Documentary : Top 10 equations that changed the world | 1080p

you [Music] equations are the lifeblood of mathematics science and technology without them our world would not exist in its present form the course of human history has been redirected time and time again by equations equations have hidden powers they reveal the innermost secrets of nature as Steve Jobs said in his iconic speech at Stanford we cannot connect the dots looking for words we can connect only looking backwards let's look back at our past and the journey up till now let's look back at the top-ten equations that has changed the world number 10 Pythagoras theorem a squared plus B squared equals to C squared this equation reaches far beyond its domain of geometry and algebra than perhaps any other equation on this list the simplicity is its power this equation revolutionized our way of perceiving distances link geometry and algebra in such a way that it gives birth to the coordinate system or more specifically how we measure distances in terms of coordinates our knowledge about its origin is very little and obscure we are not sure Pythagoras even invented it Babylonians in 2nd millennium BC 1000 years before Pythagoras knew the relations between Pythagoras triplets it is possible though that Pythagoras was the first one to prove it which he did around 530 BC it attained its first recorded proof and its most polished form in 250 BC when Euclid clearly wrote about it in his famous textbook elements he wrote in right-angled triangles the square on the side subtending the right angle is equal to the sum of the squares on the sides containing the right angle the translation being made possible by Sir Thomas Heath we don't know how Pythagoras theorem got its name but whatever and whoever the reason is behind its existence it sure paved the way for a whole new frontier of science to follow number 9 logarithms log of XY equals log of X plus log of Y at first look you might doubt its position in this countdown however look a bit deeper and you would see that nothing absolutely nothing in modern day science would work without it logarithm was developed with just one purpose in mind to make multiplications easy it does so by changing multiplication of two numbers into addition of two you might think 2 x 3 is a lot easier to solve in he raised to the power L + 2 + L + 3 and you are right it is however it was not devised for doing to cross three it was devised for astronomical calculations which is way more complex than to cross three multiplications at that level in those days were beyond tedious logarithm was invented by John Napier and he first published it in his book mirror fissile auger at Amorim canonist description description of the wonderful Canon of logarithm 1614 however it was Henry Briggs that made logarithms the way they are today he proposed the following Corrections number one the base of log should be greater than one and number two the idea that log of ten equals one thus drastically reducing the fatigue of calculating log twelve point three four five six seven eight nine if you knew log one point two three four five six seven eight nine logarithm is an indispensable tool in the toolbox of a mathematician and also calculus evolution pretty much had to come up with something like a logarithmic scale because the external world presents our sense with stimuli over a huge range of sizes a noise can be very low or very loud an ear made sensitive enough to hear the little sounds would be destroyed when hearing a loud sound conversely an ear made to hear loud sound wouldn't be able to hear little sounds at all that's the problem with being sensitive to absoluteness rather being sensitive to proportions make excellent sense logarithm does exactly that example say you can hear a sound in a range of 1 to 10 units if you perceive stimuli in absolute scale you can hear sound only up to 10 units after which your ears will be permanently damaged however if you follow the logarithmic scale which we do instead of absoluteness you will focus on ratio say you can perceive a minimum difference of 2 X then you would be able to hear sounds of units 1 to 1024 the only fault you will have is that when you hear 2 multiple sounds simultaneously and if they differ by a factor less than 2 they would sound the same also you won't be able to hear the range 0 to 1 and 1024 to infinity but it's a small price to pay comparing to what you are getting number 8 differentiation change of dependent variable with respect to independent variable is equal to the ratio of the change in functional value for an increment to that of the increment itself where the increment tends to 0 what can be said the entire mathematics and physics even parts of chemistry and biology depends on calculus which would not have been possible without derivatives let's start with the most important question in calculus who invented it while both Gottfried Leibniz and Isaac Newton discovered calculus more or less independently however we are not sure who did it first that is because none of them published their works as soon as they got the results Newton's work dates back to 16 71 while Leibniz to 1675 to make things messy the approach of Leibniz was more efficient and promising making things worse the notation we use in calculus now are borrowed from both of them by DX from live Nets and F dash of X from Newton I think it boils down to this just like Pythagoras theorem it doesn't matter much who invented it as much as who introduced it it was Newton who introduced calculus into the world who used it to