On the social construction of electrons

One interesting facts about electrons is that they are all literally identical. And I really do mean completely and literally identical, in the sense of sharing all properties. Yes, even the spatial distribution of their wavefunctions.

To illustrate how this is possible, consider a simple scenario, where we have two electrons, one at point A, and the other at point B. At first it would seem that electron 1 has a different location from electron 2. But in fact, the universe is in a quantum superposition of two states–the first state has electron 1 at A and electron 2 at B, while the second state has electron 2 at A and electron 1 at B. So even though we observe electrons at two distinct locations, the two electrons involved are actually identical.

The fact that electrons are identical has really important consequences.  One consequence is the Pauli Exclusion Principle, which states that no single state can be occupied by two electrons simultaneously. So when we have a large atom, electrons will occupy many different orbitals of the atom, instead of having all electrons occupy the one orbital with lowest energy.

Of course, it’s not really practical to think of it this way all the time. Generally we prefer to think of each electron as being at a distinct location, and then we tack on additional rules like the Pauli Exclusion Principle.

The point is that the individuality of electrons is an idea that arises from practical necessity, and not from the fundamental physics. Practical necessities arise from social context. And in principle, a different social context could have different needs that are better fulfilled by some other way of thinking about it. Therefore, the concept of individual electrons is a social construct.

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What is a symmetry group?

This is the first part of a series about symmetry in origami. Here I will explain what a symmetry group is through a series of examples.

An origami heart

This image is sourced from a video with folding instructions.

This heart illustrates one of the most basic forms of symmetry. A symmetry is a transformation that preserves the shape and orientation of the object. In this case, the transformation is a reflection. If you reflect the heart across a vertical line, you get back the same heart. But with further examples, we can see that this is not the only kind of symmetry.

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Origami symmetry masterpost

When I was very young, I remember doing some math problems where I was given a shape, and asked whether there was a line of symmetry. This seemed very basic to me even at the time, and I thought that was all there was to it. But there is, in fact, much more. This has been particularly impressed upon me by my work in modular origami. For example, some of the most basic shapes I can make are the Platonic solids, which are very symmetrical indeed.

Photos of 5 origami models, one for each platonic solid

These are models I’ve folded for each of the platonic solids. From left to right, top to bottom: tetrahedron, octahedron, cube, dodecahedron, icosahedron.

Unfortunately, if you really want to understand the kind of symmetry extant in origami, you might need to take a course in advance mathematics. Specifically, this would be taught in Abstract Algebra, and even more specifically, finite group theory.

I intend to write a series explaining some of the basic concepts behind the symmetry of origami, but in a way that people can understand even without being into math. This isn’t necessary to creating or appreciating symmetrical origami, but you may find it helpful or interesting. For the readers who are into math, I hope you enjoy a more visually-oriented discussion of a topic that is typically discussed in rather abstract terms.

Articles in this series so far:
1. What is a symmetry group?

To be continued…

Link roundup: September 2017

I used to call this monthly feature a “linkspam”, but after some consideration I am now calling it a link roundup.  But whatever, it’s the same thing.

How an Ad Campaign Made Lesbians Fall in Love with Subaru – This is a very interesting article discussing one of the first ever queer-targeted ad campaigns.  What surprised me the most is that Subaru used subtle gay-coding that straight audiences usually missed, but this was not because they wanted to hide their intentions.  Subaru was open about it, and it was widely discussed in major newspapers.  Rather, they used coded messages because market research said that lesbian audiences liked it better that way.  Of course, I’m not sure that market research would extend to today.

Is there a “Gay Agenda” in Hip Hop? (video) – Music critic Anthony Fantano answers a question from a fan. I did not know this was a serious question that people asked. Apparently some of the barriers in hip hop have been breaking down, allowing more space for openly gay and bisexual rappers. This seems significant, especially given that hip-hop/R&B is the most consumed genre of music in the US.  Of course, it doesn’t constitute a “gay agenda” in hip hop.

BTW, I don’t really listen to hip hop, but if any of you do, here’s an example song, enjoy.  (content note: video depicts blood, lyrics talk about suicide and other violence.)

Damsels in Distress vs Distressed Dudes in Jin Yong stories (also see part 2) – Sara discusses the analogue of the distressed damsel trope in the Chinese genre of Wuxia.  It seems that when male characters rescue damsels in distress, the male characters are usually regarded with suspicion.  When female characters rescue distressed dudes, the female characters tend to get fridged afterwards in order to provide motivation for the male characters.  It’s still kind of sexist but it’s a different variety of sexism from western fiction.

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What is identity politics? An empirical investigation

Every time I see people making disparaging remarks about “identity politics”, I wonder what that means. It sounds like a meaningless buzzterm, like “political correctness”. It sounds like an attack on any minority groups that dare to politically advocate for themselves.

But where did the term originate? How did it become popular? Which minority groups is it directed at? Has its use changed over time? Here I perform an empirical investigation using Google.

A line plot of the popularity of search terms over time.

Source: Google trends. This tracks the popularity of search terms over time.

As can be seen from above, the term “identity politics” has been around for a long time. I looked as far back as Google trends allows (back to 2004), and it’s still there. However, there was a big spike in popularity in November 2016–the month that Trump was elected. There’s also a broad hump around January-February 2017, and a more recent spike in August 2017. I will investigate each of these time periods by sampling from time-constrained google searches.

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Why are physics talks so bad?

As I get closer to the end of my PhD, I wanted to talk about why grad school sucks so much. For my first complaint, let’s talk about physics talks. I’m not referring to popular stuff like Stephen Hawking’s TED Talk or whatever. I’m referring to talks given by physicists to other physicists in their field.

By design, a physics talk starts out with a broadly accessible introduction, and dives into technical details that only two people in the audience understand. This is followed by a Q&A where those two people ask (apparently) extremely intelligent questions, and everyone else silently feels stupid as they listen to arguments over arcane details.

When I started out my PhD, approximately 0% of physics talks made sense. I thought that maybe when I got further into my PhD I would understand much more. Nope! Now, maybe 10% of talks make sense. And even that high rate comes from knowing when to avoid going to a talk in the first place.

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Origami: Pinwheel Dodecahedron

Pinwheel dodecahedron

Pinwheel Dodecahedron, a model by Meenakshi Mukerji

So here’s a really old model, apparently I made it in 2013?  It rounded out my set of platonic solids.  Yep, that’s the good old dodecahedron, with 12 faces, 30 edges, and 20 vertices.  I use one piece of paper per edge, so that’s 30 pieces of paper.

Looking back, I have some disagreements with how I made this model.  I chose to use patterned washi paper, but I should have used solid-colored paper instead.  The model already has patterns in it–the pinwheels, which are created by showing part of the backs of the paper.  The second problem is that I used paper with a bunch of different patterns, rather than sticking to just one or two.  The end result is a bit chaotic.  These days I try to make models with a more focused aesthetic.