Leonardo Torres Quevedo (; 28 December 1852 – 18 December 1936) was a Spanish civil engineer, mathematician, and inventor known for his numerous engineering innovations related to aerial trams, airships, catamarans, and remote control. He was also a pioneer in the fields of computing and robotics, while maintaining an active role in several scientific and cultural institutions. He held prominent positions, such as Seat N of the Real Academia Española (1920–1936) and the presidency of the Spanish Royal Academy of Sciences (1928–1934). In 1927, he became a foreign associate of the French Academy of Sciences.

His first major innovation was an improved cable car system patented in 1887 for the safe transport of passengers, an endeavor that culminated in 1916 with the opening of the Whirlpool Aero Car at Niagara Falls. In the 1890s, Torres focused his efforts on analog computation. He published Sur les machines algébriques (1895) and Machines à calculer (1901), technical studies that earned him recognition in France for his construction of machines capable of solving real and complex roots of polynomials. At the beginning of the 20th century, he made significant aeronautical contributions by developing the non-rigid Astra-Torres airships, whose trilobed structure helped the British and French armies counter Germany's submarine warfare during World War I. These works in dirigible engineering led him to become a key figure in the development of radio control systems in 1901–05 with the Telekino, through which he laid down modern wireless remote-control operation principles.

In 1912, Torres created El Ajedrecista (The Chess Player), an electromagnetic device capable of playing a chess endgame, at the Laboratory of Automatics he had established in Madrid in 1907. He demonstrated that machines could be programmed to follow specified rules and heuristics, contributing to early developments in physical automata and artificial intelligence. Expanding upon the work of Charles Babbage in his 1914 paper Essays on Automatics, he explored theories of thinking machines and designed a special-purpose electromechanical calculator that conceptually foreshadowed floating-point arithmetic. British historian Brian Randell described it as "a fascinating work which well repays reading even today." Torres later demonstrated the feasibility of an electromechanical analytical engine by successfully producing a typewriter-controlled calculating machine in 1920.

Before his retirement in 1930, Torres conceived several other innovative designs, particularly in the field of naval architecture. Among the most notable were the Buque campamento (Camp-Vessel, 1913), a balloon carrier designed to transport airships attached to a mooring mast of his invention, and the Binave (Twin Ship, 1916), a multihull steel vessel featuring flexible structural joints and independent propulsion systems that solved the stability and torsion issues of earlier catamarans. In addition to his interests in engineering, Torres also stood out in the field of letters and was a prominent speaker and supporter of Esperanto.

Early life and education

Torres was born on December 28, 1852, the Day of the Holy Innocents, in Santa Cruz de Iguña, Cantabria, Spain. His father, Luis Torres Vildósola y Urquijo (1818–1891), was a civil engineer in Bilbao, where he worked as a railway engineer. His mother was Valentina Quevedo de la Maza (1825–1891). He had two siblings, Joaquina (b. 1851) and Luis (b. 1855–1923). The family resided mainly in Bilbao, although they also spent long periods at his mother's family home in the Cantabrian mountains. During his childhood, he spent long periods of time away from his parents due to their work trips. Therefore, he was cared for by his father's relatives, the Barrenechea sisters, who declared him heir to their properties, which facilitated his future independence.

He completed his secondary education in Bilbao and moved to Paris in 1868, attending the Christian Brothers' school for two years to further his studies. There, he familiarized himself with French culture, customs, and language, an experience that ultimately benefited his scientific and technical relations with foreign figures and institutions. In 1870, his father was transferred, taking his family to Madrid. The following year, Torres began his higher education at the . He temporarily interrupted his studies in 1873 to enlist as a volunteer, along with his brother Luis, in the defense of Bilbao, which had been besieged by Carlist troops during the Third Carlist War. Once the siege of Bilbao was lifted in 1874, he returned to Madrid and completed his studies in 1876, graduating fourth in his class.