study the laws of nature and I think that is the reason Newton is often credited more than live notes also it is justified I think the world couldn't be less grateful to him for introducing calculus into physics however we cannot give all credits to Newton for his calculus for no matter how grandeur it was flawed a leading critic an anglo-irish philosopher George Berkeley Bishop of Cloyne felt Newton's discoveries as an attack on religion and attacked back by calling derivatives ghosts of departed quantities and questioned the very foundation of calculus the non-zero number H which we after calculation make equal to zero how can we divide something with zero in the first place his question was spot on the solution to this key question was limits which came in 1816 by bohemian mathematician Bernard Bolton oh but like all tragic stories it was never appreciated till 1870 when German mathematician karl weierstrass extended the formula to complex functions after the advent of limits the very foundation of calculus was reformulated nowhere in the calculation do we ever divide by zero because we never set H equals to zero moreover nothing here actually flows like Newton originally described what matters is the range of values that H can be assumed with not how it moves through that range so Berkeley's sarcastic characterization is actually spot-on the limit L is the ghosts of departed quantity by H and Newton's oh but the manner of the quantities departure approaching zero not reaching it leads to a perfectly sensible and logically well-defined ghost finally calculus had a sound logical foundation and it was now all set to redefine the world number seven Newton's law of gravity F equals two gravitational constant multiplied by m1 into m2 divided by square of the distance between the bodies Newton's influence on the revolution of science and the way we understood nature is never-ending Newton was not the first of the age of reason he was the last of the magicians the last of the Babylonians and Sumerians the last great mind which looked out on the visible and intellectual world with the same eyes as those who began to build our intellectual inheritance about ten thousand years ago Isaac Newton a posthumous child born with no father on Christmas Day 1642 was the last wonder child to whom the mage I could do sincere and appropriate homage fifth July 1687 Newton's philosophy I naturalis principia mathematica the system of worlds re-evaluated our and above all God's position in this universe Newton's law of gravitation synthesized in one simple mathematical formula millennia of astronomical observation and theories it explained many puzzling features of planetary motion and made it possible to predict the future movements of the solar system with great accuracy Einstein's theory of general relativity eventually superseded the Newtonian theory of gravity as far as fundamental physics is concerned but for almost all practical purpose the simpler Newtonian approach still reigned supreme today the world's space agencies like NASA and ESA still use Newton's laws of motion and gravitation to work out the most effective trajectories for spacecraft we cannot talk about gravity without talking about the famous Apple story which was first mentioned in 1752 memoirs of Sir Isaac Newton's life by William Stokely after a deep investigation the truth if it is even is that no Newton didn't realize gravity by the falling Apple however gravity is not that important itself words about gravity was in the air for a long time far before birth of Newton but what Apple probably did was that it made Newton realize the universality of gravitation it is this very reason why Newton more than anyone in history is credited for gravity it was he who proposed that not just son but everything that has mass attracts everything else and the force with which one body attracts another is mutual out of all the innumerable things that Newton's law of gravity made possible the latest and the most amazing one is called gravitational network tubes it's an idea straight out of sci-fi it has been observed that planets and moons of the solar system are tied together by a network of tubes whose mathematical definition requires many more dimensions that just four they can be seen only through mathematical eyes because they are not made of matter their walls are energy levels if we would visualize the ever changing landscape of gravitational fields that control how the planets move we would be able to see the tubes swirling along with the planets as they orbit around Sun without going into further details the discovery of tubes took the efficiency with which we could space travel to a whole new level and redefine the method of plotting the best trajectory for interstellar missions all of which would not have been possible without Newton and his epic law of gravity there is a tie for the number six spot it is held by I square equals to minus one square root of minus one and also by Euler's formula for polyhedral Fe plus of equals tio2 where F his face he is H and V is vertices it led to the foundation of complex analysis which is now even more important that real analysis in areas like statistics mathematics and mathematical physics especially quantum mechanics the one who knows this must hate this equation at first sight and one who doesn't know must be thinking what's so special about it well it all began in 1545 when gambling scholar Girolamo Cardno first encountered this while writing an algebra text he couldn't make sense of it and declared it useless then come Raphael bomb