Math Motive Money

One of those feel good stories today, and crossing over with my mathematics interests. But you know it!… gonna be tinged with neoliberal hate. LOL.

The story was broadcast on CBS 60 Minutes here — it is a freakin’ great story, poorly presented. Except well-presented with all the professionalism of corporate news! Poorly presented in terms of the real economy, real education and real creativity.

Two high school students, Calcea Johnson and Ne’Kiya Jackson, seniors at St. Mary’s Academy, independently discovered new proofs of Pythagoras’ Theorem using only trigonometry.

At 2min in the episode both students claim they were interested in solving the bonus question their teacher had given on a test for a monetary prize incentive. US$500. Nothing to sneeze at for high school students. But why did CBS have to air that soundbite? Cos’ they’re neoliberal.

Let me rant a bit about why this was a big deal, before getting to the core of this post, which is why the prize incentive was rotten.

Why such a big deal?

1. Trigonometry (ratios of sides of triangles) — and nothing more — had not been able to yield a proof of Pythagoras’ Theorem for over two thousand years, until Jason Zimba in 2007 . (It is well worth reading that paper, it is an easy read.)
2. Although Calcea and Ne’Kiya were given the puzzle by the same teacher, and both knew the other was trying to solve it, they worked independently, and each discovered a different new proof.
3. Finding new proofs of old theorems is hard enough itself. (Let alone finding one most mathematicians considered impossible.)

The non-circular proof

For the macroeconomists, let me just say that very, very good mathematicians had conjectured that that a proof of Pythagoras’ Theorem using only trigonometry functions would be circular, in that it would assume $$ \sin^2\theta + \cos^2\theta = 1 $$ which is of course Pythagoras’ Theorem. (You cannot assume in a proof what you are trying to prove!)

BTW, I see this a lot in crackpot physics. People often try to derive the masses of the elementary particles, but they more often than not have implicitly assumed the empirical mass. For the electron, for example, people will take the Compton wavelength as their data.

The Problem with Prize Money

(And the problem with extrinsic rewards entirely.)

Any decent mathematician would not be solving such a problem for the prize money. The effort the students put in was worth far more than US$500, if they had been paid a wage to work on the puzzle. They should have been paid to work on it if the money was the goal. But while being paid a wage does not mean one is not learning, not being paid a wage should not be the price of learning. The price of learning at school should be the real resources going in to teaching and learning. The money should not be a question. Just pay the teachers a decent living wage, and hire them locally, and hire all of them to cut down the class size ratio.

Prize monies are often like this. Except perhaps for the million dollar Clay Millenium Prizes and the Nobel, or Abel. Those bigger prizes recognize lifetime achievements, and so are fair compensation for sacrificing a lot to work on serious mathematics. For most people they are more than a wage. The problem is that they are only a wage for one person and this degrades and demeans the effort of all other people who support the prize winner. Anyone ever heard of standing on the shoulders of giants?

(No? Of course, you’re an Ayn Rand acolyte! LOL.)

Alfie Kohn , I dare say, would agree with me. Twittxr might not, but I’m no longer involved in that swamp.

The nuances of wages

I am not saying students should be paid to go to school. That issue is entirely different. Public education is an investment. It should be fully funded up to available teaching resources. We should not even worry about the pay-off, since the pay-off is incalculable, but whatever it is, it is yuuuuge! The private schools like St Mary’s Academy need to be crowded out, because they are elitist.

The placements of Calcea and Ne’Kiya are at the school mean other “less Catholic” students do not get a place. This is not their fault of course. I’m saying it is a systematic problem with private schools. Not only do they consume more resources per student than current public schools, the parents are paying for these, and they shouldn’t be. There is no reason public schools cannot be as nice and hygienic as these private schools. The private schools prove the real resources are available.

Sure, sure, admitting less desirable students into the schools messes up the pristine learning environment for these gifted kids. That’s a whole other problem though, for another day. You cannot ignore it though, otherwise you give fodder for the elites who demand their kids go to a pristine school if they pay the money. I am not trying to skirt this issue, I am just writing about a different issue today, the prizes & rewards issue.

Let me just say though, that such elitist claptrap can be defeated if we eliminate poverty and allow the riffraff kids to have a dignified living environment, a decent breakfast, and parents who are not bitterly struggling to survive, who have time to read their children Dr Suess stories, or whatever the better stories are… Spike Milligan.

Besides all this, we (society) do pay for children to go to school. We pay in terms of the real resources committed to schools — both private and public. As long as we all are paying in real terms, and the teachers especially with their labour time, I think we should demand the public schools get the premium resources. Will this crowd-out the private schools? Yes, I think so, and good riddance.

What about the motive?

