Torres Quevedo pioneered analog calculators that could solve complex equations.
Leonardo Torres Quevedo presented his electromechanical arithmometer in Paris in 1920, to celebrate the centenary of Thomas de Colmar's arithmometer.
The machine was one of Torres Quevedo's greatest contributions to the scientific community.
In the words of Leonardo himself, "My apparatus is based on the same principles as that of Thomas de Colmar, but it works in an entirely different way. In mine, all of the movements are automatic and, today, I am going to talk to you about how they are automated."
The final version of the report was published in Bilbao in June 1895, while he worked on the first model of a calculating machine.
The image shows the published report in the Public Works Journal.
Torres Quevedo's work on analog machines meant that his report, "Calculating Machines," was well-received by the Paris Academy of Sciences in 1900.
As a result, in 1901 he became a member of the Academy of Sciences in Madrid, where he gave a speech on algebraic machines.
Torres Quevedo's writings ushered in a new era in mathematical theory based on new concepts. His contributions led to the development of innovative new machines.
He built a series of analog calculating machines to complement his theoretical work, all of which were mechanical.
Torres Quevedo's theoretical ideas and inventions were based on kinematics, establishing relationships between the values of particular movements. The machine established the mathematical formulae that connect these variables.
The machine that can calculate polynomial roots is now one of the Torres Quevedo Museum's most important objects.
As the first machine to solve equations, it allowed the user to find the roots of quadratic equations involving real and complex numbers. It could be used to solve any quadratic equation.
The device works by generating a series of values, both integer and rational, for which a polynomial function is continuously reevaluated as the variable is increased or decreased.
This device finds the numerical values of the roots of an 8-degree polynomial. Its development started in 1910 and finished in 1920, and its success is proof of the persistence and genius of Torres-Quevedo.
The goal to be achieved with the device was obtaining values of a polynomial in a continuous and automatic way. Since the mechanism is analog, and not digital, it can take any value, without jumps between discrete values.
It shows two important improvements over what existed up to date: using a logarithmic scale, thus reducing to additions the evaluation of monomial expressions, and the use of the "husillos sin fin" or endless spindles, invented by Torres-Quevedo.
Diagram of the machine's relay circuits and the equations that it solves.
In a polynomial equation, the wheels representing the unknown quantity spin round and the values of the sum of the variables are given as a final result.
When this sum coincides with the value of the second member, the wheel of the unknown quantity shows a root.
View from above of the wheels that spin to give the root results, using endless spindles.
Thanks to his theories on automation and machines, Torres Quevedo was able to overcome the difficulties of creating machines that carried out calculations using exclusively mechanical methods.
This automaton is part of the calculating machine.
Torres-Quevedo introduced the simultaneous use of electricity and mechanics, which was a complete innovation in the development of calculating devices.
Detail of 2 sections from a drawing of the calculating machine.
The later development of electronics made it possible to build machines with features such as those proposed by him.
Detail of the interior sections of the calculating machine.
The endless spindle was a fundamental part of the calculation machine that could solve 8-term equations. It generated sums to solve the core equation of the algorithm. It was the most interesting and original of Torres Quevedo's inventions, and its mechanism was the first of its kind.
Torres Quevedo's calculating machine represented a significant theoretical and practical breakthrough. The endless spindle is a mechanical device that evaluates the logarithm of an expression as the sum of several logarithms, thus solving the problem of achieving enough precision with a mechanical set of parts.
The problem log(u + v) = log(u/v + 1) = log v + log(u/v + 1) is resolved, from a mechanical point of view, using 2 wheels whose angular movements are linked by way of a curve and its asymptotes.
This invention was so important that the endless spindle appears in the portrait that Joaquín Sorolla painted of Torres Quevedo in 1917.
In 1911, having already begun working on his electromechanical calculating machines, he presented his report "Mechanical Construction of the Relationship Expressed in the Formula y' = dy/dx" to the Academy of Sciences in Paris.
In this report, he presented a new machine: the integrator. It was further clear evidence of his superb imagination.
As well as carrying out calculations using the formula y' = dy/dx, the integrator produced a drawing of the result.
Torres Quevedo came to the conclusion that a machine could work independently, carrying out actions, and responding to orders and its surroundings. He applied this concept in the development of his calculating machines.
In his "Essays on Automation," he set out the theory behind what would become his arithmometers: electromechanical machines capable of carrying out calculations independently.
In this text, Torres Quevedo explores the idea of a machine that works sequentially to carry out calculations and floating-point arithmetic, enabling it to handle very large numbers.
His invention of a digital calculator made him a pioneer of automation as we understand it today.
An arithmometer was a device capable of recording numerical values, completing different processes, carrying out any calculations, printing the results, and confirming when it was finished.
With the arithmometers, Torres-Quevedo introduced new original automatic mechanical devices.
His greatest contribution, in terms of originality and novelty, was to conceive the device in such a way that it was capable of calculating and comparing without human interaction.
As Santesmases has said, “he was the first to succeed in developing an automaton which compared numbers with several figures”.
These arithmometers used a type writer as an input device.
The processing and registering unit is achieved by a system using slats, pulleys, needles, pointers, brushes, electromagnets and switches.
Detail of the inside of the processing unit.
The output device - also a typewriter - was a spectacular innovation that (as early as 1920) was the precursor to modern-day computers.
Torres Quevedo Museum (Madrid)
School of Civil Engineering
Technical University of Madrid (UPM)
Director: Francisco Javier Martín Carrasco
Secretary: Felipe Gabaldón Castillo
Museum Manager: Manuel G. Romana
Editing: Miriam Guerrero Pérez
Texts: Miriam Guerrero Pérez and Consuelo Durán Cermeño
Advisors: Francisco González Redondo, Antonio López Vega, and María Pascual Nicolás
Documentation: Manuel Romana García, Consuelo Durán Cermeño, Miriam Guerrero Pérez
Image Sources: Museum collection, Francisco González Redondo Collection, Manuel Romana Collection, National Newspaper Library, Public Works Journal, Sorolla Museum
Video Source: YouTube