The Polymath's Calculator

The polymath’s calculator

This was what is called a pinwheel calculator for the four basic arithmetic operations, which could be used to enter up to 8-digit numbers and display up to 16-digit results.

The earliest ancestor of the present-day computer, and so also of the programs that run on it, is a calculating machine which the polymath Gottfried Wilhelm Leibniz had built in Hannover between 1685 and 1690, after extensive theoretical study.

This was what is called a pinwheel calculator for the four basic arithmetic operations, which could be used to enter up to 8-digit numbers and display up to 16-digit results. Even before that, the scientist had developed the principle of binary machine language: his calculating machines were controlled only by 0 and 1.

True or false: 0 or 1

Leibniz is to Computer Science what Bach is to music,” declares Dr Manuel Bachmann, a researcher at the University of Basel and lecturer at the University of Lucerne, in his book “The triumph of the algorithm – how the idea of software was invented.” The binary or dual system, in which first all numbers and then all information in general can be written down using only the numbers 0 and 1, has the advantage of logical clarity: 0 and 1 stand simply for true and false.

What Leibniz could not have known is that his numerical system also has the advantage of being technically easy to implement. That’s because many electronic components have just two stable states and can easily be switched from one to the other by an electrical impulse. Multiplication and division are also particularly easy to perform in a binary system. Instead of representing the ten digits of the digital system by, for example, different voltages of 0, 1, 2 …9 volts, it is technically far easier and more reliable simply to distinguish between the states “voltage” and “no voltage”.

Failure to find a universal algorithm

However, Leibniz’s ambition went further: he wanted to formulate a universal algorithm for thought which would generate new and true sentences.

A logical creative method, universal knowledge and a formulation system, all in one,” is how Bachmann sums it up. In this context, the mathematician and philosopher was even interested in how games of chance work. He believed that people are never more inventive than when they are playing games.

Even though Gottfried Wilhelm Leibniz first addressed this subject in his doctoral thesis at the age of 20, and later wrote numerous draft concepts, definitions and proposals about it, he never fully got to the bottom of his idea before his death in 1716. “The problem was too ambiguous for Leibniz to have been able to reach a conclusion that satisfied him,” writes Bachmann, describing the dilemma of the polymath, who apparently said: “I wake up every morning with so many new ideas that even the longest of days would not be sufficient for me to write them all down.”

Nevertheless, with his work he created a basis which was further refined by his students and subsequent generations, who built on it in a kind of “epistemic recycling” to create something new in the long history of the algorithm.

*BINARY NUMERAL SYSTEM – “Gottfried Wilhelm Leibniz “De Dyadicis” Signature LH XXXV, III B 1, Bl. 1-4

Articles on Innovation

  • From Ada to Zuse: the computer has many mothers and fathers15.03.2018.
    Articles on Innovation

    From Ada to Zuse: the computer has many mothers and fathers

    However, many more years went by before the first real mainframe computers saw the light of day, and the final breakthrough had many mothers and fathers.

  • Artificial intelligence15.03.2018.
    Articles on Innovation

    Screw up your eyes and examine any lack of clarity

    The only identifiable principle in the over 2000-year history of the development of computer programs is: “Screw up your eyes and examine any lack of clarity in existing ideas to see if there is any as yet unrecognised potential for making them more precise.”

  • Computer Pioneers in Switzerland15.03.2018.
    Articles on Innovation

    Computer pioneers in Switzerland

    Information science in Switzerland owes its birth and early growth primarily to the farsightedness and drive of the Professor of Mathematics, Eduard Stiefel.

  • Basis For the First Programming Languages15.03.2018.
    Articles on Innovation

    Basis for the first programming languages

    “All Cretans are liars,” said the Cretan Epimenides. Is the statement by Epimenides true or false?

  • The concept of the algorithm15.03.2018.
    Articles on Innovation

    The concept of the algorithm

    Although nowadays algorithms are primarily associated with software and computers, their origins lie much further in the past.

  • Wheel Innovation15.03.2018.
    Articles on Innovation

    Innovation doesn’t happen by chance

    Even though in the history of science there have been some spectacular discoveries made by chance from time to time – from penicillin to Teflon to Viagra – these tend to be the exception.

  • Book15.03.2018.
    Articles on Innovation

    How new things come about

    The source of innovation is “epistemic” recycling. This is a term from psychology and denotes the kind of curiosity that is directed at delivering more information to the organism and enabling it to acquire new knowledge.

  • How Software Was Born15.03.2018.
    Articles on Innovation

    How software was born

    In order to compete with the German encryption machine “Enigma”, just a few weeks after arriving at Bletchley Park Turing ordered a machine to be constructed – the hardware.