This is Brad DeLong's Grasping Reality—my attempt to make myself, and all of you out there in SubStackLand, smarter by writing where I have Value Above Replacement and shutting up where I do not… Abstraction Layers: In Arithmetic & ElsewhereCounting 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...
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:
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.) Maybe you are saying “WTF?!?!?!” and are thoroughly confused. Maybe when you are asked to calculate 15 + 43 + 26 you just say “eighty-four”, nd do not think about why. Odds are—unless you are Johnny von Neumann—you don’t go through all the steps in the indented math above. (In my mind’s eye, when I do the problem I see: 5… 8… 14… push to stack… 1… 5… 7… pull from stack… 8… 4… eighty-four.) But all the steps, and shortcuts through them—the one-digit addition table, “carrying the one”, place-value for multiplying by ten, the commutative and associative properties of addition, and the distribution of multiplication over addition—are needed. All of them are needed to shift from away from having to count all the sheep one-by-one. All of them are needed to shift to manipulating the symbols. All of them are needed to shift to be able to do it much faster, and without intern, shepherd, laborers, woodcutters, and carpenters. This is an abstraction layer. Arabic-numeral math is an abstraction layer. The lower-level reality is a lot of large, smelly, furry herd mammals. But we hide the complexity and the individuality of the animals and consider them just as standard sheep. And then you further hide complexity so that you are no longer, when you turn to your clay tablet and your stylus, dealing with sheep but merely with numbers. The work-organization and laborer-bossing skills that were needed to actually get the sheep counted back in -3000 are no longer needed once you have moved up an abstraction layer. There are losses here in dealing with things this way: the cooks will not know that sheep #5 is a “year-old male, without blemish”, for example, while the intern might well have included that in his report. But if the cooks really do need more information than “eighty-four!”, they will tell you so. Good practice in being an effective and productive front-end in the real Anthology Super-Intelligence of the collective human mind—excuse me, good practice in white-collar work—involves building, utilizing, and working at as high an abstraction layer as possible in order to economize on cognitive effort. Transform problems up the chain layer by layer until the layer almost breaks, in the sense that trying to build and go up another layer will no longer produce answers your clients will find satisfactory to the questions that they will ask. Moreover, you need to not just know how to do your share of the workload as a node in the ASI at the particular abstraction layer you have chosen to work at, you also need to know a lot about how to go about things at the next-lower abstraction layer, or two. Why? Because sometimes the problem you are considering will hit a bug in your abstraction layer, and it will break, and you will still have to do your job. And most of the time all abstraction layers leak meaning and accuracy and effectiveness, and you need to be able to judge whether those leaks are a problem for you and your clients—and to fix them if they are. Now let me shift gears. I was sitting across the dinner table from one of the barons of Silicon Valley. He has been asking recent college graduates he has been running across—well-prepared and talented young people newly employed at Apple, Anthropic, and various other Behemoths and Leviathans of tech—what pieces of their recent undergraduate computer‑science education are now proving useful for them in their jobs. Their answer: none. He says they say: The undergraduate computer science curriculum has not kept up. The dominant vibe was that the right strategy was to get an internship and/or a part-time job starting as a freshman, to treat your CS courses as your side-hustle, and maybe, maybe, to spend your class time taking philosophy, art, and other things you are curious about and that you think would enrich your life. The conversation then headed off into poetry appreciation. There was a brief side-conversation among some of us elders about how we had never used any of our semiconductor physics knowledge, and did anyone remember whether you needed 10^(-6) or 10^(-4) phosphorous atoms per silicon atom for a MOSFET gate? (It is actually something like 1.5 x 10^(-3).) But the report that the usefulness of the CS courses was zero—that was something I thought about on the way home. Overstated, as young people do, certainly. But pointing at something: at a mismatch between the abstraction layer the Behemoth and Leviathans wish for their new young hires to work at, and the abstraction layers we are teaching them here at Berkeley. And now I come to the third part of today’s lesson: my colleague Lakhya Jain, who rants about the students in recent instantiations of his course CS 186: Database Systems:
But when you look at the syllabus for CS 186, my reaction is that it is not so much ChatBots that are to blame. Lakshya Jain appears to be getting caught in several sets of gears:
Back in the day it was difficult to get the credential without actually getting an education, as doing (some of) the work was not something you could largely avoid.kdl;aelkeeIf I were in charge of UC Berkeley right now, I would suggest the faculty spend this year having a roiling conversation about:
If reading this gets you Value Above Replacement, then become a free subscriber to this newsletter. And forward it! And if your VAR from this newsletter is in the three digits or more each year, please become a paid subscriber! I am trying to make you readers—and myself—smarter. Please tell me if I succeed, or how I fail…#abstraction-layers-in-arithmetic-elsewherePlease forward the email & otherwise share it to everyone you think would appreciate it…
|
Abstraction Layers: In Arithmetic & Elsewhere
Friday, 3 October 2025
Subscribe to:
Post Comments (Atom)
No comments:
Post a Comment