Category: Timeline Stories

The electromechanical relay, used as a constructive part of some early calculators and computers, was invented in 1835 by the brilliant American scientist Joseph Henry (1797–1878), known mainly as the inventor of the electromagnetic phenomenon of self-inductance and mutual inductance. Henry’s invention was based on the work of the British electrical engineer William Sturgeon (1783–1850), a former shoemaker and soldier, who began to dabble in the sciences at the age of 37, and who invented the electromagnet in 1825.

In fact, in 1835 Henry demonstrated a primitive “relay” telegraph, using a self-made electromagnet, and arranging a small intensity magnet, which works well at low power over great distances, to control a much larger quantity magnet supporting a load of weights. By breaking the intensity circuit, he also de-energizes the quantity circuit, causing the weights to crash to the floor. Students who witnessed such demonstrations by Henry at the College of New Jersey, later recalled that he described the arrangement as a means to control mechanical effects at long range, such as the ringing of distant church bells.

In the late 1830s, Samuel Morse used Henry’s relay device to carry morse-code signals over long kilometers of wire. Still, generally, the invention of Henry remained relatively unknown for several decades, but in the 1860s, and later on at the end of the 19^th century, with the development of the telegraph and phone communications, it became widespread. Especially after the invention of the rotary dial, first developed in the USA by Almon Strowger in 1890, which however used not the simple two-position switches described below, but ten-position relays, the phone companies became huge consumers of electromechanical relays.

What is the construction of a typical relay, used in telephone switching (see the nearby drawing)?
A typical electromagnetic relay consists of an electromagnet (an iron bar, marked with 7 on the drawing, and a coil of wire, marked with 6), an iron armature (8), with a fixed pin of insulator (9), and 3 contacts: normally closed (11), normally opened (12) and common (pole) contact (10). In normal de-energized status (left part of the drawing), to the electrical terminals (2) and (3) is no applied voltage, the electromagnet is not powered and contacts 10 and 12 are not connected, so the current is not flowing between common contact (10) and normally open contact (12). If a voltage is applied to the contacts (2) and (3) of the coil (right part of the drawing), then the electromagnet will be powered, thus attracting the iron armature, and insulator pin (9) will push the plate of the common contact (10), thus making a contact between it and the normally open contact (12). The electrical loop will be closed and the current will go from the common contact (10) to the normally open contact (12). When the voltage is canceled, then the armature will fall down, and the contact will be opened again.

It is clear, that the relay is an ON-OFF device, a switch, suitable for building logical circuits. By the beginning of the 20^th century, a number of inventors recognized that the ability (as well as the power) offered by electric circuits allowed one to build the machine that could not only do arithmetic but also direct a complex sequence of calculations automatically (see, for example, Leonardo Torres).

Devices of these types were in common use by the 1930s. Simple relays cost a few dollars each, and they were fairly rugged and reliable. But, for ordinary calculators, the relay offered few advantages over mechanical cams and gears. It was still cheaper and more reliable to store or add a decimal number on a train of ten-tooth gears, than on a bank of multiple-contact relays. But, for something more than simple arithmetic, relays had a crucial advantage over mechanical systems, in that their circuits could be flexibly arranged (and rearranged) far more easily. One could arrange relays on a rack in rows and columns, and connect them with wires according to what one wanted the circuit to do, then he could further reconfigure a relay system using a switchboard, with cables plugged into various sockets. Going a step further, one could use a strip of perforated paper tape (originally developed to store telegraph messages for later transmission), to energize a separate set of relays that in turn reconfigured the system just as the plugboards did.

In this latter instance, the same relays perform the functions of both arithmetic and control. This seems to confer little advantage over mechanical calculators, as it appears that arithmetic and control are two different activities. But, in fact, the two are closely related, and for anything more than simple arithmetic both are required. A calculator designer who uses relays may exploit their ability to do both tasks, thus enabling the design of a machine with the general capabilities of Babbage‘s Analytical Engine, but with a much simpler overall design.

The history of the modern computer keyboard (an input device, which uses an arrangement of buttons or keys to act as mechanical levers) begins with a direct inheritance from the invention of the typewriter. So, who was the genius, who invented the typewriter (and why the hell the layout of an English keyboard is QWERTY, but not ABCDEF:-)?

In 1714 the English engineer Henry Mill (1683-1771), received the English patent No. 395 for Machine for Transcribing Letters, see a copy of Mill’s patent from 1857 (it was not the first patent of the young engineer, as he already had the patent No. 376 from 1706 for Springs for Coaches, Chariots, and other Vehicles (it was some kind of a shock-absorber)).

The patent stated:
…Our Trusty and welbeloved subject, Henry Mill, hath by his humble petition represented, that he has by his great study, paines and expence lately invented and brought to perfection an artificial machine or method for impressing or transcribing of letters, singly or progressively, one after another, as in writing, whereby all writing whatsoever may be engrossed in paper or parchment so neat and exact as not to be distinguished from print; that the said machine or method may be of great use in settlements and publick records, the impression being deeper and more lasting than any other writing, and not to be erased or counterfeited without manifest discovery.

Unfortunately, the patent was rather vaguely-worded and contains no description of the apparatus (English Patent Laws did not, in those days, require a drawing to be submitted with the application before the letters patent was granted), so we don’t have a drawing of the machine and there is no remaining record that Henry Mill actually built a working example of it.

The first working model of a typewriter was made by the Italian Giuseppe Pellegrino Turri (1765–1828), a noble and skilled mechanic, in the early nineteenth century. Turri also invented carbon paper to provide ink for his machine. Almost nothing is known about the machine, but some of the letters written on it have survived (16 letters are preserved in a museum in Reggio Emilia).

According to the legend, Pellegrino Turri had fallen in love with the beautiful Countess Carolina Fantoni da Fivizzano. Slowly, the young contessa’s vision blurs, distorts, and fades. So, in hope of improving her illegible writing and enabling her to correspond with her friends (including him) in private, at the beginning of the 1800s Turri crafted a machine made of keys and metal arms tipped with raised characters. When the Countess pushed a key, an arm struck a piece of carbon paper atop a sheet of paper.

According to another version, the machine was invented in 1802 by Count Agostino Fantoni (1777-1847) from Fivizzano, nephew of the Italian poet Labindo (Giovanni Fantoni), to help his blind sister (maybe the above-mentioned Carolina), while Turri, only improved Fantoni’s machine and invented the carbon paper in 1806.

