Johann Helfrich von Müller

Primera Máquina diferencial, ideada por el militar, arquitecto e inventor alemán Johann Helfrich von Müller


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Máquina diferencial

Wikipedia (20130604)

"Una máquina diferencial es una calculadora mecánica de propósito especial, diseñada para calcular funciones polinómicas. Puesto que las funciones logarítmicas y trigonométricas pueden ser aproximadas por polinomios, esta máquina es más general de lo que parece al principio.


Esta máquina fue ideada por el militar, arquitecto e inventor alemán Johann Helfrich von Müller[1] y redescubierta por el matemático británico Charles Babbage, ninguno de los cuales llegó a construirla."

1 «Biography of Thomas Müller». History of Computers. Consultado el 15 de enero de 2015.



Difference engine

Wikipedia (20130604)

A difference engine is an automatic mechanical calculator designed to tabulate polynomial functions. The name derives from the method of divided differences, a way to interpolate or tabulate functions by using a small set of polynomial coefficients. Both logarithmic and trigonometric functions, functions commonly used by both navigators and scientists, can be approximated by polynomials, so a difference engine can compute many useful sets of numbers.

The historical difficulty in producing error free tables by teams of mathematicians and human "computers" spurred Charles Babbage's desire to build a mechanism to automate the process.


J. H. Müller, an engineer in the Hessian army, conceived of the idea of a difference machine. This was described in a book published in 1786, but Müller was unable to obtain funding to progress with the idea




"The German engineer and master builder—Johann Helfrich Müller (1746-1830) (see biography of Johann Müller) is a very interesting figure in the world of mechanic calculators, not only for his small calculator, an improved version of the machine of Philipp Hahn, which he created, but for his plans to build a difference engine almost 40 years before Charles Babbage. He also wanted to built a machine, that was capable of being configured to use Leibnitz's arithmetica dyadica.


…. in a book published in Frankfurt and Mainz in 1786. This 50 page booklet was edited by Müller's friend Philipp Engel Klipstein…

… under the heading "Further inventions of superior calculating machines and an arithmetical printing machine" …. In these passages, it is made clear that Müller, perhaps at an even earlier date, had invented a difference engine (to operate to the third order of difference) for the rapid production of error-free tables, by means of "whole series of numbers" and by using "difference-numbers" (Differenzzahlen). A description similar to that in the postscript to Lichtenberg is given of the printing part, which was supposed to print directly onto paper, rather than produce matrices for stereotypes. No mention is made of how the necessary mechanisms to accomplish this were to be designed. Nonetheless it is clear from this document that Johann Müller had conceived the idea of a difference engine by the year 1786. Such a machine will be proposed almost 40 years later by Charles Babbage (see the differential engine of Babbage). It is known that several chapters of the book have been translated for Charles Babbage by John Hershel. However, the date of this translation is unknown and the question remains whether some of Müller's ideas have been used for Babbage's machines"

The calculating machines of Johann Helfrich Müller