On the Count of Three

threeThe seventh post I published here, Yin and Yang, introduced my fascination with the Yin-Yang idea of duality, that life is filled with pairs of opposites (left–right, day–night, black–white). Since then I’ve written a number of posts about some of those pairs.

In that first post I mentioned that life was also filled with threes (and some of the other numbers, but especially threes). As we look around, we see an awful lot of things that do come in triplets. Today I thought I’d finally get around to tripping on life’s triples.

Ready? Then: One,… Two,… Three,… Let’s go!

Remember how a key point about Yin-Yang pairs was that there can be opposing pairs (north–south, plus–minus) or “cup” pairs (full–empty, light–dark). In a cup pair, there is the thing and the absence of that thing which creates the duality.


Peter, Paul, & Zaphod.

Triples also have two modes: They can be three distinct things (red-green-blue or X-Y-Z), or they can be two extremes with a middle (minus-zero-plus or left-center-right).

As with pairs, the distinction between the modes is that one of the “poles” is the absence of something. With triples, it’s the absence of both of the other things.

I’ll try to use the word triplet for the first mode, where there are three distinct things. As pair is the general word for two, triple is the general word for three. (As you’ll see, for the mode with a null pole, sometimes the term bi-polar works well.)

One of the most obvious observations is all the stools and small tables with three legs. And consider tripods!


Table? Foot stool? Chair?

Three legs turns out to be a very stable configuration. As we know, four-legged things wobble if the legs don’t all touch the ground (either due to the legs or the ground).

Of course, something with one or two legs needs to balance to stand. (No doubt the four-, six-, and eight-legged, animals view us humans with amazement!)

Objects with four (or more) legs have to deal with the wobble problem — only three legs is inherently stable![1]

This stability of three is fundamental to triples. Geometrically, three points define a plane. Any given three points always fit on some two-dimensional surface. (An infinite number of planes pass through any two points. A third point can only be on one of those.)

What more, on that plane, three points also define a unique circle. Given any three points (not in a straight line), you can find some circle that passes through all three. (Again, an infinite number of circles pass through any two points. A third point falls on (just) one of those.)

Consider what happens with four (or more) points: If three points define a plane, then a fourth point is either in that plane or not. If it’s not, then the table wobbles.


Lights, Camera,… wait, where’s the camera?

But the legs of a tripod can always find stable footing.

In a sense, the legs stand on the plane formed by the three points of contact, but the tripod can adjust to be level to some other reference (within reason).

This plays out in wheeled vehicles, too.

A bicycle requires a degree of balance, which is why kids start off on tricycles. Four-wheel vehicles are very stable, but the wheels have to be able to adjust up and down (via the suspension) to ensure ground contact.

The stability of three shows up in another way: Three is the smallest number of votes that never result in a tie. As such, a triumvirate, a ruling body of three, can be a useful political mode. In the USA, we have the Judicial, Legislative, and Executive, branches of government.[2]

Some computer systems use a “rule of three” to validate results in “noisy” situations. In such systems, there are three identical apps running in parallel. So long as at least two agree, the results can be considered valid (but obviously better if all three agree).[3]


Red. Green. Blue.

It’s interesting that, because of how human color vision works, all other colors may be synthesized using just three “primary” colors: red, green, and blue. (Your image display screens do this routinely. If you look closely, there are only red, green, and blue, pixels.)[4]

Baseball is filled with threes: Three strikes, three outs, three bases (plus home). Nine innings, which is three times three. Also nine players. The baseball season (162 games) is divisible by three, and so are the 54-game the thirds. To top it off, a baseball has 108 stitches. You guessed it. Divisible by three. Repeatedly.[5]

The fast way to determine if a number is divisible by three: Add up all its digits. If the sum is multi-digit, add’m up again. Keep doing that until you have only one digit left. Is that digit three, six, or nine? Then the original number was divisible by three.

