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Last Updated: Friday, 20 July 2007, 14:10 GMT 15:10 UK
New dogs and old tricks
By Clive James

Calculators have squashed mental arithmetic

Even in this wonderful world of new technology, we still have to remember the old ways of doing things, writes Clive James.

Stories on the inside pages of the newspapers can tell you a lot about a larger subject than the one they purport to be dealing with.

I was reading a story recently about car theft. There was the usual stuff about cars being stolen, instantly supplied with stolen documentation, and sold back next day to the original dealer, or something like that.

Not finding any kind of thief glamorous, even if he looks like George Clooney and steals all of Las Vegas, I was paying only vague attention until I got to a paragraph about a bunch of young American thieves who broke into a parked luxury car by night with the intention of driving it away.

Clive James
Most of these unwitting victims of a permissive non-education will graduate, because there is no machinery by which they can fail

They didn't drive it anywhere because none of them knew how to work a manual gearbox, or stick shift as the Americans used to call it when such a thing was still manufactured. I imagine the three desperadoes were still sitting there cluelessly stirring the gear-stick when the police arrived, responding to complaints from neighbours that somebody was using an angle grinder in the car-park.

It would have made a good comic scene in a frat-house movie, except that those movies, aimed as they are at hyper-hormonal teenagers, draw little of their revenue from people old enough to remember what a gearbox was like when it wasn't automatic; when, that is, it didn't do the whole thing for you.

So there would be nobody to laugh, and the post-pubescent audience would drum their heels impatiently on the heads of the people in the row in front, waiting for the next scene when the frat brats fight to take a peek through the knot-hole in the wall of the girls' washroom. Thus our path moves on irretrievably into technologically determined time, as Confucius said when one of his acolytes invented the pencil.

Calculator generation

Then again, the current issue of the seriously intellectual Australian magazine Quadrant has just carried a disturbing article by a University of Western Australia mathematics teacher recounting how some of his pupils have emerged from the high school system unscathed by any requirement to do simple mental arithmetic.

Equipped with electronic calculators since the cradle, they enter university, and even penetrate as far as the second year of a mathematical subject, unable to multiply 8 by 4 without mechanical assistance. Asked to multiply 4 by 8, they complain about having been set two problems instead of one.

Most of these unwitting victims of a permissive non-education will graduate, because there is no machinery by which they can fail, and the machinery which helps them to do their set tasks in arithmetic, the machine that does it all for them, will always be on hand.

Air traffic control
How will the next generation of air traffic controllers cope?

Presumably when they move on to become air traffic controllers or risk analysts at the nuclear power plant they will still always have calculators in their pockets. But it's daunting to think of the calculator getting stuck in an air traffic controller's pocket when he suddenly needs to figure out roughly how long it will take one blip on the radar screen to coincide with another.

One of the many advantages of learning your tables by rote and being able to do mental arithmetic is that you know what order of answer you are after for any given question. If you buy eight dinner plates at 4 each, the total outlay will be something like 30, but nothing like 3 or 300, and if the salesperson, staring dimly at the figure beeping up on her till, says the price is 32,000, you'll know that you should think twice - that's two times once - before handing over your credit card.

But without the benefit conferred by a headful of thoroughly memorised relationships, the air traffic controller will be lost, and eventually some of his pilots will get lost, not to mention their passengers. And if the pressure in the condenser pipe is rising by four psi every eight minutes and there are only 32 psi of tolerance left before structural failure, the man at the desk had better realise that he hasn't got all day before he scrambles the reactor.

Horse replacement

These are fantasy scenarios on my part, but Mike Alder, the sardonic mathematics teacher who wrote the article, thinks that the whole of modern society might soon come flickering and fizzing to a halt because the people who make and work the miracle machines can't add up in their heads. He sounds at least as convincing a doomsayer as those who hold that we'll end up under 20ft of water dotted with the corpses of roasted polar bears.

Speaking of which, it almost happened to me on a recent rainy weekend. I was away from my office for most of it. On the Monday I came back to London from Wales in the back of a car. I'm used to being in the back because I don't drive on the public roads owing to a nervous condition which other drivers contract when they see me coming.