Cableways

thumb|right|Aerial ropeway in [[Mount Ulia (1916), opened in 1907]]

Torres' experimentation in the field of cableways and cable cars began very early during his residence in the town of his birth, Molledo. There, in 1885, he constructed the first cableway to span a depression of some . The cableway was about across and transported a single person who was sitting in a chair hanging from a cable and had another traction cable. The engine used to move the human load was a pair of cows. Later, in 1887, he would build a cableway over the Río León in , much bigger and motorized, but which was intended only for transporting materials. for a cable car with which he achieved a level of safety suitable for transporting people, not just cargo. The patent was extended to other countries: the United States, Austria, Germany, France, the United Kingdom, and Italy. His cable car used a novel multiple-cable support system, in which one end of a cable is anchored to fixed counterweights and the other (via a pulley system) to movable counterweights. With this system, the axial force of the cables is constant and equal to the weight of the counterweight, regardless of the load on the car. What varies with this load is the deflection of the cables, which increases as the counterweight is raised. Therefore, the safety factor of these cables is perfectly known and independent of the car's load. The resulting design is very robust and remains safe in case of a support cable failure.

In April 1889 Torres presented his cableway in Switzerland, a place very interested in this means of transport due to its geography, between Pilatus-Kulm and Pilatus-Klimsenhorn (Mount Pilatus). It was an aerial funicular with a length of 2 km and a gradient of 300 m. In 1890 he traveled to that country to convince different authorities of its construction. He failed to convince the Swiss authorities, who did not grant any reliability to the work of a Spanish engineer due to contemporary skepticism surrounding early aerial transport systems. This disappointment, known as the "Swiss failure", led him to focus on other fields for several years. The journey was 280 meters, with a drop of 28 meters, lasted for just over three minutes, and the gondola had the capacity to board up to 18 people on each trip. The execution of the project was the responsibility of the Bilbao Society of Engineering Studies and Works, which was founded in 1906 by Valentín Gorbeña, one of his closest friends, with the purpose of developing and commercializing Torres' patents. The Ulia aerial ropeway only operated until 1917; however, it paved the way for similar passenger cableways in other countries.

left|thumb|[[Whirlpool Aero Car over the Niagara River in Ontario, Canada]]

The successful result of this type of cable car gave him the opportunity to design the Spanish Aerocar based on J. Enoch Thompson's idea at Niagara Falls in Canada. The cableway of 550 meters in length is an aerial cable car that spans the whirlpool in the Niagara Gorge on the Canadian side. It travels at about . The load per cable via is , with a safety coefficient for the cables of 4.6. and carries 35 standing passengers over a one-kilometre trip. It was constructed between 1914 and 1916. For its construction and assembly, the Niagara Spanish Aerocar Company Limited was set up from the Society of Engineering Studies and Works, with a capital of $110,000 (roughly $ million in ), and a planned concession of 20 years. The construction was directed by Torres' son, Gonzalo Torres Polanco. It completed its first tests on 15 February in 1916 and was officially inaugurated on 8 August, opening to the public the following day. The cableway, with small modifications, runs to this day with no accidents worthy of mention, constituting a popular tourist and cinematic attraction.

The Aero Car is believed to be the sole remaining example of Torres' design for an aerial ferry. Built and operated in Canada, it was a Spanish project from beginning to end: designed by a Spaniard and constructed by a Spanish company with capital from Spain. In 1991, the Niagara Parks Commission received the on the 75th anniversary of the Aero Car, in recognition of its commitment to preserving Torres' design. A plaque, mounted on a boulder in front of Aero Car Gift Shop recalls this fact: International Historic Civil Engineering Site. The Niagara Spanish Aerocar. A tribute to the distinguished Spanish Engineer who designed the Niagara Spanish Aerocar. This was only one of his many outstanding contributions to the engineering profession. Engineer Leonardo Torres Quevedo (1852–1936). Constructed 1914–1916. CSCE. The Canadian Society for Civil Engineering. 2010. Asociación de Ingenieros de Caminos, Canales y Puertos de España. Spanish aerial ferry of the Niagara.