The world’s first commercially produced typewriter was developed in 1865 and first patented and put into production in 1870 by Danish pastor Rasmus Malling-Hansen (see the nearby image).

Hansen arranged the most frequently-used letters to be pressed by the fastest writing fingers, with consonants to the right and vowels to the left. This arrangement, along with the placement of the letters on short radial pistons, made the Writing Ball a very fast-speed typing machine. The type is printed on a paper surface by means of carbonized paper or a ribbon. On the original model, the paper was attached to a cylinder, which moved with the help of an electromagnetic battery, making the writing ball in principle also the first electric typewriter.

The first commercially successful typewriter was invented in 1867 by Christopher Sholes, Carlos Glidden, and Samuel Soule from Milwaukee, Wisconsin (US pat. No. 9265). Later Sholes and Glidden being too frustrated by slow sales sold their patent for $12000 to Densmore and Yost, who made an agreement with E. Remington and Sons (a famous manufacturer of sewing machines), to commercialize the machine as the Sholes and Glidden Type-Writer.

In March 1873, Remington began production of its first typewriter. It had a QWERTY keyboard layout (the logic of the QWERTY layout was based on letter usage in English rather than letter position in the alphabet), which because of the machine’s success, was slowly adopted by other typewriter manufacturers. The first Remington typewriters even came with a foot pedal (just like sewing machines) to control carriage returns.

Acceptance of the typewriter was slow initially, but it was facilitated over the next several years by various improvements like: the shift key, which made it possible to type both capital and lower-case letters with the same keys (1878); printing on the upper side of the roller (1880); the tab key, permitting the setting of margins (1897), etc. Thomas Edison patented an electric typewriter in 1872, but the first workable model was not introduced until the 1920s.

So how did we get to where we are now, in the high-tech age of computers and plastics?

First computer keyboards were adapted from the punch card and teletype equipment. Around 1900 Herman Hollerith developed the first keypunch devices, which soon evolved to include keys for text and number entry akin to normal typewriters by the 1930s.

From the early 1940s until the late 1960s, typewriters were the main means of data entry and output for computing, becoming integrated into what was known as computer terminals. In 1948, the Binac computer had a Typewriter-Keyboard Unit. The keyboard had eight keys, representing the octal numbers (from 0 to 7), and was used to introduce either the program or data into the computer and memory. The electro-mechanically controlled typewriter was used to print the data, entered from the keyboard and data, contained in designated portions of the memory.

Biography of Henry Mill

Henry Mill was born in 1683 (or 1684), as the eldest son of Andrew and Dorothy Mill of Camois Court, Sussex. He was a relative of Sir Hugh Myddelton (1560–1631), a famous Welsh clothmaker, entrepreneur, mine-owner, goldsmith, banker, self-taught engineer, and founder of the New River Company (which managed the New River—an artificial waterway in England, opened in 1613 to supply London with fresh drinking water).

Henry Mill obtained an appointment in about 1720 as an engineer to the above-mentioned New River Company and later became Engineer-in-Chief. Mill worked most of his life as a waterworks engineer, and it is known that he erected waterworks at Northampton (and received the freedom of the borough in recognition of his services), and was employed by the prominent British statesman Sir Robert Walpole to carry out the water supply for his magnificent country house Houghton Hall, where a well sunk by him is still in use. Mill in later life employed the Scottish architect and civil engineer Robert Mylne as his assistant (Mylne was appointed surveyor to the New River Company).

Henry Mill died unmarried at his house in Strand, London, on 26 December 1771, and was buried in Breamore Church, near Salisbury, with a long epitaph to his memory. The epitaph states that he was aged 87, but he is entered in the parish register as aged 88 years. His epitaph sets forth that his capacity [was] excellent in …all the branches of the mathematicks, and other liberal sciences, and in his will, proved 6 April 1771, Mill mentions his private fancied toys, a phrase which might well include models of his inventions.

Charles Sanders Peirce (1839–1914) was a famous American philosopher, logician, mathematician, and scientist. He was an innovator in many fields, including philosophy of science, epistemology, metaphysics, mathematics, statistics, research methodology, and the design of experiments in astronomy, geophysics, and psychology, although he considered himself a logician first and foremost (he was perhaps the leading logician in the world at that time).

Charles Peirce made major contributions to logic, but the logic for him encompassed much of that which is now called epistemology and philosophy of science. He saw logic as the formal branch of semiotics, of which he is a founder. One of Peirce’s striking discoveries (made in 1880) in foundational mathematics was how Boolean algebra could be expressed via a single binary operation, either NAND or its dual, NOR.

From 1879 to 1884 Peirce was a lecturer on logic at the new Johns Hopkins University. Although his appointment at Hopkins was in logic, he was also busy there with research in psychology and philosophy. Peirce had a number of talented students in logic, whose work may be sampled in Studies in Logic, printed in 1883. Among these bright pupils was Allan Marquand (1853-1924), at that time Fellow in Philosophy and Ethics at Hopkins, until he graduated in 1880 with a Ph.D. in Philosophy. His thesis, supervised by Peirce, was on the logic of Philodemus. Marquand returned to Princeton in 1881 to teach Latin and logic. During the 1881-82 academic year, he built a mechanical logical machine, which is interesting to us. The machine was presented in 1885 and described in the 1886 article A New Logical Machine.

Marquand worked within the history of logic and upon trying to improve the design and function of what was then called logical machines, at least they were so-called within Peirce’s circle. Marquand however decided to went further and began with improvements upon the Logic Piano of Jevons. (It is unknown if Marquand was acquainted with the logical machine of British logician and philosopher John Venn (1834-1920). Venn speculates on the design of a logical machine, based on the machine of Jevons. He even gives schematic diagrams for the construction of such a machine for four propositions, but it is not clear whether the machine was ever built.)

The logical machine of Marquand (see the nearby photo) was designed to solve problems by formal logic. Construction with size 30/20/15 cm, from the wood of a red cedar post from Princeton’s oldest homestead, the machine displayed all the valid implications of a simple logical proposition by using a hotel annunciator and an arrangement of rods and levers, catgut strings, and spiral springs.

