One: the universe’s favorite digit

This is a repost of an article I wrote way back in 2011.  I’m still proud of figuring this one out.

Out of all the digits, from zero to nine, one is the most common.  This has to do with the log scale.

The log scale captures an important fact that is true of many quantities in life.  Take money for instance.  If you have one dollar, then earning another dollar is great because you’ve doubled your money!  If you have a million dollars, earning another dollar does not make much of a difference.  Small changes matter less the more you already have.

This is true on a log scale too.  On a log scale, 1 is the same distance from 2 as 100 is from 200.  The higher you go up, the more the numbers all get smooshed together.  What does that mean for the digits from zero to nine?

A picture of a log scale, highlighting the regions that have 1 as their first digit (eg 1-2 and 10-20)

In the above picture, I show a log scale.  And on that scale, I highlighted in blue all the regions where 1 is the first digit of the number.  You should see that the blue regions cover more than one tenth of the log scale.  In fact, they cover about 30%.  And so, if we pick numbers randomly on the log scale, about 30% of those numbers will have 1 as their first digit.

Just for fun, let’s apply this concept on the fundamental constants of nature.  I will compare two hypotheses: [Read more…]

I am graduating

I have been hinting for months that I am close to graduating.  Well, the time has come.  I am graduating with a Ph.D. in physics.

In the immediate future, I will be unemployed.  I am taking my time looking for a job in data science.  That means I’ll find some tech company and analyze data for them.  And before you comment on that career choice, let me just say that I know more physics students moving into data science than staying in physics.  When I do find a job I probably won’t make any announcement about it.

Given that most of my time blogging has been while I was at grad school, the impact on my blogging is unknown.  I may have more free time while unemployed, but I won’t necessarily spend that time blogging.  (Note that I often take a blogging break near Christmas, and that has nothing to do with graduating.)

Ah, one thing that might make an impact on blogging, is that I will lose journal access.  I can still get physics papers on ArXiV, but most of what I’d want to blog about would be in social sciences or humanities.  So, that’s a bit tougher.

After this post, I intended to write at least a couple more blog posts about why grad school can be such a bad experience.  It’s not too late, I’ll get around to it eventually.

If you are unwise enough to wonder what my dissertation is about, I’ll tell you.

I worked on photoemission spectroscopy of cuprate superconductors.  Photoemission spectroscopy is the technique of shining light on a material, and measuring the electrons that come out.  The technique tells us about how the electrons were behaving in the material.  A superconductor is material in a special state where electricity is conducted with zero resistance.  Cuprates are a particular class of superconductors.  Cuprates are famous for being in a superconducting state up to relatively high temperatures (but “high temperature” still means minus ~170 degrees Celsius).  Cuprates are not fully understood, and have been a longstanding mystery since they were discovered in the 80s.

Photoemission spectroscopy of cuprates sounds very specific, but it’s a well-established and competitive field of research.

Link Roundup: December 2017

Unpacking Some of the Extreme Distress I Experienced Last Week – Some of you may have heard about the murder-suicide of Scott Smith, who was a podcaster for Recovering From Religion.  Well, here is an account from the cohost of the podcast.  I think this could be helpful if you knew Scott Smith, or if you just want to learn about trauma.

Cuphead: The Fake Outrage (video) – Anti-feminist gamergate-types have recently been outraged over people calling Cuphead (a video game) racist and ableist.  Except… nobody is saying that.  Amongst game critics, there has been discussion of the racist history behind the animation style used by Cuphead, and there has also been discussion about it’s high difficulty, and what that might mean for accessibility.  That really isn’t the same, and Shaun goes into depth about it.  I recommend Shaun’s YouTube channel if you need an antidote to anti-feminist and alt-right YouTubers.

Video game difficulty and accessibility is an interesting topic, maybe I will write about it in the future.

The Fine-Tuning Argument and Base Rate Fallacy – The author is not a physicist, but articulates very well some of the reasons why as a physicist I am very skeptical of fine-tuning arguments.  Predicting how the universe would look with different fundamental constants sounds like an incredibly difficult question!  And the more “fine-tuned” the universe is, the more difficult the question is.

