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Strange Numbers Found in Particle Collisions | Quanta Magazine

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Motives are in a sense the fundamental building blocks of polynomial equations, in the same way that prime factors are the elemental pieces of larger numbers.

If the period of a motive arising in one system of polynomial equations is the same as the period of a motive arising in a different system, you know the motives are the same.

“Once you know the periods, which are specific numbers, that’s almost the same as knowing the motive itself,” said Minhyong Kim, a mathematician at Oxford. One direct way to see how the same period can show up in unexpected contexts is with pi, “The most famous example of getting a period,” Cartier said.

Pi shows up in many guises in geometry: in the integral of the function that defines the one-dimensional circle, in the integral of the function that defines the two-dimensional circle, and in the integral of the function that defines the sphere.

“The modern explanation is that the sphere and the solid circle have the same motive and therefore have to have essentially the same period,” Brown wrote in an email.

To calculate the probability of a specific outcome from a specific set of starting conditions, you consider all possible diagrams that could describe what happens, take each integral, and add those integrals together.

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Article originally posted at www.quantamagazine.org

Post Author: Kim Lachance Shandrow

2 thoughts on “Strange Numbers Found in Particle Collisions | Quanta Magazine

    Daniel Jeyaraman

    (January 25, 2018 - 6:14 pm)

    A cup of rice indicates infinity in the number of grains? Now that is really strange. How is that possible?

    Matthew Beckner

    (January 25, 2018 - 6:14 pm)

    Jason Valentine

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