Iteration

Overview

Iteration is a process of calculation that is repeated again and again, each time improving the accuracy of the result by using the output of each step for the input of the next iteration. By repeating the process and analyzing successes and errors, humans and even some machines can improve at performing the action.

Fundamental Mathematical Concepts and Terms

An example of problem solving by the process of iteration could be found in the following set of computer programming instructions: "While a number is less than 15, continue printing that number but increase its value by one. Upon arriving at the number 15, activate the programmed screensaver." These instructions could well relate to the set up of a screensaver to come on after a computer screen was been inactive for 15 minutes.

Let's look at the nuts and bolts of the above set of instructions in a bit more detail. If the starting number was two, for example, it would be less than 15, and so the statement would be judged as being true (i.e. less than 15). That would be a signal to go through the process again, and again, until the number was 14. At that point the number plus one would no longer be less than 15. That would be the signal for the computer to switch to another set of instructions that activates the screen saver.

Real-life Applications

ITERATION AND SPORTS

You do not have to be a big basketball fan, or even have much of a knowledge of the game, to recognize the name Michael Jordan. Michael Jordan was an aweinspiring basketball player. One big reason was talent, but another was iteration. A particularly relevant example of this process was Jordan's routine at the end of each practice. Jordan would shoot the basketball at the hoop from various locations, near to the basket and further away. His practice was not over until he sank 100 shots in a row. If he made 92 baskets and missed one, he would start over again. This routine, which must have been frustrating on a less-than-accurate day, is analogous to mathematical iteration. By performing the action over and over again, using the results of each shot to refine the performance of the next shot, Jordan fine-tuned a technique that predictably put the ball through the hoop.

Similarly, Tiger Woods has used thousands of hours of golf practice to perfect a golf swing that is consistent from one day to the next. This consistency propelled him to become the number one ranked golfer in the world in 2003.

But even the best golfer in the world likes to tinker with his swing, to try out slightly different changes in hopes of producing a swing that is even better than before. That is the essence of iteration. By repeating an action again and again, changes can be evaluated and, if they are successful, can be incorporated into the action.

ITERATION AND BUSINESS

Not surprisingly, iteration is a favorite buzzword of computer programmers. Computer programmers often make available trial software programs on the Internet, called beta versions. Beta programs are a form of practice versions of a new program. Usually this iteration of a program has more features built in that presumably will make people want to buy it and use it instead of the current version of the program. The purpose of a beta version program is to encourage people to try the software, figure out its good points and, most importantly, discover what needs changing or what does not work. The software programmers can then change the beta version to produce the final improved program that is widely sold.

In another business application, iteration is an important feature of accomplishing a project that involves a large team of people. Again, in the realm of computing, an ideal example of iteration involves extreme programming, or XP. Like an extreme sport, XP is a difficult-to-accomplish form of programming that often involves dozens of programmers. These programs are updated frequently and made available much more often than, for example, a program for a video game that might be updated once every three or four years.

In the XP iteration process, the total project is usually broken into chunks. Each chunk can have a back-and-forth process where the component of the program is written, tested, and returned for tinkering. A tight schedule allows the iteration process for each chunk of the project to be accomplished by a deadline, so that all the chunks can be put together to produce the final product. As well, the back-and-forth contact between people that is part of this type of iteration allows for better tracking of minute details in the frenzy of the project.

ITERATION AND CREATIVITY

Creativity involves the ability to look at something in a different way, to find a new idea. A necessary part of creative thinking is gathering information, and then trying to put that information together in a new way. This is where

iteration comes in. New product ideas come to the forefront after cycles of inventing a design, testing the design, and, as usually happens, discovering and fixing problems.

Iteration in creative product design can be illustrated by considering a new CD from a popular music group. The tracks on the CD do not usually happen in one recording session in the studio. When the band first starts to record a song, the musicians, songwriters, and producer may have different ideas of what the final version will sound like. Different versions (iterations) of the song are tried out, discussed, and changed until the artist is pleased with the final version. The final track that is heard on the CD is often very different from what a band member thought it sound like months before.

People who are known for their creative approach to their work often say that the process they use to come up with all those great ideas is very structured. They take the same approach to each problem, knowing that doing the steps in much the same order (there has to some flexibility in how things are done) helps their mind get ready to think. In other words, their whole approach to being creative involves iteration. Similar actions are repeated.

ITERATION AND COMPUTERS

In a computer program, iteration is the recycling of a set of instructions, known as looping. A single iteration is one pass of the instructions. Once the set of instructions has been written, a computer will quickly pass through the loop over and over again without making mistakes (unlike humans).

Another real-world example of iteration in computing is a macro. A macro is the putting together of a series of commands that responds to one signal (like the pressing of a designated key on the keyboard). Macros are not necessary to do work on a computer, but they make time go more quickly. Instead of typing in the same commands over and over, this iteration is taken care of by the one action of pressing that designated key.

Iteration and Nature

In nature, repeating patterns are common. From the spirals of a seashell to the icy beauty of a snowflake, to the many hexagons of the honeycomb of a beehive, a basic unit is repeated again and again to produce the final structure. This repeat of the basic unit is iteration.

A cutting-edge example of iteration in the laboratory is molecular cloning. Molecular cloning involves creating a genetic twin from the genetic material obtained from a living creature. Experiments in plants and animals have shown that scientists have not yet perfected the cloning process. When they do, then cloning will be a living example of iteration. Whether this form of iteration is desirable or not is being debated at the present time.