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# Calculemus!

Celebrating 25 years of celebrating computation

# Inquisitive Computing

Let me be clear about what kind of programming I have in mind. I'm not talking about software development. In software development, the end product is the program itself. The developer builds a web browser, say, or a word processor—a program that others can then put to use. In my kind of programming, the product is not the program but the result of running the program. That result might be a number or a graph or an image; in general, it's an answer to a question. Let's call the whole process inquisitive computing .

The earliest computers were all used in an inquisitive mode. One of those innovative machines was the EDSAC, built at Cambridge University under the direction of Maurice V. Wilkes. On May 6, 1949, a punched paper tape was threaded into the EDSAC's input device, and a few seconds later a nearby teleprinter began typing out the numbers 0, 1, 4, 9, 16, 25, 36, continuing on to 9,801. Clearly, this was computing for answers, although I suppose the Cambridge dons assembled for the demonstration weren't really there to learn the squares of the integers from 0 through 99. A few days later another program generated a table of prime numbers up to 1,021.

If these accomplishments seem trifling, keep in mind that the first EDSAC programs had to take control of the machine at the level of bare metal. There were no operating systems or programming languages. Every step in an algorithm had to be specified in excruciating detail. Merely getting the teletype to print out a number took a dozen instructions.

Over the next decade, the EDSAC had a distinguished career in inquisitive computing. The statistician Ronald A. Fisher used the machine to solve a problem in genetics, quantifying the effect of selective advantage on gene frequency. The Danish astronomer Peter Naur came to Cambridge to calculate orbits of planetoids and comets. Naur was knocked out of his own orbit by this encounter with EDSAC; he left astronomy and became a distinguished theorist of computing. The biologist John Kendrew relied on the EDSAC to analyze x-ray diffraction patterns of the myoglobin molecule, thereby elucidating the three-dimensional structure of the protein.

In the 1970s, the hobbyists who built or bought the first microcomputers faced a predicament much like that of the EDSAC pioneers. The machines came with little or no software. If you wanted to do anything interesting with your new toy, your only option was to write a program. Thus another generation entertained themselves by printing out lists of squares and primes; the ambitious and persistent ones went on to plot the dizzy contours of the Mandelbrot set or to search for patterns in John Horton Conway's game of life.

Inquisitive computing has a less prominent role today, if only because so many other applications of computers have upstaged it. These days, if I suggest that you answer a question by consulting a computer, you would think I meant to go ask Google. Nevertheless, programming for answers is still a living art. In large-scale scientific computing, clusters with hundreds or thousands of processors are put to work modeling the planet's climate and simulating collisions of protons or collisions of galaxies. Studies of proteins have gone far beyond Kendrew's crystallography; computers now try to predict from first principles how the long strand of a protein molecule will fold up into a three-dimensional tangle.

Climate models are a bit too ambitious for most of us. I want to focus on smaller and more casual programming challenges—computational problems or puzzles you might play with for a few minutes or a few days. Here are three examples that involve nothing more than simple arithmetic applied to integers.