We are taught that if at first we don’t succeed, we should try, try again. This proverb embraces the power of iteration, the act of repeating a process. A repeated process can accumulate change over time- either progress towards solving a problem, or physical progress as in climbing a mountain one step at a time.

Lao Tzu said, ‘A journey of a thousand miles begins with a single step’. He meant that iteration of single steps can take you a thousand miles.

Darwin introduced his ideas on the origin of species in this way:

‘As many more individuals of each species are born than can possibly survive; and as, consequently, there is a frequently recurring struggle for existence, it follows that any being, if it vary however slightly in any manner profitable to itself, under the complex and sometimes varying conditions of life, will have a better chance of surviving, and thus be naturally selected. From the strong principle of inheritance, any selected variety will tend to propagate its new and modified form.’ [My emphasis]

The complexity of the natural world with its bewildering variety of species defied explanation, because while it’s clear how these things are maintained by reproduction, it’s not clear how each different type first appeared.

Darwin knew that the origin of complexity lay in reproduction as an iterative process– as long as there is variation, mortality, inheritance and lots of time. By understanding the effects of iteration over millions of years, Darwin realized that the first simple living things, as long as they didn’t die out, had no choice but to diversify and evolve into many and diverse types.

The really interesting thing about the controversy stirred up by Darwin is why something that was so obvious to him (and his supporters) was not at all obvious to everyone else. I don’t mean the controversy in the sense of evolution being contrary to religious beliefs– that was inevitable. I mean that the argument against evolution often involved a counter argument that so much complexity could not arise from simple living things by chance alone. Regardless of what actually occurred, the capability of the process of natural selection to generate complexity over time is both undeniable (and can easily be modeled by simple example or realistic computer models) and obvious to anyone who takes the time to read and understand Darwin’s simple explanation of the power of iteration.

The effects of iteration are everywhere, as if hiding in plain sight. Car engines repeatedly turn car wheels. Lifetimes of heartbeats and breaths. Computer central processing units performing billions of calculation cycles a second. The polishing of pebbles being rolled up and down a beach by the action of waves.

Iteration is also the foundation of human learning. The characteristic skills of childhood, walking and talking, are acquired by repeated attempts, honed by parental correction and encouragement. The English language has several words for iterative learning: drill; experience; nag; practice; rote; rehearse; repetition; train. Iteration is vital because so many apparently ‘basic’ units of human learning are actually highly complex processes- making a step or saying a word are both extremely delicate dances by many muscles acting in precise choreography. No matter how efficient the brain is at observing and processing the incoming information, it’s impossible for it to coordinate the necessary commands to do all these things in one go, the first time. It has to observe, attempt an approximation, modify the first attempt, repeat, modify, repeat until the skill or knowledge is learnt.

Curiously, the nature of learning by iteration necessarily plays down its own importance. Personally, I can’t remember being able to walk badly; I can’t remember struggling to speak; and the best way I can appreciate what it’s like to not be able to play tennis is to try to play with my left hand. In order to improve by iteration, you need to emphasize in your memory the latest or most successful attempt and discard previous attempts. I don’t know whether this is reflected in the reality of how the brain works, but it certainly feels like I naturally forget the bulk of learning iterations and remember only the most recent- as if there is only one pigeonhole for that learning and the latest attempt fills the pigeonhole at the expense of the last. It feels like any skill or kowledge, be it walking or talking or solving quadratic equations, is something I’ve learnt in one go even though I know that I have actually done those things many times. Learning seems to leave no fossil record of previous understandings in our brain.

It is of course entirely possible to learn things in one go. Our responses to near death situations were honed from brushes with predators in our deep prehistory. Nowadays if we cross the road without looking and narrowly avoid being hit by a car, we experience such a moment of fear that we never forget the incident and are much more likely to take care in the future.

In normal, non-emergency situations, learning is less simple. I think it’s fair to say that repetition gives an opportunity to reinforce learning in most situations, and that the lack of repetition makes it more difficult to learn well.