But the upside is that I can work. Reading and writing are what I do for a living, and while travelling as a passenger I can do both.

I barely knew how to switch the stricken monster off, and had no idea at all of how to fix it - I thought briefly of aiming my microwave oven at it

I had an article to finish that day for a magazine in Chicago. Drafting the piece in my notebook with a biro, I got most of it done during the trip, which took about three and half hours. As usual I spent almost no time reflecting that the same journey would have taken Jane Austen more than a week, and that covering the same distance was even slower before the invention of the horse. I took the speed for granted, and if we had been slowed up for an hour by the rain I would have thought that abnormal.

We weren't. I got to my desk safely by early evening and I sat down at my computer to begin the task of transforming the draft in my notebook into a document, which I could do the final work on before sending it off by e-mail to Chicago, where it would arrive at the speed of light before close of business in the mid-West.

I pressed the button that lights up the screen and nothing happened. Strange, I thought. All the diodes are glowing correctly and I can even hear the thing hum.

I poked around among the cables and sockets, testing with my fingertips to make sure everything was a tight fit. It was only then that I noticed the whole thing was wet. I looked up and saw that the rim of one of the recessed light fittings in the ceiling was stained with water.

At this point a director of a frat-house comedy would have staged the scene differently. I would have found out that I had my hands in a lake of electricity when I lit up all over with crackling blue cobwebs and was blown backwards into the closet where my roommate was hiding with my naked girlfriend.

What happened instead was a mental revelation, much harder to film. I realised that the technology was miles ahead of me. I barely knew how to switch the stricken monster off, and had no idea at all of how to fix it. I thought briefly of aiming my microwave oven at it.

Harsh reminder

During the rest of that week, before I left for a business visit to Australia, I slowly grasped that I was more helpless than I had ever thought. The hard drive eventually got saved by my young friend Idris. His principal instrument of salvation was a hairdryer, which personally I thought only one step up from my microwave oven notion, but Idris knows how a computer works.

Since I don't really know how a hairdryer works, I needed this harsh reminder of just how irreversible the road has become. As the proprietor of a state of the art multi-media money losing website I'm in awe of the new technology, but I'm also in almost complete ignorance of it.

For day after nail-biting day I couldn't send or receive e-mails. Finally I had to fly to Sydney with no clear idea of whom I was supposed to meet at the other end, because all my schedules were attached to e-mails I couldn't read. Getting to Australia and back in roughly the time it took Magellan to leave harbour, I regained my office to find a new flood ready to hit my computer - all the e-mails that had piled up in cyberspace over the past fortnight.

There were more than 150 of them, practically all decorated with that little red exclamation mark that looks like the droppings of an angry sparrow.

Yes, I could have accessed them in my Sydney hotel, but I didn't know how. I don't know how to do anything the machine does and there's a limit to how far I can go back down the one-way path. I can still write an article by hand, but do I really want to copy it on to a typewriter, and then mail the typescript, and then wait?

I can't go back to all that, any more than the young mathematicians can go back to doing arithmetic in their heads, or the young car-thieves can go back to treading on the clutch pedal before shifting the gear-stick, and then - this is the hard part, as I remember - letting the clutch pedal come up slowly while they steadily tread on the accelerator. All too primitive.

So we let the machines do it, and more and more they make us feel powerful enough to forget how helpless we really are. Let's call that a plus.

Below is a selection of your comments.

Last night, my toddler sat on the TV and DVD remote controls, sending a variety of signals to both devices. 12 hours of trial-and-error later, we've managed to get TV reception back, but I fear the DVD may be lost forever. Is it sending to the TV, which is not receiving? Is it sending on the wrong SCART lead? Is it not sending at all? How do I find out? I'll have to wait until the toddler is old enough, in 3 or 4 years, to tell me.
John, Portsmouth

Don't forget, some of this is cultural; no young Brit would have any difficulty using a manual, because 95% of European cars are manuals; American technology is geared, forgive the pun, that way because American driving requires less work than European, which has harder geography to contend with. If the author doesn't know how to access his email in a hotel, that is his flaw; the young wouldn't think twice about it.
John Smith, Somerset, UK

