Entries by andrewkirk

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…

Acoustic ‘beats’ from Mismatched Musical Frequencies

Introduction In late high school physics courses and first-year university courses, the phenomenon of acoustical ‘beats’ (digital audio) is often covered. This is an interesting phenomenon, but it is usually only skated over, leaving the students with not much more than a feeling that the beats somehow arise from the two waves moving in and…