BTW, the author mentions William Lane Craig’s claim that the gravitational constant is sensitive to a change of one part in 10^60.  I would not believe Craig’s claims without independent investigation.  I cannot stress this enough, William Lane Craig is an extremely unreliable source of information on math and physics, even on matters that are neutral with respect to his apologetic arguments.  Seriously, if you’re going to believe in God, you might be better off just believing in God rather than accepting Craig’s arguments, because then at least you will only be wrong about one thing.

[Read more…]

Republicans screwing over grad students

For those of you who are in grad school, you’ve likely already heard that the Republicans’ proposed tax plan hurts grad students. Specifically, grad students would be taxed on their tuition waivers. On top of being bad for grad students, it simply doesn’t make sense to me. As far as I’m concerned the tuition waiver is just an exchange of money between the grant providers and my university. I never see the money. So why should I be taxed on it?

I intend to graduate before any of this could possibly affect me personally. But I went ahead and estimated how much additional tax I would have to pay. In 2016 I earned about $33k, and paid $3k in federal taxes. I had a tuition waiver of $13k, so the proposed tax plan would treat my total income as $46k. My marginal tax rate was 15%, so if I paid taxes on the tuition waiver, my taxes would go up from $3k to $5k. Now, I’m omitting some details, as the tax proposal also shuffles around tax brackets and deductions. But some students at UC Berkeley made a calculator, and it comes out the same.

For some grad students it can be even worse. For example, the calculator estimates that for a typical MIT student, taxes would go up by 240%, amounting to more than a third of their true income. The reason is that MIT has a higher tuition than my own public university.

[Read more…]

Somebody else had it worse

[cn: Non-explicit discussion of sexual violence.]

Last month, I mentioned my past experience with sexual assault and rape. And I said I was fortunate to have never suffered from PTSD, unlike many other victims who have suffered from PTSD. This is my way of saying that other people had it worse than me.

If you’ve heard any number of accounts of victims of sexual harassment or sexual violence, you know that “somebody else had it worse” is a common trope. Saying, “I don’t want to take up space from other people with more extreme stories.” Or, “I don’t want anyone to think I’m making a huge deal over something so little.” Or, “I’m not sure this even belongs in the category of sexual assault.”

In the other extreme, some people argue that we shouldn’t ever compare different experiences of sexual violence at all. We’re told that there is only one kind of rape, all sexual violence is bad, end of story.

I have issues with both of these sides, and wish to find a happy medium.

[Read more…]

Origami: Compound of Five Octahedra

Compound of Five Octahedra, by Meenakshi Mukerji.  From the book Exquisite Modular Origami.

At first when you look at this it just looks like a many-pointed star.  But look carefully: each color forms an octahedron.  Yep, it’s five octahedra arranged symmetrically.  Classic.  I’ve already talked your ear off about symmetric colorings and polypolyhedra, so I’ll just leave it at that.

 

If you’re wondering, yes those are the aro flag colors (or at least the most common version).  Black, gray, white, light green, dark green.  It’s a good color scheme.

How to make symmetric colorings

This is the fourth part of a series about symmetry in origami.

Given an origami model, what are the possible symmetric colorings?

This is a question I posed in an earlier post, and I said I didn’t know the solution.  I thought about it a lot, and I found the solution. I will write up a mathematical proof in a later post.  Here I will just explain the result.

A brief review: Each origami model has an associated shape symmetry group, which is the set of all transformations (rotations and reflections) which leave the shape unchanged. There is also an associated color symmetry group, which leaves the shape and colors unchanged. Then there is the pattern symmetry group, which may swap the identities of some of the colors, but leaves the color patterns unchanged. In this post, C is the color symmetry group, and P is the pattern symmetry group.

I defined a “symmetric coloring” to be one where P is “large” and C is “small”. I didn’t say how large P needed to be, or how small C needed to be, but it doesn’t matter. I found a method that can construct any and all symmetric colorings.

Fundamental domains

Suppose we want to find a symmetrical coloring of a cube. First question: Are we assigning a color to each face, each vertex, or each edge? We want to find a general solution that will work in all three cases, as well as any more complicated case. So the first thing we need to do is divide the cube into fundamental domains.

A cube. Each face of the cube has been divided into eight triangles.

Each triangle on the cube’s surface represents a fundamental domain. In total, there are 48 fundamental domains.

[Read more…]