This essay by my brother-in-law is presented with his permission. John, now retired, was a professional economist and mathematician. He loved to play with numbers and words. The Buffalo Pundit Club was founded in 1892 and John was a frequent contributor.
THE NUMBER THREE
by Dr. John Boot
for the Buffalo, NY Pundit Club, circa 1985
Birds can count to three.
This was determined by removing eggs from the nest while the breeding bird was aforaging. If the number of eggs was reduced from 6 to 5, or from 5 to 4 or from 4 to 3, or in one fell swoop from 6 to 3, the bird, upon return to the nest, happily continued hatching as if nothing were remiss. The bird was happy as a bird.
But heaven forbid if 3 eggs were reduced to 2. The bird now displays great consternation. The bird is all aflutter. The bird misses an egg.
Although ethology, the systematic study of animal behavior, is a twentieth century science, our forefathers long ago not only knew of bird’s counting capacities, they even were able to use this knowledge to advantage.
A 1710 book published by the venerable house of Elsevier advises the following ruse when going duck hunting. Four hunters should enter a blind; shortly after, three should leave. “The ducks will now think the coast is clear,” the book advises. It may be their last thought, as the hunter who stayed behind transforms them to duck paté.
People do better than birds. We can see the number 6 the way a bird can see the number 3.
If there were only 5 players on one side of a volleyball net, we’d immediately spot that a player was missing. Yet, don’t try this with numbers much larger. We never “see” it when there are twelve men on the field in football.
And bridgeplayers, when given a hand with 12 or 14 cards routinely spot the discrepancy from 13 only at the very end of the hand.
So while we do better than birds, we don’t do a whole lot better. It is, in fact, the thesis of this paper that 3 is, even for us, the largest number we are truly comfortable with. It may be a link in the chain of evidence suggesting that birds were one of our evolutionary stepping stones.
Our primary awareness of the number three is anchored to the three dimensions of space – length, width, and height. It is a constant reminder of the number three. Thinking vertically, we have the sky above, land afoot, and water below. Thinking horizontally, we have a neighbor to the left, ourselves in the middle, and a neighbor to the right.
Three is a number with a beginning, a middle, and an end. We have a lower class, a middle class, and an upper class. We have a first name, middle initial, last name. We are young, middle age, and old.
Along the time axis, the number three is equally pervasive. The past, the present, the future. Yesterday, today, tomorrow. Before, now, later. Past tense, present tense, and future tense — was, is, will be.
Languages not only have three tenses, they also have three modes, the positive, the comparative, and the superlative, as in good, better, best. There is no compelling reason why one could not have good, better, best, bestest, or perhaps black, blacker, blackest, blackiest. But we don’t have four steps, just three. And “we” is not only the English speaking, but any and all speech known to mankind.
Nature is also partial to the number 3. All physical phenomena, gravity, energy, electricity, whatever, have a dimensionality premised only on length, mass, and time, usually measured in centimeters, grams, and seconds. The basic building block of matter, the atom, has neutrons, protons, and electrons. The neutrons and protons, in turn, are built from three quarks each. There are just three primary colors, red, blue, and yellow.
In chemistry, one has acids, bases, and salts. Chemical elements can manifest themselves in three ways: as a solid, as a fluid, and as a gas, as in ice, water, and vapor. In life sciences, we divide the biota in animal, vegetable, or mineral. A plant has a root, a shaft, and a flower. A fruit has a husk, the flesh, and a kernel. Nature likes the number three.
Shortly after birth, we become aware of a papa, a mama, and ourself. All through life, we are aware of three generations, grandparents, parents, and children. Great grandparents, if extant, are plausibly out of sight, and in any event beyond comprehension: both ways. We grow from child to parent to grandparent in three generations, but four is just one too many.
Early on we realize that there is a morning, an afternoon, and an evening, with breakfast, lunch, and dinner, consumed with knife, fork, and spoon. Dinner may well consist of soup, entree, and dessert, which dessert may be cake, fruit, or ice cream, which ice cream will be vanilla, chocolate, or strawberry: for despite rumors that there are 28, real ice cream comes in but three flavors, the three flavors of Neapolitan.
Early on we hear about three blind mice, three little pigs, and three little kittens who lost their mittens. We are told about goldilocks and the three bears, whose porridge was too hot, too cold, or just right, whose bed was too hard, too soft, or just right, and whose chair was too high, too low, or just right. And then we are lulled to sleep with Winken, Blinken, and Nod.