Analog calculating machines

Since the mid-19th century, several mechanical devices had been devised—including James and William Thomson's integrators, various multipliers, and Charles Babbage's never-completed analytical engine—setting the stage for Torres' own developments in the field. In 1893 he presented the "Memória sobre las máquinas algébricas" ("Memoir on Algebraic Machines") at the Spanish Royal Academy of Sciences in Madrid. This paper was commented on in a report by Eduardo Saavedra in 1894 and published in the '. Saavedra, who considered Torres' calculating machines as "an extraordinary event in the course of Spanish scientific production", recommended that the final project be financed. In 1900, he presented a comprehensive study, "Machines à calculer" ("Calculating machines") to the Paris Academy of Sciences. An abstract was published in its Comptes rendus that same year, followed by the full memoir in the Mémoires de l'Institut de France. The commission formed by Marcel Deprez, Henri Poincaré and Paul Appell, asked the academy for its publication, where they reported favorably: "In Mécanique analytique, Joseph-Louis Lagrange considers material systems whose connections are expressed by relationships between the coordinates or parameters used to define the position of the system. We can, and this is what Mr. Torres does, take the opposite point of view." Concluding: "In short, Mr. Torres has given a theoretical, general and complete solution to the problem of the construction of algebraic and transcendental relations by means of machines; moreover, he has effectively constructed machines that are easy to use for the solution of certain types of algebraic equations that are frequently encountered in applications."

His works examined mathematical and physical analogies that underlay analogue calculation or continuous quantities, and how to establish mechanically the relationships between them, expressed in mathematical formulae. The study included complex variables and used the logarithmic scale. From a practical standpoint, he showed that mechanisms such as turning disks could be used endlessly with precision, so that changes in variables were unlimited in both directions. Torres developed a whole series of analog mechanical calculating machines that used certain elements known as arithmophores, which consisted of a moving part and an index that made it possible to read the quantity according to the position shown thereon. The aforesaid moving part was a graduated disk or a drum turning on an axis. The angular movements were proportional to the logarithms of the magnitudes to be represented. Between 1910 and 1920, using a number of such elements, Torres built an algebraic machine that was able to compute the roots of arbitrary polynomials of order eight, including the complex ones, with a precision down to thousandths. This machine could calculated the equation:

<math>\alpha = \frac{A_1 X^a + A_2 X^b + A_3 X^c + A_4 X^d + A_5 X^e}{A_6 X^f + A_7 X^g + A_8 X^h} \,</math> where X is the variable and A<sub>1</sub> ... A<sub>8</sub> is the coefficient of each term. Considering the case of α = 1, it becomes the following formula, and the root of the algebraic equation can be obtained:

<math>A_1 X^a + A_2 X^b + A_3 X^c + A_4 X^d + A_5 X^e - A_6 X^f - A_7 X^g - A_8 X^h = 0 \,</math>

By calculated each term on a logarithmic scale, they can be calculated only by sums and products like A<sub>1</sub> + a × log(X), which can handle a very wide range of values, and the relative error during calculation is constant regardless of the size of the value. However, to calculate the sum of each term, it is necessary to accurately obtain log(u + v) from the calculated values log(u) and log(v) on a logarithmic scale. For this calculation, Torres invented a unique mechanism called the "endless spindle" ("fusee sans fin"), a complex differential gear using a helical gear shaped like a wine bottle, which allowed the mechanical expression of the relation <math>y=\log(10^x+1)</math>. Putting log(u) – log(v) = log(u/v) = V, then u/v = 10 V, and the following formula is used to calculate log(u + v):

<math>\log (u + v) = \log (v (u / v + 1)) = \log (v) + \log (u / v + 1) = \log (v) + \log(10^V + 1)\,</math>, the same technique which is the basis of modern electronic logarithmic number system.

Torres also devised another machine around 1900 with a small computing using gears and linkages to obtain the complex number solution of the quadratic equation X<sup>2</sup> – pX + q = 0, and an integrator to solve first-order differential equations. This mechanical phase evolved into electromechanics, which he used to design and construct analytical machines. Nowadays, all these analog machines are kept in the Torres Quevedo Museum at the School of Civil Engineering of the Technical University of Madrid.

