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Babylonians Were Math Whizzes

January 31, 2016 By Brian Galloway Leave a Comment

"a ancient clay tablet that belongs to the Babylonian people"

The ancient Babylonians were using geometrical calculus to observe Jupiter’s movements

The recent discovery of some clay tablets belonging to the ancient civilization of Babylon revealed the fact that Babylonians were math whizzes. It seems that they used complex geometrical calculations 1,400 years before they were officially invented in order to track the movements of the planet Jupiter.

It seems that calculus was not invented where we originally thought it was. Gottfried Leibniz and Isaac Newton were not that original in the 17th century when they devised the calculus method. It seems that they were actually really late with their findings compared to what ancient Babylonians were carving on their clay tablets while looking for Jupiter.

A team of researchers found a couple of clay tablets that date back from 350 to 50 BC. The symbols carved into them proved to be nothing other than geometric calculations meant to track the movements of the gas giant, Jupiter.

According to the recent findings published in the Science journal last Thursday, the Babylonians used a technique that tracks the distance traveled by a body using a graph of the time lapse and velocity. Originally this technique was supposed to be developed in 1350 in England. The time lapse between the two civilizations is enormous.

The author of the study published in the Science journal, Mathieu Ossendrijver, says that the calculus method employed by the ancient Babylonians is rather similar to the modern day integral calculus. The ancient people were using a rectangle with an inclined top and a trapezoid. The trapezoid was used to represent the area under the curve. They computed the area of the trapezoid that is used to describe how the velocity of an object changes with time. The area described is equal to the distance traveled by Jupiter.

This is the first evidence found by archaeologists and scientists that proves that the ancient people were using calculus and geometry for astronomical observations. This means that the Babylonians were math whizzes all on their own.

Jupiter was, in the case of the Romans, the god of thunder and sky, ruler of all the other gods. The Greeks attributed the planet to Zeus, the equivalent of Jupiter. The ancient Babylonians thought that the bright star in the sky was none other than Marduk, their own supreme deity, master of all others.

It is interesting how all of these different civilizations attributed the role of supreme deity to the exact same planet. And that the twinkle in the sky could predict water levels or the status of the next crop.

Image source: www.wikimedia.org

Filed Under: Tech & Science Tagged With: Astronomy, Babylon, babylonians were math whizzes, Geometry, Jupiter, math, Tablets

Math Proposed Substitute to Quantum Tenet

September 13, 2014 By Brian Galloway 18 Comments

math-quantum-tenet

It has been observed by the scientists that the central ambiguity of quantum mechanics is that small portions of matter from time to time appear to act like particles, at times like waves. For most of the past century, the widespread explanation of this conundrum has been what’s called the “Copenhagen interpretation” which believes the fact that, in some sense, a sole particle in fact is a wave soiled out athwart the earth that disintegrated into a determinate place.

An alternative elucidation, known as “pilot-wave theory,” which posits that quantum particles are borne beside some specific type of wave, according to some founders of quantum physics particularly Louis de Broglie. The pilot-wave theory stated that, the particles have specific routes, though since of the pilot wave’s sway, they still demonstrate wavelike statistics.

The pilot-wave theory be worthy of a second look, John Bush, a professor of applied mathematics at MIT, believes. It’s just because Yves Couder, Emmanuel Fort and colleagues at the Univ. of Paris Diderot, who have lately revealed a macroscopic pilot-wave system whose statistical behavior, in certain conditions, reminds that of quantum systems.

Certainly, the system developed by Couder and Fort’s consists of a bath of liquid quivering at a rate just below the threshold at which waves would begin to form on its facade. A droplet of the same liquid is out above the bath; where it strikes the facade, it causes waves to emit outward. The droplet then begins moving crossways the bath, pushed by the very waves it generates.

Bush says, “This system is undoubtedly quantitatively different from quantum mechanics. He further stated that, it is also qualitatively different: there are some features of quantum mechanics that we can’t imprison, some features of this system that we know aren’t present in quantum mechanics. Although are they philosophically distinct?”

Tracking Trajectories

The Copenhagen explanation sidesteps the technical challenge of scheming particles’ trajectories by refuting that they subsist, Bush says. He further added “The key question is whether a real quantum dynamics, of the general form suggested by de Broglie and the walking drops, might underlie quantum statistics”. “Whereas certainly composite, it would put back the theoretical vagaries of quantum mechanics with a tangible dynamical theory.”

