seven equations that rule your world - what is the best car alarm
The alarm sounded from Ian Stewart.
You looked at the clock. The time is 6. 30 am.
You haven't even got up yet, and at least six mathematical equations have affected your life.
Without a critical equation in quantum mechanics, it is impossible for a memory chip that stores time in a clock to be designed.
Its time is set by a radio signal, and if it weren't for James Kohler Maxwell's Foursquare, we never dreamed of inventing the signal.
The signal itself travels according to the wave equation.
We float in a hidden ocean of equations.
They work in the areas of transportation, financial systems, sanitation and crime prevention and detection, communications, food, water, heating and lighting.
Walk into the shower and you will benefit from the equation that regulates the water supply.
Your breakfast cereal comes from crops cultivated with statistical equations.
Driving to work, the aerodynamic design of your car depends in part on navi-
The Stoke equation that describes how air flows above and around it.
Turning on its satellite navigation system involves quantum physics again, plus Newton's laws of motion and gravity, which helps to launch positioning satellites and determine their orbits.
It also uses the random number generator equation of the timing signal, the triangular equation for calculating the position, and the special and general relativity for accurately tracking satellite motion under Earth gravity.
"We float in a hidden ocean of equations.
They work in transportation, sanitation, communications, food, water, heating and lighting "and most of our technology will never be invented without the equation.
Of course, important inventions like fire and wheels are made without any mathematical knowledge.
Without equations, however, we would fall into a medieval world.
The equation is far beyond the technology.
Without them we will not be able to understand the control of tides, the breaking of waves on the beach, forever
Changing weather, the movement of planets, the melting pot of stars, the spiral of galaxies-the vastness of the universe and where we are.
There are thousands of important equations.
The seven I'm focusing on here-the wave equation, the four equations of Maxwell, the Fourier transform, and the schröröringer equation-illustrate how empirical observations lead to the equations we use in science and everyday life. Graphic:
See equation seven first, wave equation.
We live in a rough world.
Our ears detect compressed waves in the air like sound, and our eyes detect sound waves.
When an earthquake struck a town, the damage was caused by seismic waves passing through the Earth.
It is difficult for mathematicians and scientists not to think about the waves, but their starting point comes from art and the colon;
How does a violin string sound?
This problem dates back to the worship of the bidagolas in ancient Greece, and he found that if two strings of the same type and the same tension have length in a simple proportion, such as 2 & colon; 1 or 3:
Together they sent out notes that sounded unusually harmonious.
The more complex ratio is discord and unpleasant for the ears.
The Swiss mathematician, John burnuli, began to understand these observations.
In 1727, he imitated a violinist string into a mass of closely spaced dots connected by springs.
He wrote the equations of motion of the system with Newton's law and solved them.
Based on these solutions, he concludes that the simplest shape of the vibrating string is the sine curve.
There are other modes of vibration, as well as sine curves, in which more than one wave fits the length of the string, which the musician calls harmonic.
About 20 years later, Jean Le Rond d'Alembert followed a similar procedure, but he focused on simplifying the equations of motion rather than simplifying the solutions of the equations of motion.
What appears is an elegant equation that describes how the shape of the string changes over time.
This is the wave equation, which states that the acceleration of any short segment of the string is proportional to the tension on which it is acting.
This means that waves whose frequency is not a simple ratio produce an unpleasant buzz called the "beat.
That's one of the reasons why a simple digital ratio gives a note that sounds harmonious.
The wave equation can be modified to deal with more complex and confusing phenomena such as earthquakes.
The complex version of the wave equation allows the seismologists to detect what is happening hundreds of miles under our feet.
As one plate slides below the other, they can map the Earth's tectonic plates, triggering earthquakes and volcanic eruptions.
The biggest gain in this area will be a reliable way to predict earthquakes and volcanic eruptions, and many of the methods being explored are based on wave equations.
But the most influential insight from the wave equation is from studying Maxwell's emc equation.
Most people lit their house with candles and lanterns in 1820.
If you want to send a message, you write a letter and put it on the back of the Horsedrawn carriage;
You omitted shipping for emergency information.
In 100, families and streets had electric lights, and telegrams meant that information could be spread across continents, and people even started talking to each other over the phone.
Radio communications got a demonstration in the lab, and an entrepreneur set up a factory to sell "wireless" to the public.
The discovery of two scientists triggered the social and technological revolution.
In about 1830, Michael Faraday established basic physics.
Thirty years later, James Clark Maxwell began seeking to lay the mathematical foundation for Faraday's experiments and theories.
At that time, most physicists who studied electricity and magnetism were looking for an analogy with gravity, which they thought was the force that worked in the distance between objects.
Faraday has different ideas & colons;
To explain a series of experiments he carried out in terms of electricity and magnetism, he assumes that both phenomena are fields that are filled in space, change over time, and can pass through the forces they produce
Faraday put forward his theory in terms of geometric structure, such as magnetic lines.
By analogy with the mathematics of fluid flow, Maxwell restates these ideas.
He inferred that the Force line is similar to the path followed by the fluid molecule, and the strength of the electric field or magnetic field is similar to the speed of the fluid.
By 1864, Maxwell has written four equations for the basic interaction between the electric field and the magnetic field.
The two tell us that electricity and magnetism can't leak.
The other two tell us that when an electric field region rotates inside a small circle, it generates a magnetic field, and the rotating area of the magnetic field produces an electric field.
But the next thing surprised Maxwell.
By doing some simple operation on his equation, he successfully deduced the wave equation and deduced that light must be a sound wave.
This is an amazing news in itself, because no one can imagine such a fundamental connection between light, electricity and magnetism.
The light has different colors, corresponding to different wavelengths.
The wavelength we see is limited by the light chemistry of the eyes.