Aerostatics

right|thumb|[[Astra-Torres airship|Airship Astra-Torres No.1 at an air show in 1911]]

In 1902, Torres started the project of a non-rigid, trilobed-shape dirigible designed to solve the serious problem of gondola suspension by including an interior framework of flexible cables that provided rigidity to the airship through internal pressure, a principle known as "autorigid". He applied for a patent in France entitled "Perfectionnements aux aerostats dirigibles" ("Improvements in dirigible aerostats"), wrote a "Note sur le calcul d'un ballon dirigeable a quille et suspentes interieures" ("Note on the calculus of a dirigible balloon with interior suspension and keel"), and presented both to Madrid and Paris' Academies of Science. By the end of that year the report at Paris's Academy of Science was included in the French magazine L'Aérophile, and an English-language summary was published in the British The Aeronautical Journal.

left|thumb|Torres with a model of his airship in 1913

Torres was appointed director of the Centre for Aeronautical Research in Madrid in 1904, a civil institution created by the government of Spain "for the technical and experimental study of the air navigation problem and the management of remote engine maneuvers." From March 1905, with Army Engineer Captain Alfredo Kindelán as Technical Assistant, he supervised the construction of the first Spanish dirigible in the Army Military Aerostatics Service, located in Guadalajara, which was completed in June 1908. The new airship, named Torres Quevedo in his honor, made successful test flights with passengers in the gondola. However, Torres parted company with the Army and found himself forced to leave the Park in Guadalajara. Despite this, in 1907 and 1909 he had requested an improved patent for his airship in France. He moved all the material to a rented hangar in Sartrouville (Paris), beginning a collaboration with the Société Astra, a new Aeronautical Society integrated in the conglomerate of French petroleum businessman Henri Deutsch de la Meurthe and directed by Édouard Surcouf, who had been familiar with Torres' work since 1901. The Astra company managed to buy the patent with a cession of rights extended to all countries except Spain, making the use of said system free in the country. In 1911, development began on dirigibles known as the Astra-Torres airships, and Torres would receive royalties of 3 francs for every m<sup>3</sup> of each airship sold. and the United Kingdom in 1912—the system was officially titled "Improvements in Mooring Arrangements for Airships." Towers based on his design became standard industry practice, significantly improving aircraft accessibility and eliminating the labor-intensive process of manual hangar storage.

left|thumb|Statue of Leonardo Torres Quevedo at the [[Museum of Aeronautics and Astronautics (Madrid)|Museum of Aeronautics and Astronautics in Madrid]]

In February 1911, trials of the Astra-Torres No. 1 conducted at Issy-les-Moulineaux, south-west of Paris, proved successful. The airship, with a volume of 1,590 m³, reached speeds of up to 53&nbsp;km/h. In May 1911, it won the Deperdussin Prize after recording the fastest time for a dirigible over a predetermined 100-kilometre circular course. Following this achievement, the airship participated alongside French military forces in the Bastille Day parade at Longchamp on 14 July 1911. Subsequent Astra-Torres designs included the Astra-Torres XIV (designated HMA No. 3 to the Royal Naval Air Service), which in September 1913 set a new world speed record for airships by reaching 83.2&nbsp;km/h, and the Pilâtre de Rozier (Astra-Torres XV) named after the aerostier Jean-François Pilâtre de Rozier, which at 24,300 m3 was the same size of the German 'Zeppelins', reaching speeds of around 85&nbsp;km/h.

The distinctive trilobed envelope was also employed in the United Kingdom in the Coastal, C Star, and North Sea airships. The Entente powers used these dirigibles during the First World War (1914–1918) for diverse tasks, principally to the escort of convoys, the continuous surveillance of coasts and the search, from bases in Marseille, Tunisia and Algeria, for German submarines in the Bay of Biscay, the English Channel and the Mediterranean Sea.

In 1919, based on a proposal by engineer Emilio Herrera Linares, Torres also designed a transatlantic dirigible named Hispania. The project aimed to achieve the first transatlantic flight for Spain, and was patented in both Spain and France, but was ultimately abandoned due to financial difficulties. The success of Torres' trilobed design during the war even drew the attention of the Imperial Japanese Navy in 1922, who acquired the Nieuport AT-2 with almost 263&nbsp;ft long, maximum diameter 54&nbsp;ft and with a hydrogen capacity of 363,950&nbsp;ft 3. This type of non-rigid airship continued to be manufactured in various countries during the postwar era, notably by the French Zodiac Company in the 1930s, and its trilobed structure influenced most later dirigibles.

