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---------------------------- #1953 - Math was Invented to Solve Problems?
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- Mathematics is a language. It can be used to explain observations, to solve problems, to find results and to predict results coming in the future. Its effectiveness in explaining nature is totally unreasonable. Why does it work so well? It is a wonderful gift that we neither fully understand nor deserve.
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- Isaac Newton invented Calculus to explain “motion” and to explain things that “change“. He breaks change down into infinitesimally small frame by frame sequences in order to solve problems. Lots of things change so Calculus has wide application in today’s world. Calculus is used to calculate the change in the value of money with time, for example.
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- When Calculus is the rate of change of quantities it is interpreted as the slope of curves.
Example: velocity is the slope of distance versus time. This is called Differential Calculus. When the math is used for lengths, areas, and volumes of objects it is called Integral Calculus. Example: Calculus can add up the areas of circles and get the volume of a sphere.
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- Quantum Electrodynamics is a more recent math invention that explains how light and matter interact. Scientists used this math to calculate the magnetic moment of an electron. Their answer agrees with experiment to an accuracy of a few parts per trillion.
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----------- electron’s magnetic moment = 1.0011565218073
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- Quantum Mechanics is a math concept that assumes matter and energy behave as particles as well as waves. It states that measurements at the atomic level are always uncertain. Position and velocity, time and energy are pairs that can not both be known with precision. There is always a trade-off in play between these pairs.
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- Group Theory was a math invented in 1800 to solve polynomial equations . Groups are algebraic structures made up of sets of objects, say a set of integers, united under a specific operation, say addition, that obeys a specific set of rules, say adding zero to any number does not change the number. Now, in the 21st century this same Group Theory is used to develop the Standard Model in Particle Physics. It models the building blocks of matter. The fundamental particles of matter are given a specific group called SU(3) that can be used to describe how atomic nuclei are held together. Example: SU(3) math predicts that there is a Higgs Boson, a force carrier particle that gives matter its mass. The Large Hadron Collider in CERN, Switzerland, is a particle accelerator smashing protons and anti-protons together with 14 trillion watts of energy. Physicists hope to discover the Higgs Boson in the debris. And, I think they have already discovered the Higgs Particle.
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- Group Theory becomes a way to represent symmetry in nature. Lie Groups represent symmetries of solutions to differential equations that are infinite. There is a Monster Group that defines the structure of the Universe at the subatomic level.
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- Then, there is Knot Theory that studies knots, closed curves in 3 dimensions. The math was born out of attempts to model the atom. Today it is used in String Theory, Topology, DNA research and molecular biology.
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- Topology is the math that describes objects that remain unaffected by smooth deformations, such as stretching or squeezing, but do not involve tearing or cutting. Example: a doughnut is the same Topology as a coffee cup.
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- Number Theory is the math used in cryptography .Quantum Entanglement has recently been added to make cryptography messages unhackable and uncrackable.
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- The General Theory of Relativity uses the math of non-Euclidian geometry. Non-Euclidian are spaces where parallel lines converge and diverge.
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- String Theory is math that describes fundamental particles as musical notes of vibrating strings. The strings are very tiny , 10^-33 centimeters in length, but, they have no thickness. The strings are 1 dimensional, yet the math needed to describe their behavior must use 10 dimensions. Space-time has 4 dimensions, the other 6 dimensions are called Calabi-Yau spaces. All the properties of elementary particles such as mass, spin , charge can be mathematically described in vibrating strings. The faster the vibration the greater the energy. Since matter and energy are the same thing, the faster the vibrations the greater the mass.
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- Loop Quantum Gravity is Knot Theory math that is trying to reconcile space -time relativity with quantum mechanics The math for one describes the Universe of big things. The math for the other describes small things, things at the sub-atomic level. But, the two math’s are not compatible. Neither one will work in the other’s domain.
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- Chaos Theory uses math whereby the tiniest change in the initial conditions can produce entirely different end results. Example: A butterfly wing flap in the Amazon can cause a tornado in Kansas.
