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We No Speak Mathematicano

November 11, 2016

I have always found numbers ugly. For me, they have forever been black, spiky shapes devoid of meaning.

I know there are people out there who find numbers neat, even elegant; satisfyingly coordinated, even beautiful.

To those people, the idea of someone completely untouched by prime numbers is a mystery.

They imagine that I’m bereft of something special. But if you were blind from birth, you couldn’t miss the colours you have never seen. I have never been able to see the colour in maths.

Among people who get on all right with numbers, I’m often faced with the insistence that if I only try hard enough, I will eventually understand them and see their value.

Considering a person with an aptitude for numbers usually shows this by the age of seven and knows it by the age of 12, if this is the case for me, I’m a decade and a half late (if my maths is right – don’t quote me on it). When will this mysterious appreciation of numbers appear to me in a blaze of white light – at the age of 50, 60, 70?

The fact is that maths, unusual among the subjects, is mainly about aptitude and not mainly about knowledge. A child with an IQ in the 99th percentile could learn all the maths in the world by their seventh birthday, starting at the age of two, if they dedicated enough time and effort to it. That may even be an underestimate.

Their intuitive understanding makes the formula simple and easy to remember. There aren’t many principles. Compare this to fact-based, knowledge-gathering subjects like the humanities and social sciences. You could never become an expert on politics in just five years of reading.

These trial-and-error subjects are the ones that we get better at as a society, provided we do the reading to make sure we understand the key concepts, which with each successive generation become more comprehensive.

Anyone with an average IQ could, with a decent explanation, understand the basis of our political systems, legal systems, and other important points of knowledge.

Having a high IQ gives you a head start, but ultimately can’t aid you much, because the subject matter in question doesn’t have the kind of complexity a high IQ helps you deal with. Your advanced problem solving ability may make you able to determine the answers to complicated social questions, and it may help you retain important information. But the margin of difference will be significantly smaller.

Despite this, we still live in a society that values mathematical ability and IQ more than it values education; the acquiring of facts and the ability to look at them critically that determines a person’s ability to make informed choices.

Whereas the high IQ problem solver can be a great political leader, they are nothing without the informed support of voters in a democracy. It is humanities and social sciences that create this informed society of voters, not algebra and trigonometry.

This is why I get aggravated when I open a book called “Economics for Dummies”, which starts so slow as to be patronising, and by Chapter 4 leaps into three lines of algebra.

For all the mathematical people out there: understand that non-mathematical people would rather read dozens of pages of text explanation than have to fathom one algebraic equation. Even though a simple equation is much faster and clearer for you, to non-mathematical people, it is neither.

A book dedicated to explaining a set of concepts as clearly and carefully as possible makes a drastic error when it jumps into algebra. It alienates its own audience, who as likely as not avoid more comprehensive economics books because they are afraid of tables, graphs and algebra.

Dummies pays some lip service to this, but the writer could not have fully understood what he was dealing with. If he had understood, he would have known that the non-mathematical person’s aversion to numbers and equations runs deeper than can be fixed by jocular comments about how the nasty algebra isn’t so nasty, really.

I’m afraid it is. For non-mathematical people, algebra is more than difficult. It’s unpleasant, it’s cruel. It feels malevolent. It makes us feel stupid; it’s supposed to be simple, the simplest possible format of transferring information, yet try as we may, we cannot find it so. It brings back unwanted memories of struggling in maths class.

Many of us just scraped O levels, GCEs and GCSEs in maths. And when we quit compulsory maths class, we did so with a sigh of relief. We knew we had wasted our time. We knew, from the age of 12 as clearly as today, that however much our patient teachers explained to us that Pythagoras theorem is useful, it would be never be useful to us.

The amount of pain we had to go through do scrape through meant that we would never be in a position to challenge or match the jammy bastards who sailed through maths class and pursued numerate careers. By the time we had calculated anything – slowly, drudgingly – it would be irrelevant.

That type of maths is useless to most people, for that reason. It cannot help them as it can help others. They will always know that they spend hours of their life learning to do something that to them is closer to housework than it is to academic work; something you drag yourself through, questioning the point of it all, gaining no proper understanding or fulfilment. For the final reiteration for people who still don’t get it: anti-maths attitudes are not made. They are born.