le and thought he could certainly do better by 1572 he had noticed that these numbers despite being baffling and nonsense they did lead to perfectly correct results when used blindly it took almost 18th century for scientists to finally get an idea of what it is by 19th century scientists started feeling comfortable about it however by the time they were truly understood they had already become indispensable in mathematics and science and it's definition hardly mattered with the dawn of 20th century the so called imaginary numbers seemed no less real than their older cousins the real numbers it all started when there was a concept that squares are always positive and defined it was Renaissance time and the concept sprang from their logic that no matter what you do to a square double it or vanish it hole the least you can reach is zero not negative ie even square doubling is always greater than equal to zero live nets on 1702 wrote the divine spirit found a sublime outlet in that wonder of analysis that portent of the ideal world that amphibian between being and non-being which we call the imaginary root of negative unity the first one to make sense of them was Wallace 1758 his idea was then improved upon by vessel 1797 Argand 1806 and gauze eighteen oh eleven it came to gain wide acceptance when calculus was expanded to complex realms Euler also contributed by merging the realm of complex and trigonometry by giving his formula he raised to the power i z equals to COS of Z plus I sin of Z for Z equals to PI e raised to the power I pi equals minus 1 plus 0 or e raised high pi plus one equals zero this equation has been voted time and time again as the most beautiful equation in mathematics it unifies calculus es e trigonometry spy complexes I and algebras one to give the ultimate number zero it is based so deep into the current model of mathematical analysis and modern physics that you cannot do anything without them you either learn it or close your eyes to see nature as God mean it to be you need an eye while I changed one pillar of mathematics Euler changed the other Euler was the man who single-handedly changed the very face of mathematics he published more papers than any other scientist in the history and has also contributed most number of equations to mathematics thus making him the rightful owner of the title the greatest mathematician of all time why is this formula important well before it the three pillars of pure mathematics were algebra analysis and geometry after this formula it became algebra analysis and topology this founded a whole new branch of mathematics where shapes never matter only the points do for the sheet here is elastic this revolutionized the way we approach any problem related to geometry when asked Euler said this has nothing to do with maths it's just observation don't know how anyone never noticed it I do not think this can be explained in simple terms here for the time and knowledge required to know more about it is way beyond many of us for now let's just end by saying that when a formula results in equation of a whole new pillar of mathematics you can guess how important it is number five wave equation del square of u by Del T square equals to v square into del square of u by Del X square where u equals to X T very basically say a wave is propagating Delta x equals tove of delta T for a parameter u X T del u by del x equals to tell u by V del T again del square u by Del X square equals to del square u by V square del T Square for limit Deltans to 0 del square u by Del T square equals to b square del square u by del x square this helps us visualize how a wave propagates the greatest use of this is in the study of earthquakes and tsunamis thus you can understand how important it is this gave birth to acoustics the interdisciplinary science that deals with the study of all mechanical waves in gases liquids and solids including topics such as vibration sound ultrasound and infrasound or the other way around you this equation exists only because scientists wondered why does the strings of violin create sound it took birth from the fundamental elements of music that is harmonics for same tension to string different lengths produced different sounds some were unpleasant and some touched the hearts it is this curiosity to reveal the secret of music that leads scientists to discover a formula which now predicts the height of its tsunami wave it all started with Pythagorean x' the cult founded by Pythagoras it was reported by around hundred and fifty ad however it was Dalembert who proved the equation in 1746 by applying Bernoulli's approach to Newton's second law of motion from then it spread across the world of science like a forest fire it is extensively used to drill out all the quadrillion dollar industry nowadays explosions are made at the surface and using the principle of returning echoes of the seismic waves they map out the underlying geology and hence find where oil is number four Fourier transformation F of epsilon equals to integration minus infinity to plus infinity f of X he raised to the power minus two pi X epsilon DX where epsilon is frequency what is this well what it does is that it transforms any function into a function of multiple sinusoidal waves which when drawn superimposes to give back the original function why is it important well without a genetical development would have stopped at the foot of the ever-popular DNA molecule it is the series that led to the analytical study of DNA and thus pushed the mankind to a whole new level of intelligent species for a more