Is 34,782,576,470,928 divisible by three? Let’s see:

3+4+7+8+2+5+7+6+4+7+0+9+2+8 = 72
7+2 = 9

So, yes. It is. (Incidentally, if the final digit is 9, then the number is also divisible by 9 — which this one is.)

Science fiction has The Trilogy. In writing in general, a common structure is the three act story (introduction, conflict, resolution), and that’s all SF trilogies really are — long stories told in three acts.

Foundation Trilogy by Isaac Asimov

To name just one.

On a finer-grained scale, writers often list examples in triplets (you’ll find them throughout this post). It has a substantive feel to it (like pointing with two fingers).[6]

The Christian religion revolves around the Holy Trinity, the Father, the Son, and the Holy Spirit. The Hindu religion revolves around Brahma, Vishnu, and Shiva. There is, again, the sense of a triumvirate.

Our stories, our myths, and our religions (even baseball) abound with triples!

On a more technical level, three pops up in interesting places. The neutrons and protons that make up the nucleus of the atom each consist of three quarks. Further, in sub-atomic physics, there are three families of matter (excitingly named: I, II, & III).[7]


The Fermions. All atoms consist of up and down quarks and a bunch of electrons!

Each family has a heavy quark, a lighter quark, an electron species, and a neutrino species. So there are (as far as we can tell, only) three neutrino species, three electron species, three heavy quarks, and three light quarks.

There are two common types of electrical power supply. The standard “cup-pair” single pole supply that provides ground (0 volts) and some voltage (often +5 VDC), and the bipolar supply that provides ground and plus and minus voltages (e.g. -12 VDC, 0, +12 VDC).

Pretty much all the triples mentioned so far are triplets. The bipolar power supply is an exception. So are signaling systems with three states, usually plus, minus, and zero. There are also three-wire systems with one send, one receive, and one ground (zero) wire.

In math, base three (ternary) is a little bit more efficient digit-wise than base two (binary), but is still “verbose” compared to our more comfortable decimal:

201510 = 22021223 = 111110111112

It turns out that it’s pretty easy to calculate the motion of two bodies, but the three-body problem raises the difficulty level significantly. A third planet (dwarf or not) complicates the picture almost to the point of intractability.

love triangle

(no comment)

Which, perhaps, is a little reminiscent of the third wheel — the unwelcome third-party who complicates matters. Let alone the complications of trying to date two people (a whole different three body problem)!

The ultimate three might be that, as far as we can tell, we live in three-dimensional space. Modern physics thinks there might be a number more that we just haven’t seen for some reason. (String theory currently is thinking ten, but one version went up to 26!)

Regardless, as with spotting all the pairs of things around us, we can also spot many triples of things. See how many you can start noticing!

This post was brought to you by the number three.

[1] Makes you wonder why there are no three-legged animals. Two, yes; four, six, or eight, common; even five. But no tripod critters! (Outside of certain classic science fiction.)

On the other hand, six legs can act like a pair of opposing tripods, which gives an animal a very stable gait. Once again, be glad insects can’t get too large!

[2] The movie Minority Report featured another kind of voting triumvirate. It’s rare that I like Spielberg’s work, but I did like this one. Perhaps because it’s based on a Philip K. Dick short story.

[3] In critical situations all three must agree or the system shuts down. I was in line at Disney World’s Space Mountain one time when one of the three systems monitoring the system suffered a glitch and thought one of its sensors reported an error. That was enough to shut the system down. The ride stopped, the work lights came on (those rides look weird and ugly in bright lighting), and workers had to go get all the stranded riders down before the ride could reset and start again.

[4] I’ve posted about color perception before. See: Color My World and Color Redux.

[5] In both cases, the thirds (18-games and 36 stitches) are divisible by three, and so are those thirds (6 and 12 respectively), and so are those thirds! Lotta threes in baseball!

[6] In science fiction, such triplets usually have two items the reader will know but the third one will be made up and science fiction-y. For instance, naming favorite authors an SF character might name: “Mark Twain, Stephen King (both Terrans), and Rass Yugturwar (the Scoracxian).”