Depending on your definition of smart, non-mathematical can be smart. If smart is just an IQ score to you, we’re all stupid. But I contest this definition, because I don’t think it’s in the best interests of society.

A good mathematician must surely understand that the higher the overall critical intelligence and knowledge, the better; a good economist understands that the opportunity cost of teaching non-mathematical people maths when you could be teaching them two humanities subject in the same amount of time is a dreadful use of resources.

Recognising that non-mathematical people make up a large and important section of society who are articulate, literate, critical and analytical is an important step towards better education in society as a whole. Let’s start with the understanding that there are two ways to analyse something; with equations (traditional maths) or with words (indirect maths).

Every analysis involves some kind of mathematical comprehension. Where economics is taught as a social science, this is understood. It is only maths that is written in numbers which unnerves non-mathematical people, who cannot ascribe or remember meaning given to those shapes.

You would think that remembering numbers, equations and letters would be the same as remembering words, but for whatever reason, the two are different. A literate person uses etymological pattern spotting to interpret new words, engages with the phonetics of the words, and forms an appreciation of those words which makes them interested in them and therefore aids their memory of them.

I’m sure we can all agree that enthusiasm for a subject boosts willingness to learn and rehearse, and subsequent retention. Wherever this enthusiasm is absent, the processing power is compromised by a lack of will power. That is what non-mathematical people experience when they see a string of numbers and equations.

To some extent, this can apply to acronyms, which strip words of their memorable content and make them mere representative symbols, like in algebra, where often the choice of letter doesn’t even follow an apparently intuitive pattern. In economics for example, Y represents total income. The reason was never explained.

Often, if you ask a mathematical person why X is Y, they are flummoxed by the very existence of the question and will say: “It just is.”

They cannot understand why these pesky non-mathematical people need identifiable reasons why things are called what they are called. Those with good mathematical retention remember symbols which have no rhyme or reason, and accept them as representing the content ascribed to them without any trouble.

For them, algebra and other forms of short hand help to simplify. For non-mathematical people, they complicate matters. The mathematical person asks: “Why would you use a six-page explanation where a short equation will do?” The non-mathematical person asks: “Why would you use a string of meaningless numbers, where a clear explanation would do?”

This difference in opinion is just a difference in brains, but economics books do not account for it. Of all the economics books, Dummies should have accounted for this difference. The six-page explanation could have been boxed underneath the equation, with a note to say that the reader need only look at one or the other, as per their preference.

It’s easy to see how something works when you already know how it works. What teachers have to do is try to understand what it’s like to have a brain empty of their years of experience. But the writer of Dummies was unable to do one crucial thing; he couldn’t see the world through the eyes of the non-mathematical person.

He did not predict that his future readers would understand every word he said when he was writing pages and pages about diminishing returns and marginal costs, using simple visual examples, but that they would become instantly unable to follow his logic as soon as he crossed over into Yd = Y0 x C – c (1) r = R + C0 – Y.

My goodness, what an ugly thing.

It’s a made-up equation of course, because I don’t understand (and therefore obviously can’t remember) the real one. But the choice of letters – including the change of case, indicating something completely different – is all within the accepted economics language. It’s the sort of thing that drives non-mathematical people to despair.

To be clear, it is not mathematical theory, particularly, that is alienating. It’s a formatting problem. Mathematics defines the entire natural world, entire systems, anything with order, symmetry, or any kind of pattern. It governs all logic and analysis. The world is maths.

But the world is not numbers. All these systems I have come to admire and appreciate, and have some solid understanding of, I have done so outside of numbers. Wherever numbers have been used to explain any of these, I have politely excused myself.

If anyone asks me what my aversions of, I might tend to mention bugs of various kinds. Now that I think about it, I think numbers are my biggest aversion, and I doubt this is the kind that can be fixed with cognitive behavioural therapy.

I have always thought of it as more like a difference in language and culture that can’t be crossed. Every generation has a preoccupation with one of these. In the 90s people were obsessed with the differences between men and women. Then it was all about introverts and extroverts. These days it’s all larks and owls.

