Is this an imaginary number which I see before me?

First the math.

The BBC report today that equations can be beautiful. Apparently it took a few cognitive psychologists and an fMRI scanner to show what the more enlightened among us already knew (yes, I know its yet another fMRI story, but what the heck, it starts my post off). As I said here, Eulers Identity is, unquestionably, a thing of beauty.

Then the literature.

Talking to my year 9 daughter about her day she tells me that today they were studying Macbeth, specifically the “Is this a dagger which I see before me…” soliloquy. Also, clearly, a thing of beauty.

Both Eulers magnificent equation and Shakespeares glorious writing stand at the pinnacle of their respective domains. And I wondered. Why do we teach one to 13 year olds but not the other?

I’ll leave it to better and more literate people to deconstruct the soliloquy (and having, many years ago, seen Ian McKellen do a similar thing with “But soft! What light through yonder window breaks…” it will take a better person than I) but I can do the job on the equation. The knowledge requirements to even begin to understand it are immense. We’ll take as read the basics. Addition, subtraction,  the concept of equality and zero. It starts to get tricky with pi, but even that shouldn’t be too difficult. Moving onto the concepts of exponentials and then we veer into the insane territory of imaginary numbers. All that just to explain the symbols used.

It all starts to get a bit leery when we add in sine and cosine and explain that they can be described by an infinite series. And that there are methods of adding up (convergent) infinite series. Actually, just have a look at a video (if you want to).

Even if you don’t understand the maths fully, I think you can see that it is complex (no pun intended).

Now, whilst I’ve often thought it would great to construct a maths course, the sole purpose of which would be to converge on an understanding of Eulers Identity, I have also been sure that it would be wrong to start with it.

So here’s my question. Is that what we are doing with the way literature is taught? Before you think, “Here we go, here’s a mathematician telling us how to teach everything”, I’m not. The question is not rhetorical, it’s genuine. I think the Macbeth soliloquy is complex, as complex in its domain as Euler is in math. Why do we teach one (the literature) to all students at the start of their understanding of the field, and the other (the math) only to those who clear all the previous hurdles – up to and including, usually, Further Maths.

I can see the obvious differences. In the main, a year 9 student can, at the very minimum, usually read the soliloquy and understand the individual words and their discrete meaning. The emotional and intellectual meaning can then be overlaid (look, I’m not an English teacher, i’m reaching out here). We don’t do that with the maths. Why?

So there it is. It is a real question. I’m making no point. I’m genuinely interested in why we approach these two subjects in such dissimilar ways.


2 thoughts on “Is this an imaginary number which I see before me?

  1. This is my wild guess of an answer. Literature is, as you say, dependent on language: words and their meaning. The 13 – 18 y.o. youngsters I teach (as a part time amateur) seem reasonably comfortable with the spoken word, if not so much with the written word.

    Mathematics starts with numbers. My pupils cannot deal with numbers. I am tempted to say that they have never been taught about numbers.

    Mathematics then goes on to replace numbers with symbols.
    The idea of replacing numbers (which my pupils do not understand) with symbols (which I am fairly sure they interpret as sounds; thinly sliced words) is roughly analogous to telling them that their mobile phone is the same as a rock.

    I regard (perhaps wrongly) distance-speed-time problems as the first step to mathematics. My pupils have a roughly 50:50 chance of getting any DST problem correct. It seems to be the word “divide” which throws them into a panic.

    Most of the pupils I attempt to teach attend mainstream Comprehensive schools. Very few of them have a recognised learning difficulty.

    Please pardon the rant.

    In answer to your question, I believe that we are doing the mathematical equivalent of trying to teach Shakespeare to youngsters who have no vocabulary.

    A quick anecdote to end: in an “In Our Time” program Lord Melvin Bragg was asked if a coin had come up tails on every one of the previous 100 tosses, what the chances would be of getting heads on the 101st toss. He got it wrong. He described that thought experiment as “a trick”.
    You’re up against a society in which the likes of Lord Bragg are highly respected intellectuals.
    In my opinion far too many influential people are openly proud of their ignorance of mathematics and science. How many are proud of not knowing Shakespeare?
    I could go on for ages (and frequently do).
    Good luck. You’ll need it.

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