Maxwell's equation has led to a dramatic prediction that waves of all wavelengths should be present.
Some wavelengths are much longer than we can see, changing the world & the colon; radio waves.
"The Maxwell equation has led to a dramatic prediction that waves of all wavelengths should exist.
Heinrich Hertz demonstrated radio waves in an experiment in 1887, but he didn't realize that they were the most revolutionary applications.
If you can impress in such a wave, you can talk to the world.
Nikola Tesla, Guglielmo Marconi and others have turned dreams into reality, and the entire modern communication system from radio and television to mobile radar and microwave links naturally follows.
It all stems from four equations and a few short calculations.
Maxwell's equation is not just changing the world.
They opened a new one.
As important as Maxwell's equations are, they don't describe things.
Although these equations reveal that light is a wave, physicists quickly find that the behavior of light is sometimes inconsistent with this view.
It glows on metal to produce electricity. this phenomenon is called photoelectric effect.
It only makes sense when light behaves like a particle.
Wave or particle alone?
In fact, there's one thing about both.
Matter is made up of quantum waves, and a closely arranged wave is like a particle.
In 1927, an equation for quantum waves is written by Elvin schörörörörörör.
It fits the experiment perfectly, and at the same time depicts a very strange world in which elementary particles like electrons are not very good --
Defined object, but probability cloud.
The spin of the electron is like a coin, which can be half a head and half a tail before hitting the table.
Soon, theorists began to worry about all sorts of quantum quirks, such as the cat who escaped at the same time, and the parallel universe in which Adolph Hitler won World War II.
Quantum mechanics is not limited to such philosophical mysteries.
Almost all modern electronic devices-computers, mobile phones, game consoles, cars, refrigerators, ovens-have transistor-based memory chips, and the operation of transistors depends on quantum mechanics of semiconductors.
New uses of quantum mechanics are available almost every week.
Quantum dots are a small piece of semiconductor that can emit light of any color for biological imaging, replacing traditional toxic dyes.
Engineers and physicists are trying to invent a quantum computer that can perform many different calculations in parallel, just like a cat that is alive and dead.
Laser is another application of quantum mechanics.
We use them to read information from small pits or markers on cd, dvd and Bluray discs.
Astronomers use lasers to measure the distance from the Earth to the moon.
It is even possible to launch a space vehicle from Earth on the back of a powerful laser beam.
The last chapter of the story comes from an equation that helps us understand the waves.
It began in 1807 when Joseph fuliye designed a heat flow equation.
He submitted a paper about it to the French Academy of Sciences, but was rejected.
In 1812, the college set the theme of the annual awards as a hot topic.
Fu Liye submitted a longer revised paper and won the victory.
The most attractive aspect of the Fu Liye Award-
How he solved the problem, not how to win the paper.
A typical problem is how the temperature along the thin rod changes over time, given the initial temperature distribution.
If the temperature changes along its length like a sine wave, Fourier can easily solve this equation.
Therefore, he expressed the more complex profile as a combination of sine curves of different wavelengths, solved the equations of the sine curves of each component, and added these solutions.
Fu Liye claims that this method is applicable to any profile, even the profile with a sudden change in temperature.
All you have to do is add an infinite number of contributions from more and more winding sine curves.
Still, Fu's new paper was criticized for not being rigorous enough, and the French Academy again refused to publish it.
In 1822, Fu Leye ignored the objection and published his theory as a book.
Two years later, he was appointed college secretary, scoffed at critics and published his original paper in college magazine.
Critics do, however, have a point of view.
Mathematicians began to realize that infinite series are dangerous beasts.
They don't always perform well, limited and.
It turns out that it is very difficult to solve these problems, but the final conclusion is that the idea of Fourier can become strict by excluding highly irregular contours.
The result is a Fourier transform, an equation of processing time.
Change the signal to the sum of a series of component sine curves and calculate their amplitude and frequency.
Today, the Fourier transform affects our lives in various ways.
For example, we can use it to analyze the vibration signals generated by earthquakes and to calculate the frequency at which the vibration ground transmits the maximum energy.
Take a wise step to the earthquake
Proofreading of buildings is to ensure that the preferred frequency of buildings is different from that of earthquakes.
"Today, the Fourier transform affects our lives in many ways, from finding structures in DNA to compressing digital photos," Other applications include removing noise from old recordings, using X-
Image of light, improve radio reception, prevent unnecessary vibration in the car.
Also, most of us use this inadvertently every time we take a digital photo.
If you calculate how much information is needed to represent the color and brightness of each pixel in a digital image, you will find that the amount of data on a digital camera seems to be 10 times that of a memory card.
The camera does this using JPEG data compression, which combines five different compression steps.
One of them is the digital version of the Fourier transform, which processes signals that change not over time but over images.
Mathematics is actually the same.
The other four steps further reduce the data to about one-
A tenth of the original amount.
These are just seven of the many equations we encounter every day, not realizing that they are there.
But the equation has a much greater impact on history.
A truly revolutionary equation has a greater impact on human survival than all kings and queens, and their plot is filled with our history books. There is (or may be)
Most importantly, physicists and cosmologists like an equation that puts their hands on the colon very much;
The theory of unifying quantum mechanics with relativity.
Among the many candidates, the most famous is the super string theory.
But as far as we know, our equations for the physical world may just be too simplistic to capture the deep structure of reality.
Even if nature follows the universal law, they cannot be expressed by equations.
Some scientists believe that it is time for us to completely abandon the traditional equation and instead support the algorithm-a more general way to calculate things involving decision-making --making.
But before that day comes, if any, our greatest insight into the laws of nature will continue to take the form of equations, and we should learn to understand them and appreciate them.
The equation is recorded.
They really changed the world and they will change the world again.