The 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.
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!
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!
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.
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.
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).
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.)
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.
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.
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).
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).
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.
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.
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.
 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!
 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.
 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!
 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).”
 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.
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