The Bit

The key to the digital age is also the key to learning algebra.

Despite what many of us may believe, our digital age did not began with the microprocessor, or the personal computer, or even the iPhone; it began with a single amazingly simple idea by a quiet man who few of us would today recognize. Claude Shannon grew up in Minnesota when radio was becoming the means of communication to all, broad cast. It was the age when sound was added to movies, when phonographs and records storing sound became a must in every home, when the first facsimile machines were used to transmit photographs and text, and when everyone could take their own pictures with the Kodak Brownie camera.

Each of these transforming inventions used a different analog means of storing or transmitting data. Analog data is continuous; on a graph it is a line, sometimes smooth, sometimes jagged. All of these inventions had to deal with the problem of noisy data and of separating the noise from the data. This was the problem Claude chose to work on. Before him the common way of dealing with noisy data was to turn up the volume. If the radio static was bad, make it louder. If the picture was muddy, increase its contrast. If the telephone call was hard to understand, yell.

To solve this problem of noisy data both in storage and in transmission, Claude came up with a truly brilliant, surprising, and original idea. Think about all data as digital. Think about it as being broken down into discrete bits, a collection of just 1’s and 0’s. No longer would data be stored or transmitted as a wave like the grooves in a phonograph record, a continuous quantity. In Claude’s new world it would be like atoms, discrete, separate, objects. Bits, the word he chose, came from binary digits; where his “atoms” took two and only two forms. It was transmitted in bits, stored in bits, and processed in the same bits. He then figured out how to find corrupted noisy data, how to minimize it, and how to replace it. When he died at the turn of this century, his vision for data was just becoming an overwhelming reality. Because today, we have the bandwidth, the storage, and the processing power to handle all data digitally, and the processes that make noise no longer a problem we concern ourselves with.

Isn’t it time our schools deal with its noise problem by becoming digital and focusing on discrete data? Today’s “analog” continuous variable algebra makes the concept of variable abstract and difficult for many students to understand. It requires students to learn a complex set of special cases to solve abstract equations. It turns algebra into collection of mechanical processes focused on cases that are easy to solve. What if we were to follow Claude Shannon’s lead and treat variables as discrete, digital quantities? Spreadsheets make this easy. Variables become concrete, easy to understand, iterate, build into functions, and use those functions to build models. They give us the means to focus on real, messy, interesting data to solve fascinating problems.

Try this new way of thinking for yourself. Go to our Tour to see apply the digital world to algebra. Try it with your students. Tell us what you think.

Art

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