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A Formal Definition of Large-Scale Isotropy

This Insight is part of my attempt to develop a formal definition of ‘large-scale isotropy’, a concept that is fundamental to most cosmology, but that is nowhere that I have seen properly defined. The definitions of isotropy are as precise as one could wish, but the ‘large-scale’ bit is in every case I have seen…

Learn Partial Differentiation Without Tears

Differentiation is usually taught quite well. Perhaps that’s because it is the first introduction to calculus, which is considered a big step in a student’s mathematical education, so teachers mostly take a lot of care with that step. Unfortunately, the same cannot be said for partial differentiation. It is often glossed over in a rush…