There’s a very interesting article by Ian Steward in the February 13, 2012 New Scientist. Stewart explains how seven equations changed the world and are central to modern life. These equations are
Wave Equation
Johann Bernoulli (using Newton’s Laws) developed this equation from the ancient Greek Pythagoreans, and subsequently Jean Le Rond d’Alembert used both of these preceding formulae to produce the wave equation.
Maxwell’s Four Equations for Electromagnetism
The wave equation was central to the work of Jam4es Clerk Maxwell, particularly assisted by Michael
Faraday’s work on the basic physics of electromagnetism. Faraday framed his theories as geometric structures – lines of magnetic force. Maxwell reformulated these using the mathematics of fluid flow. He developed two equations showing that magnetism and electricity don’t leak away. A third says that an electrical field spinning in a small circle creates a magnetic field, and the fourth says that a spinning magnetic field creates an electrical field.
By manipulating these four equations, Maxwell derived the wave equation and deduced that light itself must be an electromagnetic wave. This was a revolutionary link between light and electricity and magnetism. This approach led to a prediction that electromagnetic waves of all wavelengths should exist, not just those visible to the human eye.
Some of these invisible long-wave forms would become radio waves as demonstrated in 1887 by Heinrich
Hertz and used to carry information by Nikola Tesla and Guglielo Marconi. This research opened the door to radio, television and microwave towers for cell phones – all derived from four equations and a couple of calculations.
The Schrodinger Equation
In 1927, Erwin Shrodinger wrote an equation for quantum waves, in which electrons were viewed not as particles but as probability clouds. Memory chips and semiconductors are based on this equation. Lasers and laser-based CDs and DVDs are also founded on this equation.
The Fournier Transform
In 1807, Joseph Fournier submitted an equation for heat flow to the French Academy of Sciences. It was rejected. In 1812, the Academy made heat the subject of the annual prize. Fournier submitted a revised paper and won the prize, but the academy wouldn’t publish it because of the way that Fournier resolved the problem. Fournier assumed the temperature varied like a sine wave along its length, so he assembled a more complicated combination of different sine waves of different lengths for each component sine wave and added them together. Fournier’s solution added together an infinite number of waves, and the Academy found this solution unrigorous and therefore improper to publish. In 1822, Fournier published his theory himself.
From this knowledge, an added element became the excluding of highly irregular profiles, resulting in the Fournier transform, which treats a signal that varies with time as a series of component sine waves and calculates the amplitudes and frequencies of the series.
The Fournier transform is used today to analyze earthquake signals, remove noise from old sound recordings, prevent unwanted vibration in automobile design, and save modern digital photographs in five-step JPEG compression.
Here are the Equations
Conclusion
Scientists seek new equations, especially one that unites quantum theory with relativity. Such unifying equations have proven elusive so far.
Summarized from:
http://www.newscientist.com/article/mg21328516.600-seven-equations-that-rule-your-world.html?full=true
Comments by the Blog Author
Without diminishing these accomplishments, they are standing on the shoulders of other mathematical knowledge, physics insights and some brilliant chemistry.
Euclidean geometry is central to modern science, even though we now know that other geometries are also valid, such as Riemannian and Lobachevskian geometries.
It is unlikely that the wave equation could have been formulated without Newton’s laws of physics, itself a profound breakthrough in the hard sciences.
We couldn’t make these things (such as semiconductors, zener diodes, and precise compounds) without the modern Periodic Table [itself a Daily Quiddity post] and stoiciometric chemistry.
Speculation: Einstein won a Nobel Prize for demonstrating the photoelectric effect: certain structures react to the addition of an electron by ejecting an electron. This proven insight may ultimately prove more valuable than the Shrodinger equation.
- The wave equation
- Maxell’s 4 equations
- The Schrodinger equation
- The Fournier Transform
Wave Equation
Johann Bernoulli (using Newton’s Laws) developed this equation from the ancient Greek Pythagoreans, and subsequently Jean Le Rond d’Alembert used both of these preceding formulae to produce the wave equation.
Maxwell’s Four Equations for Electromagnetism
The wave equation was central to the work of Jam4es Clerk Maxwell, particularly assisted by Michael
Faraday’s work on the basic physics of electromagnetism. Faraday framed his theories as geometric structures – lines of magnetic force. Maxwell reformulated these using the mathematics of fluid flow. He developed two equations showing that magnetism and electricity don’t leak away. A third says that an electrical field spinning in a small circle creates a magnetic field, and the fourth says that a spinning magnetic field creates an electrical field.
By manipulating these four equations, Maxwell derived the wave equation and deduced that light itself must be an electromagnetic wave. This was a revolutionary link between light and electricity and magnetism. This approach led to a prediction that electromagnetic waves of all wavelengths should exist, not just those visible to the human eye.
Some of these invisible long-wave forms would become radio waves as demonstrated in 1887 by Heinrich
Hertz and used to carry information by Nikola Tesla and Guglielo Marconi. This research opened the door to radio, television and microwave towers for cell phones – all derived from four equations and a couple of calculations.
The Schrodinger Equation
In 1927, Erwin Shrodinger wrote an equation for quantum waves, in which electrons were viewed not as particles but as probability clouds. Memory chips and semiconductors are based on this equation. Lasers and laser-based CDs and DVDs are also founded on this equation.
The Fournier Transform
In 1807, Joseph Fournier submitted an equation for heat flow to the French Academy of Sciences. It was rejected. In 1812, the Academy made heat the subject of the annual prize. Fournier submitted a revised paper and won the prize, but the academy wouldn’t publish it because of the way that Fournier resolved the problem. Fournier assumed the temperature varied like a sine wave along its length, so he assembled a more complicated combination of different sine waves of different lengths for each component sine wave and added them together. Fournier’s solution added together an infinite number of waves, and the Academy found this solution unrigorous and therefore improper to publish. In 1822, Fournier published his theory himself.
From this knowledge, an added element became the excluding of highly irregular profiles, resulting in the Fournier transform, which treats a signal that varies with time as a series of component sine waves and calculates the amplitudes and frequencies of the series.
The Fournier transform is used today to analyze earthquake signals, remove noise from old sound recordings, prevent unwanted vibration in automobile design, and save modern digital photographs in five-step JPEG compression.
Here are the Equations
Conclusion
Scientists seek new equations, especially one that unites quantum theory with relativity. Such unifying equations have proven elusive so far.
Summarized from:
http://www.newscientist.com/article/mg21328516.600-seven-equations-that-rule-your-world.html?full=true
Comments by the Blog Author
Without diminishing these accomplishments, they are standing on the shoulders of other mathematical knowledge, physics insights and some brilliant chemistry.
Euclidean geometry is central to modern science, even though we now know that other geometries are also valid, such as Riemannian and Lobachevskian geometries.
It is unlikely that the wave equation could have been formulated without Newton’s laws of physics, itself a profound breakthrough in the hard sciences.
We couldn’t make these things (such as semiconductors, zener diodes, and precise compounds) without the modern Periodic Table [itself a Daily Quiddity post] and stoiciometric chemistry.
Speculation: Einstein won a Nobel Prize for demonstrating the photoelectric effect: certain structures react to the addition of an electron by ejecting an electron. This proven insight may ultimately prove more valuable than the Shrodinger equation.
photosynthesis
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