The puzzle solving motive is the only motive the students needed.

Would they then bother to solve the problem?

Who knows? But they did not need the money prize motive. Why not? Because they should have been take care of materially, or their parents should have been taken care of, with decent wages.

Take the money incentive off the table — unless it is a socially necessary sh1t job.

Since solving mathematics puzzles is not a sh1t job, we can, and therefore should, take the money off the table, by providing for the students needs, by providing for their parents’ or guardians’ needs.

“But,” the pedant asks, “what if the students then did not bother?” I say two things to this foolishness:

1. So what? If they did not bother to work on the puzzle then no one dies, and they lose out on the chance of discovery. People lose such chances all the time. What you do not know you lost will not hurt you.
2. This would more likely than not reveal the students were not truly motivated by the money prize, because I bet were finances not an issue they’d still have worked on the puzzle.
3. Everyone is capable of providing their own incentive. If you crack the puzzle treat yourself to a movie — or whatever floats your boat.

(I guess I suck at arithmetic.)

It is a profound lack of creativity to think the students had no motive other than the money.

It is a reality they were in fact motivated by the monetary prize, because to them US$500 dollars was a lot of dinero. But that’s utterly beside my point.

But don’t wages encrudify labour?

I don’t know about that! As I stated, for sh1t jobs wages are bl00dy good.

For enjoyable jobs we still compensate workers because it is the right thing to do, even if the worker is having such a wonderful larking time of it they cannot care about the money. In this case, we${}^\ast$ take the money off the table by paying a wage that is fair and just above what the worker considers fine enough not to care about the amount and care more about the work (enjoyment or utility or both).

(${}^\ast$Who is this “we” you might ask? I mean the We if I were supreme dictator. Or failing that, a simple democracy, full of nasty plebs who simply want their fair say in the rules of our society.)

But then the neoliberal wank3r utters, “The wage destroys the competition!”

I mean… sure. With a wage the student can take their own fw33t sucking time trying to crack the mathematics puzzle.

But what student you know would be taking their sw33t a$$ time?

None I know. There is always competition in sciences because others can discover the thing first, and then you’ve really cocked it up. Discoveries are not like hamburgers, the first one made is the only one made. Unless you get lucky and the original hamburger gets lost in the sands of time.

(There is an exception for school pedagogy: it is a great thing to give students a solved problem, but get them to try to rediscover a solution. There is still a marvellous thrill in this, but it’s not the same. However, this pedagogical thrill of re-discovery is even more important than original discovery, precisely because it is the hamburgers and fries of mathematics and science. Feeds the masses.)

But again, it is profound lack of creativity to think students cannot motivate themselves when they are waged, or have their financial cares met. How would I motivate myself with some pressure? That’s so easy, I can think of a million ways — which is to say, the million ways my girlfriend and I can achieve orgasm.

What about the teacher wishing to motivate their students?

Well, for heavens sake do not offer a prize. You can put a deadline on the puzzle for “recognition”. But even deadlines are for dummies.

You can instead just talk to the students! Shock & horror! Does “talking” even work? I cannot imagine.

“Hey Calcea and Ne’Kiya, so you like this challenge problem? Well, this is a tough one, it might take a long time, much effort, many daydreams, and at the end of six months you might get nowhere, like all humankind for two thousand years. Except in the process you’ll have learned so much interesting geometry your brain will swell and your mind will be both humbled and proud. Think about that!
     “Now… do you want to give yourself a constraint as a challenge. Say 9 months, but then move on to a new puzzle?”

and then you might say,

“… look, if you also want some candy as a prize, we’ve got $500 from the school kitty. That’ll get all the chocolate you need for a year. Give yourselves that if you crack the puzzle, but work on it because it’ll grow your mind, not your belly.”

But I personally would not add that bit, it’s the real enshittification. Am I a mean & nasty teacher? Maybe. But no student of mine ever told me so.

To be clear, if we are not making whole the families of the students, then yeah, would should damn well offer a wage or a prize. For open puzzles I prefer a wage, because there is a lot of work to be done, and no guarantee of success. But it is a poor system that requires this enshittification.

The neoliberalization of education cuts deep, and has created a festering wound on our society.

(“Here kids, work on this and teacher will give you candies, but if you cannot solve it then pi55 off, because you deserve the f-all proportion of a billion times your present wage.”)

Summary based-MMT Thoughts

(Well… $I$ think they’re based. 😂)

Most people are perfectly capable of motivating themselves with scarcity. I do it all the time with food — I will exercise to earn my meal. The CBS story reported the high creativity shown by Calcea and Ne’Kiya, which is rightly celebrated, but does not stop to ponder how uncreative the idea of the monetary prize was, and how insidious.