First Application of Boolean Algebra

When we think of Boolean algebra (the maths of dealing with TRUE and FALSE, the operations of AND, OR, NOT), we think of it as only being relevant to the way digital computers work. And yet the first application of Boolean algebra wasn’t to do with computers at all! Here is that story from Jimmy Soni and Rob Goodman’s biography of Claude Shannon (the founder of Information Theory) titled A Mind at Play.

When Shannon was a student at MIT, he was studying electrical circuits:

1)      A switch could be used to turn on or off the current;

2)     Arranging the circuit elements in different ways allowed for current to flow only when, say, two switches were On, but not if zero, one or three switches were On.

But designing such circuits was an art in those days, not a science, “with all the mess and false-starting and indefinable intuition that “art” implies”.

Shannon also learnt Boolean algebra, the algebra from over a century earlier:

“(Boolean algebra) was taught to generations of students mainly as a philosopher’s curiosity.”

It had no practical application at that time.

Until, that is, Shannon connected the dots of Boolean algebra with the problem of designing electrical circuits. It was a “leap from logic to symbols to circuits”. In his master’s thesis in 1937, he wrote:

“Any circuit is represented by a set of equations, the terms of the equations corresponding to the various relays and switches of the circuit.”

And conversely:

“The circuit may then be immediately drawn from the equation.”

That last part was what transformed the design of circuits from an art form to a science.

What was even more useful to engineers (and companies)was that applying the rules of Boolean algebra on (some) circuit equations allowed one to combine the terms to come up with a simpler equation that had fewer items and fewer operators (AND, OR, NOT) in it. For example, the circuit defined by:

x’y’z + x’yz + xy’z + xyz’ + xyz

could be reduced by applying the rules of Boolean algebra to just:

xy + z

The revised, simplified equation could be translated back into a circuit, which by the rules of Boolean algebra, was functionally equivalent to the original circuit! It was a reduction in that example from 11 connections to just 2. Which meant price saving and ease of maintenance.

Of even greater importance in the long run was the beauty of his system:

“As soon as switches are reduced to symbols, the switches no longer matter. The system could work in any medium, from clunky switches to microscopic arrays of molecules.”

And how did Shannon remember this for-all-time methodology?

“I think I had more fun doing that than anything else in my life.”