Multi-command radio remote control

Torres began developing remote control technology around 1901 or 1902, as a way of testing his airships without risking human lives. Between 1902 and 1903, he patented a radio control system in France, Spain, United States, and Great Britain, under the name "Systéme dit Télékine pour commander à distance un mouvement mécanique" ("Means or method for directing mechanical movements at or from a distance").

On 3 August 1903, Torres presented the Telekino (a term derived from two Greek words: tele (far away, in the distance) and kino (force, movement)) at the Paris Academy of Sciences, together with a detailed memoir, and making a practical demonstration to its members. He created a family of different and easily readable code words by using the signal generated with a common wireless telegraph transmitter, building a completely new type of receiver, which was able to react in a different way to each codeword sent by the transmitter. José Echegaray praised the Telekino as a material device capable of interpreting instructions "as if it were intelligent", referring to its operation as a form of "disciplined intelligence". For the construction of this first model, Torres received help from Gabriel Koenigs, the director of the Laboratory of Mechanics at the Sorbonne, and Octave Rochefort, who collaborated by providing wireless telegraphy equipment.

In 1904 Torres chose to conduct initial Telekino testings in the Beti Jai fronton of Madrid, which became the temporary headquarters of his Centre for Aeronautical Research until 1907, first in an electric three-wheeled land vehicle with an effective range of just 20 to 30 meters, which has been considered the first known example of a radio-controlled unmanned ground vehicle (UGV). and later testing a dinghy on the Bilbao Abra bay from the terrace of the Club Marítimo in the presence of the president of the Provincial Council and other authorities. The successful trials attracted significant international press attention.

thumb|left|Telekino working

On 25 September 1906, in the presence of the king Alfonso XIII and before a crowd, Torres successfully demonstrated the invention in the port of Bilbao, guiding the boat Vizcaya from the shore with people on board, demonstrating a standoff range of 2&nbsp;km. By applying the Telekino to electrically powered vessels, he was able to select different positions for the steering engine and different velocities for the propelling engine independently. He was also able to act over other mechanisms such a light, for switching on or off, and a flag, for raising or dropping it, at the same time. Specifically, Torres was able to do up to 19 different pulse-coded actions with his prototypes. These experiences encouraged Torres to apply to the Spanish government for financial aid to use his Telekino for steering submarine torpedoes, a technological field that was just emerging. The government denied his application, leading him to abandon further improvements to the Telekino. Nevertheless, the Telekino laid the groundwork for his pioneering research in automatics, anticipating many of his later theoretical and practical developments.

thumb|right|Commemoration of Early Developments in Remote-Control at the [[Technical University of Madrid. IEEE Milestone Plaque.]]

In early 1907, French inventor Gustave Gabet presented a wireless telemechanics device to the Paris Academy of Sciences based on a "delayed contact" principle. Torres formally contested Gabet's claims by submitting a note titled Le télékine et la télémécanique. Réclamation de priorité, which was received during the Academy's session on 4 March. In the text, Torres stated that this operating principle and its technical solutions were identical to those he had already patented for his Telekino in France in 1903. The Academy officially recognized his claim by publishing the note in the Comptes Rendus on 6 May.

On 15 March 2007, a century later, the prestigious Institute of Electrical and Electronics Engineers (IEEE) dedicated a Milestone in Electrical Engineering and Computing to the Telekino, based on the research work developed at Technical University of Madrid by Prof. Antonio Pérez Yuste, who was the driving force behind the Milestone nomination.

Symbolic language for machine description

In 1907, Torres introduced a formal language in Vienna designed for the description of mechanical drawings and devices. He had previously published the concepts of this method in a paper titled "Sobre un sistema de notaciones y símbolos destinados a facilitar la descripción de las máquinas" ("System of notations and symbols intended to facilitate the description of machines") in the Revista de Obras Públicas. According to Austrian computer scientist Heinz Zemanek, this was equivalent to a programming language for the numerical control of machine tools.

