From “One Goat” to “The Number One”
How the birth of math changed everything
Anthropological studies all over the globe have confirmed that in the most primitive cultures, numbers as abstract entities have no meaning at all. In other words, you can talk about one tree, two bananas or three goats, but the words “one,” “two” and “three” are just adjectival modifiers, used in the exact same way we use modifiers like “large” and “round.”
Ask a person in one of these cultures to draw a representation of the concept of “three,” and this person will draw you three trees or three goats: The number exists strictly as at attribute of the thing described. Asking the person to “just draw a three” sounds as nonsensical to them as a request to “just draw a round.” The person can draw a round shape, but has no way to represent the abstract quality of roundness without reference to some object, real or imagined, that is round.
The conceptual leap from “three goats” to “the number three” — or even from “one goat” to “the number one” — may well be the single most significant leap that’s happened so far in the history of human mental evolution. To put this in perspective, the universe had gotten along just fine for billions of years — from quarks and planets and DNA all the way to intelligent brains — without any abstract numbers at all. Some scientists like to say that mathematics is the language of the universe; but until mathematicians came long, the universe’s mathematical laws existed only as properties of physical phenomena.
But then, on some long-forgotten paleolithic morning, one goat-herder turned to another and said something like, “If I have one goat and I get two more, how many goats do I have?”
“Three goats,” the other goat-herder answered.
“And if I have one rope and I get two more,” the first goat-herder said, his face now clouding with a strange concentration, “how many ropes do I have?”
“Three ropes, of course,” the other answered, now barely trying to conceal his boredom.
“You see?” the first herder answered, a triumphant look flashing in his eyes. “No matter if we’re talking about goats, ropes or anything else in the wide world — the numbers one, two and three are always governed by the exact same laws! Maybe the gods are trying to send us some sort of coded message!”
The second goat-herder probably remained unimpressed that morning, but the difference between “one goat” and “the number one” is the difference between goat-herding and rockets to the stars.
