Gus Grissom hung a "LEMON" on the simulator, commenting on how infeasible Apollo really was, and met his gruesome end? The (LEM) was covered in MAGICAL GOLDEN "Tinfoil" space blankets?

    Tokamak = "Bullock's"
    Wisps of plasma, at 200 million Celsius to Fahrenheit reveal the obvious. …"if part of it, (plasma) touches the walls, it cools"
    Well people, if part of the containment was even in the proximity of 200 million (anything's). … it couldn't possibly hold?

    So insuring the plasma = (SHAPE) or (MOLD) remains stable is critical. …? ("Every magician needs to control there illusion")?
    There's actually 360 million reasons WHY "Tokamak" is a lie? (2e+8°C × 9/5) + 32 = 3.6e+8°F 360000032 = (666)?

    Digressing back to our "Psychonaut" experiment orchestrated by DAVID their (beloved dark god) Scott …
    Q: How come the feather fell at the same rate as the hammer? a.) Gravity, b.) Dielectric Acceleration?, c.) Californication?
    A: Red Hot Chili's: "Space may be the final frontier but it's made in a Hollywood basement?" (✓)

    Another great video, congrats you must be proud. …~Inertia

  41. How mad would we be if reality was haphazard and made absolutely no sense? We would not be who we are .. but something different, something lost and sad. Thankfully or universe is very ordered like a ladder., that we can slowly climb knowing there is always another rung.

  42. @33:28 they just finish talking about how space has many possible variations … and they happen to be platonic solids … which all have a common root generic shape … so the lowest common denominator between all of the platonics is a part of the very first shape primarily … which is 4 equilateral triangles … so whatever is making waves in the universe for creation happen uses that pattern to transmit it's basic shape … from there energy level ( electro magnetic force ) takes over and makes everything from there … now it's just a matter of figuring out the energy levels and frequencies and poof you can make or replicate anything from a power source using a base substrate of a primary constituent to what you want to make …

  43. Before the Gods of the Infinite heavens noticed Earth, they sent the wind to kiss your beautiful hair, and that's how maths was born, or so Leonard Cohen might sing it up there, in the Tower of Song.

  44. Prof James Gate finding binary error codes ,the exact same code behind the internet compression files-EXACT SAME CODE , in the maths of super string theory . It doesn't necc mean we live in a computer sim but it should make you think …. i mean what the hell ??

  45. you could ask everyone at the Infinity Hotel to move down a room so you could have the first one, but it would take forever.

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