Conjugate variables, in thermodynamics and elsewhere

When I wrote an explanation of cap and trade, I had a strong temptation to make a physics analogy, to an idea in thermodynamics. The trouble is nobody would understand the analogy, and I would be obliged to explain the physics instead of the economics. Well I’d still like to explain the physics, but in a separate article.

There are certain thermodynamic quantities that are considered to be paired with one another. For example, pressure and volume, or temperature and entropy. These pairs are called thermodynamic conjugate variables.

The concept of conjugate variables can be challenging for physics students to understand because the examples we use are unintuitive. The connection between pressure and volume is unclear, and most people don’t wholly understand what temperature or entropy even are. Therefore, I’d like to use a more down-to-earth example.

So, let’s consider a pool of water. The pool is described by two conjugate variables: the volume of water, and the height of the water.
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Cap and trade

In my series discussing capitalism and socialism, a commenter said that both frameworks have problems with externalized costs.  According to the internet, “Externalized costs are costs generated by producers but carried by society as a whole.”  For example, pollution.

I want to discuss externalized costs through the lens of a specific concrete example: cap and trade policies in California.  I choose this example because I have a friend willing to explain it to me because I live in California and know all about it.

Generally speaking, cap and trade is a policy to reduce carbon emissions (or greenhouse gasses).  The government auctions off “allowances” that give companies permission to produce a certain amount of carbon emissions.  There are a fixed number of allowances available (that’s the “cap” part), and further carbon emissions are restricted.  The companies are free to buy and sell the allowances at prices of their own choosing (that’s the “trade” part).  The number of allowances decrease over time in order to meet the government’s pollution reduction goals.

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On color theory

This is a repost of an article I published on Tumblr in 2017.  As many things I publish there, it was written somewhat extemporaneously, but it stood out as something I wanted to eventually import here.

There are really two color theories, the scientific theory of color perception, and the aesthetic theory of choosing color palettes.

The former is quite interesting, containing some surprising facts: yellow is the brightest color, many shades of green can’t be produced by modern displays, white is defined arbitrarily.

The latter is a hodgepodge of various historical ideas and a collection of overgeneralized advice. When I’ve read about aesthetic color theory online my impression is that much of it is either already taught to children or else it is not very good. Here is my attempt to identify some non-bullshit principles of color theory.

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The primary election is the election

I’ve seen many people lamenting that the US has this two-party system, and since one of the parties is a garbage fire, we basically have the one Democratic candidate foisted upon us, regardless of whether we actually like them. And, well, yes. That’s what democracy is, the foisting of popular candidates upon people who don’t necessarily like them.

But if I may point out the obvious, we do in fact get a say in the Democratic candidate, during the primary election. Heck, we don’t even have to vote for a Democrat during the primaries, since one of the major candidates is still an independent. As far as my own vote is concerned, the primary election is the election, and the general election is a formality.

I think everyone knows this, so what I’m really advocating is a shift in thinking. The primaries, which occur between February and June 2020, are the time to pick your favorite candidate, and let your political ideals shine. The general election, in November 2020, is the time to put out the garbage fire.

Of course, thinking about it this way, there are certainly aspects of the Democratic primaries that are disappointingly undemocratic. In 2016 there was a lot of talk about superdelegates, but I don’t actually think that’s the worst problem. (Anyway, superdelegate rules have been reformed since then.)

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Exploitation of labor, part 2

This article is part of a series discussing capitalism and socialism.  Remember, the point isn’t to conclude that socialism or capitalism is good or bad.  The point is to discuss which aspects are good or bad, and why.  Don’t treat me as an authority, tell me how wrong I am, discuss.

Last time, I introduced the idea that labor has a certain maintenance cost, and creates a certain amount of value.  The “surplus” is the difference between the value output and maintenance cost.  In the discussion, we agreed that it’s difficult to define the productivity of each worker.  Usually, many workers are cooperating to make the final product, and you may even have workers who are there to improve the efficiency of other workers.

There are two responses to this.  One response is, even if we can’t define it on an individual basis, we can look at worker productivity and worker pay on a macro scale, and see that workers are getting paid less and less of the surplus.

Another response, is a question.  In the current capitalist system, how do we evaluate worker productivity for the purposes of determining their wages?  The answer lies in the idea of marginal productivity.

A graph whose axes are "number of workers" and "wages". The graph has two curves, labeled "marginal cost" and "marginal revenue". The intersection of the two curves determines the equilibrium wage and workforce size. Two regions of the graph are labeled the employer surplus and worker surplus.

Image mine. Use with permission.

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Link Roundup: May 2019


Skepchick is back! – That is, to say, they’ve collected a lot of their former writers, and relaunched the site.  (Although, even when Skepchick was “inactive”, Rebecca Watson was still there with some good vlogging.)

Terrible Graphs of Orientation – I collected a bunch of graphs, primarily made by ace people.  And I tried to “outdo” the graphs by drawing hypercubes labeled with comic sans.

“No romo”: An overanalysis – I wrote in great depth about “no romo”, which is an occasional meme among aromantic people.  Mostly I end up talking about the history of “no homo”, and all the different ways it has been used.

A commenter pointed out that you can hear the beating frequency between two notes, even if each note is played in a separate ear.  If you have headphones/earbuds, you can hear it for yourself.  This is fascinating, because there is no real beating frequency in the air, so the beating frequency you perceive is somehow created in your brain.


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“Shipping” is a fandom term that refers to a desire to see two fictional characters in a relationship. Shipping includes many behaviors, such as…

  • Wanting canon to bring the characters together.
  • Wanting to interpret canon in such a way that it makes sense for the characters to be together, or that they’re already together.
  • Fantasizing about two characters being together, regardless of whether that would make sense.
  • Wanting to produce or consume fan works that portray the characters together.
  • Rooting for a particular relationship over the alternatives, similar to how sportsball fandoms root for teams.

As a person who has always been on the outside of fandoms, shipping doesn’t really make sense to me. That is, I have difficulty imagining ever feeling that way about characters. Sometimes I like romantic arcs in fiction, and I even enjoy stories in the romance genre, but I don’t fantasize about counterfactual relationships between characters.

But perhaps it’s something I can understand after all. Because you see, I have fantasies in the opposite direction.

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