Basic epidemic math

We are living in an epidemic of armchair epidemiology, and far be it for me to contribute by giving my own feverish take as an expert of an unrelated field. Therefore, I solemnly swear that I will make no predictions about the present pandemic. I am not paid enough to make such predictions–and if you did pay me I would consider it my professional duty to find you a better expert.

What I can do for free, is read up on basic epidemiology, and digest the maths for you, dear reader. My sources: Wikipedia’s article on mathematical modeling and compartmental models, and some lecture notes I found. My expertise: during my PhD in physics, I frequently worked models like the one I’m about to discuss, only with electrons instead of people.

The SIR Model

The very first epidemiological that one learns about, is the so-called SIR model. This model divides the population into three groups (“compartments”): susceptible (S), infected (I), and recovered (R). Susceptible people are those who could be infected; infected people are those who are currently infectious; recovered people are those who are no longer infectious, and are immune to infection. “Recovered” can be a bit euphemistic, since one method of “recovery” is dying. Another method of “recovery” is by developing symptoms strong enough that the victim knows to quarantine themself (becoming less infectious).

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Factorial experiments

cn: It’s math

When I was an experimental physicist, one of the difficulties was the sheer number of different knobs you could tune… the power of the laser, the rate of laser pulses, the angle of the laser, the material being measured, the temperature, and numerous other knobs more difficult to explain. The search space was too large, and I had to judiciously choose what things to measure.

But in some ways, it’s easier in physics. I had a lot of physics theory to inform my expectations. Suppose you’re designing a website for a personal business, there isn’t quite as much theory to tell you what design features will drive business. You might be stuck trying everything, throwing stuff at a wall until something sticks.

It turns out there’s some interesting math behind this. If you throw everything at a wall, that’s an awful lot of things. But there are ways to throw fewer things at the wall and get about the same information from your experiment.

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Fractals from Newton’s Method

This is a repost of an article I wrote in 2008, over ten years ago!  This is the one that explains where my avatar comes from.

Today, I will explain how I created this:

Three-colored fractal

This is a fractal. A fractal is a pattern that contains smaller versions of itself. But it’s not just any fractal. It’s a fractal I created from something called Newton’s method.

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Intrinsic value of choice

I know that this question has practical and political implications, but for now, I’m treating it as a “just for fun” philosophical question.  Just wanted to be upfront.

What is the value of freedom of choice?  Does it have intrinsic value, or is its value purely instrumental?

A thing has “intrinsic value” if it is valuable in itself.  It has “instrumental value” if it is valuable because it is a means to get something else of value.  For instance, suppose we have a choice between mushroom and cheese pizza.  This choice has instrumental value, because it’s a means for people to have the kind of pizza they most prefer.  But does the choice also have intrinsic value?

Under an initial analysis, I thought the answer was “no”.  If I’m presented with a one-time choice between A and B, and I choose A, did the other option B do any good?  At least within a consequentialist ethical framework, it sure doesn’t seem like it.  After all, option B had no bearing on the consequences.

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Chess involves luck, and other propositions

I find the concept of luck vs skill in games to be fascinating, because the common intuitions are just so wrong. The common intuition is that some games involve more luck, and some games involve more skill. On the extreme end of luck, we have the lottery; on the extreme end of skill, we have chess. The orthodox view was best expressed by a Vox article/video, which included the following image:

An image depicting a continuum, with lottery and roulette being on the left "luck" end, and chess being on the right "skill" end. In the middle, we have hockey, football, baseball, socker, and basketball in that order. Each sport is depicted with an image of the ball/puck, and the name of an associated league.

The Vox image also shows several sports, and the position of each sport is based on the statistical analysis of Michael Mauboussin.  The details of analysis aren’t explicitly described, but it’s basically analyzing the national tournaments for each sport, and estimating how much of the variance in outcome is explained by luck or by skill.

Mauboussin did not analyze chess.  Vox added chess in themselves, pulling a claim out of their ass.  Without doing any analysis, I can guarantee that if you applied the same statistical analysis to chess, you would not find that chess was 100% skill.  The analysis will only show that a game is pure skill if the same people consistently win all their games.  I quickly checked the US Chess Championship winners, and while some names show up repeatedly, it is not 100% consistent, and therefore would not be deemed a pure skill game by this analysis.

So what gives?  Is the statistical analysis bogus, or is the claim that chess is 100% skill bogus?  Trick question.  Both of them are bogus.

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Measuring musical dissonance

An empirical approach

When we hear two musical notes played together (either in succession, or simultaneously), we often characterize those notes as “dissonant” or “consonant”. But instead of having a sharp dichotomy between dissonance and consonance, it might be more useful to speak of a spectrum between the two. Then, the question before us is how to quantify the dissonance of any pair of notes.

12tone is a cool music theory channel, and he recently published a video discussing the solution thought up by the 18th century mathematician Leonhard Euler. I include the video below, but be warned that I’m going to trash Euler’s answer. I believe that any measure of musical dissonance must, at some point, refer to empirical observations of dissonance. Euler’s answer relies on mathematical supposition, and thus I would deride it as numerology.

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