What is the “Theorema Egregium of the Universe”?

Egregium: because Nature is remarkable, beautiful. Through the testimony of our limited senses and guided by our evolving mathematical minds, a deep panorama unfolds.

How can we be certain that Nature is the way we think it is? What is Nature? Is there an ultimate answer?

The Gaussian curvature of a surface embedded in a three-dimensional space is an intrinsic geometrical property of the surface. The curvature could be measured by two-dimensional creatures living on it, without the need of a third degree of freedom. The “remarkable theorem” of Gauss inspires the naming of this weblog.

The Universe in the ultimate sense is “everything that exists”. Will we be able to understand it at all? One is tempted to feel that we are like those two-dimensional creatures, somewhat in principle able to learn about a maximum possible set of intrinsic “facts” [*] about our Universe. But could there be “extrinsic” facts as well, about which our own Nature is destined only to infer vaguely?

What is the “Theorema Egregium of the Universe”?

–[*] The reader may have noticed that my use of the word “fact” here carries the idea of a more abstract notion of a set of observables and, although being inspired by, does not refer to the specific differential geometry aspects of the Theorema Egregium of Gauss. It is intended as a step towards a much more abstract and wider ontological framework. This idea evidently must be worked out.

Ref: [Ber] — for an outline of the Theorema.