daily example Fourier series is used in image processing the thousands of selfies you take would not have been possible without it the very format of JPEG would not have been possible without this how well first let's see how it was discovered it all happened when Fourier in 1807 submitted an article on heat flow to the french academy of sciences based on a new differential equation although that prestigious body declined to publish the work it encouraged Fourier to develop his idea further and try again at that time the academy offered an annual prize for research on whatever topic they felt was sufficiently interesting and they made heat the topic of the year for the 1812 prize Fourier Dooley submitted his revised and extended article and won his heat equation was del u by del T equals to alpha into del square u by Del X square where u is the temperature function and alpha is constant of thermal diffusivity it is almost similar to the wave equation except it has del square by Del T square the difference is huge it means that in wave energy is conserved but in heat flow it was not so however while solving this equation for trigonometric profile from there sprang out this brilliant conclusion that any function continuous or discontinuous can be represented as superposition of sinusoidal curves provided we have enough of them that is an infinite series of sine curves after all the solution was insufficiently rigorous and every scientist discarded his prize-winning formula we now know that although Fourier was right in spirit his critics had a good reason for worrying about rigor the problem was when does the Fourier series converge to the function it allegedly represented that is if you take more and more terms does the approximation to the function get even better even Fourier knew the answer was not always resolving it was tricky it required a new theory of integration by unruly Bess q a reformulation of the foundation of mathematics in terms of set theory was made by Georg Cantor and major insights from towering figures like Raymond fast-forward the time and now it is being used everywhere stripping out unnecessary frequencies from the source signal to reduce your telephone cost to making buildings that can efficiently absorb earthquakes its greatest impact is perhaps in the digital revolution you can follow the links to know more about them for now we end by saying that the equation which took birth from heat flow has literally set the world on fire this number two well the second position is a tie again between Maxwell's equations divergence of electric field equals to Rho by epsilon not divergence of magnetic field equals to zero curl of electric field equals to Del of magnetic field by del of time curl of magnetic field strength equals to current density plus del of electric displacement by del of time and black Scholes equation at the start of 19th century most people lit their houses using candles and lanterns gas lighting which dates from 1790 was occasionally used in homes and business premises mainly by inventors and entrepreneurs gas street lighting came into use in Paris right een 20 at that time the standard way to send messages was to write a letter and send it by horse-drawn carriage for urgent ones keep the horse and omit the carriage the main alternative was mostly restricted to military and official communications which was optical Telegraph the first extensive system of this type dates from 1792 when the French engineer Claude chap built 556 towers to crave 4800 kilometer network across France it remained operational for 60 years fast-forward 100 years homes and streets now had electric lighting Electric telegraphy had come and gone and people could talk to each other by telephone radio communication was at the verge of being commercialized and Wireless had become the hottest word among the elites all this can be traced back to two scientists whose monumental insights into how universe could work in the most magnificent scale brought upon physics the greatest revolution ever since Newton discovered gravity they were anglish man Michael Faraday and Scotsman James Clerk Maxwell Faraday was a son of blacksmith and was trained as a booksellers apprentice he lacked formal education but that's okay for history remembers him as one of the great experimentalist ever his extensive experiments in electricity and magnetism led him to conclude one of the fundamental equations of electromagnetism EMF induced equals to minus del Phi by Del T equals to minus del by Del T of closed surface integral of B vector EMF induced equals to closed contour integral of e vector equals to minus del by Del T of closed surface integral of B vector equals to minus surface integral of del a B vector by Del T therefore closed contour integral of e vector equals to minus closed surface integral of del a B vector by Del T using Stokes theorem surface integral of curl of e vector equals to minus closed surface integral of del a B vector by Del T or curl of e vector equals to minus del B vector by Del T what this tells is that over a closed surface area if the magnetic field changes a voltage will be introduced over that area and it will be in a direction opposite to that of the magnetic potential for the first time in history two completely different seeming quantities were unified however this was not how he described it he described in analogies of machine and theories like he invented this concept of static field lines penetrating the fabric of space which relays the effect of field to that subject and results in a force along its