Logic runs deeper than arithmetic

My old classmates would be tickled pink to hear that I failed a math test.  Okay, so maybe I didn’t fail, I scored below average and failed to get a job because of it.  Big difference.

Back in the day, some would want to copy my homework, but the more competitive students were annoyed when I got the highest mark.  As a teenager, I put myself into game mode; so for me, math was like playing cards.

I won’t make excuses.  This time I wasn’t on form.

Am I getting old?  Nah, next week I could probably ace the same test. I simply wasn’t in game mode.  And, when you’re out of game mode, you can get distracted by things that don’t fit.  What distracted me? The poor logic of some of the questions.

  1. Helen can write 3000 words in three hours;  Assuming she works at a steady pace, how many hours does it take her to write 20000 words? 

Or was it 50000?  I forgot the exact numbers, but I disagreed with the question.

Assuming you work at a steady pace, you still can’t answer that question with simple arithmetic.

Why?  Let’s use a simple form of research called I-Search, where we search our own experience for the answers.  When I was an undergrad studying film and French, students wrote between 10 and 20 essays a year of 3000 words each.  (Unless we had practical courses: those required equivalent work in the form of films or screenplays.) Maybe more. Meanwhile, a PhD student would write one 50000 word paper in three years.  Yes, I’ve read PhD dissertations that were that short. That’s less than 20000 words a year. Wait a minute, you did the arithmetic. It doesn’t make sense with only arithmetic.

Are PhD students lazier?  Less talented? No, to qualify for a PhD you need to be an above-average undergrad, with an upper second-class or first-class degree.  

So, why do the best slow down?  Is it old age? Not really. Many could still crunch in a three-thousand-word essay at top speed.  Besides, lecturers who have PhDs have to work much faster than undergrad students do. Ask your friends who have PhDs about all the extra work that goes into writing a long paper.

First, short papers can usually be completed with a handful of sources.  Watch a film, read a few reviews and a book and listen to a lecture, and you have enough material for a 3000-word paper.  If you’ve been paying attention in class and doing your reading and viewing assignments, you already know most of what you need to know before you put the pen down.  What you’re doing for three hours is searching your memory, checking your sources and proofreading. You’re reheating a ready-made soup, the bulk of the work is behind you.

Back when I was a student at Aberystwyth University, we also had to write essays in exams.  We rehearsed those essays ahead of time, so we were pretty much rewriting two or more short essays in a three-hour exam, without any reference works or spell checks.  Those weren’t 3000-word essays, but they had to be fairly long if we wanted to pass. The idea was that the average student could remember about 3000 words on a topic if they paid attention in class and did the reading (or viewing) assignments.

If you’re writing a doctrinal dissertation, (or a feature-length screenplay, or a novel,) then your research needs to dig much deeper.  Rather than just picking up the recommended texts at the library or on the internet and watching the popular documentaries, you’ll need to look where most people don’t.

Unfortunately these days, (as a side note), students no longer have to sit exams in many UK universities.  The word length for undergraduate essays has gone down over the years, as indeed has the total workload for undergrads.  But strangely, the word length for postgraduate essays seems to have gone up. Perhaps the dean of the University of Essex and others took the same test I did and used arithmetic to create their curriculums rather than logic.

Television and film also defy simple arithmetic.  People expect more from a movie that they pay to see at the cinema than they do from something they see on Netflix.  Netflix, a blog, or a magazine article might be relatively shallow, like a university undergraduate essay. However, a feature film, a novel, or an expert’s presentation goes into more detail. 

On the other hand, sometimes you can be faster with longer projects.  Some people get off to a slow start, but speed up when they know where they’re going.  Some skills have a learning curve, where we start slow, but pick up speed as we learn the tricks of the trade.

That may seem to be getting off-topic;  but, try to stay on topic for 20,000 words or more.  You’ll need some original material in order not to repeat yourself.  

Where do you get that original material?  That depends on your subject, but it’s not always quick to build a new path.  It’s much quicker to walk along the beaten trail, going the short route that many others have gone down, than to risk the hidden dangers of quicksands, monsters and freezing deserts while you cut through the overgrown wilderness of the unexplored.

So, how long does it take to write a longer essay “at a steady pace?”

Normally, I’d ignore the silliness of such a question and just play along.  However, it was related to a job test. And that test expected us to answer something like 20 questions in four minutes.  I guess I imagined a future employer seeing me do a task in ten minutes, and expecting me to keep up that speed for 8 hours straight, day after day.  It’s happened before where I’ve been punished for working faster than normal. So, I ended up spending too long on a few questions. Then, I rushed through the rest.

But, if it was a twenty-minute test then I would have probably had time to get over it and get into game mode to catch up with the pack.  Oh well. There will be more opportunities.

That wasn’t the first math question to throw me off, though.  In a teacher training course that I started many years ago, there was a cooking question that also defied logic.  It went something like, this:

  1. If it takes Mary 50 minutes to cook lamb at 300°F (degrees Fahrenheit), how long would it take to cook the lamb at 100°F?

Now, even though I’m a vegetarian, I know you can’t cook meat at 100 degrees Fahrenheit.  I objected to that question because it taught stupid logic. Others might object to the stereotype of a cook named Mary or the eating of lamb.  But to me, this question was teaching students to become an accessory to food poisoning.

  1. If it takes water ten minutes to boil over a stove set to 100°C, How long will it take to boil water at 2°C?  

See how silly it can get?

Yet, when people plan, many do put simple arithmetic before logic.  Or, they do the math without first realising that real life doesn’t exist in a vacuum.  They think if they make a ten-minute short film in one month, they can use the same sized crew to make a 120-minute feature in twelve months.  Or, if they win that 72-hour film contest, they can win a larger film festival in… well, you get the idea.

I’ve seen talented filmmakers create short films quickly. but when pieced together like Frankenstein’s monster, these group-effect films just lack that coherent sense of oneness that a true feature has. Four Rooms was terrible, even though the same filmmakers worked together on much better films later.  

I’m reminded of the Penns who allegedly bought Pennsylvania from the Indians by claiming the entire territory was what a man could walk in a day.  The Penns hired the fastest men in the area to run in a relay, each “walking” a fraction of the distance, to claim an unjust share of land.  

The Delaware Indians should have made Richard Penn walk the distance himself, in a day.  He’d probably have died of exhaustion before lunchtime.

Sure, some things can be scaled with simple arithmetic.  If you’re buying something made from a factory, it makes sense to pay per unit.  Even then, prices may go down in large quantities. So sorry, you can’t rely on arithmetic alone to figure out prices.  If it costs ten dollars to ship a 100 of something, it will still cost more than ten cents to ship one. If you create things in bulk, the unit price is normally lower, as the development costs (including building a mode and training anyone who works at a factory) are spread over multiple units.

If I’d only ignored these facts for four minutes, and pretended like I was playing Super Mario Brothers or something, I would have scored higher on that math test.   Oh well, next time I’ll do better.

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