Some of them are likely hogwash, but some may have grains of truth. I’m waiting for a day where smart, non-mathematical people are not regarded as mythical beings.

So different are mathematical and non-mathematical people in my opinion, if I could work my will, I would rate all education books with a system which unpacked how mathematical they were, and their literary complexity.

That way, people who know their limits don’t get caught out by falsely reassuring introductions, followed by a steeply inclining difficulty curve. Dyslexic people will not then find themselves suckered into buying a book that come Chapter 5 suddenly jumps reading age by about a decade.

This is not to discourage people from challenging themselves. Ultimately, people are responsible for determining their level of challenge, particularly when self-educating in adulthood.

It’s not as if us non-mathematical doofuses need to be led by the nose to better things, because our plebeian consciousnesses are unable to appreciate fine arts, culture and high knowledge without first being tricked into it.

In this world over-saturated in media, it’s easy, expected and desirable that educators compete to create a greater variety of products to choose from. There’s always a better way to explain something, as time moves on. I’ll wager economics without algebra certainly has a market.

That level of complexity is for people who already have an aptitude, and aren’t just looking for some understanding of what the people in navy suits are talking about when they wax lyrical on interest rates and housing bubbles.

These financial issues are increasingly relevant to our society, yet many of us are out the loop because there’s nowhere to start; all the starting points assume you’re hunky dory with numbers and graphs.

Expressing concepts in multiple ways, including the simplest way (not to be confused with “the shortest way” which is very often not the simplest way) to explain an inherently complicated subject like economics is a step forward in education, because it makes learning easier and less daunting.

Better to have more people with a simple base understanding than to have most people unable to follow major newspaper stories. Your average news consumer has no wish to study economics at degree level, but they do want to know how depressions, recessions and financial crashes happen, since these things are best avoided.

Recessions are, after all, not inevitable like damage from tsunamis, or circumvented by changes in city structure decided by authorities, like earthquakes. They are prevented by sensible economic behaviour by the public. Far from increasing the level of education, complicated elements that require a high IQ impoverish it by putting people off trying.

They see an equation, assume this is something they’ll never get the hang of, and miss the fact that the lessons of economics were mainly learned from trial and error. Phrased this way – with the simple history of commerce laid out chronologically – anyone could understand (given enough time and content) how we’ve got to now, without looking at a scrap of algebra.

The bottom line that can’t be overstressed is that you can teach somebody to like politics of certain kinds, you can teach them to care about law, and you can show them the value of the social science part of economics – the psychology of how people spend money. But there’s just no way to make a non-mathematical person comfortable with maths.

We accept that some people have a hard time remembering spelling, dates, factoids, and names. For some reason, we have a block about accepting that some people really don’t have a working memory of maths.

I am against the concept of trying to garner up enthusiasm that is permanently unattainable, and especially for a subject as socially useless as maths. We have a lax attitude about many more useful subjects; or we govern them by social pressure, even though no one learns the basics at school and can’t reasonably be expected to know Jack about them.

I’m not trying to diss maths. Non-mathematical people understand that maths has value, without feeling the warmth of its value. I feel about maths the same as I do about giant wasps. I don’t begrudge its existence, recognise its function, and encourage others to study it. I don’t wanna.

It is not compulsory to care about wasps. It’s not required to love all aspects of history. Nor is it necessary to appreciate modern art. If you can’t see the beauty of these, people accept that. If you can’t sing a note or play an instrument, people accept that. Really, then, people should know that maths is the same, since musical ability – or at least, compositional ability – is closely related to maths ability.

I believe it is an ideological, cultural attachment to maths that makes us insist that young people learn it beyond the point of basic numeracy – which is a drag, but required, constantly useful and easy to remember.

We think that mathematics ought to be useful to everybody, despite the fact that it isn’t, simply because most people can’t and don’t make use of it, any more than they make use of the knowledge that English operates under a subject, verb, object construction.

We speak English as a first language. We don’t need to know that to speak it. Yet, this is the kind of stuff that’s compulsory in our schools, while we can choose to wave away recent history, politics, the social science of spending, our rights in law, cooking and nutrition, and other subjects arguably fundamental to our full engagement and maximum possible well-being in society.

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