Initially, the machine of Marquand was met with disappointing reception. Peirce tried to encourage his pupil and friend (they were so close, that Marquand was lending him money) and proposed some possible ways for improving. One of them was to use electricity. It is possible even the whole electromagnetic design of the machine to have been made by Peirce, because Marquand after 1886 wrote no more on logical machines, while Peirce wrote in 1887 an amazing article (Logical Machines) on that topic for the American Journal of Psychology. The article mentioned Marquand’s work in a positive way, but Peirce continued to make comments on the problem, the latest known one being in 1906.

There is a circuit diagram for the electromagnetic logical machine in Marquand’s archive, made around 1890 (see the nearby image). The operating core consists of 16 electromagnetic elements—an electromagnet with five separate coils, an armature with an air gap, and a spring to maintain a position for the unenergized armature (the armatures are shown only at the upper left position of the diagram). The information is represented as states of magnetic energy in each of the 16 elements.

The machine is used in this general way:
First the programmer “resets” the machine, using the operating switch. Then a premise is entered by depressing the appropriate programming keys. Now using the control switch and the operate switch, the result is that the machine will remember all the elements previously programmed by key entries. One can now enter a new premise with the program keys, then use the operate switch to see the result of two premises entered. The operator can save that again, and see the result of a third premise entered, and so on. At the proper point, he can stop, inspect the read-out facility, which in this case is the pointers of element armatures, and from that determine what conclusion is consistent with the premisses entered.

The machine is easily expandable to any size (any number of terms), hence this seems to be a design for a general-purpose, truth-functional, logical computer.

In a conclusion—the first electrical logical machine was invented in 1886 by Charles Peirce and Allan Marquand.

William Stanley Jevons (1835–1882) was an English economist and logician, a major figure, both in Britain and internationally, in the fields of political economy and social reform. Jevons is most often credited with being the first theorist to make economics a mathematical discipline, and he is regarded as one of the founders of the form of neo-classical economics, that dominates our current economic thinking and political discourse.

The most interesting for us aspect of his life is the designed in 1869 logical machine for doing logic inference, called Logic Piano, which is the best-known logic machine of the 19^th century.

The work of Devons on Logic Piano was inspired by Stanhope’s Demonstrator. The construction of the device was announced in his 1869 logic textbook, Substitution of Similars. It was the culmination of a long series of inventions and aids to the calculation of syllogisms: logical alphabet, logical slate, logical stamp, and logical abacus-all tools to write quickly the lines of a truth table in a logical argument.

The interest of Jevons to Logic as a science began as early as in 1860, when he worked as an assayer at the Sydney Mint, Australia. Jevons wrote in his 1860 diary:
As I awoke in the morning the sun was shining brightly into my room, there was a consciousness on my mind that I was the discoverer of the true logic of the future I felt a delight such as one can seldom hope to feel. I remembered only too soon though how unworthy and weak an instrument I was for accomplishing so great a work and how hardly I could expect to do it.

Jevons’ serious involvement and subsequent passion for Logic came about when, on his return to England, he met up with his former undergraduate teacher of mathematics, the famous logician Augustus de Morgan. It seems Jevons was one of the first in Britain to catch on to the importance of the newly developed formal logical systems of Boole and De Morgan.

Jevons read the Mathematical Analysis of Logic and An Investigation of the Laws of Thought of Boole and was fascinated. But he also saw problems with it, and by 1861 he was developing his own system of logic based on what he eventually called the Substitution of Similars, whereby philosophy would be shown to consist solely in pointing out the likeness in things. In 1863 he published his first work on the subject, Pure Logic, which was hardly a success, with four copies sold in 6 months. But Jevons was a great one for persistence.

In his 1869 logic textbook, The Substitution of Similars Jevons described the Logical Abacus: as a series of wooden boards with various combinations of true and false terms. It was intended that they be arranged on a rack and a ruler used to remove certain excluded combinations. This was the basic outline of the device that, with the addition of levers and pulleys, Jevons had a Salford clock maker construct for him in 1869. Fitted within a wooden case, and with a keyboard mounted on the front to operate the substitution mechanism, this was his Logic Piano.

The logic piano (see the nearby image) was a wooden box approximately 90 cm high. A faceplate above the keyboard displayed the entries of the truth table. Just like a piano, the keyboard had black-and-white keys, but here they were used for entering premises. As the keys were struck, rods would mechanically remove from the face of the piano the truth-table entries inconsistent with the premises entered on the keys.

The Logic Piano can deal with up to 4 terms. Jevons had in fact wanted to build a machine capable of dealing with up to 16 terms, but it would have been too large and taken up a whole wall in his office. The logic expressions are typed (or perhaps played) via the keys of the keyboard (see the nearby image), and hitting full stop removes all impossible combinations from the screen. The copula is the equals key, while the finis key resets the machine.

A truth-table for n proposition requires 2ⁿ entries. The table for n = 4 has 16 entries and is as follows if we represent the truth of a proposition by an upper case letter, and its falsity by the same letter in lower case:

The truth-table for n=4
PQRS	PQRs	PQrs	PQrs
PqRS	PqRs	Pqrs	Pqrs
pQRS	pQRs	pQrs	pQrs
pqRS	pqRs	pqrS	pqrs

The proposition if P, then Q, is true just in case P is false or Q is true. If this proposition were entered on the keyboard of the logic piano, the face would show:

The truth-table for proposition if P, then Q, is true just in case P is false or Q is true, when n=4
PQRS	PQRs	PQrs	PQrs
(second line is removed)
pQRS	pQRs	pQrs	pQrs
pqRS	pqRs	pqrS	pqrs

As propositions were entered on the keyboard, representing additional premises that must be satisfied simultaneously, other inconsistent entries would disappear from the face.

The action of the logic piano actually did not result in a conclusion stated in the form of a proposition, but only in the truth table entries consistent with the conclusion. Jevons worked unsuccessfully to resolve this problem, which he termed the inverse problem and which he somewhat misleadingly associated with the process of mathematical induction.

As Jevons’ adversary John Venn noted, the logic piano has no practical purpose, for there are no circumstances in which difficult syllogisms arise or in which syllogisms must be resolved repeatedly enough to justify mechanization of the process. Jevons countered that it was a convenience to his personal work and useful in his logic classes.

People love legends, even in the world of computers. And Ada Lovelace is the perfect person for such a legend—she was a beautiful, intelligent, and rich young (she died only 36 y.o.) lady, who had the chance to be in the right place at the right time and reflected some of the light of one of the greatest persons in the world of computers—Charles Babbage.