Early on we play games like tic-tac-toe, with three squares to a vertical, horizontal, or diagonal line. We play paper-stone-and-scissors, with paper wrapping the stone, stone crushing the scissors, and scissors cutting the paper. We try to get the fox, the goat, and the lettuce head to the other side of the river.
All along, we notice that there are three traffic lights; that there are three phalanges to a finger; three months to a season; three bands in a typical flag; three feet to a yard; and three movements to a concert.
In every language the number three resonates. A Greek dogma admonishes to keep one’s tongue, one’s stomach, and one’s genitals in check. Caesar boasted veni-vidi-vici. The French rallied around liberté, egalité, fraternité. The Germans are fond of Wein, Weib, and Gesang; while these Weib ought to occupy themselves with Kinder, Küche, and Kirche: children, kitchen, and church.
Churchill, meanwhile, had nothing to offer but blood, sweat, and tears; and applauded so few who did so much for so many. And the Americans have a government of the people, by the people, for the people, with the executive, legislative, and judicial branches providing for life, liberty, and the pursuit of happiness. Meanwhile, monkeys see no evil, hear no evil, and speak no evil.
Any number of expressions have three words. We have feast or famine, now or never, sink or swim; stop the nonsense, perish the thought, pass the buck; heaven and earth, short and sweet, down and dirty; tit for tat, all for naught, up for grabs; sad but true, naughty but nice, slow but sure. We have time is money, time will tell, and just in time. We have praise the Lord, peace on earth, and rest in peace. We have easy does it, haste makes waste, and never say never. We have I love you, head over heels, and love conquers all. Such pithy three-worders are a dime a dozen.
In auctions, it all ends with going, going, gone. In races it all begins with on your mark, get set, go. Religions admonish to do justice, love mercy, and walk humbly. In logic one has the thesis, the antithesis, and the synthesis. Literature revolves around the three primary emotions love, hate, and jealousy, — amor, odium, invidia,
In church one concludes with amen, amen, amen. In real estate all that counts is location, location, location. And a rose is a rose is a rose.
In song London bridge is falling down, falling down, falling down. And one could have danced, danced, danced all night. And just one kiss would not do: kiss me once, and kiss me twice, and kiss me once again.
Why cannot anyone just be calm and cool? Why are all those who are cool and calm also collected? Why cannot we share a confidence just between you and me? Where is that lamppost coming from? We all have some notion as to who the father might well be, and the son, but what woodwork is the holy ghost coming out of?
In the same vein, it is not enough to have just heaven and hell: rather, heaven, hell, and purgatory. It is not enough to have a body and a soul: we have a body, a soul, and a spirit. It does not quite do to have an id and an ego without super ego. Only when we add the third component does the sentence seem whole.
In the Olympics we have a gold, a silver, and a bronze metal. In all other arenas of human endeavor we similarly focus on the number three: we ask for the three best. The three best authors are Homer, Dante, Shakespeare. The three best composers are Bach, Brahms, and Mozart, although many would rank Beethoven above Brahms, and some go with the three B’s.
But the point is not whether we agree with the ranking, but whether we agree that such questions are phrased in terms of three. In recruiting, we are asked to rank the top 3 candidates.
The three most compelling fairy tale figures are Little Red Riding Hood, Cinderella, and Snowwhite. Don’t even think about Goldilocks. The three winning literary creations are Sherlock Holmes, Don Quixote, and Robinson Crusoe. Odysseus, anyone?
There is a similar emphasis on the number three in jokes, involving perhaps the antics of a Brit, a Frenchman, and an Italian; or a parachute jump by a Priest, a Rabbi, and a Reverend; or a General, a Colonel, and a Captain debating the effort involved in sex; or again the graduate in economics, who wonders what should be done, in engineering who wonders how it should be done, and in liberal arts, who wonders whether you would like fries with your order.
The globe itself is rife with threes. For one, there are the three prominent globes themselves, the sun, the moon, and the earth. Then there are the three circles around the globe, the equator and the two tropics. There are the three oceans, Atlantic, Indian, and Pacific. There are the three major political powers: USA, Russia, and China; and the three primary economic powers: Europe, North American, and the Pacific Rim. We have an old world, a new world, and a third world.
The three cities of the USA are New York, Los Angeles, and Chicago. The three cities of Europe are London, Paris, and Rome. The three cities of Holland are. Amsterdam, Rotterdam, and the Hague. There is no earthly reason why three should not be two or four cities, but there it is.
