Abstraction Layers: In Arithmetic & Elsewhere
Counting to 84 by offshoring much of the real work to your information-technology ASI arabic-numeral symbolic copilot, and other topics about variation in proper education for the kind of numeroliteracy worthwhile to help you function in society over the past 5000 years…
Let us try to think, once again, about: the real ASI, we East African Plains Apes of (relatively) little brain, and our ability by drawing on the real ASI to apply the massive mental force multipliers that we call abstraction layers.
Cast your mind back five thousand years to the days of Gilgamesh, 2/3 god and 1/3 man, King of Uruk-the-Sheepfold. Climb the walls of Uruk, walk their length, survey their foundations, and study the brickwork. Is it not all made of solidly-crafted oven-baked bricks? Did not the Seven Sages lay the cornerstone? Two thousand acres for the city! Two thousand acres for the orchards! Two thousand acres for the pits of brick-clay! And one-thousand acres for the Temple of Ishtar! At peace is the city of Uruk protected by its wall. Prosperous are its people, well-provided with tools of bronze made of tin from Afghanistan and copper from Jordan well-mixed, well-fed on grain and mutton, well-clothed in wool and linen, well-housed by skilled builders.
Imagine that you are one of the understewards of King Gilgamesh, in charge of informing the cooks who are to prepare the feast for the climax of the Great Festival of Ishtar—the one in which Ishtar demonstrates that Gilgamesh is still he upon whom her favor rests. You need to tell the cooks about the sheep that they are going to roast. Fifteen sheep have arrived from the north, forty-three from the west, twenty-six from the south, and there is report that the barbarian of Elam have stolen those that were supposed to come from the east.
How do you figure out what to tell the cooks? You need to count the sheep.
The most straightforward way would be to send a shepherd, a numerate intern, plus a couple of laborers with mobile fence-sections and a gate out to the sheepfold where the sheep are. Have the shepherd drive the sheep into one corner of the sheepfold, have the laborers set up the mobile fence and the gate across the corral, let the shepherd drive the sheep one-by-one through the gate into the other half of the corral, and have the intern count them as they pass, and then report the total number as eighty-four, plus include in his report notations on the individual characteristics of the sheep, where those are thought to be at all likely to be relevant to the jobs of the cooks.
Or—provided you trust the reports of the sheep-drivers, you could use what we call arabic numerals cognitive addition technology, thus:
15 + 43 + 26
= (10 + 5) + (40 + 3) + (20 + 6)
= (10 +40 +20) + (5 + 3 + 6)
= (1 x 10 + 4 x 10 + 2 x 10) + 14
= (1 + 4 + 2) x 10 + (1 x 10) + 4
= (1 + 4 + 2 + 1) x 10 + 4
= 8 x 10 + 4
= 84
The same eighty-four.
No need for shepherd, numerate intern, laborers, mobile fence-sections, gate, and—upstream in the production process—woodcutters and carpenters. Just you at your table with your clay tablet and your stylus. With your stylus and your ability to draw on and utilize the arabic numerals cognitive addition technology that is in the possession of the ASI, the Anthology Super-Intelligence which actually exists and which gives you your meal-ticket by virtue of your ability to interface with it. (Never you mind that we are 4300 years anachronistic here.) OH NOES!!!! JOB DESTRUCTION! (Or, maybe, the woodcutters and carpenters could make other also useful things, the shepherd could perform an extra health check on the flock, the laborers could be put to work storing beer, and the intern could goof off.)