The universe is expanding. Into what ?

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SUMMARY

The universe is expanding without the necessity of a surrounding space, as established by mathematical models of cosmology. In 1850, mathematician Bernie from Göttingen developed tools for defining and measuring spatial curvature and expansion intrinsically, eliminating the need for external reference points. Cosmology relies on fitting data to mathematical models rather than verbal descriptions, emphasizing the importance of understanding the underlying mathematical concepts rather than solely relying on language. The absence of evidence for a surrounding space leads cosmologists to reject the assumption of an external environment for the universe.

PREREQUISITES
  • Understanding of intrinsic geometry
  • Familiarity with mathematical models in cosmology
  • Knowledge of spatial curvature concepts
  • Basic grasp of data fitting techniques in scientific research
NEXT STEPS
  • Research intrinsic geometry in mathematical cosmology
  • Explore the mathematical tools developed by Bernie in 1850
  • Study the implications of spatial curvature on cosmological models
  • Learn about data fitting techniques used in cosmology
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Cosmologists, mathematicians, and anyone interested in the mathematical foundations of the universe's expansion and the nature of space.

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The universe is expanding. Into what ?
 
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The math model of expansion does not need any surround to expand "into".

BTW the math model of the cosmos can be curved without having to sit in some surrounding space to be curved "in".

In 1850 a young guy in Göttingen named Bernie discovered the math tools needed to define and measure both spatial curvature and expansion *internally* without the need for surroundings. You just work within the space itself. You do geometry intrinsically.

So the upshot is that cosmology is a mathematical science---you fit data to math models. It is not a verbal science. So when they say "expands", the word is only the best available English language approximation for the idea. You can't automatically go by words, you have to ask what is really meant. Dig down to the underlying mathematical meaning.

There could be a surround, but since there is no evidence of one, it is more a speculative fairytale fantasy. Cosmologists normally do not assume any surrounding space in which our universe is embedded because there is no indication that one exists, nor is there any conceptual need to assume one.
 
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