In history, we have the Old Ages, the Middle Ages, and the Modem Age. In the Old Age the world was governed by three Gods. Jupiter, with three forked lightning, ruled in the heavens. Neptune, with his trident, ruled the sea. And Pluto, with his three-headed dog, was master of the Sea underworld, Hades.
We have the three sons of Charlemagne, who divided Europe in three parts, still recognizable today as France, Germany, and a buffer zone of puny countries like Holland, Belgium, and Switzerland. Just like Gaul in Caesar’s day, Europe is still divided in partes tres.
And we have the three famous women leaders, whose fame extended to the boudoir: Empress Theodora, who knew not a particle of modesty; Queen Christina, who resigned the throne in Stockholm to cavort with cardinals in Rome; and Catherine the Great, the Russian empress of German blood and French culture, who never denied herself the needs of her passionate nature.
We have royalty, presidents, and popes. If their lives are truncated, royalty is beheaded, presidents are shot, and popes are poisoned.
Three is also the sexual number. The fundamental reason is premised on a brute count: a man has one prick and two balls, a woman has one twat and two tits. It may be coincidence, and it is not true in all languages, but sex has three letters. And men are divided in leg men, ass men, and tit men — whichever way the spirit moves, it moves to another three letter word, leg, ass, tit. 1 will not, however, belabor this aspect, for fear of scarring sensitive souls. Rest assured there is more to it than here reviewed.
In mathematics, there are the three problems of antiquity, that of trisecting an angle, squaring a circle, and doubling a cube. The modern day problem which stymies mathematicians is the three body problem, which asks how three bodies move when subjected only to each other’s gravity. We also have the three elementary geometric figures, the square, the circle, and the triangle
Speaking about triangles, in each triangle one can draw three bisectors; three perpendiculars; and three median lines. In each case these three lines go through one point, for every triangle. These three points will always lie on a straight line.
Still mathematically speaking, the three mathematical formulas a2 + b2 = c? (stating that in a right triangle the sum of the squares of the sides equals the square of the hypothenuse), A = 11, (giving the area of a circle as a function of its radius), and V-E + F= 2, (stating that for any polyhedron the number of its Vertices or comers minus the number of its Edges plus the number of its Faces or sides equals 2) all involve precisely 3 symbols, as does the most famous formula of all, E = mc.
Also, numbers are either negative, or zero, or positive. And the two most famous transcendental numbers, roughly speaking numbers with an infinite number of unpredictable decimal points, the numbers i = 3,14159… and e = 2.71828… are both, when rounded to the nearest integer, equal to 3.
In baseball, we have three strikes and you are out, and three base hits, and triple plays.
We play a best of three in tennis, and we play tennis with three balls: two is too few, four is too many. We have the triple crown in horse racing, and the trifecta bet in horse betting. In athletics, we have the triple jump, also known as hop-step-jump, and the triathlon, with swimming, bicycling, and running. In poker we have three of a kind. And overriding all this, matches or games tend to end in a win, a loss, or a draw.
Other threes, or threesomes, in a more or less random grab bag include the three R’s of elementary education, reading, ‘riting, and ‘rithmetic; the three areas of higher education, humanities, social sciences, hard sciences; the three precious metals, gold, silver, and platinum. There are three witches and three stooges and three French hen. There are three magi, three musketeers, and three McMurray’s sons. There are three fates, three furies, and three graces.
There is a three-way bulb, a three-piece suit, and a three-minute egg.
There are three cigarettes to a match, three slices to a club sandwich, and three moves are as bad as one fire. A house guest and a fish stay fresh for three days, when two dogs fight for a bone the third dog runs away with it, and to give one three times three is to give a standing, rousing, tumultuous ovation of cheer after cheer after cheer.
A date gives month, day, and year. An address gives street, city, state. A phone number is given as a 3-digit area code, a 3-digit exchange, and a 4-digit number. A social security number is given in 3 sets of 3, 2, and 4 digits. And on letterhead one has a name, an address, and a phone number.
And yet, I hear you think, these are selective matters. Surely you can select a three leaf clover, a three toed sloth, or a three ring circus, but equally surely you can take one for the road, and you can go to a one-horse town with a one-track mind for a one-night stand. We have two parents, there are two poles, we can add two and two together, or have two strings to our bow, and two can keep counsel, provided one of them is dead. Then again, two heads are better than one.
There are four wind directions and four corners of the world, there are four horsemen of apocalypse, there is a four minute mile, there is a four-letter word, and there is the fourth of July.