[7] Everything we see and touch is made from particles in the first family of matter. The particles in the other two families only exist in very high-energy situations and normally decay to first family particles almost instantly.

[8] This footnote intentionally left blank.

About Wyrd Smythe

The canonical fool on the hill watching the sunset and the rotation of the planet and thinking what he imagines are large thoughts. View all posts by Wyrd Smythe

9 responses to “On the Count of Three

  • SelfAwarePatterns

    In SF&F, trilogies are increasingly passe, with many series going into tetralogies, pentalogies, heptalogies, decalogies, or even longer. Sometimes there are trilogies of trilogies with nine books overall in the series. The Wheel of Time eventually went for 14 books (with the last three being written by another author after the original died). A Song of Ice and Fire (the source for Game of Thrones) is supposed to wrap up at 7, but we’ll see. (It was originally supposed to be a trilogy.)

    I’ve personally sworn off these epic series except when the books are each a discrete story, such as in the Expanse series (now at 5 books with number 6 on its way, along with a TV show adaptation).

    So, is Footnote 8 a test to see if anyone looks at the footnotes? 🙂

    • Wyrd Smythe

      The passing on of trilogies owes a lot, I think, to how SF has become a commodity. It’s sometimes not about telling a story that bursts from the author’s heart but about creating a salable product.

      In other cases it’s fan demand (which translates eventually into the publisher offering “can’t turn down” sums of money — another consequence of the commoditization). You and I were just talking about how Anthony’s Xanth was intended to be a trilogy. There are many other examples, including A.C. Doyle. (Farmer’s Riverworld saga was the canonical example for a long time.)

      I hung with Jordan until somewhere around book #10. I’d been losing interest for a while. I think it started with book #6 where I realized I’d read an entire (damned thick) novel that hadn’t really advanced the plot (or been interesting) must at all. Talk about milking it! I’ve never been moved to go back and try again.

      I’m inclined these days to just wait until a series is complete. Singletons that take place in a common reality is another kettle of space fish. Niven did that a lot; Brin does it now. I do enjoy those.

      In point of fact, I often throw in a not-quite-right fact or oddity to see if anyone says something. Sort of my version of: “[tap] [tap] [tap]… Is this thing on?” As a general rule of thumb, I seem to be talking to a mostly empty room, so it’s nice when someone pays attention! 😀

      • SelfAwarePatterns

        Readers do seem to enjoy series. They sell extremely well. In the indie markets, they are even more prevalent, although I’m not sure how many are continuous stories or just multiple stories with the same settings and characters.

        In one of the writing podcasts I listen to, a writer lamented about readers who wait until a series is done before buying the books, pointing out that if too many readers do it, the series can get cut short. My reaction was that maybe some of those series should be cancelled.

        Myself, I gave up on WoT around book 3 or 4 sometime in the 90s. Like you, with all the bloat, I’ve never been tempted to go back to it.

      • Wyrd Smythe

        “Readers do seem to enjoy series.”

        There’s the sense of familiarity. If you like the characters, you naturally want to see more of them. I was thinking about series last night after seeing your comment. Hammett’s Thin Man, Doyle’s Holmes, there are many others that go way back. Asimov has a YA series, Lucky Starr, that was some of my first SF as a kid.

        TV shows have always tapped into that. Each episode is another chapter in the serial. (Then Roots showed producers people would return time after time for a continuing story, and now much of TV has season-long and even series-long story arcs.)

        It is the goal of many authors to create a character well enough liked to spawn a series. (Sue Grafton must have expected Kinsey Millhone to be successful. The first book was A is for Alibi. She’s up to X now.) Even I had an idea for a character and a series, but could never think of any actual plots that didn’t sound tired and cliche.

        But like any idea, it has both a loving, positive expression and a cynical, negative expression, and I suppose those two reflect two fundamental aspects of making art: Doing it because you’re an artist and you have to create and you have things inside you demanding to be released. Or doing it because it seems like a fun way to make money. Art for love versus art as income (even profit).

