New Physics 🧵! Ludwig Boltzmann was not just a father of Statistical Physics but also a master of Thermodynamics. That’s how he got his name on the Stefan-Boltzmann law. If you allow me, I would love to walk you through a magic moment in physics history. /1
The single most undervalued fact of linear algebra: matrices are graphs, and graphs are matrices.
Encoding matrices as graphs is a cheat code, making complex behavior simple to study.
Let me show you how!
Given samples from a distribution consider the
mean x̅
median m
range [a,b] = [min, max]
standard deviation σ
sample size n
Then for modestly large n (>50 or so)
x̅ ≈ (a+2m+b) ⁄ 4
σ ≈ (b-a) ⁄ 6
Notably, these are distribution-free results & do not require knowledge of n