I believe many modern educational regimes, especially those emphasizing personalized learning, heavy use of ICT, and directed learning paths reduce the opportunity for students to receive iterative learning. One GCSE ICT course, for example, is assessed by means of coursework undertaken in ICT suites, where the assessment is of printed screenshots prepared by students while carrying out tasks demonstrated by the teacher. So, the ability to send an email to someone, to use cc, attach documents to the email, reply and forward are proven to the examination board by means of screenshots of single instances of these activities. Since there is no testing of the context in which any of these uses of an email is required, nor any need for the student to choose and use these features in a real world example, nor any requirement for the student to perform these tasks more than once, the qualification is really only proof that the student was able to carry out single tasks under the supervision of a teacher. In contrast, the traditional teaching of arithmetic requires students to perform calculations of each required type many times, using different numbers, and in different contexts; and the students are tested in entirely novel situations in which they have to choose the types of calculation they use and apply them correctly.

Automation and simplification of student syllabuses and assessments have many subtle effects on end results. The showing of a video may well be able to explain a topic clearly and simply, yet the one-way, one-time flow of information may well teach differently to a teacher explaining the same topic directly to the class with more class involvement and practice.

I believe that as education is radically transformed in the 21^st century, care must be taken to examine the loss of iterative learning– often dismissed as ‘rote’ and ‘old fashioned’– from the syllabus.

Information can certainly be found quickly on the internet for copying and pasting into a document. On the other hand, traditional repeated interactions with books, finding and sifting related information, précising and writing by hand may have encouraged different types of learning that occurred invisibly alongside the direct acquisition of a particular piece of information. While a sum can easily be done on a calculator, mental agility and internal understanding of number systems may be better improved by the need to memorize times tables and estimate results on the way to calculating sums by traditional methods.

It’s difficult to create shortcuts to learning physical skills. That’s why drills and practice are still commonplace in music, drama and PE. It’s commonplace to hear teachers of these subjects tell their students that there is no substitute for hard work and practice. Art courses still not only use iteration, but are judged by students showing evidence of iterative progression in coursework. It’s therefore a little surprising to find educators in other subjects more willing to discard iterative practices, as if there actually are substitutes for hard work and practice.

Children are instinctively aware of the power of iteration, and use it almost as a default technique to achieve their objectives. In an episode of the TV animated series The Simpsons, Bart orders a toy spy camera, which takes a long time to arrive in the post. Every day he waits at the door for the postwoman and pesters her: ‘Where’s my spy camera?’ After many repetitions, the box finally arrives and the frustrated postwoman throws the package at Bart, shouting with relief, ‘Here’s your stupid spy camera!’ The interaction is funny because watching adults immediately recognize the futile but automatic use of the pestering tactic (= iterated request) by Bart, on a completely intractable and un-modifiable process. They also recognize with possibly subconscious discomfort that the arrival of the camera inevitably rewards and reinforces Bart’s pestering behaviour.

Children effortlessly use iteration to learn and perfect their skills at computer games and mobile phone texting. Marketing campaigns routinely target child audiences in order to increase sales of products to adults, because ‘pester power’ is such an effective motivation for parents.

Educators are often confronted with children who are unwilling to perform repetitive tasks. The complaint is that it is ‘boring’. I think that is a very interesting area for research, since children are clearly happy to perform many iterative and apparently boring tasks. It may be because the iteration, the hard work and practice, is only willingly undertaken when the target of the work is sufficiently attractive.

In life, at first you usually don’t succeed. We know the life skill that solves this problem. We’ve known it since we were children and our children know it now. Our education system should be structured to reinforce, not bypass, the willingness and ability of students to iterate when appropriate.

Darwin ends his ‘On the Origin of Species’ by describing again the various observations that make evolution inevitable, and then finishes with this wonderful evocation of deep time– the reference to the apparently endlessly repeating days and years that give evolution the time to do its work:

‘There is grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.’

When I ask if anything is wrong, the method I use which is most fun is called Reductio ad absurdum. Wikipedia gives this useful definition:

… a type of logical argument where one assumes a claim for the sake of argument and derives an absurd or ridiculous outcome, and then concludes that the original claim must have been wrong as it led to an absurd result.

