Retrotechtacular: Pascal Got Frustrated At Tax Time, Too

While necessity is frequently the mother of invention, annoyance often comes into play as well. This was the case with [Blaise Pascal], who as a teenager was tasked with helping his father calculate the taxes owed by the citizens of Rouen, France. [Pascal] tired of moving the beads back and forth on his abacus and was sure that there was some easier way of counting all those livres, sols, and deniers. In the early 1640s, he devised a mechanical calculator that would come to be known by various names: Pascal’s calculator, arithmetic machine, and eventually, Pascaline.

The instrument is made up of input dials that are connected to output drums through a series of gears. Each digit of a number is entered on its own input dial. This is done by inserting a stylus between two spokes and turning the dial clockwise toward a metal stop, a bit like dialing on a rotary phone. The output is shown in a row of small windows across the top of the machine. Pascal made some fifty different prototypes of the Pascaline before he turned his focus toward philosophy. Some have more dials and corresponding output wheels than others, but the operation and mechanics are largely the same throughout the variations.

Operation of the Pascaline is quite elegant in its simplicity. For example, in order to add 3 and 5, one would insert the stylus between the ‘3’ spokes and turn the dial clockwise until encountering the stop. At this point, the display would read ‘3’. To add five to it, the process is repeated on the same dial by placing the stylus between the ‘5’ spokes and turning clockwise until the stop is reached. This adds five to the accumulator, and the output now reads ‘8’. Before performing a new calculation, the outputs must all be cleared. This is done by setting all of the input wheels to their highest digit, the spokes of which are marked with small slots. Once this is done, entering ‘1’ on the one’s place dial causes all of the accumulators to roll over to zero.

The Pascaline simulator shown in the video has simplified input dials. The actual surviving models show inputs that corresponded with the currency divisions of the time period. The French livre, which equaled one pound of silver, was subdivided into 20 sols. Each sol comprised 12 deniers, the smallest unit. To handle the arithmetic carry operation, each input dial connects to a 10:1 accumulator on the output drum. That is, when input exceeds nine (or in the historical case, 19 sols or 11 deniers), the output drum in the next place advances by one and the input drum resets to zero.

This four-banger in a brass chassis really only performed addition and should probably be called an adding machine. Subtraction is done using nine’s complement arithmetic. Each of the output drums has two sets of digits. Zero through nine appear on the bottom, and the nine’s complement of each digit appears in line above it. For the subtraction operations, a sliding bar is pushed down to reveal the nine’s complement digits on the output drums. Much like the Curta mechanical calculator we covered a few months ago, the Pascaline performs multiplication and division through repeated addition and subtraction operations.

Pascal’s machine was arguably both the first mechanical calculator and the first piece of office technology. It was a remarkable advancement whose carry mechanisms live on in odometers, gas meters, and much more. However, the Pascaline was a fragile creation that was prone to jamming and unintended carry operations. As Pascal himself was the only certified repair technician, it was also somewhat cost-ineffective. A more robust Pascaline could be made out of, say, LEGO.

Retrotechtacular is a weekly column featuring hacks, technology, and kitsch from ages of yore. Help keep it fresh by sending in your ideas for future installments.

13 thoughts on “Retrotechtacular: Pascal Got Frustrated At Tax Time, Too

    1. You are right Rob.

      Pascal certainly led the way for valve then silicon computers of today
      by discovering his mechanical computing machines the 16th century.

      Still, there was equally clever machines earlier than 16th century,
      in the remote case you did not know, I present you:

      (Kristina, is the issue worth a hackaday retrotechtachular of its own ?)

      1. Respectfully unless there’s evidence that the creators of the first modern computers where aware of Pascal’s machine and built on it, it has to be false it effected modern computers. For some reason man has to dismiss modern achievements . In that vein we should also dismiss Pascal’s machine because of the existence of this Grecian device, even if we don’t have evidence if he was aware of it or not. Sorry just a peeve I have, not meant to distract from Pascal. Although I think an experience person could calculate faster using slate and chalk, if paper was affordable there would be record of the calculations.

        1. We should differentiate between analog & digital mechanisms, look at Pascal’s machine and ask yourself why he didn’t he simply use gears for the carry operation making additions and subtractions without all the complication he has done.
          The goal of his more complicated engine, is to avoid bad readable output (like 2 numbers in the same spot), see my post below, making calculations faster and less prone to misreading.
          I call this digital mechanism where the Antikythera (and others) are analog one.

          1. An analog computing machine could have been a device with wheels linked with belts that does not compute something useful.
            The Antikythera mechanism was made of gears designed to compute positions of stars and viewer at specific times. That output was more than useful to people on ships at that time. All that worked because of well designed gears advancing next stages etc.
            The dial displaying output was very specific rather than analog quantities.
            The British researcher stated that if this knowledge was not lost for more than a millenium, human kind would have advanced more than imaginable.
            As for Pascal (moving towards Turing’s work), his work was well known and not lost.

  1. What I find most interesting, is the way that this mechanics “schmitt trigger” numbers, p.ex. it’s either 4 or 5 you can enter/display, nothing between, even the carry does only change by 1 whole digit.
    This thing is made to make input easier, Pascal as first UI designer?

Leave a Reply

Please be kind and respectful to help make the comments section excellent. (Comment Policy)

This site uses Akismet to reduce spam. Learn how your comment data is processed.