“For the Third Time…”

First there was On the Count of Three, which introduced the fundamental notion of triples. There was actually a prequel of sorts years before — very appropriately a trifecta challenge — about the actual Count of Three and his rabbit fur cloak).

Then came the sequel, Three-peat, which explored the world of triples in more detail. That world spans the gamut from witches to transistors to music theory. (Triples cover a lot of ground!)

Now, at last, the exciting final post of the trilogy! Will the three heroes finally find the three keys, defeat the three dragons, and save the Three Kingdoms?

I have no idea, and you won’t find out here, because this isn’t about that. I just got a little carried away. What this is about is either the third time paying for all or being a charm (hopefully both).

The truth is rather prosaic (no dragons). Ever since the second post, I’ve been noticing and noting triples. The first post scratched the surface. The second one dug a little deeper. The third time pay for all charm is a consolidated list of all the triples from those posts and the notes. Just to have it all in one place.

It’s rather a long list; I’m sure I’m just scratching the surface; no doubt I’ll think of more good ones later.

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The fundamental metaphor of triples extends the binary notion of a Yin-Yang duality to a ternary concept perhaps best thought of as a triangle or tripod. The former are important on many counts — for example, the three corners pick out a unique plane and a unique circle in that plane. (Triangles also ground trigonometry.) Tripods allow a stable platform on uneven or rough ground.

In fact, many true Yin-Yang pairs, in contrast with “cup” Yin-Yang pairs, lead naturally to a triple when there is a middle, both, or neither, option. Then duality naturally segues into trinary.

With cup Yin-Yang pairs, the middle ground is often the canonical glass half full, but it can also be the “just right” of Goldilocks. (A very general triple: Too Little, Just Right, Too Much.)

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Triples also highlight the 2D+ nature of configuration spaces. While duality, with just two sides, can be cast as a tug-of-war, trinary demands a different metaphor.

At the very least, triples generally work best with two orthogonal axes. And as I’ve many times pointed out, even Yin-Yang pairs often benefit from two orthogonal axes (see Window with a Worldview), so it should be no surprise that triples do. As just mentioned, many Yin-Yang pairs naturally segue into triples.

Other triples (for example: Red, Green, Blue; or Vanilla, Chocolate, Strawberry) require three orthogonal axes, because each term is a completely separate thing. (See: 3D Ice Cream)

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According to my notes, the following may be something author Terry Pratchett wrote and may be paraphrased (or even re-phrased) or an approximate quote. I don’t know where it came from. (In my notes it says: “Terry Pratchett??”) Regardless, it’s right on point:

Writers throughout history have relied on a simple belief: everything’s better in threes. Hence “The Rule of Three”. Things are funnier, easier to remember, generally more meaningful, if you combine things in threes.

It is, indeed, an ancient device. In a lot of science fiction, the third item listed will be fictional and futuristic. A story character might mention, for instance, the three greatest presidents of the USA as being: Washington, Lincoln, and Applegate. In comedies, the third item is usually played for laughs.

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I mentioned a list. Here it is:

• One, Two, Three,… (Go!)
• On your mark, Get set,  Go!
• Birth, Life, Death.
• Begin, Middle, End.
• Three Act Story.
• Three Volume Novels (Trilogies).
• Three Blind Mice (see how they run).
• Three Blind Men (and one elephant).
• The Three Little Pigs (straw, wood, brick).
• The Three Little Bears (too much, just right, too little).
• Lions, Tigers, and Bears (oh, my).
• Sun, Earth, Moon (star, planet, moon).
• Mother, Maiden, Crone: A coven of witches.
• A Priest, a Minister, and a Rabbi…
• Yes, Maybe, No.
• Pro, Neutral, Con
• True, Unknown/Undecidable, False.
• High, Middle, Low.
• Left, Center, Right.
• Forward, Stopped, Backward.
• Start, Go, Stop.
• Big, Medium, Small.
• Hard, Medium, Soft.
• Too Hot, Just Right, Too Cold.
• Black, Gray, White.
• Red, Green, Blue (Yellow, Cyan, Magenta).
• Breakfast, Lunch, Dinner.
• Animal, Mineral, Vegetable.
• Vanilla, Chocolate, Strawberry.
• Executive, Legislative, Judicial.
• Rock, Paper, Scissors.
• Fuck, Marry, Kill.
• Good, Bad, Ugly.
• I came, I saw, I conquered (veni vidi vici).
• Stop, Drop, Roll.
• Words, Words, Words.
• Theist, Agnostic, Atheist.
• Father, Son, Holy Ghost. (Brahma, Vishnu, Shiva.)
• Isaac Asimov, Arthur Clarke, Robert Heinlein.
• The Beatles, The Rolling Stones, The Who.
• Spock, Kirk, McCoy.
• CBS, NBC, ABC.
• Lights, Camera, Action!
• The Pledge, The Turn, The Prestige.
• A Triangle — a geometric instance of three.
• Three points define a plane, a circle, and a triangle.
• X, Y & Z: Three dimensions of physical space.
• Three-body Orbitals (two is easy; three is a game-changer).
• A Triumvirate.
• A Trifecta.
• Triple Redundancy — at least two must agree.
• Tripods & Tricycles: stability without unevenness.
• Three-chord songs (using the I, IV, and V-7 chords).
• A Waltz has three beats per measure.
• Neutrons & Protons (all Baryons) are made of three Quarks.
• Three Weak Bosons: W+, W-, Z0.
• Three families of matter.
• Baseball: three strikes; three outs; three bases (plus home).
• Electrical Power Supplies: +V (plus), ground/neutral, -V (minus).
• Transistors: Emitter, Base, Collector. (In FETs: Source, Gate, Drain.)
• Three-phase Electrical Power: 0°, 120°, 240°.
• Telecommunications: Send, Receive, common.
• Files: Open, Read/Write, Close.
• Dynamics: Input, Process, Output (IPO).
• Cis, Bi/Ambi/Non, Gay (plus many other letters).
• A Third Wheel (meaning an unwanted extra).
• Ménage à trois (when a third wheel is wanted).

The list is not anywhere near being exhaustive. The point is that triples are just as fundamental as pairs. Zero, One, Two, and Three, are extremely important constants. when it comes to the structures of reality. (Note they are prime numbers, although the first two are prime by fiat.)

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I noted the threeness of baseball in the first post, but for completeness (and because I just think it’s cool) I’ll note it again here:

• A player gets three strikes during an At Bat.
• A team gets three outs during an inning.
• There are three bases. (1st, 2nd, and 3rd, plus Home)
• A game is nine innings; a team has nine players. (9=3×3)
• A season is 162 games. 162÷3=54÷3=28
• A baseball has 108 stitches. 108÷3=36÷3=12÷3=4

There is a lot of threeness in music and dance, too. “Three-quarter time” and waltzes!

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There’s an old joke that we computer geeks get a real roar from…

There are 10 types of people:

• Those who understand binary…
• And those who don’t.

In the context of the Rule of Three, the joke becomes…

There are 10 types of people:

• Those who understand binary…
• Those who don’t…
• And those who didn’t expect a joke in trinary.

Of course the joke expands recursively…

There are 10 types of people:

• Those who understand trinary…
• Those who understand binary…
• Those who don’t…
• And those who didn’t expect a joke in quaternary.

And so on to quinary and beyond…

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Stay in triplicate, my friends! Go forth and spread beauty, light, and joy.

∇