direction he lacked the knowledge of mathematics and then was ridiculed upon it is then that Maxwell came into action after getting his mathematical degree from Cambridge he went for post graduation at Trinity College where he read about Faraday's experiment in 1860 he moved to King's College London where he could sometimes meet faraday finally Maxwell embarked on his most influential quest to formulate a mathematical basis for Faraday's experiment and theories rest is history they changed everything about how we perceived electricity and magnetism and the uses endless what's important though is the correction Maxwell made remember those static field lines Faraday talked about they would be dynamically emanating from the source and traveling to infinity secondly they would be spherical and not lines although eventually they changed into lines at infinity also curiously when solved for free space Maxwell's equation gave the wave equation where v square came out to be 1 by mu naught epsilon naught or v equals to 1 by square root of mu naught epsilon nought or equals to 3 into 10 to the power 8 or the speed of light thus this proved that light is an electromagnetic wave formed by two mutually perpendicular Li varying electric and magnetic field while this revolutionized the world of physics there is yet another equation that affected the world in an equal scale however in a completely different way the black-scholes equation this equation describes how the price of financial derivative change over time based on principle that price is correct the derivative carry no risk and no one can make profit by selling it at different price why is it important well it makes it possible to trade a derivative before it matures by assigning an agreed rational value to it so that it can become a virtual commodity in its own right what does that mean for the world well it leads to one massive growth of the financial sector - ever more complex financial instruments three surges in economic prosperity punctuated by crashes for the turbulent stock market of the 1990s 5 the 2008 to 0-9 financial crisis 6 and also the ongoing economic slump since the turn of the century the greatest source of growth in the financial sector has been in financial instruments known as derivatives derivatives are not money nor are they investments in stocks and shares they are investments in investments promises about promises here's a simplified example due to rules about market stability you have agreed to buy 200 tons of rice every year from the market however you see the value of rice Rises every year so you can buy now and sell it next year at higher price then you become greedy and you want even more money what you do is that you use the black Scholes equation to estimate the value of rice in two years you then go to another guy and say that hey look after two years 200 tons of rice will be thrice as costly I have promised the market to buy from them 200 tons rice every year so if you pay me double the amount of what it's worth now I will give you 200 tons of rice which I have promised to buy from the next year which by then would cost thrice the money it costs no that way I make profit now and you make profit then this is the mess that the equation created what was its effect in 1998 the international financial system traded roughly 100 trillion dollar in derivatives by 2007 this amount grew to one quadrillion dollar the problem was these all were a mess of virtual money in real the total value of all products ever manufactured for last 1,000 years is about 100 trillion dollars adjusted for inflation if you can see the problem at some point the entire system will fall like a house of cards it happened in 2008 to 0-9 when the world lost 17 trillion dollars the only difference being this was real money who would have imagined what a disaster an equation can cause this equation became so important that it won Merton who modified it later and Scholes black being already dead the 1997 Nobel Prize in Economics we have finally reached number one so far we have seen equations that changed the courses of history left and right which makes us wonder which equation can overpower all of them what can be more important than all previous ones how much more powerful and impactful can an equation get well to begin with our winner of number one spot for the equation that changed world is not one but rather it's a tie again it's a tie between the two pillars of modern physics the equations on which the entire universe rests from quarks to supermassive black holes wormholes to bending of time and light they can make anything possible they are Einstein's relativity and Schrodinger's quantum mechanics let's start with Einstein the man synonymous to genius his theory of relativity consists of special relativity and general relativity both of them consists of more than one equation however out of all those comes out these two equations which made this dude with crazy hairs into the greatest scientists and even more the greatest minds of all time they are number one he equals mc-squared and number two this how they came and what they do there are billion videos about that on internet and there's a good reason for that equation so powerful cannot be explained in short rather they shouldn't be explained in short one must know them in their full glory or don't know them at all I will leave links to some of the best videos for you to check out if you wish to what I will tell you though is what they meant for the world his special theory of relativity redefined the laws of conservation