That's right Clive, no young people have any brains, we're all pathetic specimens of humanity in comparison to generations past. The fact that most decently educated young people can do such basic arithmetic doesn't seem to dawn on Mr James (who I assume reads the Daily Mail and spends life mainly moaning), but being as all old people are apparently splendid intellects, I'll do a deal, I'll draw a pension and they can apply there computer programming and code writing skills to my job. Then they'll suddenly find that just because we no longer do trigonometry in our heads, doesn't mean we haven't got useful skills. I can write in numerous languages of computer code off the top of my head, without a reference guide and that includes doing arithmetic calculations and complicated logical operations, as can everyone who was on my course, can Clive do that? Or is it just possible that while our educations were different, both are relevant?
Peter Jay, Newcastle

i love this article, it brings us down to the reality of life now and dares us to face it. i am 24, have done maths from the age of 5 from tables and manual calculations. I have continued with science subjects and just finished a mechanical engineering degree from London - I have personally witnessed the changes in my brains to maths, how I can (or cannot) do calculations in my head and rely constantly on the calculator. This is no good when I have to make simple calculations to save my skin and I realise how we have all surrendered to the automation of calculations.
vashi, london

Excellent article. I myself had discussions about it with my friends...Im 35 years old. My generation was the last one in my country that had to learn the tables by rote or learn how to obtain square numbers...etc...
Yamil Camilo, Dominican Republic

I would totally disagree, the way forward for the human race IS to rely on things we don't understand, teaching every new generation the same stuff over and over is utterly pointless. The human brain has so much more to offer when we release it from the mundane task of remembering facts. When we can instantly draw on any knowledge, learning it ourselves will become completely irrelevant. It'd just a matter of convention, individually we don't know how our brain moves our arm, it just 'does', if we had to teach each newborn the whole process from neuron to muscle we would get nowhere. Well learning all facts is just as restrictive. learn it once, archive it for all to use. Just like Google has ended the office quiz banter, total information avaliability will end the need to 'Learn'.
Chris, Hull

"The Machine stops" by Joseph Conrad. Nothing new... The answer is to LEARN at least the basics of what you use. Not enough to get a job as a Gadget repairer or Gizmo maker, but just enough to understand what the pretty lights actually mean.
Technophile, Lonodn, UK

I take issue with this! I'm 25 and came through the so called calculator generation at school. Not only can I rattle off times tables perfectly but always add up my shopping in my head and match the till total by the penny. This seems like another (it's not as good as in my day) winge!
Lee Jones, London

I had a happy permissive non-education in which I never learned my times tables by rote. My inability to reel off six times seven in an involuntary compulsive noise bothers me not a bit. Then I got into computer programming and learned my 2 to the power of N table. What's 2 to the power of 5, Clive?
Felix, Nottingham

Reminds me of a conversation I had with my dad many moons ago when I was still (just about) a teenager, inquisitive and explorative of the world and the way things work. In short, I was musing on the idea that if we had some sort of catastrophe along the lines of total infrastructure destruction all our high tech gizmo's and the massively advanced fabricating processes that give us 'x' nano-meter precision electronics won't be worth the plastic and metal they're made from, as all the more basic foundation technologies have long since been built on top of, without the regard given to them that is due.
Ian, High Wycombe, Bucks

The best way to learn mental arithmatic is scoring a darts game. Working out the doubles, triples, summing each throw and deducting them from a total gives the brain a decent workout. Figuring out the finish gets division involved. Unfortunately you don't get that with a playstation!
Richard, Bristol, UK

I was in a shop recently and a 10p bag of crisps had been swiped an extra time by mistake (I knew this because the equal number of items bought came to 90p and no item ended in 5p i.e not 80p or 1.00) And the teenage girl on the till looked at me as if I was a 14th Century Wizard denouncing Christianity! She was stunned and couldn't work out WHY I was challenging the computer! She couldn't add the items up - so her manager was called and after they both tried - they just gave me the 10p as if I was cheating them.
Hurst Vanrooj, Sheffield


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