If, when you hear the name Johnlock, you think of the 17th century poltical philosopher, John Locke, then keep reading. This guide is for you.

My daughter, who is a freshman in high school, informs me that Johnlock is not, as I had presumed, the "Father of Classical Liberalism", but rather the "Father of All Gay Ships". In fact, it is a "gateway ship" for all sorts of "slash" couples. Confused? I was too. Like I said, keep reading.

Johnlock is John Watson and Sherlock Holmes, paired as a gay couple. More specifically, it is Martin Freeman/Benedict Cumberbatch (hence the term "slash"), in their roles as John and Sherlock, living in a fanfiction story arc (a sort of alternate universe) and being in a romantic relationship (hence the term "ship'") with each other. This is a VERY popular concept among young people (I can pretty much guaranty that my mother NEVER shipped Basil Rathbone and Nigel Bruce). Fangirls (and fanboys, to a certain extent), who are devoted to the BBC series Sherlock, are obsessed with this fictional relationship. Apparently, Mr Cumberbatch and Mr Freeman make an incredibly cute couple.

Shipping does not end there. As I said, for many, Johnlock is merely a gateway to shipping...that is, to fantasies about your favorite characters (or real people, in some cases) getting romantically involved with each other. Take Thorin Oakenshield and Bilbo Baggins, for instance. We all saw them hug at the end of The Hobbit. Obviously, it was the start of an epic ship...an "unexpected journey" that Peter Jackson may not have intended (and JRR Tolkien certainly did not). The humble hobbit and the dwarf king, are, in fact, a very popular slash couple.

This all sounded funny to me (in both the "haha" and "strange" sense), but my daughter assures me it is not. She warns me that if the producers of BBC's Sherlock have Watson get married in season 3, there will be a major revolt among the fandom.

Are all ships gay? No, but they are far more common than hetero ships. Other than that, I wonder how different this is than other fan-based fantasies of decades ago. John Steed and Emma Peel...that was a ship if there ever was one. Major Nelson and Jeannie? Absolutely. I'm sure people were shipping Oscar and Felix, just not so openly. What about Rob and Laura Petrie? Oh wait, they actually were in a relationship, but some fans might have fantasized about them getting rid of their twin beds. If you grew up in the 60's and 70's, you know what I'm talking about.

So I thought aloud to my daughter, who of my cultural icons would I ship? For some odd reason, the first couple that came to mind was Dimitry Shostakovich and Aaron Copland. Okay, interesting couple, but no. Ishmael and Queequeg? Probably not too popular among my daughter's generation, but she assured me that it would be a good one, and probably had already been documented somewhere. I needed to think of something more modern. Call me old-fashioned, but the gay male slash thing doesn't really work for me. Maybe Black Widow and Pepper Potts?

My apologies to all those serious shippers out there, but I'm afraid it's still funny to me. My daughters and I enjoy Sherlock together, as well as The Hobbit (and even Moby Dick), and now we can also talk about shipping. I'm a lucky guy.

A series of occasional articles on the intersection of art, math, and computers

Everything you know is wrong.

That's the title of an old Firesign Theater album, and I think of it often as I watch my kids progress through high school.  Maybe it should read, "Many of the things you are taught have been dumbed down because teachers didn't think you could handle them."  Whether it's glossing over quantum physics when teaching the nature of the atom, or stating that Socrates killed himself, because getting into the whole trial thing is too complicated, examples abound.

Anyway...most people, when asked to name the primary colors, would respond "red, yellow, and blue", and, when asked to define what a primary color is, would respond with something like, "they are the colors which can be used to make all other colors". That's what many of us were taught in school at a young age, but it's only partially true. People involved in printing know that the truest primary colors are cyan, magenta, and yellow, with black added to get a full range of darks (that's the familiar CMYK color model, with K representing black).

Are We Adding or Subtracting?

But even that is only half the answer to the question of primary colors.  We see colors on a piece of paper or canvas because they absorb certain wavelengths of light and reflect others. Red appears red because it absorbs most light and reflects only the "red" wavelengths.  This is called reflective color.

If you mix two colors together on a piece of paper, they absorb a greater range of wavelengths, and together, reflect less.  The mixed color is darker.  Mixing reflective colors together is a subtractive process.

On the other hand, the color you see on a computer monitor is transmitted (by thousands of tiny LED lights). If you add transmitted colors together, the result is a brighter color, so it's called an additive process.  The primary colors in a transmitted color system are not cyan, magenta, and yellow, but rather red, green, and blue, which is the RGB we are all familiar with when describing colors in a program like Photoshop or GIMP.  Combine all three transmitted colors at their full intensity, and you get white.

On a computer monitor, a single unit of transmitted color -- a pixel -- is the product of 3 LEDs (red, green, and blue), each shining at varying levels of intensity.

Your Digital Palette

The range of colors available on a computer screen depends on the range of intensities that can be defined for each of the color channels (red, green, and blue). In a typical system, the values for each channel are defined by eight bits of information. Each bit is binary, having two states, defined as 0 and 1, so two bits together can represent four different values (00, 01, 11, 10); eight bits together can represent 256 different values (2⁸). The intensity of a single channel, for example the red LED, is defined by eight bits, and so can have 256 levels of intensity.

Thus we have the familiar RGB notation of 3 numbers, each with a value between 0 and 255. Each number represents the intensity of one of the color channels. This is commonly called 24-bit color, and can represent 16,777,216 different values (256³).

HTML Notation, or the Beauty of Math

We (humans) have chosen to represent numbers, which are empirical things, with ten different characters, namely the digits 0 through 9.  We can represent any number (including numbers greater than ten) using these ten characters, if we combine them. It's a base ten, or decimal system.  Just like eight binary characters can represent 256 numbers (2⁸), 8 decimal characters can represent 100,000,000 numbers (10⁸).

In a decimal system, twelve is 12.  In a binary system, where we only use two characters (0 and 1), twelve is 1100.

RGB notation represents each of the 256 available levels of intensity using a decimal (base ten) system. But what about HTML notation, where RGB values of 226, 243, and 229 become e2f3e5?  This is actually three numbers (e2, f3, and e5) that are used to represent the 256 different values for each of the three channels in base 16 notation, or using 16 characters for each number instead of ten.  The 16 characters are 0-9 and a-f. In this system, 01 is one, 0f is fifteen, and 10 is sixteen.  Why use base 16?  Because it only takes two base 16 characters to represent 256 values (16²).

So What? or 16 Shades of Gray

Do you need to understand all this to produce a nicely colored picture on your computer?  No.  If you do understand it, will it guaranty that you use colors well?  No (I'm a prime example of this).  I just like the elegantly logical structure of the system.  And it opens a door to a greater understanding of color.  For instance, if the LEDs for all three channels are shining at the same intensity, you get gray.  In HTML notation, 999999, aaaaaa, and bbbbbb are all shades of gray.  Only when you vary the intensities among the individual channels, do you get different hues.

Or better yet, think about this: The RGB system is based on how human eyes work.  We generally have three types of color receptors, roughly correllating to red, green, and blue.  We are known as trichromats.  There are some animals that are tetrachromats; they have four types of color receptors. So when we see green grass rendered on a computer screen, and it looks realistic to us, it's because the monitor is replicating our own limited way of seeing color. A tetrachromat, seeing the same image, would probably think that it doesn't represent the true coloring of grass.

I think this is all fascinating and...ummm..enlightening, but admittedly, I'm a geek.  If you've made it this far, thanks for reading.