Cosmologic philosophy:strange number relationships (Introduction)

by David Turell @, Saturday, November 19, 2016, 01:44 (1366 days ago) @ David Turell

Math is a way we understand the universe, but we don't know why the numbers have the values they have. Are they arbitrary or follow a pattern?

https://www.quantamagazine.org/20161115-strange-numbers-found-in-particle-collisions/?u...

"Over the last decade physicists and mathematicians have been exploring a surprising correspondence that has the potential to breathe new life into the venerable Feynman diagram and generate far-reaching insights in both fields. It has to do with the strange fact that the values calculated from Feynman diagrams seem to exactly match some of the most important numbers that crop up in a branch of mathematics known as algebraic geometry. These values are called “periods of motives,” and there’s no obvious reason why the same numbers should appear in both settings. Indeed, it’s as strange as it would be if every time you measured a cup of rice, you observed that the number of grains was prime.

“'There is a connection from nature to algebraic geometry and periods, and with hindsight, it’s not a coincidence,” said Dirk Kreimer, a physicist at Humboldt University in Berlin.

"Now mathematicians and physicists are working together to unravel the coincidence. For mathematicians, physics has called to their attention a special class of numbers that they’d like to understand: Is there a hidden structure to these periods that occur in physics? What special properties might this class of numbers have? For physicists, the reward of that kind of mathematical understanding would be a new degree of foresight when it comes to anticipating how events will play out in the messy quantum world.

***

"This process first involved looking at the geometric objects (known as algebraic varieties) defined by the solutions to classes of polynomial functions, rather than looking at the functions themselves. Next, mathematicians tried to understand the basic properties of those geometric objects. To do that they developed what are known as cohomology theories — ways of identifying structural aspects of the geometric objects that were the same regardless of the particular polynomial equation used to generate the objects.

"By the 1960s, cohomology theories had proliferated to the point of distraction — singular cohomology, de Rham cohomology, étale cohomology and so on. Everyone, it seemed, had a different view of the most important features of algebraic varieties.

***

"'What Grothendieck observed is that, in the case of an algebraic variety, no matter how you compute these different cohomology theories, you always somehow find the same answer,” Brown said.

That same answer — the unique thing at the center of all these cohomology theories — was what Grothendieck called a “motive.” “In music it means a recurring theme. For Grothendieck a motive was something which is coming again and again in different forms, but it’s really the same,” said Pierre Cartier,

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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. Motives also have their own data associated with them. ... mathematicians ascribe essential measurements to a motive. The most important of these measurements are the motive’s periods. And 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.

***

"Periods and amplitudes were presented together for the first time in 1994. The work led mathematicians to speculate that all amplitudes were periods of mixed Tate motives — a special kind of motive named after John Tate, in which all the periods are multiple values of one of the most influential constructions in number theory, the Riemann zeta function.

***

"This classification of periods by weights carries over to Feynman diagrams, where the number of loops in a diagram is somehow related to the weight of its amplitude. Diagrams with no loops have amplitudes of weight 0; the amplitudes of diagrams with one loop are all periods of mixed Tate motives and have, at most, a weight of 4.

***

"The fact that the periods that come from physics are “somehow God-given and come from physical theories means they have a lot of structure and it’s structure a mathematician wouldn’t necessarily think of or try to invent,” said Brown."

Comment: Is there an underlying set of math from God that ties all this together? I wouldn't be surprised that He had it all planned out.


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