Excellent Men

"It is unworthy of excellent men to lose hours like slaves in the labors of calculations" - Leibniz, on the machine he invented to calculate trigonometric and astronomical tables. So leads an article from 1975 about the debate over introducing calculators into the classroom.

Pro argued the case that calculators would create room to explore more complexities, con that rudimentary skills of basic arithmetic would be eroded as kids perform them less often. Furthermore, the NYT worried that children seemed to be having fun with their silicon, writing 07734 for HELLO, just wait until they discover 80085.

"Kids like hamburgers not only because they taste good but because they're something they can hold and control, they are a master of eating a hamburger. They can do it with nobody else around. It's the same with pocket calculators. They are like electronic hamburgers," said definitely not robot, Henry Mullish of NYU. Meanwhile James McKinney, professor of mathematics, Cal Poly lamented, "I have yet to be convinced that handing them a machine and teaching them how to push the button is the right approach... I see a lot of low-level math among college students who still don't understand multiplication and division. You take away their calculators and give them an exam in which they have to add 20 & 50, and they get it wrong. And I'm talking about business majors, the people who will soon be running my world."

Plus ça change...

Fifty years later these prognostications turned out basically correct. (Except for Mullish's observations about hamburger eating. Those will never be right.) In my decade of teaching math, I have witnessed the hopes and concerns of yesteryear. I have seen the compounding interest of early failures. The students who struggle with algebra struggled with division, and prior they struggled with multiplication and additionally with addition. The weakest students, often introduced earliest to the calculator, are the most slavish to it.

It is also true that we can do all sorts of cool things like finding more digits of pi than anyone will ever care for, calculating greater numbers far quicker than any man of moderate intellect can in his head, finding exact answers to trigonometric and exponential functions that I would have given up on due to sheer tedium (what was once the labor of grad students & professional calculators and filled the pages of ancient tomes, is now accessible at the push of a button) and perhaps most importantly the modern ones can draw very pretty graphs, certainly much prettier than whatever Frankenstein or Picasso I slap on the board. (Preferably a chalkboard, with the good chalk that melts onto the board like butter, a whiteboard is fine but the problem is the markers. They are fine right up until they're not when they spit and sputter like an untuned carburetor. I abhor PPT and look down upon all you that teach from them, shame and a pox upon thine house)

All that said, I hate them. I use them all the time. And I hate them. I'm surprised I hate them. At least younger me is surprised I hate them because he was always going to be cool, he would never worry about silly things like the process. We both agree old people bitch about things just because they are different, him from speculation me from experience. It's terra cognita. The luddites, the internet's latest rehashed insult/badge-of-honor depending upon where one sits. (I disagree, proper luddites would burn down the data centers rather than gripe about them at their local planning commission.) Going further back Socrates lamented the advent of writing "For this invention will produce forgetfulness in the minds of those who learn to use it, because they will not practice their memory. Their trust in writing, produced by external characters which are no part of themselves, will discourage the use of their own memory within them. You have invented an elixir not of memory, but of reminding; and you offer your pupils the appearance of wisdom, not true wisdom, for they will read many things without instruction and will therefore seem to know many things, when they are for the most part ignorant and hard to get along with, since they are not wise, but only appear wise." (No notes.)

I hate them because when the calculator goes on the brain goes off. Without fail, there's always that kid (you know which one. If you don't, I've got some news.) with the confidence of youth, who will call out or if they're polite raise their hand to tell me I'm wrong. Fair enough, I've been wrong many times, at least five times today, just ask my wife. Pray tell, good sir, (it's always a boy, if it's a girl I actually fucked up) why am I wrong? I'm wrong because thou hast punched in the numbers and thy calculator divined from heaven THE ANSWER. And lo' it was said unto thee that THE ANSWER must be correct and the fuckwit at the board (me, registered fuckwit class of '09) has nary a clue what he's talking about because THE ANSWER has been delivered on high from thy righteous calculator. And that thou must halt for what has been written is false, it is a heresy, it is not...THE ANSWER. So I ask them, does it make sense that a car traveling from Cleveland to Austin is traveling at 46,578 mph? And the answer is indubitably: well no... but my calculator said... and I, as a good teacher with care and understanding and patience, suggest that they encourage the neurons in their brain to try introducing themselves to each other some time, just as my teachers did to me when I was that kid. Teaching is punishment for the sins of youth.

I loathe them because, excepting those children of preternatural talents or preparedness, McKinney, and Socrates a millennia prior, were absolutely correct. We trade off one skill for another. Few among us, certainly not I, anymore memorize a few stanzas of poetry let alone chapter and verse of full books, perhaps excepting the bible or other religious texts wherein recitation is rewarded with good marks and the promise of everlasting bliss because well I can just google it. The calculator has deleterious effects on the ability of students to calculate, to manipulate numbers and information in one's head because the process has been offloaded to a machine. I've seen it in the students when you ask what's 8+5 and they respond with blank stares, followed by panic, and the subsequent desperate rummaging of backpacks. They were robbed of their confidence before they had the chance to earn it.

It's a classic extrapolation error. We extend Leibniz to children and teens who have yet to become excellent men. The calculator is a boon for someone who knows the ins and outs. The repeated process, once difficult, has become tedious. For a novice, difficulty is mistaken for tedium.