What is Ada’s place in computer science? Some people used to call her the World’s First Computer Programmer, and even the Founder of Scientific Computing. In 1980, the U.S. Department of Defense settled on (in honor of Lady Lovelace) the name Ada for a new standardized computer language. The truth is somewhat different.

Foreseeing almost a century of the modern general-purpose programmable computer, in the 1830s Charles Babbage designed his Analytical Engine. He was not a diligent writer, however, especially concerning documentation of his ideas (actually he was a rather careless and impractical man, which will end in some friction developed between Ada Lovelace and him during their later mutual work), thus we know little of Babbage’s programming ideas.

In August 1840, Babbage visited Turin in Italy and gave a series of seminars on the Analytical Engine at the Academy of Sciences. One of the listeners—the Italian engineer and professor Federico Luigi Menabrea (1809-1896), who later on will become the Prime Minister of Italy, wrote up the lectures, modified with ideas from the discussions, in the paper Notions sur la Machine Analytique de M. Charles Babbage, which was published in French in Bibliothèque Universelle de Genève in October 1842. This paper was the first extensive publication on computers and programming in the world.

Ada first met Charles Babbage in June 1833, through their mutual friend Mary Somerville. Later that month, Babbage invited her to see the prototype for his Differential Engine. Soon Babbage became something like a mentor of the young lady (and vice versa, as Ada was an extraordinary celebrity, and later as the wife of a prominent aristocrat, she was in a position to act as patron to Babbage and his engines, though she never, in fact, did so), and helped Ada to begin mathematical studies with the great mathematician Augustus de Morgan in 1840 at the University of London. Babbage was impressed by Lovelace’s intellect and writing skills. He called her The Enchantress of Numbers and in 1843 he wrote:
Forget this world and all its troubles and if
possible its multitudinous Charlatans—every thing
in short but the Enchantress of Numbers.

After the publication in 1842 of the paper of Menabrea, Babbage was asked to write a paper for two British scientific journals (The Ladies Diary and Taylor’s Scientific Memoirs). Thus he decided to ask Ada Lovelace to translate Menabrea’s article into English but to append extensive notes to the translation, prepared under Babbage’s close guidance. These deal with the familiar modern ideas of the flow of control in programs, particularly the formulation of simple loops and nested loops controlled by counters. However, the paper (see Sketch of The Analytical Engine) and notes carefully and deliberately skirt around any discussion of details of the means by which these are to be implemented, yet it was written for a journal audience.

Babbage wrote the following on the subject, in his book Passages from the Life of a Philosopher:
I then suggested that she add some notes to Menabrea’s memoir, an idea which was immediately adopted. We discussed together the various illustrations that might be introduced: I suggested several, but the selection was entirely her own. So also was the algebraic working out of the different problems, except, indeed, that relating to the numbers of Bernoulli, which I had offered to do to save Lady Lovelace the trouble. This she sent back to me for an amendment, having detected a grave mistake which I had made in the process.

Babbage considered this paper a complete summary of the mathematical aspects of the machine, proving that the whole of the development and operations of Analysis are now capable of being executed by machinery.

Ada also expanded upon Babbage’s general views of the Analytical Engine as a symbol-manipulating device rather than a mere processor of numbers. She brought to the project a fine sense of style that resulted in the frequently quoted analogy, “We may say most aptly that the Analytical Engine weaves algebraic patterns just as the Jacquard-loom weaves flowers and leaves.” She suggested that it “might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations… Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible to such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent… Many persons who are not conversant with mathematical studies, imagine that because the business of the engine is to give its results in numerical notation, the nature of its processes must consequently be arithmetical and numerical, rather than algebraic and analytical. This is an error. The engine can arrange and combine its numerical quantities exactly as if they were letters or any other general symbols; and in fact, it might bring out its results in algebraic notation, were provisions made accordingly”.

So, what about Ada’s title the world’s first programmer? Well, this is nonsense! Babbage was, if programmer is the right term at all. After Babbage came his mathematical assistant, his eldest son—Benjamin Herschel, then Menabrea, and possibly Babbage’s two younger sons. Ada was probably the fifth or sixth in this row. Moreover, all she did was to rework some calculations Babbage had carried out years earlier. It is out of the question, however, that Ada was Babbage’s fairy lady—interpreter, adviser, collaborator, and confidante, supporting his work financially, intellectually, and emotionally. As such her achievement was certainly remarkable.

The English mathematician and philosopher George Boole (1815-1864) was one of the first men, after the great Gottfried Leibniz, who believed that human thinking is mastered by laws, which can be described through mathematics. Boole is the inventor of Boolean logic, which is the basis of modern digital computer logic, thus he is regarded in hindsight as a founder of the field of computer science.

The child prodigy and self-taught genius George Boole first became interested in mathematics as a tool to solve mechanical problems in his instrument-making occasions. His interest quickly blossomed and he soon began an elaborate project of self-education in mathematics. In 1838 Boole wrote his first mathematical paper. In 1841 he founded a new branch of mathematics called Invariant Theory, which later inspired Einstein. Boole was awarded the first Gold Medal of the Royal Society of London in 1844 for a paper on Differential Equations, whose methods are still used today.

Speculations concerning a calculus of reasoning and applying algebra to the solution of logical problems had at different times occupied the thoughts of the great mathematician, but it was not till the spring of 1847, that he put his ideas into the essay, called Mathematical Analysis of Logic (see the nearby title page). It was the ground-breaking work that laid the foundations for what is known today as Boolean algebra and propositional calculus. It not only expanded on Gottfried Leibniz’s earlier speculations on the correlation between logic and math but argued that logic was principally a discipline of mathematics, rather than philosophy.

It seems Boole has been motivated in his research by his intense religious convictions. At the age of 17, he had a mystic experience in which he felt God called on him to explain how the mind processes thought. He decided to do this in a mathematical form, for the Glory of God.

Boole afterward regarded the Mathematical Analysis of Logic as a hasty and imperfect exposition of his logical system, and he desired his much larger work. In 1854 he wrote the monograph An Investigation of the Laws of Thought, on which are founded the Mathematical Theories of Logic and Probabilities, which should alone be considered as containing a mature statement of his views.

Boole did not regard logic as a branch of mathematics, as the title of his earlier essay might be taken to imply, but he pointed out such a deep analogy between the symbols of algebra and those that can be made, in his opinion, to represent logical forms and syllogisms, that we can hardly help saying that (especially his) formal logic is mathematics restricted to the two quantities, 0 and 1.