        Being who I am (essentially an anti-materialist in this context), I tend to have some disdain for the latter although I do fully recognize the need to make a living. But I just tend to have less regard for those who “want to be writers” than for those who “want to write.” In a (real) artist, the need to create burns bright and unquenchable.

        “In the indie markets, they are even more prevalent,…”

        That doesn’t surprise me. Fan fiction runs rampant. The TOS Star Trek novels had reached over 100 released before I finally managed to stop collecting the damned things. Luckily I never got hooked on the TNG or DS9 or Voyager (no real danger of getting hooked there) ones.

        The love of serials, and all the re-boots and re-makes, impresses upon me how much people like the comfort of a known setting. Hollywood has learned that most movie goers want a pretty good handle on the film before they go, which is why trailers give so much away. It’s what most people want.

        You and I have discussed whether, and if so, how, SF has changed pre- and post-Lucas. I know you feel it hasn’t, whereas I’m quite sure it has. I’ve been doing some basic research trying to put my finger on what I (and many others I’ve read) think has changed.

        I think some of it is purely the result of mainstreaming and the resulting commoditization of SF. Some of it is the high-volume world of today. Everything — including fiction — is mass produced for a very hungry, very large, audience. I would agree Sturgeon’s Law (technically, Sturgeon’s Revelation) holds in any period. There’s always going to be crap. I think I’m focused on the quality and nature of the stuff that isn’t crap.

        There is also the “new ground” aspect. SF is fairly well-explored territory by now, so it’s hard for new fiction to stand out. As I just mentioned, I couldn’t think of a single plot that didn’t seem hackneyed to me. (That could be my limitation as a fiction maker.) And I don’t like people enough to create really interesting character studies. So I’m just not a fiction writer.

        I think my bottom line is that, for whatever reasons, when I compare the best SF Before Lucas (B.L.) to the best SF Anno Stella Bella I think the new stuff doesn’t hold a candle. I do think the biggest reason might well be that the first ones to show up at the party get all the best hors d’oeuvres.

        Maybe someday will do a post on the topic. (If for no other reason than to introduce the terms B.L. and Anno Stella Bella.)

        “…readers who wait until a series is done before buying the books,…”

        That’s a good point. (And I agree that maybe many of them should be cut short.) Perhaps the trick is to write a good stand-alone novel that introduces the characters and see if it flies. Let the public say, “Hey, that was pretty good… got any more?”

        “Myself, I gave up on WoT around book 3 or 4 sometime in the 90s.”

        Heh! Smarter man than me! It took a really long gap between books (perhaps due to the author’s health?) to make me decide it wasn’t worth waiting for more. OTOH, I’ve dodged the George Martin thing completely, and nothing I’ve heard about the series generates any level of interest (not my cuppa).

        (Well, okay, not dodged completely. I did watch the first two seasons on HBO and wasn’t whelmed.)

      • Wyrd Smythe

        Tch. These comments never seem that long when I’m writing them!

      • SelfAwarePatterns

        “but could never think of any actual plots that didn’t sound tired and cliche.”

        From what I’ve read, that’s actually a very common sentiment among writers. All of the plot patterns have existed for thousands of years. The trick is to find new variations. I’m coming to realize that the idea is just the beginning, it’s what you do with the idea that makes the difference. All of which is to say, I wouldn’t give up on trying to develop it (if you have any aspirations in that direction at least).

        And remember, readers actually like familiar plot patterns. I don’t advise it, but Terry Brooks made a ton of money by pretty blatantly copying the plot of the Lord of the Rings; readers knew Sword of Shannara was a blatant ripoff but didn’t care, because they wanted that pattern so badly.

        “Art for love versus art as income (even profit).”