of energy mass and momentum and his general relativity redefined the entire definition of space and time and how they interact together they redefined everything we knew about world it was the birth of a new modern physics when Einstein first came up with his theory of general relativity he said that the theory is so beautiful he would feel sorry for God if it doesn't turns out to be true luckily for God it did turn out to be true and made Einstein the Einstein remember how I said there are millions of videos out there about his theory well for a few things there are none they are the exact reason for conducting michelson-morley experiment in different season and different locations how the results threatened to dispose of Maxwell's equations itself the difference between Galilean Newtonian and Einstein's relativity what Minkowski space-time distant formulae actually means and about how he explained the orbit of mercury which Newtonian gravity failed to do on this let me know down in the comments if you want to know them and I will publish a blog post about them then for you hardcore science nerds for now we end by saying that Einstein more than any other person in the world deserves a universal hats off he taught himself to think not just out of the world but out of the universe in an age where we already thought that we knew everything he superseded Newton's theory of gravity when even today it works perfectly fine for 99% of cases only when gravity comparable to that of Sun or above comes into play does Einstein's relativity show it's true color with no actual clue or frame to work upon with just sheer power of his intellect he single-handedly showed God how men doesn't need to always learn from problems they face how men can see through the same eyes as that of God into the future and beyond to reveal what God has hidden under the table while Einstein towered above all to see through galaxies things went differently at the smaller scale by smaller I mean much much smaller welcome to the world of quantum mechanics where nothing actually exists all that exists is the probability of everything's existence these probabilities interact with each other and the energy around them in ways no classical or relativistic physics can explain it demanded a new branch of physics on its own in 1900 the great physicist Lord Kelvin argued that the then-current theory of heat and light considered to be an almost description of nature was obscured by two clouds the first involves the question how could move through an elastic solid such as luminiferous ether the second cloud was doubt about the maxwell-boltzmann doctrine regarding partition of energy he was spot on we saw how the first question was solved by Einstein's relativity now we will see how the second equation pans out to be it all began with light bulbs when a german physicist named Max Planck was hired in 1884 to design the most efficient light bulbs possible in short this led him to throw away the then-current theory of radiation and energy distribution the equipartition theorem and reinforcing thermodynamics assumptions he proposed that energy distribution cannot be continuous it has to be discrete since then Einstein proved how light has particle nature - by then people had accepted that light is both a particle and wave then came this equation which became the central equation of quantum theory the equation bears the name of her when Schrodinger in 1927 he wrote down the differential equation IH cross del shy del T equals H cap shy where H crosses H by 2 pi and H cap is Hamiltonian operator one way to interpret this is that quantum waves are linked pairs of real waves as if a complex ocean that actually is made up of real waves of different heights with the two direction of height being at right angle to each other also as time passes the wave cycles through a whole series of shapes and each is mysterious linked to the other it's like two waves are two faces of same wave which spin steadily around a unit circle in complex plane the real and imaginary parts vary sinusoidally we can solve the equation like one solves for EA's equation however here we get eigenfunctions unlike the functions of space and time which we get in furry and classical wave equation an eigenfunction is a multiplication of two functions one of only space and other of only time despite all the complications it would just have been a fancy form of classical wave equation if it wasn't for a puzzling twist you can observe classical waves and see what shape they are even if they are a superposition of multiple Fourier modes but in quantum mechanics you can never observe the entire wave function all you can observe on any given occasion is a single component eigenfunction roughly speaking if you attempt to measure two of these components at the same time the measurement process on any one disturbs the other there are so so much more but we end here some are extra easy some cannot be expressed even in thoughts some are small some are big but they all single-handedly change the course of human history [Music] you [Music]

Channel: Scrivial

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Keywords: Equations, Scrivial, Five Equations That Changed The World, Documentary (TV Genre), Production, History, Media, Best, Quality, 1080p, change the world, top 10 equations that changed the world, 4k, Top, Revolutionary, HD, of all times, full HD, Equation, Greatest, top 10, 720p, Definition, top 10 equations, Revolutionary equations

Id: 0K-t090uvL4

Length: 40min 20sec (2420 seconds)

Published: Sun Oct 25 2015