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- Math is a language that just works. We can not really explain why. We just use it because it is reliable in learning stuff about our Observable Universe. There appears to be fundamental symmetries that Nature uses in her own math. There appears to be a grand design that we are discovering, not inventing. An announcement will be made shortly, stay tuned.
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- To learn more math, request these reviews:
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- #1952 - Transcendental numbers “ e” and “pi”. This Review covers imaginary numbers. “Pi” is an irrational number. Compound interest uses “e”. e^i *pi +1 = 0 is world’s most amazing equation.
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- #1935 - How fast is the satellite? How to calculate the speed to be 18,557 miles per hour
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- #1865 - Equations are just another language. There are a least 6 differed proofs of the Pythagorean Theorem. Logarithms are designed to make the math simpler. Calculus ws invented to calculate rates of change. Fourier transforms describe time as a function of frequency. Chaos Theory models copulation growth.
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- #1844 - Pascal’s Wager on climate change. Decision Theory - what is the best and the worst with any two alternatives.
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- #1780 - How fast to orbit? The same math as Review #1935.
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- #1750 - Math for fun. Short cuts you can do in your head for math calculations. How to add up all the numbers in a multiplication tale up to 100? The answer = 3,025. Pick any 4-digit number, scramble the order of the digits, subtract, add, the answer you get is always “9”.
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- #1661 - Math is food for the brain. The sum of he cubes of aa series of numbers is equal to the square of the sum of those numbers. How to win at craps and roulette tables, Blackjack and Poker. What is your probabilities when gambling?
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- #1649 - The power of combinations. Factorials is multiplication is a descending sequence of numbers down to the number one. When you get 23 people in a room the probability is 49% that none have the same birthday, 51% that 2 of them do have the same birthday.
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- #1565 - How fast is that satellite?
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- #1521 - Math’s most powerful equations. E=mc^2. and FV=PV( 1+i )^t
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- #1493 - Puzzles in astronomy
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- #1467 - The growth and decay of money . Interest is really the price of money. Put one penny in a kitchen jar on December 1st and double it every day.. How much will you have by Christmas? $117,772 and you could buy an airplane.
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- #1324 - How politicians use math. They tend to use math to get the numbers they want. 2008 financial crisis at Lehman Brothers and AIG
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- # - Presidential poles. I don’t believe the poles but the math is fun.
- #1235 Equations are sentences in short hand. Frequency times wavelength equals a constant = 300,000,000 . Energy divided by frequency equals a constant = 6.6*10^-34. The force of gravity times distance squared equals a constant = 79*10^43.
- #1213 How to calculate odds for poker hands. The logic for these calculations is “ combinations. There is a “rule of sums” and “ rule of products”. The odds of a Flush are 0.198%.
- #1086 Formulas for space time, velocity, galaxies, solar systems, light , atoms, Quantum Mechanics, Energy, Action, Work, Momentum, Geometry, and more.
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- #1095 Math is a learned discipline.
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- # 1042 Calculate areas by connecting the dots, Pick’s Theorem
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- # 1041 The star with the golden ratio. (a /b ) = (a + b) / a 1/1.618 = 1.618
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- #853 Math, the golden ratio
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- #805 Gambling, math for craps, roulette, blackjack.
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- #803 Transcendental numbers, “e” and “pi”.
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- #796 Science and Math, Part I
- #798 Science and Math, Part II.
- #799 Science and Math, Part III.
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- # 745 The calculus of a circle.
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- #649 The Greeks invented numbers.
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- Transcendental - is a function that is not an algebraic function. It is a number that is real but not an algebraic with rational roots.
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- Irrational - not expressible as a ratio of two integers having an infinite and nonrecurring expansion when expressed as a decimal.
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- Rational - number expressed as a quotient, a fraction, a ratio.
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----- 707-536-3272 ---------------- Tuesday, January 16, 2018 -----
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