(Roughly) Daily

“Many of the things you can count, don’t count. Many of the things you can’t count, really count”*…

Still, we count… and have, as Keith Houston explains, for much, if not most of human history…

Figuring out when humans began to count systematically, with purpose, is not easy. Our first real clues are a handful of curious, carved bones dating from the final few millennia of the three-​million-​year expanse of the Old Stone Age, or Paleolithic era. Those bones are humanity’s first pocket calculators: For the prehistoric humans who carved them, they were mathematical notebooks and counting aids rolled into one. For the anthropologists who unearthed them thousands of years later, they were proof that our ability to count had manifested itself no later than 40,000 years ago.

Counting, fundamentally, is the act of assigning distinct labels to each member of a group of similar things to convey either the size of that group or the position of individual items within it. The first type of counting yields cardinal numbers such as “one,” “two,” and “three”; the second gives ordinals such as “first,” “second,” and “third.”

At first, our hominid ancestors probably did not count very high. Many body parts present themselves in pairs—​arms, hands, eyes, ears, and so on—​thereby leading to an innate familiarity with the concept of a pair and, by extension, the numbers 1 and 2. But when those hominids regarded the wider world, they did not yet find a need to count much higher. One wolf is manageable; two wolves are a challenge; any more than that and time spent counting wolves is better spent making oneself scarce. The result is that the very smallest whole numbers have a special place in human culture, and especially in language. English, for instance, has a host of specialized terms centered around twoness: a brace of pheasants; a team of horses; a yoke of oxen; a pair of, well, anything. An ancient Greek could employ specific plurals to distinguish between groups of one, two, and many friends (ho philosto philo, and hoi philoi). In Latin, the numbers 1 to 4 get special treatment, much as “one” and “two” correspond to “first” and “second,” while “three” and “four” correspond directly with “third” and “fourth.” The Romans extended that special treatment into their day-​to-​day lives: after their first four sons, a Roman family would typically name the rest by number (Quintus, Sextus, Septimus, and so forth), and only the first four months of the early Roman calendar had proper names. Even tally marks, the age-​old “five-​barred gate” used to score card games or track rounds of drinks, speaks of a deep-​seated need to keep things simple.

Counting in the prehistoric world would have been intimately bound to the actual, not the abstract. Some languages still bear traces of this: a speaker of Fijian may say doko to mean “one hundred mulberry bushes,” but also koro to mean “one hundred coconuts.” Germans will talk about a Faden, meaning a length of thread about the same width as an adult’s outstretched arms. The Japanese count different kinds of things in different ways: there are separate sequences of cardinal numbers for books; for other bundles of paper such as magazines and newspapers; for cars, appliances, bicycles, and similar machines; for animals and demons; for long, thin objects such as pencils or rivers; for small, round objects; for people; and more.

Gradually, as our day-​to-​day lives took on more structure and sophistication, so, too, did our ability to count. When farming a herd of livestock, for example, keeping track of the number of one’s sheep or goats was of paramount importance, and as humans divided themselves more rigidly into groups of friends and foes, those who could count allies and enemies had an advantage over those who could not. Number words graduated from being labels for physical objects into abstract concepts that floated around in the mental ether until they were assigned to actual things.

Even so, we still have no real idea how early humans started to count in the first place. Did they gesture? Speak? Gather pebbles in the correct amount? To form an educated guess, anthropologists have turned to those tribes and peoples isolated from the greater body of humanity, whether by accident of geography or deliberate seclusion. The conclusion they reached is simple. We learned to count with our fingers…

From an excerpt from Houston’s new book, Empire of the Sum: The Rise and Reign of the Pocket Calculator: “The Early History of Counting,” @OrkneyDullard in @laphamsquart.

* Albert Einstein


As we tally, we might send carefully calculated birthday greetings to Stephen Wolfram; he was born on this date in 1959. A computer scientist, mathematician, physicist, and businessman, he has made contributions to all of these fields. But he is probably best known for his creation of the software system Mathematica (a kind of “idea processor” that allows scientists and technologists to work fluidly in equations, code, and text), which is linked to WolframAlpha (an online answer engine that provides additional data, some of which is kept updated in real time).


Written by (Roughly) Daily

August 29, 2023 at 1:00 am

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