Ali’s blog

Mostly quant stuff with occasional digressions

A Luddite argument

Posted by alifinmath on April 12, 2009

This post is provisional and I may come back and clean it up or amplify and extend some of the arguments.

I came across an interesting blog by one John Kozy (which I have added to my blogroll). In one of his essays there, he makes the claim that the hand-held calculator has destroyed Americans’ knowledge of arithmetic:

There is little doubt that technology has contributed to the dumbing-down of America. The first assault may have come with the hand-held calculator which has almost extinguished Americans’ knowledge of arithmetic, not to mention higher mathematical disciplines.

I couldn’t agree more. In my short stint as a schoolteacher, I abolished use of calculators on the very first day. Calculators and computers are crutches that prevent students from being able to do arithmetic. People need to be able to multiply 16 by 14 on a piece of paper. More importantly, only in doing lots of such calculations will they figure out shortcuts such as, for example, that 16 by 14 has to be 224 because 15 by 15 is 225 (and likewise 17 by 13 has to be 4 less than 225, i.e., 221). But they are not going to acquire this number sense if they use calculators. Likewise, almost no-one today — including most math teachers — can calculate square roots anymore. Ask for the square root of 5 calculated to three decimal places and even the teachers will look at you with a blank face.

Without the background in arithmetic, how are students ever going to learn algebra on a sound basis? For example, the fact that 19 by 21 = 399, which is 1 less than 20 by 20 is a particular example of a general identity: (x -1)(x+1) = (x^2) -1. How are they going to master the multiplication of polynomials when they never learnt how to multiply two two-digit numbers? And with non-existent foundations in both arithmetic and algebra, how are they expected to learn more advanced material (assuming they go on to it in the first place)?

An innumerate population can be hoodwinked by real estate salesmen, by credit card companies, by pharma companies making bogus statistical claims, by Wall Street firms, and by the government itself. And that is exactly what is happening. This is probably the principal reason why there is not more concerted resistance to the government’s bailout package: no-one understands the numbers involved and the significance these astronomical figures will have on people’s everyday lives. Americans do not even have enough arithmetical sense to calculate annual rates of interest on their credit card debt or other loans. Indeed, in a thought-provoking essay by Sasan Fayazmanesh, those who have known arithmetic have swindled those who have not over centuries:

… as I have argued in my book, Money and Exchange: Folktales and Reality, and in some other essays, in medieval trade merchants regularly tried to cheat one another in the market place. [3] In so doing they used other merchants’ ignorance of arithmetic to swindle them. Arithmetic—which at the time consisted mostly of knowledge of the Arab numerals, four basic mathematical operations and the “golden rule,” or the “rule of three,” where a missing fourth number in two equal ratios is found—had just reached Europe by way of Arab merchants. Between the 13th and 16th centuries a group of merchants in Europe, particularly in Italy, wrote manuscripts to teach merchants’ children, who attended special training schools, the newly received arithmetic. But what is perhaps most interesting about these manuscripts is that almost all of them teach how to use arithmetic, particularly in the act of barter, to cheat their trading opponents and increase what they called the “overprice.” As such, these medieval manuscripts taught that the rule of exchange was to come out ahead in transaction and that barter was “nothing but giving a good for another in order to get more.”

To make a long story short, in the medieval markets arithmetic became a tool, a “financial innovation” to use the language of the modern market, to make more money. The rule of the game was to take advantage of arithmetical ignorance of others to gain as much profit as possible. This was how capitalism was born. It was born not of honesty, equality, justice or fairness in exchange, but of deceit, swindle, inequality, injustice and unfairness.

An innumerate population that cannot cope with multiplication, division, percentages, averages, and so on is putty in the hands of a financial oligarchy in the same sense that an illiterate population that cannot cope with logic and sustained arguments and rebuttals is putty in the hands of that same financial oligarchy’s political puppets. We can’t have a healthy democracy without an informed and critical citizenry. And to be such, this citizenry has to be au fait with calculating square roots and multiplying polynomials.

I was intending to say a few words about Heidegger’s outlook on technology but to be frank it’s at a different level of seriousness and abstraction to the (relative) fluff I’ve written above. More can be found here and I’ll restrict myself to a couple of extracts:

Instead, technology enters the inmost recesses of human existence, transforming the way we know and think and will. Technology is, in essence, a mode of human existence, and we could not appreciate its mental infiltrations until the computer became a major cultural phenomenon.


He (Heidegger) put forward an analysis that loaded technology with a determinate existence and an impetus of its own beyond any direct control of the “will to power.”

In short, technology develops a life, will, and purpose of its own like Frankenstein’s monster (or the replicants in Bladerunner) and as such is not amenable to individual and collective human will. But this kind of discussion goes way, way beyond my entreaty that tech should be kicked out of the classroom because it breeds innumeracy, illiteracy and the inability to think for oneself.

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