Counting in Imaginary (featuring Irrationals) #SoME3

An introduction to imaginary and complex numbers as counting units, built from first principles in plain language accessible to people with elementary school level of math and a cursory understanding of algebra. We'll be talking about uniformity, relativity, continuity, units, the stuff that in my opinion gets clarified much too late, way past the point that most people decide math is not for them. If you're looking for a tighter intuitive understanding of these numbers, you've got a good shot right here. If you already get it, but wonder how to bring others into the fold, I think you'll find some hacks you might appreciate. Enjoy! This video has been submitted to the 3rd installment of the Summer of Math Exposition, hosted by @3blue1brown. Further info: https://some.3b1b.co/ 00:00 Psychologically Charged Names 01:03 Hidden Properties of Counting 06:16 Between the Things We Count 13:12 Irrational Imperfection 16:53 Relativity of Numbers 22:12 Collapsing Degrees of Freedom 26:36 What is This i? 31:23 (Ac)counting Imaginary Things 36:13 It's All in the Unit CORRECTIONS: 2:18 the symbols between the counting numbers should be less than instead of more than Resources (because the video leaves you hanging on most of algebra): ========================================================= Easy and practical overview of basic algebra with complex numbers: https://www.mathsisfun.com/numbers/complex-numbers.html Intuitive introduction to Euler's formula https://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/ Thorough overview of complex algebra https://brilliant.org/wiki/complex-numbers/