Who is behind this geometry idea anyway

While the use of geometry goes back to prehistory, its power in modern culture comes in large part from the world's most famous geometer, Euclid. He or she—nobody knows much about Euclid's real identity lived in Alexandria around B.

The suggestion that the physical world obeys an ordered, hierarchical logic came as welcome news to world leaders at the time. The power of that idea — of a fixed order, beyond question — explains many of the designs of palaces and capital cities. She points out that geometry has symbolized different things in different times and places. While Middle Eastern leaders used simple geometrical design to project power with big, imposing buildings, artists also saw in geometry a humbler message.

So that, for some philosophers, really worked very well to contemplate God's perfection and harmony. Euclid's geometry couldn't live up to the promise of complete perfection. But as Alexander points out, that's not really the point. The point, Alexander adds, is akin to Plato's ambitious pure rational principle: it's not about achieving, but rather on the profound effect that striving for perfection has on us.

The historian anticipates that future leaders will always rely on geometry for its powerful resonance. Recently, a strange duality has been found between string theory and quantum field theory, indicating that the former which includes gravity is mathematically equivalent to the latter which does not when the two theories describe the same event as if it is taking place in different numbers of dimensions.

No one knows quite what to make of this discovery. But the new amplituhedron research suggests space-time, and therefore dimensions, may be illusory anyway. This work is a baby step in that direction.

Even without unitarity and locality, the amplituhedron formulation of quantum field theory does not yet incorporate gravity. But researchers are working on it. They say scattering processes that include gravity particles may be possible to describe with the amplituhedron, or with a similar geometric object. Physicists must also prove that the new geometric formulation applies to the exact particles that are known to exist in the universe, rather than to the idealized quantum field theory they used to develop it, called maximally supersymmetric Yang-Mills theory.

Beyond making calculations easier or possibly leading the way to quantum gravity, the discovery of the amplituhedron could cause an even more profound shift, Arkani-Hamed said. That is, giving up space and time as fundamental constituents of nature and figuring out how the Big Bang and cosmological evolution of the universe arose out of pure geometry. The object is basically timeless. While more work is needed, many theoretical physicists are paying close attention to the new ideas.

Note: This article was updated on December 10, , to include a link to the first in a series of papers on the amplituhedron. This article was reprinted on Wired. Get highlights of the most important news delivered to your email inbox. Quanta Magazine moderates comments to facilitate an informed, substantive, civil conversation. Abusive, profane, self-promotional, misleading, incoherent or off-topic comments will be rejected.

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We care about your data, and we'd like to use cookies to give you a smooth browsing experience. Please agree and read more about our privacy policy. A Jewel at the Heart of Quantum Physics. Read Later. Illustration by Andy Gilmore. The Quanta Newsletter Get highlights of the most important news delivered to your email inbox. Show comments. This little gem of reasoning foreshadows the man he became, scientifically, stylistically, and temperamentally. It concerns right triangles, meaning triangles that have a right ninety-degree angle at one of their corners.

Maybe you never did, either. Once you do, though, the questions start coming. What makes it true? How did anyone ever come up with it? For a clue to that last question, consider the etymology of the word geometry. Officials needed to assess how much tax was to be paid, how much water they would need for irrigation, how much wheat, barley, and papyrus the farmers could produce. How much land is that? The meaningful measure would be the area of the field.

For a thirty-by-forty lot, the area would be thirty times forty, which is twelve hundred square yards. Surveyors, by contrast, do care about shapes, and angles, and distances, too. In ancient Egypt, the annual flooding of the Nile sometimes erased the boundaries between plots, necessitating the use of accurate surveying to redraw the lines.

Four thousand years ago, a surveyor somewhere might have looked at a thirty-by-forty rectangular plot and wondered, How far is it from one corner to the diagonally opposite corner?

The answer to that question is far less obvious than the earlier one about area, but ancient cultures around the world—in Babylon, China, Egypt, Greece, and India—all discovered it. The rule that they came up with is now called the Pythagorean theorem, in honor of Pythagoras of Samos, a Greek mathematician, philosopher, and cult leader who lived around B.

It asks us to imagine three fictitious square plots of land—one on the short side of the rectangle, another on the long side, and a third on its diagonal. Next, we are instructed to calculate the area of the square plots on the sides and add them together. The Pythagorean theorem is true for rectangles of any proportion—skinny, blocky, or anything in between.

The squares on the two sides always add up to the square on the diagonal. More precisely, the areas of the squares, not the squares themselves, add up.

The same rule applies to right triangles, the shape you get when you slice a rectangle in half along its diagonal. In pictorial terms, the squares on the sides of a right triangle add up to the square on its hypotenuse. But why is the theorem true? Actually, hundreds of proofs are known today. Garfield, which involves the cunning use of a trapezoid. Einstein, unfortunately, left no such record of his childhood proof.

Walter Isaacson, Jeremy Bernstein, and Banesh Hoffman all come to this deflating conclusion, and each of them describes the steps that Einstein would have followed as he unwittingly reinvented a well-known proof.

Twenty-four years ago, however, an alternative contender for the lost proof emerged.