Boole proposed that logical propositions should be expressed as algebraic equations. The algebraic manipulation of the symbols in the equations provides a fail-safe method of logical deduction, i.e. logic can be reduced to algebra. He replaced the operation of multiplication by the word AND and addition by the word OR. The symbols in the equations can stand for collections of objects (sets) or statements in logic. For example, if x is the set of all pink pigs and y is the set of all fat pigs, then x+y is the set of all pigs that are pink or fat, and xy is the set of all pigs that are pink and fat.

Similarly, if z = the set of all Hampshire pigs, then z(x+y) = zx+zy, in other words, the set of Hampshire pigs that are either pink or fat is the same as the collection of pigs, that are Hampshire and pink or Hampshire and fat.

Why is Boolean algebra so important for computer science and digital circuitry?

Boolean algebra provides the basis for analyzing the validity of logical propositions because it captures the two-valued character (binary) of statements that may be either true or false.

In the 1930s, many researchers noticed that Boole’s two-valued logic lent itself to a description of electrical switching circuits. They showed that the binary numbers (0 and 1), combined through Boolean algebra, could be used to analyze electrical switching circuits and thus used to design electronic computers. Today, digital computers and electronic circuits are designed to implement this binary arithmetic.

In the mid-1850s, the Swede Martin Olsson Wiberg (1826-1905), a Doctor of Philosophy from Lund University and an amateur mechanic, became very interested in the printing business and had the intention of developing a composing machine. In 1854, Wiberg was in London to show off a setting machine, i.e., a line casting machine that set and cast a line in lead. In order to raise money for this venture, he decided to publish a set of interest tables, hoping to use the machine of his compatriot Pehr-Georg Scheutz for computing and printing these tables. The machine of Scheutz was, however, already sold to the Dudley Observatory, and that’s why Wiberg decided to construct his own raknemaskin (calculating machine).

Wiberg wanted to build a machine, similar to Scheutz’s, but that would be much smaller. In the late 1850s, after only six months of work, he managed to build a successful desk-size (one-tenth the size of Scheutz’s machine) calculating machine, and the interest tables appeared in 1860. This enterprise, however, became a failure for Wiberg because the tables failed to sell due to their bad looks.

It was a bad start, but fortunately, later, Wiberg managed to obtain the support of a group of influential Swedes, including the Duke of Östergötland (the future King) Oscar II of Sweden, and a group of scientists and capitalists formed the Wibergska Tabell-Aktiebolaget. The company took over ownership of the machine and future publications. Wiberg received 120 shares and 40000 riksdalers. With capital and heavy backing, Wiberg’s life was at least temporarily secured, and he was able in 1875 to publish logarithm tables in Swedish, German, English, and French. The Riksdag gave him 8000 riksdaler as a national reward, and the King gave him the Order of the North Star. The machine received several medals at expositions, and the French Academy of Sciences invited the inventor to Paris to demonstrate his calculator, where it received favorable notice, was described in a special report, and Emperor Napoleon III awarded him the Legion of Honor.

Wiberg’s machine had the same capacity as the machine of Scheutz, it could compute fourth differences of 15-digit numbers. Instead of the rectangular array of number wheels, that had characterized the Scheutz machines, however, the machine of Wiberg was made more compact (weight= 16.6 kg, width 220 mm, length 420 mm, height 230 mm; materials used: metal, copper alloy (copper, brass, bronze)) by substituting identical metal disks for the counting wheels used by Babbage and Scheutz, and by arranging these linearly along a common axis. This meant that 75 disks were arranged in 15 groups of 5, each group corresponding to the tabular values and the first, second, third, and fourth differences, arranged from left to right. A second axis, parallel to the first, carried thirty hooks, which could cause as many of the disks to be acted upon at the same time, making possible the simultaneous addition of two sets of 15-digit figures. Thus, one of the operating features of the Scheutz machine had been preserved: one turn of the crank caused even differences to be added, another turn, odd ones; carrying was again effected separately after the rest of the addition had been completed. Results were once more impressed on lead or papier-mache, from which stereotype plates could be produced.

The academy’s reporting committee pointed out in his report from 1863 that the machine could do nothing that the Scheutz machine had not done but commended it for its efficient mechanical construction, which had led to a substantial saving of space and utmost reliability.

Martin Wiberg was an outstanding inventor whose contributions ranged from mechanical letterboxes, heating devices for railroad carriage components, speed controls, match-manufacturing machines, self-propelled torpedoes, automatic breech-loading weapons, a cream separator, etc. His calculator became especially well known through a set of logarithm tables, which included logarithms of the trigonometric functions, and appeared in 1875. It was published in Swedish, German, French, and English editions, appearing in 1876, in time to be included among Sweden’s contributions to the International “Centennial” Exposition held at Philadelphia that year, where it joined his “bull-dog apparatus” for deep-sea sounding (this machine was awarded a prize at the Exposition) and railway control device.

Biography of Martin Wiberg

Martin Olsson Wiberg was born on 4 September 1826 in Viby, a locality near Kristianstad, Scania County, Sweden. He was the first son of the local farmer Ola Jeppson (Wiberg) (1802-1879) and Elna Trulssdotter (1803-1876). Before Martin, the family had a daughter (who died in infancy), and after Martin, they had two more girls, Marna and Kjersti, and five boys: Nils Olof, Truls, Jöns, Pehr Olof, and Anders. Wiberg was a well-to-do farming family, and with great sacrifices, the parents ensured that four of the six sons became “educated men”.

Martin was so fragile as a child that he was not expected to live for a long time, but he survived. The skinny and shy boy had no interest in anything but books. After attending a high school in Kristianstad, where he was noticed, in the autumn of 1845, Martin Wiberg enrolled at Lund University to study medicine, but for financial reasons, after three terms, he turned to the study of science and became a Doctor of Philosophy in 1850. Martin’s academic career was open, but he chose the inventor’s path.

