My son, a mathematician at the University of Louisville, has a new hobby: restoring mechanical calculators. These machines were obsolete long before he was born, but a visit this past weekend brought back a wave of nostalgia. I was a student just before the advent of electronic desktop calculators (the ubiquitous personal calculators came along a few years later) and I spent a substantial part of my life doing statistical analysis on a mechanical calculator and a spreadsheet, which in those days was a ledger-sized sheet of ruled paper.

Mechanical calculators were conceptually simple and mechanically extremely complex. They were basically glorified adding machines which did multiplication as repeated addition and division as repeated subtraction. On the early manual machines, to multiply, say 135 by 25, would enter a number to be multiplied from the keyboard or by rotating pinwheels. You would then turn the crank 5 times, move the carriage one place to the right, and turn the crank twice. The answer would appear in the accumulator register. Division was a bit more complicated, but was basically the same process in reverse and could be carried out to as many decimal places as you had digits in the register. Later models replaced the crank with an electric motor and moved the carriage automatically. The last generation of Friden mechanical calculators had a square root function built in, an enormous benefit in stat work, which requires computing lots of square roots.

These calculators made a marvelous noise–motors whirring, gears meshing, bells ringing. The stat labs at the University of Michigan where I would were big rooms filled with dozens of machines, all going at once, making a glorious racket. The space at the Rackham graduate school included a plugboard-programmed IBM accounting machine (ancient even then), a counter-sorter, and a printer, and when everything was running at once, it sounded more like a stamping plant than a lab.

Mechanical calculators were painfully slow by electronic standards and needed lots of maintenance (those levers in the photo of the Friden, top, represent the complex mechanical logic of the machine.) It was generally a blessing when they were replace by electronic calculators and, ultimately, by software such as Mathematica, Maple, Matlab, and Sage.

But those wonderful old machines created a intimacy between analyst and data that doesn’t exist anymore. So I am happy that some in the younger generation are willing to do the work of restoring these beauties.

(Jake recently acquired a Curta, the Ferrari of crank-operated calculators. It looks a bit like an slightly oversized peppermill, if Swiss watchmakers made peppermills. Plus, there’s the amazing story of its inventor, Curt Herzstark, who designed the machine while a prisoner in the Buchenwald concentration camp. And the Curta is proudly marked “Made in Liechtenstein,” possibly the only industrial export of that postage stamp-sized coiuntry (which, of course, issued a postage stamp to honor the device.)

Looking at the photo I can’t imagine how those mechanical calculators were ever designed and built.

The key to their logic is a carry flag, inmost cases a pin that pops out to indicate that an addition has overflowed (or a subtraction underflowed), requiring an adjustment of the next decimal place. Pin-wheel calculators are significantly simpler than keyboard models. But mechanical logic is a lot more complex than its digital equivalent.

This is when being a “technology veteran” really pays off ;-). Fascinating snippet about the Pre-digital world. Thanks. Plus it makes an over-40 feel young!

I wonder if the inventors also concluded that no ordinary person would need one of these for the home?

Joe

They were too expensive for most consumers to consider. And they required significant real estate on a desk.

I read your column for those 15 years and am fortunate to know Jake. I am not surprised to see him undertaking this fascinating project. He is always one of the most interesting folks I have the pleasure of having a conversation with.

I’m rather fond of him myself.