Long ago I thought that curvature was a deep concept we owe to Carl Friedrich Gauss. Then I saw that phase-space was deep also. It seems that now more people are coming to the same conclusion. Here I try a simple interpretation in my understanding of Julian Barbour's ideas.
Pattern is time. We know what comes next because of our expectations. The arrow of time is as real as the persistence of objects. Linear predictions are called common sense, but Ray Kurzweil has shown us to extrapolate with non-linear functions. Gauss then is the master of prediction. If we know the curvature in a local region, we know if linear or non-linear predictions are needed. Einstein also saw in curvature the key to a theory of physics.
Thermodynamics, General Relativity, and now Perelman's Theory of Ricci Flows, must be related. The relation may be Barbour's idea that there is no time, only patterns.
More to come.
Pattern is time. We know what comes next because of our expectations. The arrow of time is as real as the persistence of objects. Linear predictions are called common sense, but Ray Kurzweil has shown us to extrapolate with non-linear functions. Gauss then is the master of prediction. If we know the curvature in a local region, we know if linear or non-linear predictions are needed. Einstein also saw in curvature the key to a theory of physics.
Thermodynamics, General Relativity, and now Perelman's Theory of Ricci Flows, must be related. The relation may be Barbour's idea that there is no time, only patterns.
More to come.
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