There are five fingers to a hand, there are five senses: hearing, sight, smell, taste, and touch; there are five wits: common sense, imagination, fantasy, estimation, and memory; there are five boroughs in New York, and five-year plans in Russia, and five nations in the old British Empire, Canada, Australia, South Africa, and India being the other four.
We have six of one or half a dozen of the other, six sides to a die, six runs for the batsman in cricket who hits the equivalent of a home run in baseball; we have six-packs, and we have six inches.
The number 7 is second only to the number three in prevalence. There are seven days in the week, seven virtues: faith, hope, charity, justice, fortitude, prudence, and temperance; and seven deadly sins: pride, wrath, envy, lust, gluttony, avarice, and sloth. There are seven hills of Rome, seven seas, seven heavens, and seven wonders of the world.
The number 8, sandwiched between the very popular numbers 7 and 9, plays hardly any role at all.
Nine is three times three, and one of the three mystical numbers, 3, 5, and 9. It is a trinity of trinities. There are nine muses, the hydra is a nine-headed monster, there are nine rivers in hell; a cat has nine lives, possession is nine points of the law, and nine men’s morris is a sophisticated version of tic-tac-toe.
None of that is denied. There are numbers other than three. They have their uses. And yet, numbers larger than three are quite matter-of-factly brought down to size. The six sides of a room are referred to as the floor, the ceiling, and the walls. The seven days of the week are Saturday, Sunday, and weekdays. The seven virtues are truncated to the three Christian graces of faith, hope, and charity. Humans have a body, a head, and extremities. The sky’s myriad points of light are sublimated in a sun, a moon, and the stars. There may well be four wind directions, but the United States has just an East, a West, and a South: the North is called Canada. And as for the four corners of the world, Shakespeare speaks of the three comers of the world — although Dryden speaks of the four corners of the sky. Confusion in all corners.
And though the cock crowed but once, as in “You will deny me thrice before the cock crows once,” virtually everybody thinks the cock crowed three times. More confusion.
When Gertrude Stein said Rose is a rose is a rose is a rose, it was just one rose too many, and it is quoted as a rose is a rose is a rose. Compare the awkward UNLV with the smooth MIT or USC. Four is just too much. When BOAC changed its name from British Overseas Airline Corporation to BA, British Airways, they went from too many to too few: KLM, TWA, and SAS do it better. Three is where it is at. Some think there are four basic food groups, dairies, veggies, meats, and grains. But in truth there are but three, chocolates, fats, and salts.
There are trilogies galore, but no bilogies or tetralogies. One can practice triage, but not biage.
There is many a triptych, but no tetratych.
There are, you guessed it, three morals to this story.
The first is that more-than-three is too many. David Letterman made a real blunder when he went for ten of this or that. What on earth possessed him. Nobody can keep the interest up for ten points. Even seven is way too much. Who knows the names of the seven dwarfs? Who cares about justice, fortitude, prudence, and temperance, after faith, hope, and charity have said it all? The three deadly sins of pride, wrath, and envy would do much better by themselves than when watered down with gluttony and sloth: gimme a break. No flag has four horizontal bands.
The second moral is that one or two is not enough to give a sense of wholeness, stability, and comfort. A concert with two movements would not a concert be; a dinner with two courses is too sparse; a family without three generations feels empty; a child with just one parent feels deprived; a tripod missing a leg would keel over.
The third moral is that three is just right. Don’t tick off six points to your boss explaining why you need a raise; three will be more persuasive. To prove guilt, show motive, opportunity, and wherewithal, don’t fuss around with gloves. To tell your son to shape up tell him not to leave his clothes on the floor, wash his hands before meals, and write thank you notes to aunts.
Anything beyond that will go in one ear and out the other. More to the point, even these three admonishments will be lost when you tack on other complaints. It is not only useless overkill, it is killing overkill. The human mind can grasp three with ease and elegance. Three as in quack quack-quack. What is good enough for the birds, is good enough for us. And that is not for the birds.
Disclaimer and acknowledgment: This paper has not reviewed the prominent role of the number three in other than western cultures and religions, for I wanted it to relate to your own experiences and knowledge. Nonetheless, other civilizations show much the same partiality to the number three.
Also, and separately, a goodly number of earlier versions have been around, and input from many sides is gratefully acknowledged. By name I want to single out Valerie Limpert, who provided many telling examples as she got bitten by the “three-bug.”