        I think it’s a combination in most artists. People who are in it solely for the money would likely just write romance, since it’s the biggest market segment by far. I think anyone who writes fiction for smaller niches has to, at least to some degree, do it because they enjoy it. (Although in some cases, like Piers Anthony, they may grow tired of their successful franchise.) And so few authors make even a living wage from their writing, that it’s hard to imagine too many of them are just in it for the money. (If they are, they’re in the wrong profession.)

        On Star Wars, I do think it had an effect on the amount of SF we get. (Most of which has always been dreck.) Although it’s probably more accurate to say that it was the beginning of a trending increase in SF&F media that continues today. I was talking with someone yesterday, and we noted that when we were kids (pre-Star Wars), we pretty hungrily watched any sci-fi shows or movies that came out. Now, there’s so much of it that we can (indeed must) pick and choose. My 1976 self would have been astounded.

        On Martin, I actually bailed on ASoIaF after book 3. I felt the third book was bloated. (The TV producers apparently agreed since they cut most of it from the show.) It helped that it was 4-5 years after I finished that book before book 4 came out; the series was completely out of my system by then, at least until the show came out. Now that the show’s caught up with the books, and will likely finish before they do, I’ll likely never return to the books.

      • Wyrd Smythe

        “The trick is to find new variations.”

        Yep. True of all art. And it exists on a spectrum. Some art forms are very restrictive (Haiku, for example), so the variations are necessarily small. Other forms are more free-form (cinema, for example) and more prone to new ground.

        As for me, I really have no aspirations to write SF. I write a blog, and that’s enough. As a writer, I think I’m far more inclined to commentary and analysis than fiction. (The plots would have to be interesting enough to me to write them, and so far nothing has popped. And it’s not like I’m really trying, anyway.)

        “And remember, readers actually like familiar plot patterns.”

        That’s another tension each artist must resolve. To what extent does your audience matter compared to what your heart wants to express. It’s really another form of the tension between expressing your art your way — what I think of as truly being an artist — and creating something someone will buy — what I’d call a craftsman.

        I respect craftsman, but love artists (and am one). One of my favorite workspace signs reads:

        One who works with their hands is a laborer.
        One who works with their mind is a craftsman.
        One who works with their heart is an artist.

        If you are an artist, there is almost always compromise involved. You just have to decide what you can live with. (I think they’re a little crazy, but I have to on some level admire artists who would rather starve or never sell anything than compromise at all. That only ever works if you’re really, really good.)

        “I think anyone who writes fiction for smaller niches has to, at least to some degree, do it because they enjoy it.”

        Sure. And it’s not binary. Both motivations can exist. The question is which is the primary one.

        As for making a living at it, don’t forget all the other professional writing. Ad copy, press releases, kids shows scripts, various corporate departments… all these hire writers. Let alone media, medical, legal, and government organizations of all kinds. And someone’s writing all that trash that shows up in supermarket check out lines.

        But as far as making a living as a novelist? Yeah, good luck with that. It does happen.

        “I was talking with someone yesterday, and we noted that when we were kids (pre-Star Wars), we pretty hungrily watched any sci-fi shows or movies that came out.”

        Yep. Likewise. Star Wars did two things: made SF mainstream (think of the children); and showed the bean counters SF was profitable. That was a game-changer. SF was pretty niche up to that point. It wasn’t vaguely disreputable anymore, but we were definitely still outsiders. SW brought us inside.

        The inevitable result of mainstream popularity and a large population is commoditization, and the inevitable result of that is a certain cheapness in the production process. Once something is a commodity, profit becomes a guiding star, so minimizing expense becomes a key ethic.

        (We’re lucky that the economics of storytelling aren’t the same as those of hardgoods manufacture!)

        Put another way, a lot of SF now is created by people for whom the heart is a smaller fraction of the equation, and that can’t help but have some impact on its quality.

  • wakemenow

    Hmmm. Interesting post, Wyrd. Hadn’t given much thought to how triples are all over the place.

    • Wyrd Smythe

      Thanks! It’s like a lot of things… once you start looking for them… then you’ll find them everywhere!

      Kind of like when you learn a new word and suddenly everyone else is using it a lot.

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