All his life, Wiberg has been employed almost exclusively in practical mechanics and has made numerous beautiful inventions in this area. However, like many other inventors, Wiberg lacked business acumen and the ability to make his ideas profitable for himself. For example, in 1896, Wiberg received a patent (pat. No. 7304) for a “spectral instrument”, equipped with a keyboard so that different colored light rays could be evoked when different keys were pressed and thereby “create a play of colors which, according to the changing of the colors, evokes different impressions on the eye and different physiological effects on the objects, which is thereby affected”. Wiberg considered that the effect of light on the sense of sight should, under certain circumstances, be able to produce as pleasant sensations as the air-valley rings, converted into tones, have on hearing. Intending to create a “tone opera”, Wiberg devoted himself to the invention, and Alfred Nobel himself is said to have been willing to assist with the necessary capital (in May 1896 Nobel wrote a letter to the inventor, stating The idea is so ingenious, that I’d like to congratulate the author of it), but the completion was thwarted by Nobel’s death in Dec 1896.

Being widely famous but still poor, Wiberg considered moving to the United States and wrote to the famous American naval engineer and inventor John Ericsson (1803-1889), who gave him praise but also a very discouraging picture of the possibilities in the USA:
“If the tables sent were calculated and printed by the same machine, I consider this machine the greatest triumph of human understanding over matter… As for America, I can assure you that such an invention would not induce capitalists to risk the slightest. A new rat trap or a new way of making shoe nails would arouse more interest here than your admirable calculating machine.”

Martin Olsson Wiberg was married two times. With his first wife, Sofia Augusta Knutsson (1830-1859), he had one son, Knut Alexis (born Dec 1854 and died May 1918). After the early death of Sofia in 1859, in 1863 Wiberg married a second time, to Emma Wilhelmina Lindskog (1843-1905). They had eleven children—five daughters: Sigrid Maria Wilhelmina (1865–1915), Ellen Emma Martina (1867–1938), Alma Ingeborg (1869-1950), Ebba (1871-1871), and Nanny Emilia (1872-1941), and six sons: Axel Algot (1868-1920), Nils Albert (1870-1870), Gustav Lennart (1874-1932), Philibert (1875-1906), Torsten (1876-1934), and Ragnar (1877-1934).

The remarkable inventor Martin Wiberg died in his home in Hedvig Eleonora Parish of Stockholm on 29 Dec 1905, only several months after his wife Emma Wilhelmina. As evidence of the vitality and the will-power he possessed, can be mentioned, that when the doctors told him he had only a couple of hours in this world, he gave instructions on how a bed should be constructed so like, that it is prepared for a sick person to the greatest possible rest period.

The Swede Pehr Georg Scheutz (1785–1873) was a remarkable man—a lawyer, translator, and inventor. When he read a description of the differential engine of Babbage in 1834, he decided to build such a machine. And, despite the fact, that he was neither a mathematician (like Babbage), nor an engineer, he didn’t have enough money at his disposal, and he lived in a country, that was much behind England from a technological point of view, nevertheless, he succeeded. Pehr Georg (with his son Edvard) managed to build the first workable differential engine, and the first printing calculating machine in the world.

Scheutz initially learned about Charles Babbage and his machine, when he started to translate several chapters from Babbage’s very successful book Economy of Machinery and Manufactures, for his Journal för Manufakturer och Hushållning in 1832. From this book Scheutz learned also about the technique of computing mathematical tables, using the “method of differences”. Intrigued by this account in Babbage’s Economy, Scheutz discovered a more detailed discussion of Babbage’s machine, which appeared in the July 1834 issue of the magazine Edinburgh Review, in which the author of the article “Babbage’s calculating engine”—the Irish popularizer of science Dionysius Lardner (1793-1859), reviewed a set of seven publications pertaining to the machine, ranging from Babbage’s accounts of 1822 and 1823 to the 1829 report by a committee of the Royal Society. Lardner not only presented a sketch of several major tables produced over the preceding fifty years, using these to illustrate the difficulty and importance of producing large quantities of error-free copies, but also described in a relatively non-technical fashion, the working of the machine, and Babbage’s concept of mechanical notation.

After familiarizing himself more closely with computational techniques and the construction of Babbage’s difference engine, at the beginning of 1837, Scheutz built some provisional models in wood, pasteboard, and wire, which appeared to prove the point. In the summer of the same year, his son Edvard, a student at the Technological Institute in Stockholm, asked and was granted his father’s permission to enlarge upon the rough model of a difference engine, and produced a metal version. By the end of summer, Edvard had made so much progress with his work, that it seemed perfectly feasible to produce a complete engine. Edvard’s progress pleased his father sufficiently, so on the 3^rd of October 1837, he sent a long letter to the Royal Academy of Sciences. In it, he stated that he had discovered a simpler and cheaper design for a difference engine than Babbage had done and offered to build such an improved engine, which inclusive of the stereotype printing unit would be 19 times smaller than Babbage’s! While Babbage’s engine cost 15000 pounds in 1829 “and was still unfinished”, Scheutz (so he claimed) was able to build an engine for 20000 riksdaller banco (circa 1638 pounds) within an estimated time of one to two years at most. The Academy refused to support the request because it would cost “too much for a country like Sweden with its limited resources”.