Torres defined a table of symbols, established a set of rules, and applied them to a concrete example to demonstrate their technical viability. Through this symbolic language, he sought to address the limitations in contemporary mechanical description and design methods. Regarding the challenges of this endeavor, Torres noted:

Despite the independent efforts of Babbage, Reuleaux, and Torres, the engineering field continued to rely primarily on descriptive geometry as its standard symbolic language.

Laboratory of Automatics

As a member of the steering committee of the (Junta para la Ampliación de Estudios e Investigaciones Científicas (JAE))—established in Madrid in 1907 to promote scientific research and education in Spain—Torres played a leading role in creating three key state agencies. These agencies served as models for the JAE's multidisciplinary research support: the Laboratory of Automatics (1907), of which he was appointed director; the Association of Laboratories (1910), which unified state laboratories and workshops for instrument construction; and the Institute of Scientific Materials (1911), which managed budget allocations.

The Laboratory of Automatics produced a wide variety of instruments, building its own inventions while providing essential support and services to JAE universities and researchers. Torres, physicist Blas Cabrera, and workshop head Juan Costa jointly designed several scientific instruments, including a Weiss-type electromagnet, an X-ray spectrometer, a remote-control mechanism for a Bunge scale, and a variable-height reservoir with micrometer movements for magneto-chemical measurements. Additionally, prominent scientists commissioned custom equipment from the workshop: —head of the Spectroscopy Section of the Laboratory of Physical Research and mentor to Miguel A. Catalán—ordered a spectrograph; requested a Michelson-type variable-distance interferometer; Juan Negrín acquired a stalagmometer; and Santiago Ramón y Cajal commissioned both a microtome and a panmicrotome, alongside a film projector.

The development of the Laboratory of Automatics reached its peak with the reform of the , to house the School of Industrial Engineers and the JAE, and the National Museum of Natural Sciences, also expanding the own Laboratory.

El Ajedrecista

In 1910, Torres prepared the designs for a chess-playing device—which he dubbed El Ajedrecista (The Chess Player)—and in 1911 he began its construction in his laboratory. As opposed to The Turk and Ajeeb, El Ajedrecista was an electromechanical automaton capable of playing a king and rook endgame against a human opponent. Operating without any human intervention, the automaton achieved true integration of its mechanical and logical components from any starting position.

The pieces had a metallic mesh at their base, which closed an electric circuit that encoded their position in the board. When the black king was moved by hand, an algorithm calculated and performed the next best move for the white player. If an illegal move was made by the opposite player, the automaton would signal it by turning on a light. If the opposing player made three illegal moves, the automaton would stop playing. Due to the simplicity of its move-calculating algorithm, the automaton does not always deliver checkmate in the fewest moves possible, at times requiring more than the fifty moves permitted by the rules. However, it consistently defeated its opponents in every match. Claude Shannon, in his paper Programming a Computer for Playing Chess (1950), pointed out that Torres' idea was quite advanced for that period.

This FEN configuration and move sequence show how White executes Torres' algorithm to checkmate the black King:

<nowiki></nowiki><pre>

[FEN "8/8/1k6/8/R7/8/5K2/8 w - - 0 1"]

1. Rh4 Kc5 2. Kf3 Kd5 3. Ke3 Kd6 4. Rh5 Kc6 5. Ke4 Kd6 6. Rg5 Kc6 7. Kd4 Kd6 8. Rg6+ Kd7 9. Kd5 Ke7 10. Rh6 Kf7 11. Ra6 Ke7 12. Rb6 Kf7 13. Ke5 Ke7 14. Rb7+ Kd8 15. Ke6 Kc8 16. Rh7 Kb8 17. Rg7 Ka8 18. Kd6 Kb8 19. Kc6 Ka8 20. Kb6 Kb8 21. Rg8#

</pre>

Following its completion in 1912, the automaton was first demonstrated in 1913 at the Asociación Española para el Progreso de las Ciencias in Valladolid. It had its official public debut at the University of Paris in 1914, where it drew great interest and was featured on the front page of Le Matin. Its internal construction was published by Henri Vigneron in the French magazine La Nature. On 6 November 1915 Scientific American magazine in their Supplement 2079 pp.&nbsp;296–298 published an illustrated article entitled "Torres and His Remarkable Automatic Devices. He Would Substitute Machinery for the Human Mind". It was summarized as follows: