For my first interview on the show, I spoke to Max Hawthorne, author of the paleo-fiction thriller, Kronos Rising, about his writing and his experiences with science fiction as a whole. Max's website. Max's peer-reviewed scientific paper on Plesiosaurs. Max's book recommendations: The Bug Wars by Robert Asprin Hiero's Journey by Sterling Lanier

For my first interview on the show, I spoke to Max Hawthorne, author of the paleo-fiction thriller, Kronos Rising, about his writing and his experiences with science fiction as a whole.

The Recamán sequence, or more properly Recamán’s sequence, is one of the more unusual sequences to make the rounds in the internet math community. The way it works is that the first term in the sequence is 1. Then, for each term, you either add or subtract the number of that term from the previous one. There are two rules to this.

First, the numbers have be greater than 0. So for the 2nd term is 1+2=3. The 3rd term is 3+3=6. But the 4th term is 6-4=2. Second, if you subtract, the resulting number may not have appeared in the sequence before. You can include repeats when you add (otherwise, you’d get stuck), but not when you subtract. So the next term is 2+5=7. But then, you can’t subtract 7-6=1 because that there’s already a 1 in the sequence. Instead, you have to add 7+6=13.

This sequence was featured in a video by the YouTube channel Numberphile in 2018, which gave an interesting visualization of the sequence by connecting each term to the next one on the number line with a semicircle, which gave an interesting swirly pattern like the one below:

For my first interview on the show, I spoke to Max Hawthorne, author of the paleo-fiction thriller, Kronos Rising, about his writing and his experiences with science fiction as a whole. Max's website. Max's peer-reviewed scientific paper on Plesiosaurs. Max's book recommendations: The Bug Wars by Robert Asprin Hiero's Journey by Sterling Lanier

Despite his often inconsistent writing, Philip K. Dick is notable for having more film adaptations of his novels and short stories than almost every other sci-fi author, making him one of the most important writers of the New Wave. Here, we explore an overview of his work.

Today, January 2, is the observed birthday* of Isaac Asimov, one of the most prolific science fiction (and science fact) authors of the twentieth century.

In Asimov’s honor, January 2 is celebrated each year as National Science Fiction Day. (Which honestly feels like a questionable move because it’s so overshadowed by New Year’s Day.) So, kick back with some Star Trek or something as we ease in to the task of trying to make sense out of 2021. Enjoy!

* Asimov’s actual birthdate is uncertain because he was born to a Russian Jewish family in 1919-1920, and there were several different calendars to complicate things. He may have been born as early as October 4, 1919, but January 2 is the day he celebrated.

Previously, I described how the weak nuclear force really is a force even though it’s almost never described as one. Instead of a simple inverse square law like gravity and electromagnetism, it decays exponentially so that it weakens over a very short distance.

But there’s one more piece to this puzzle. At the popular science level, no one ever explains what the equation for the strong nuclear force is, either. It does have one, and it’s simple enough to explain, but no one ever mentions it, which is a shame because it’s actually kind of cool.

This equation is called the “Cornell potential” or the “funnel potential”:

Here, α and σ are constants associated with the strong force. The main function of the strong force is that it holds the quarks inside a proton or neutron together. It holds atomic nuclei together, too, but that’s a side effect. The Cornell potential tells us how this works when we take a derivative to convert it to a force:

The first part of this is an inverse square law. In other words, inside a proton or neutronmeson, quarks actually undergo a gluon-mediated scattering interaction governed by an inverse square law just like Coulomb’s law. The difference is that there’s a second term in the equation, and it’s a constant. Regardless of the distance between them, two “unpaired” quarks will be attracted to each other with a constant force on top of the inverse square law of about 10,000 newtons^{[1]} (which is a weirdly normal-sounding number equal to about one ton of force).

It’s time for another physics explainer. In an earlier post, I explained Lagrangian mechanics and why it uses the weird (to physicists) equation L=T-V. I thought I might do some more posts like that, and I found a topic that should make a good one. So, let’s jump over to nuclear physics and figure out what on Earth is going on with the weak nuclear force.

Physics says there are four fundamental forces of nature. There’s gravity, which pulls masses toward one another. There’s electromagnetism, which pulls opposite electric charges toward each other (and pushes like charges apart). There’s the strong nuclear force, which holds the quarks together inside protons and neutrons. And then, there’s the weak nuclear force, which…causes radioactive decay?^{[1]}

♫♪ One of these things is not like the others. ♫♪

In any popular science book or really even undergraduate textbooks (to my memory), you’ll see the four forces described this way, and you may be thinking: “Wait a minute, one of those isn’t actually a force.” Three of the fundamental forces are described how forces are always supposed to be described: by how they push or pull on particles. But the weak force isn’t. It causes this other process to happen, and no one ever mentions it pushing or pulling.

