Monthly Archives: March 2020

Deadly Vacation Cabin

I’m not that into horror, on the page or the screen. For instance, I’ve never seen any of the Jason, Freddie, or Chucky, movies. Maybe it comes from having a different set of fears, but slasher movies never did anything for me. The gore doesn’t bother me. It’s more finding it all kinda silly and ultimately tedious.

But there are definitely exceptions. Some horror stories — usually comedies or parodies — manage to find a new spin on old tropes. When it comes to storytelling, I am a big fan of new spins, almost regardless of genre.

Which is why I really enjoyed The Cabin in the Woods.

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The Heart of the Mandelbrot

In recent posts I’ve presented the complex numbers and the complex plane. Those were just stepping stones to this post, which involves a basic fact about the Mandelbrot set. It’s something that I stumbled over recently (after tip-toeing around it many times, because math).

This is one of those places where something that seems complicated turns out to have a fairly simple (and kinda cool) way to see it when approached the right way. In this case, it’s the way multiplication rotates points on the complex plane. This allow us to actually visualize certain equations.

With that, we’re ready to move on to the “heart” of the matter…

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The Complex Plane

In the first post I explained why the mathematical “imaginary” number i is “real” (in more than one sense of the word). That weird number is just a stepping stone to the complex numbers, which are themselves stepping stones to the complex plane.

Which, in turn, is a big stepping stone to a fun fact about the Mandelbrot I want to write about. (But we all have to get there, first.) I think it’s a worthwhile journey — understanding the complex plane opens the door to more than just the Mandelbrot. (For instance, Euler’s beautiful “sonnet” also lives on the complex plane.)

As it turns out, the complex numbers cause this plane to “fly” a little bit differently than the regular X-Y plane does.

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“Imaginary” Parabola

Graph of ax2 for diff a values.
(green < 1; blue = 1; red > 1)

This is a little detour before the main event. The first post of this series, which explained why the imaginary unit, i, is important to math, was long enough; I didn’t want to make it longer. However there is a simple visual way of illustrating exactly why it seems, at least initially, that the original premise isn’t right.

There is also a visual way to illustrate the solution, but it requires four dimensions to display. Three dimensions can get us there if we use some creative color shading, but we’re still stuck displaying it on a two-dimensional screen, so it’ll take a little imagination on our part.

And while the solution might not be super obvious, the problem sure is.

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“Imaginary” Numbers

Yes, this is a math post, but don’t run off too quickly. I’ll keep it as simple as possible (but no simpler), and I’ll do all the actual math so you can just ride along and watch. What I’m about here is laying the groundwork to explain a fun fact about the Mandelbrot.

This post is kind of an origin story. It seeks to explain why something rather mind-bending — the so-called “imaginary numbers” — are actually vital members of the mathematical family despite being based on what seems an impossibility.

The truth is, math would be a bit stuck without them.

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Cloud Library

Here’s yet another unplanned post, mostly because there was something important I forgot to mention yesterday, but also because I started watching three different Netflix shows (or maybe call it two-and-a-half), and all three are fit for a Sci-Fi Saturday post, so here I am again.

I dither about three because one of them was wasn’t new, it was season two I started of Siempre Bruja. But I hadn’t yet seen any of Lost in Space or the new Chilling Adventures of Sabrina. I’ve been suspicious of the former, and the latter isn’t quite my cup of tea on several counts.

But first you should know about (Your) CloudLibrary!

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Cooled Lava Hellscape

Fissure #8.

Wow, for the third time this month (third time in a week) I’ve realized the day calls for a post I hadn’t planned. The first time was when the MLB delayed the baseball season. The second time — the very next day — was Pi Day and Albert Einstein’s birthday.

This time it’s the equinox (and a friend’s birthday; shout out!). For those of us in the northern hemisphere it’s the spring (vernal) equinox, and that’s my favorite of the four annual solar node points (two equinoxes; two solstices). It means we have a whole half a year of light ahead.

So I just had to post something.

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Tiny Measurements

When possible, I try to find a theme for the Wednesday Wow posts. Last time, for instance, the theme was aviation and fireworks (two things you wouldn’t normally think went together, but in one case they delightfully did).

The problem is that I’m jaded and have seen a lot, so I can be hard to impress. Not lots of things raise to my highest rating, Wow! Fortunately, I’m not so far gone I can’t still see a world filled with wonder, some of which drops my jaw.

The theme, such as it is, concerns measurements, especially tiny and precise ones. Like, for instance, Planck Length tiny.

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Capable of Greatness

I’ve been slowly going through the NPR Tiny Desk Concerts. Most of the musicians and groups are unknown to me (it’s been decades since I even attempted to keep up with music). Truth is, most of the acts are interesting, but don’t really grab me. Maybe one in ten engages; none have made me a new fan.

Which is a whole other story. I mention it because many of these music makers are sweet, gentle, loving people who just want everyone else to be sweet, gentle, and loving. It’s a common sentiment. Banish the bad forever!

But balance is required. There is a Yin-Yang aspect to life.

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The Hexagon

I hadn’t really planned to, but it’s both Pi Day and Albert Einstein. As a fan of both the number and the man, it seems like I should post something.

But I’ve written a lot about pi and Einstein, so — especially not having planned anything — I don’t have anything to say about either right now. In any event, I’m more inclined to celebrate Tau Day when we double the pi(e). I do have something that’s maybe kind vaguely of pi-ish. It’s something I was going to mention when I wrote about Well World.

It’s just a little thing about hexagons.

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