(enter AI stage left) All the same arguments are being had again. The boosters are right, just as they were with calculators and writing. Undoubtedly AI will expand the surface area of capability to the previously incapable. Exhibit A. This website. It's all AI-generated. I can't code. I'm an idiot. I run it on an iPad. So I had to set up a shell and a droplet and a bunch of other annoying workarounds because as I've found out iPads are not computers. But I did all that because the machine held my little meat-sack hand and walked me through step-by-aggravating-step and I followed along nodding, whatever you say George, and I talked to the magic box and it went off cajoled and rigamaroled and figitated and voila the site was built. (This belies the reality of hundreds of iterations to get to something that I'd say is good enough. Maybe it's just a skill issue at least that's what the internet seems to claim, that if I just had been more organized, more precise in my prompting, had written more explicit .md files the machine would one-shot it no problem. So maybe I'm a bit picky, but I expect my AGI, or almost AGI, or one maybe two steps removed from AGI to be a little more, I dunno, generally intelligent. I mean it can solve Millennium problems! Which, of course, is incredibly impressive but at the same time when I work with the machine and ask it to create a bunch of problems that cover an AP exam - also math last I checked - the clanker responds by getting maybe 50% of the way there. It skipped multiple sections, only created single step problems, without any graphs or tables or problems that really involved interpreting anything, and it used the same four functions twenty times. So while it's awesome it can solve some hard math problems it's also the worst kind of employee that absolutely needs to be micromanaged and followed up on Every. Single. Thing. It. Has. Done. It. Is. Exhausting. It's like building a website by herding cats. But I digress) The reality is it is much faster and cheaper to build things today than it was yesterday. The barrier to entry to get an idea into working production is approaching zero. It's cool and it's fascinating, and as a hobbyist and weekend warrior I'm all about it.

On the other hand Socrates and McKinney, the modern luddites and all your Nancys' negative, are also right. I built the website. I've "done" it. But ask me to do it again. I can't. I can't reproduce any of it. Not without the crutch. I did something. I learned nothing.

I've tried using it to do research and I've found that a fool's errand. It's not that it can't do it, it can, sometimes even decently but it's a pointless exercise. I'm treating myself like some politician who wants a couple talking points for my cable news hit and then I can go back to not knowing and not caring. I'm doing the thing but not holding onto anything. In hindsight this should be obvious because the hippocampus has to get stretched and poked and prodded in order to absorb new information and retain it. When we offload that entire regimen to AI it's like watching someone else lift lots of weights and wondering why our muscles aren't getting bigger.

The kids are just doing the same thing. Choosing between sitting down spending hours on work thinking or offloading the labor of thought to the chatbot is like choosing between scrubbing the bathroom with a toothbrush or a pile of cocaine. One cocaine please.

More tasks are getting done. In fact the homework looks fantastic. Probably because it's become a handwriting exercise. The children of Stepford aren't alright. In my classroom I've witnessed their ability to understand and explain decrease. We're starting to see it in the data too. A recent study out of China showed AI use among students increased homework scores by 18% while reducing completion time by 30%. Great but... monthly test scores dropped by 20% after six months and college and high school entrance exam scores dropped 18% & 24%, after two years. They've handed over their thinking to the machine hoping it would set them free to watch TV and play video games. And it has.

After a decade of watching people learn I've come to the conclusion what you think about is what you remember. The truism is obvious and dumb and won't make for a good contrarian think piece in Slate. The reality is boring. Why can we keep up with all the Kardashians, yet struggle to find Botswana on the map? It's what we spend our time doing. If we spend lots of time watching TV and little looking at maps then it should be little wonder why we don't know any geography (there's only one country that matters after all and if anything Botswana should be grateful we can't find them it means we haven't tried bombing them, actually you're welcome Botswana. Try showing some gratitude) but we can pick Khloé out of a lineup.

Jensen Huang, in an interview with Ezra Klein, says so what. Do kids really need to know how to add or do long division? Do they need to do surface integrals? To paraphrase him, isn't this just mathematicians clutching their pearls because they think they're special little snowflakes? When he was young he stressed over individual transistors while engineers today are systems thinkers fretting over layers of abstraction far removed from those simplicities. There is a difference between completing a task and the purpose of completing a task. He doesn't even bother to know his own address. It serves no purpose for him to know. I agree. (This is the ultimate in billionaire ignobraggadocio. I no longer bother myself with menial trivia. Let that pollute the mind of my assistant. Haha right guys doesn't everyone do that? Guys...?)

The point of homework was never the output. We weren't waiting for Becky to finally finish reading Macbeth to share the ending with the rest of us. Writing is, and has always been, about the writer wrestling with one's thoughts; pinning them down and conveying them in an articulate manner. In math the answer is worth maybe 10%. What we're always searching for is the why? How did you get there? What's your reasoning? That's why the fuckwit at the board is always pestering you to show your work. Jensen's engineers didn't become great systems thinkers without learning about transistors. Brain surgeons don't limit their studies at the neck. As Mao waxed, "Those who have never been to the Great Wall, are not true men." Flying there just ain't the same.

Despite all the doomerism, much of it from the CEOs no less (1. We're going to build an AI god 2. The AI god will kill us all 3. ??? 4. Profit $$$) or the worries of agentic AI hacking everyone and destroying the world (anti-hacking laws, maybe use them?), I don't lose much sleep. I think the far greater concern is to the population that will never be. In our excitement to prepare them for the future, we will hand them the chains in which they will shackle themselves. AI is a boon for the excellent men, who needn't labor anymore as slaves; it is a yoke for the yet to be excellent who unwittingly give up their powers of cognition.