Last year, Bush and Jan Molacek (one of Bush’s students – now at the Max Planck Institute for Dynamics and Self-Organization) did for their system what the quantum leads the way couldn’t do for theirs: they derived an equation relating the dynamics of the pilot waves to the particles’ trajectories. Bush and Molacek had two advantages over the quantum pioneers in their work, Bush stated.

At First, in the fluidic system, both the vigorous droplet along with its guiding wave is clearly evident. If the droplet bypasses from a slot in a barrier as it does in the re-creation of a canonical quantum experiment then the researchers can precisely find out its place. The only way to carry out a dimension on an atomic-scale particle is to hit it with another particle, which eventually changes its velocity.

When it comes to the second improvement, it believes to be comparatively recent growth of chaos theory. The chaos theory holds that many macroscopic physical systems are so sensitive to initial conditions that, even though they can be described by a deterministic theory, they evolve in unpredictable ways, pioneered by MIT’s Edward Lorenz in the 1960s. For example, a weather-system model may yield totally different results if the wind speed at a specific place at a specific time is 10.01 mph or 10.02 mph.

Furthermore, it is also believed that the fluidic pilot-wave system is chaotic too. It’s not possible to measure a vigorous droplet’s place correctly enough to forecast its trajectory very far into the future. However, Bush, MIT professor of applied mathematics Ruben Rosales, and graduate students Anand Oza and Dan Harris in a recent series of papers, applied their pilot-wave theory to demonstrate how chaotic pilot-wave dynamics leads to the quantum-like statistics seemed in their experiments.

The Real Story:

Bush discovers the link between Couder’s fluidic system and the quantum pilot-wave theories anticipated by de Broglie and others, stated in a review article appearing in the Annual Review of Fluid Mechanics.

According to the Copenhagen interpretation, it is basically the claim that in the quantum monarchy, there is no explanation deeper than the statistical one. He further said that when a measurement is made on a quantum particle, and the wave form crumples, the originated condition of the particle is totally random. The statistics don’t just explain the reality; they are the reality, Copenhagen interpretation says.

However in spite of the dominance of the Copenhagen interpretation, the perception that physical objects, no matter how small, can be in only one location at a time has been hard for physicists to quiver. Albert Einstein, who notably suspicions that God, plays dice with the universe, worked for a time on what he called a “ghost wave” theory of quantum mechanics which was believed to be an elaboration of de Broglie’s theory. The Nobel Prize lecture held in 1976, Murray Gell-Mann stated that Niels Bohr, the main exponent of the Copenhagen interpretation, “brainwashed an entire generation of physicists into believing that the problem had been solved.” John Bell, the Irish physicist whose famous theorem is often mistakenly taken to repudiate all “hidden-variable” accounts of quantum mechanics, was, in fact, himself a proponent of pilot-wave theory. He further added, “It is a great mystery to me that it was so soundly ignored.”

After that, there’s another physicist named as David Griffiths who’s “Introduction to Quantum Mechanics” is standard in the field. Griffiths says that the Copenhagen interpretation “has stood the test of time and emerged unscathed from every experimental challenge,” in that book’s afterword. Nevertheless, he finds, “It is entirely possible that future generations will look back, from the vantage point of a more sophisticated theory, and wonder how we could have been so gullible.”

Keith Moffatt, a professor emeritus of mathematical physics at Cambridge Univ says “The work of Yves Couder and the related work of John Bush offer the opportunity of understanding previously incomprehensible quantum phenomena, involving ‘wave-particle duality,’ in purely classical terms. I think the work is brilliant, one of the most exciting developments in fluid mechanics of the current century.”

Filed Under: Tech & Science Tagged With: Albert Einstein, Anand Oza .Dan Harris, Bush, Cambridge Univ, Copenhagen, Copenhagen interpretation, David Griffiths, de Broglie, elucidation, Emmanuel Fort, fluidic system, Griffiths, Jan Molacek, John Bush, Keith Moffatt, Louis de Broglie, macroscopic pilot-wave system, math, Max Planck Institute, MIT, Murray Gell-Mann, Niels Bohr, Paris Diderot, pilot-wave theory, Quantum Mechanics, quantum particles, Quantum Tenet, Substitute, vigorous droplet, weather-system model, Yves Couder

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