Edvard and his father continued their efforts, despite this initial rejection. The work progressed slowly, because of a lack of good instruments and money. Edvard continued to tinker on the model, while the older Scheutz tried to get financial support. In 1838 Georg tried to sell the machine in France but without success. By 1840 they had already a five-place machine that would compute one order of differences. Within another two years, the machine had been increased to compute up to three orders of differences. At the beginning of 1843, the printing mechanism was completed. With the proper integration of the printing component, in the summer the complete machine model was ready for trial. In the same 1843, a commission from the Royal Swedish Academy of Sciences was invited to inspect the machine. Following is a part of their statement:
The undersigned take leave to issue the following statement concerning a calculating and printing machine, which they were requested to inspect and which was conceived by the Auditor Mr. Georg Scheutz and brought to a finished form by his son Edvard Scheutz, a student at the Royal Technological Institute, who also has invented several important parts of the machine.
The general purpose of the machine is to provide a solution to the same problem for which the English Calculating Machine constructed by Babbage was designed, namely to present in tabular form and to print in stereotypes the successive terms of arithmetical series. It can thus be used for the construction of tables where the difference of a certain order becomes constant. The machine in question consists of three parts:
1^st—The Calculating unit. This is certainly unable to deal with arithmetical series of a degree higher than the third, and it cannot give complete terms, where more than five digits are called for, but there is nothing in the nature of the mechanism to prevent one from extending its performance to include series of arbitrary degree and terms with as many digits as required. To accomplish this, it is only necessary to supply additional machine-parts, similar to those already existing, i.e. the machine’s height and length are increased. In its present state, he [sic] can nevertheless, under certain circumstances, print 10-digit numbers. The last five digits are already given correctly and provided the terms do not grow too rapidly, the 6th together with all the digits to the left of it, are increased by 1 or alternatively, several of the subsequent terms become constant. This mechanism of the machine was supplied with another device, which allowed the missing digits in terms greater than 99999 to be displayed. In our presence, specific terms were correctly presented for five different series of the third degree, supplied by us. Here it may be observed that in the case of decreasing series the machine gave not the negative terms themselves, but their complements relative to 100000. However, if the machine is halted at the term where the series changes from positive to negative and the complements to the differences, arising from that point onwards, are inserted, the negative terms and not their complements result.
2^nd—The Printing unit. Each term supplied by the calculating unit is presented in the form of printed digits, arranged in rows close to one another, as in a printed table and the rows are immediately printed in some material, which allows galvanoplastic or stereotype copies to be made. The printing is accomplished by means of ordinary printer’s type, which, however, in the case of a larger machine or where the digits had to be printed in copper, would require to be made of steel or some other hard metal, and the rows are set with great accuracy, one beneath the other in the same vertical column. In the test carried out, the digits were printed in a thin layer of lead.
3^rd—The Numerator. The printing unit is combined with another mechanism, which before each term prints its corresponding argument.
The machine is operated by turning a handle by means of which, without any additional measure, one can carry out both the calculation, arrangement and printing of the digits and rows. In its present form, it occupies a case 2 feet 8 inches long, 2 feet wide and 8 inches high. When placed on a table large enough to support it, it can be lifted and moved, together with the table, by two persons.
Finally, it may be noted that the machine, being merely a model, has been built without access to those mechanical tools required for more accurate metal work and it does not therefore possess that perfection which a larger scale model, designed for actual use and executed in more favorable circumstances, would and must possess. Nevertheless, in its present form it is capable of evaluating certain classes of mathematical formulae when the variables involved receive steadily increasing definite values.

The abovementioned statement of the scientific committee certified the conceptual and technological soundness of the proposed machine. What remained to translate the working model into a saleable product was supporting capital. This was beyond the means of the Scheutzes. The attempts of Georg Scheutz to find a buyer for a full-size machine abroad (in England and France) failed continuously. In 1844 he applied again for a grant of 10000 riksdaller from the Swedish crown to construct a full-scale model. But the academy, while attesting to the physical possibility of building such a machine, was not prepared to guarantee from its construction an advantage to the nation commensurate with the cost. Lacking assurance that building a difference engine would be in the national interest, the government denied Scheutz’s request, and the model lay dormant for some years.

In 1851 Georg Scheutz applied again to the crown, this time for a smaller grant of 3333 riksdaller. And again failure, the crown denied for lack of funds. This time, however, the Royal Swedish Academy of Sciences endorsed them, and the Swedish parliament (Diet) advanced 5000 riksdaller on the condition that the inventors finish the project by the end of 1853. Otherwise, the money would have to be returned.

Unlike Babbage, the Scheutzes were an eminently practical pair, and the Tabulating Machine, as they called it, was completed on schedule (though not within the budget and prone to error). The first machine, which was ready in October of 1853, was built under the supervision of Edvard Scheutz in the workshop of the industrialist Bergström. The machine (see the lower photo) could handle numbers of 15 digits and tabulate functions with 4 orders of differences (the fourth being constant) and print out results, rounded off to eight digits, on molds from which metal printing plates could be cast.

The overall measurements of the machine are 56 cm x 170 cm x 58 cm.

All the units and movable parts in the machine were operated by hand through a crank. The force applied was transmitted by a system of gears to the cams, arms, and racks that operated the calculating unit. Beneath this were two carriages (one of them on wheels), which ran along rails, that were suitably curved to give the five vertical axles their up-and-down movements. The printing table in the printing unit was acted upon by a crank mechanism.
The calculation of a table was carried out in four stages:
1. The start values of the table in question were calculated manually.
2. The number wheels in the calculating unit were set at the start values with the help of a special tool.
3. A piece of matrix material, wax, pasteboard, or lead, was fastened to the slide on the printing table. Then the slide was pushed in until the feeding hooks reached the first notch of the ratchet. The numerator was set at zero.
4. The handle of the engine was cranked and after every 6^th revolution, a result was printed.
The tabular values and differences were represented by a number of toothed wheels arranged horizontally in a 15 by 5 array. The top row of 15 figures represented the tabular values; the second row, the first differences; the third row, the second differences; the fourth row, the third; and the fifth row, the constant fourth differences. At the outset of the computation, the number wheels were set manually. Each wheel had an adding mechanism, consisting of a “catch-and-trap” combination. There is an upward catch, attached to the upper part of the wheel, the corresponding trap to the central axis surrounded by that wheel, at a point approximately midway between it and the wheel above it. As the axes rotated, the traps revolved within the calculating wheels. Each trap had an arm that touched the catch of the wheel below it as the trap revolved.
Depending on the direction of this revolution, it either pressed down a portion of the catch and passed it freely, or was caught by it and raised. When the trap was raised, it engaged the number wheel above it, thereby turning it. A related stud and lever mechanism were provided for carrying as the upper wheel passed from 9 to 0 (or 5 to 0, in the case of the “sexial” wheels. A small stud between these two digits pushed against a lever when a wheel passed from 9 to 0. This lever extended to the left in front of the preceding wheel. The carrying action was prompted by a moving upright “pillar.” If the stud had pressed against the lever, this then came into contact with the pillar, causing a pivot arm on that pillar to engage the wheel behind the lever and to move it forward one unit, thus performing the carry.

The printing mechanism (see the nearby photo) was joined to the top row of the machine because only final values must be printed. A set of horizontal shafts was placed at right angles to the rows of number wheels. By means of a set of eight cams and “snails” (stepped cylindrical segments), these shafts linked the vertical axes corresponding to the eight leading digits to a set of racks geared to eight type wheels. The racks were parallel to the rows of number wheels. A bar kept the type wheels stationary while the machine added. Once the calculations had been completed, the bar was removed, releasing a set of weights. Being suspended from disks attached to the horizontal shafts, these weights were connected to the eight leading number wheel axes by the snail and cam combinations. Upon release, they set the type wheels into action, impressing 8-digit figures onto 8-inch-long strips of paper. These strips were usually covered with black lead to facilitate the production of stereotype plates from them.

The Scheutz Difference Engine was powered by falling weights, as can be seen in the photo below.

