WOW. This was an outstanding episode of Veritasium on the Power Law probability distributions (i.e. probability distributions described by an *exponential* relationship between the variables). I never realized these types of probability distributions are so common, and that they behave in such similar ways to each other.

Even more bizarrely to me, there appear to be many systems in nature that *spontaneously* organize themselves in a way to exhibit Power Law probability distributions. In fact, I suspect that “black swan” events are possibly a symptom of mistakenly perceiving a Power Law distribution phenomenon as one exhibiting a Normal or even Log-Normal distribution.

#math #physics #probabilities #blackSwan

youtube.com/watch?v=HBluLfX2F_…

#Noisevember! I revisited the Littlewood polynomial sound from day 2 of Noisevember. I thought to investigate a different sort of polynomial. Here, instead of polynomials with coefficients all ±1, the polynomials have coefficient ±1/(n+1) on the x^n term. As before, all roots of all such 15th degree polynomials are considered. (I really should create a gallery of these root plots so we can easily compare them.) Along the way, I realized I was making an error with the way I created "random" stereo that introduced a bunch of unneeded noise. So that's something! I'll have to go back and replace the Littlewood polynomial sound. soundcloud.com/matthew-m-conro…

Here's a plot of the roots (essentially the spectrogram of the sound).

#noise #sound #audio #math #maths #mathematics #polynomials #roots