⚠️ What is space and how can it be distorted?

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Probably only the lazy have not yet seen how the distortion of space (or space-time, if you like) is depicted on the diagrams. It looks like a dent in a checkered sheet. Moreover, both teachers and authors of popular science articles often resort to this visualization technique. But this idea of space distortion is not entirely correct. Which one is correct then?
Let's try to understand two important issues. What is space from a physical point of view and how does the distortion of this space occur, which, for example, then causes gravitational interaction. We are looking for a clear analogy and will try to figure out why mathematics is no less important for a physicist than physics itself.
This argument will have some parallels with simulation theory. Is this true or not? You be the judge. And I will tell you how I myself understand this issue. The conclusion was made based on the study of a number of sources, from which it follows that my version has every right to exist. I hope that this logic will help you in studying physics and in finding answers to interesting questions.
Content:
01:00 - Space in physics
02:29 - About the connection between physics and mathematics
03:19 - The role of “mathematical forecasting”
03:30 - About models and shortcomings. A singularity that may not have existed
05:05 - Trying to imagine space
05:50 - And again about virtual worlds
08:15 - If space is a mathematical model, then everything is very simple
09:10 - What is physically distorted when space is distorted?