Читать книгу Riemannian space. Recognition of formulas (structures) of riemannian manifolds by a neural network - Ludmila Naumova - Страница 3

In 1854, in Gottingen, Riemann gave the famous lecture “On hypotheses underlying geometry”, where he gave an extended concept of space. This lecture was a messenger in shaping Einstein’s future theory of relativity in physics. Penetrating into the depth of Riemann’s thought and developing it, the author logically states the following: Riemannian manifolds in the broad sense, in the concept that Riemann himself attached, are innumerable and exist in the real world. It remains to comprehend and accept the fact of their existence in the real world. As a proof of the existence of Riemann spaces in reality, the author shows how, before our eyes in the XXI century, artificial neural networks already reveal the structure of Riemannian manifolds (manifolds in an extended concept, as Riemann imagined). Our geometric metric space is a special case of Riemannian manifolds. Mathematicians are still discovering new spaces in mathematical symbols that have nothing to do with reality. But real spaces and their structure (formula) are revealed in the symbolism of programming languages using neural networks.