Of course, if we make a claim that doesn’t lead to an absurd result, we can often come to interesting and unexpected conclusions.

When I was selling computers in 1988, a typical (Macintosh) specification was 2Mb RAM, 20Mb hard disk and 30Mhz processor speed. Today, a typical low end specification would have about a thousand times more RAM, a thousand times larger storage, and a hundred times more processor speed. Today’s cost would be about a tenth in actual currency, before inflation.

In 1988, the main applications used on the computer would be word processing (with e-mail to follow soon afterwards), spreadsheets, and presentations. These, with web browsing, are still the main applications today, although the greater power of modern computers allow us to handle sound and video as well. Nevertheless, we are now at a point where TV quality video can be handled by computers, and we can store vast numbers of photos and songs as well- in fact this point was probably reached a few years ago. Most of the extra power available in new computers is used to drive new operating systems and applications written in an environment of apparently limitless memory and storage- much of the rigour of ‘old school’ programmers has been lost in the last ten years.

We are still being offered ever more speed, memory and storage, and yet the average user has no requirement for improvement in these areas- for them the ability to archive properly, or to accomplish whatever they want to do is much more important. So- here’s the reductio ad absurdum claim. Manufacturers are now at the point that their R & D has produced more powerful machines than most consumers require, and that therefore they have no intelligible way of marketing these machines in the standard way of identifying problems for which the machines are a solution. The absurd result of this claim is that their marketing would be such complete gibberish that the average consumer would have no way of judging whether the computer they’re about to buy is actually any good to them. Now, all we have to do to disprove the absurd claim is to show that computer marketing material isn’t unintelligible gobbledigook, but actually makes sensible descriptions of the products for sale. Let’s have a look.

HP DX2250 Micro Tower PC / Sempron 3000+ (2.0Ghz) / 1GB RAM / 80GB SATA HDD / DVD ROM / Win XP Pro / MS Office Ready / 1-1-1 Wtny

The HP Compaq dx2250 Microtower PC offers essential features and power efficient AMD technology to help deliver reliability and performance for basic business requirements to help your business run more effectively. Industry standard features and proven technology from AMD and ATI exceed basic business requirements, ensure reliability, and help lower overall cost of ownership by helping to increase power efficiency and productivity.

A full-featured, affordable computer, the dx2250 features the latest industry-standard parts and components, and offers a large and varied range of certified PC upgrades and options to help optimize business computing. With simplified set-up and use, this compact microtower offers convenient audio ports for greater flexibility, front USB 2.0 ports, and optional 16-in-1 media reader for quick access to digital files help provide out-of-box productivity.

A quality product engineered to deliver a low total cost of ownership, HP provides consistent system improvements in quality, and leads in lower than industry standard hardware failure rates – bringing peace of mind to business computing. Quick and easy access to experts you can trust and personal assistance through the channel you prefer throughout the lifecycle, from acquisition to transition, providing the freedom to focus on what matters to your business success.

Features
AMD Sempron 3000+ Processor Technology
1GB DDR2 RAM / 80GB Hard Disc Drive
DVD-ROM
Microsoft Windows XP Professional
Microsoft Office 2007 Ready 60 Day try before you buy         

I don’t know- is it really absurd? Well, the marketing copy isn’t completely unintelligible, but it certainly isn’t plain English, and it doesn’t make much reference to the real everyday functionality of computers. Could it be that computer development is now completely out of step with the requirements of consumers? Cars are equally complex pieces of technology, marketed at much the same people. Here’s an introduction to the Fiesta from the Ford website:

The latest Fiesta range features striking new exterior styling, with a fresh, bold look thanks to distinctive new headlights. Inside, a wide choice of stylish new trims and fabrics gives the cabin a spacious, sophisticated feel. Impressive high-tech options include Bluetooth®, satellite navigation and voice control.

Everywhere in the Ford site, the English is of that standard of clarity. Is it absurd to think that cars actually have selling points worth communicating, but computers do not? Later posts will apply Reductio ad absurdum to computers more specifically in a school context.