Imagine if someone said, “Gravity is a force that makes things change shape.” And it’s true; gravity makes stars and planets form into spheres, and it makes a raindrop splatter into a pancake on the ground. But that sentence is still completely missing the point (even if it doesn’t sound like total nonsense). It would be silly to talk about gravity just making things change shape and not even mention the main aspect of it—the actual force part of it—which is that it pulls masses together.

That’s how weird it sounds to me to say, “The weak nuclear force causes radioactive decay.” So, what gives? Well, that’s what I’m hoping to explain with this post.

(And I’ll get to the strong force in the next post. Ironically, that one is more complicated, even though it sounds simpler.)

One year ago today, I posted a Challenge to Flat Earthers on this blog. I proposed an experiment that could photograph the curvature of the Earth directly without having to worry about camera distortions, which is what Flat Earthers usually point to to explain away such images. If you hold a ruler against the horizon in view of the camera, it will give you an absolute standard for what is straight. With a ruler to measure against, you don’t have to be at the edge of space, but only up in an airplane to see a little bit of curvature in the horizon.

I was going to put my proverbial money where my mouth is and do this experiment myself the next time I flew, but then 2020 hit, so I haven’t flown since then–nor have I have any takers on the challenge.

However, this is about a different topic. I admitted in that post that there is one other thing that could cause an apparent curvature in the horizon: refraction. Refraction is the bending of light through…anything, really, but in this case, it’s mostly to do with air. In various weather conditions, air can bend light so that distant objects appear higher or lower than they should be. This is the basis for a various phenomena that are colloquially called mirages.^{[1]} Refraction can also make the horizon appear lower than it really is, and thus the edge of a flat disk would look more curved that it should be.

More generally, one thing Flat Earthers like to say, possibly the clearest^{[2]} positive evidence to support their claims,^{[3]} is that they can take photographs that show distant objects that should be behind the horizon.

Take this photo of the Chicago skyline, for example. It taken from the other side of Lake Michigan, 60 miles (100 km) away. If you do the math, the skyline should be behind the horizon on a round Earth. What’s going on?

For my first interview on the show, I spoke to Max Hawthorne, author of the paleo-fiction thriller, Kronos Rising, about his writing and his experiences with science fiction as a whole. Max's website. Max's peer-reviewed scientific paper on Plesiosaurs. Max's book recommendations: The Bug Wars by Robert Asprin Hiero's Journey by Sterling Lanier

In the 1960s, science fiction went through a major change as the New Wave moved it away from the hard sci-fi of the 50s into a softer, but more socially conscious space. In this episode, we overview the new ideas, themes, and authors of this period.

And, in the spirit of the season, you can see Santa Claus Conquers the Martians free on YouTube. It’s public domain in the United States due to various errors on the part of the studio, including releasing it without a copyright notice. Or, there are RiffTrax out there, too.

Actually, I posted this video a couple weeks ago, but between my podcast and professional stuff, I haven’t gotten around to reposting it here. I’m trying to catch up on actual blog posts I have planned, so I thought I should share it. Check it out.

This video is a tribute to Mathologer’s video about multiplication tables and the Mandelbrot set a few years ago. You can see it here.

This is an animation of modular arithmetic, which is basically the kind of arithmetic you do on a clock, except instead of 12 hours or 60 minutes, the circle adds up to an arbitrary number. In this case, there are 360 points on the circle.

The lines show multiplication by the number in the top left corner. Take multiplication by 2, for example. Go around the circle, and draw a line connecting 0 to 0 (which is just a point), 1 to 2, 2 to 4, 3 to 6, and so on. When you get to 180, you have to start over, so you connect it to 0, 181 to 2, and so on. You can see this at 00:06 in the video. The resulting heart shape formed by the lines is a cardioid, which is the largest bulb in the Mandelbrot set. Each number up to 360 produces a different pattern, many of which are interesting.

This isn’t the only video of animated modular multiplication tables on YouTube. Mathologer’s original video spawned many copycats, a few of which are larger and more complex. But I did do something that no other video I saw does. My version pauses at many of the interesting numbers so that you can see the patterns more clearly. Without that, it’s hard to tell what’s going on, much less appreciate the complexity of the structures.

I animated this whole thing using Python. Maybe I’ll post the code later if I decide on an appropriate venue. The music comes from Tchaikovsky’s“Pathétique” Symphony, specifically the second movement, which is a waltz in 5/4 time instead of the usual 3/4. I thought the odd time signature befitted the strange spinning of the patterns in the video. Public domain recording courtesy of Musopen.

I have another, more complex math animation that I’m working on. If you want a sneak peak…well, I haven’t rendered anything yet. But you can click here for the inspiration.

For my first interview on the show, I spoke to Max Hawthorne, author of the paleo-fiction thriller, Kronos Rising, about his writing and his experiences with science fiction as a whole. Max's website. Max's peer-reviewed scientific paper on Plesiosaurs. Max's book recommendations: The Bug Wars by Robert Asprin Hiero's Journey by Sterling Lanier

Like books, movies and television also went through a golden age in science fiction in the 1950s. In this episode we explore the trends in the visual medium at the time and how they compared to print.