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2022

Train Whistles

A quick post tonight – just relating an interesting observation that I made about train whistles.

I set outside and work any time the weather is fair. And in doing so I often hear one of the local trains in the distance blowing their whistle as they cross at an intersection. I realized one day that if you listen carefully, you can tell which direction they're going – toward you or away from you – according to the sound of their whistle. Now obviously, there's the Doppler effect, so that the sound of their whistle is higher pitch if the train is coming towards you and the lower pitch if the train is going away from you. But the Doppler effect by itself isn't that helpful because you (or I at least) don't have perfect pitch and don't know what the normal pitch of a train whistle should be.

  • in Math
  • 8 min read

Playing with a Rational Distribution

(Note to reader: I think I wrote this post for myself. From an outside perspective, it's by far the most boring one I've ever written. But it's math that's been occupying my mind for a week and from an inside perspective it's been quite fun. Maybe you'll find the fun in it that I did.)

For a project I'm currently working on at GitHub, I ran into my first statistical distribution defined on rational numbers and I found it weird and interesting when compared to the continuous distributions that I'm used to. We were looking at feature adoption on a per-repository basis. We defined adoption to be

\[\textrm{adoption}=\frac{\textrm{number of people using feature in a given repo}}{\textrm{number of people active in that repo}}\]

The question is, what should the distribution of feature adoption look like across all repos? Pause here and think about it. (Don't even scroll down!) Leaning upon my normal intuition with continuous distributions I was initially a bit surprised with what I found.

"Who da Boss" Graph Clustering

I've been playing with my Twitter social graph recently, and it occurred to me that the people that I'm friends with form several clusters. I wanted to see if I could come up with some sort of clustering algorithm to identify these clusters. Why? Well for one, it could be of practical use; maybe I can find some good use for it. But, perhaps more than that, I was curious if I could make a clustering algorithm – I've kinda got a thing for reinventing wheels.

Evolution of Jiggly Stuff

I like positing hypotheses that are completely unverified and poorly examined. Why? Because it's easier to play with ideas when you don't have to check your work. 🤣 Here are two somewhat related hypotheses about how evolution has made two very different jiggly things more durable and resistant to distress: your brain and trees.