At the end of 1854, Scheutzes and their machine traveled to England with the help of the firm of Bryan Donkin, a famous English engineer, and industrialist, who in 1829 assisted Charles Babbage in creating his differential engine. They immediately applied for a patent, which was granted the next year. The machine was opened for demonstrations and a number of English newspapers and magazines presented reviews of the patent and descriptions of the machine. In 1855 a committee appointed by the Royal Society examined the machine and noted that although Scheutz had adopted Babbage’s suggestion of operating oppositely on odd and even differences, so these could be handled simultaneously, the mechanism of the Scheutz machine is different from Babbage’s. To the surprise of many, Babbage (ever the gentleman) himself not only demonstrated a positive attitude to the machine but in the following years, he will support quite strong Scheutz, despite many problems.

In August of 1855 the machine was transported and installed at the Exposition Universelle des produits de l’ Agriculture, de l’Industrie et des Beaux-Arts in Paris, France. Babbage also arrived in Paris and touted the machine to the public. The machine won a gold medal, thanks, in part, to Babbage, who was a highly respected member of the Institute of France and who had lobbied on their behalf. Interestingly, in July 1855, a French patent for a machine similar to Scheutz’s (Machine à calculer et à imprimer, pat. N° 23577) was granted to Count Nils Ludvig Ferdinand Barck (1820-1887), a Swedish businessman and adventurer, a personal friend of Napoleon III. Next year the Scheutzes received a gold medal (Medaille d’Honneur) for the invention of their difference engine at the Paris Exposition from Prince Charles in ceremonies at the Royal Palace in Stockholm. The machine was described by the French journalist Baron Léon Brisse as follows:
This machine, among the most ingenious, solves equations of the fourth degree and of even higher orders; it operates in every number system; in the decimal system, in the sexagesimal system (for trigonometry), or in any other system… Scientists who vaunt their calculating powers, as divination of the laws of nature, will be advantageously replaced by a simple machine, which, under the nearly blind drive of an ordinary man, of a kind of movement, will penetrate infinite space more surely and profoundly than they. Any man knowing how to formulate a problem and having the machine of the Messieurs Scheutz at his disposal for solving it will replace the need for the Archimedes, the Newtons, or the Laplaces. And observe how in the sciences and arts, all is held together and intertwined: this nearly intelligent machine not only effects in seconds calculations which would demand an hour; it prints the results that it obtains, adding the merit of neat calligraphy to the merit of calculation without possible error: the stereotyped numerals emerge grouped at the will of the operator, and separated, as he desires, by blanks, lines or any arbitrary typographic symbols. If a simple machine can tell us the distance of stars, the extent of celestial globes, the path which the great comets traverse on their parabolic course, what limit can henceforth be assigned to mechanism? What world of impossibilities will not be cleared?

The gold medal gave the Scheutzes the recognition they deserved. It also attracted a buyer, which the pair had been searching for almost from the day they had completed the machine. In 1856 the machine was purchased for £5000 by Dudley Observatory at Albany, New York, USA, and the next year was transported to the USA, where it was used for the first practical work—a computation of the True Anomaly of Mars.

At the same time in England, a second Scheutz difference machine was being put to work. In 1857 the British government authorized the sum of £1200 for a full-scale difference engine with an attached printing apparatus based on the design of Scheutz to be constructed by Donkin’s company. The new machine was almost exactly as first (with only small variations in design) and handled 15-place numbers to 4 orders of differences and could transmit 8 places to the printing mechanism. Costs overran and Donkin delivered the machine in July 1859, several weeks past the deadline, incurring a loss of £615. The machine was used at the General Register Office to compute life tables, which were published in 1864.

Biography of Pehr-Georg Scheutz and Edvard Scheutz

Pehr Georg Scheutz was born in Jönköping, Sweden, on 23 September 1785. His father, Fredrik Christian Ludvig Schieutz, was born in Copenhagen to German parents. Together with his wife, Johanna Christina Berg (the daughter of Petter Berg, the Inspector at Limmareds glasbruk, Sweden’s oldest still running glassworks, founded in 1740), he ran the popular inn and wine merchant’s business Fortuna in Jönköping. Besides the inn, Fredrik Schieutz was responsible for providing refreshments for the guests at Medevi Spring, the most frequented spa in the country at that time. It was in this stimulating, cosmopolitan spot at the southern end of Lake Vättern that Georg Scheutz, his parents’ only son, grew up.

In 1796, when he was eleven years old, Georg Scheutz entered Jönköping elementary school. There he followed the normal course of instruction, which included theology, history, and political geography, and in addition, he made the acquaintance of classical authors. Afterward, Scheutz moved on to the Gymnasium in Wexiö, where the subjects on the curriculum were much the same as before. He showed a particular interest in languages and read the New Testament in Greek and even picked up somewhat outside the normal routine a fair amount of Hebrew. The main emphasis of Scheutz’s schooling was on languages and the humanities and this was to be of great use to him in his future career.

Georg Scheutz began his study at the University of Lund in the autumn of 1803, where he obtained a law degree in 1805, in preparation for more senior posts in mining, which had become his main goal. In 1800 his father died and in order to pay his way, Georg had been compelled to tutor junior students. In 1805, he became a probationer at Göta Hovrätt (court of appeal) in his hometown. At various times, he also served as deputy actuary, provisional magistrate, and on one occasion as mayor in Ulricehamn.

In 1811 Scheutz moved to Stockholm where he was employed in the chancellery of Justitie-Revisionen för Sjöärendena, the body charged with the preliminary investigation of Supreme Court cases dealing with maritime affairs. Scheutz was appointed the second auditor with the Svea Artillery Regiment and in November 1814, he received “Royal authorization as Auditeur”. This type of post carried with it more honor than money, which led Scheutz in 1816 to resign. He had given eleven years of his life to the Law and now he left it forever.

Scheutz decided to start publishing and printing business and in 1817 he bought a printing press and Stockholm’s newspaper Anmärkaren, becoming a printer and journalist. As an editor and columnist of his newspaper, Scheutz became famous as a political journalist. In 1825 he started the first technical journal in Sweden, the monthly Journal för Manufakturer och Hushållning (see the nearby photo). This magazine contained descriptions of useful inventions and discoveries in physics, chemistry, and technology, which could be simply put to practical use by the intended readers’ cottages, and tradesmen. It was in this journal, in November 1833, that the Swedish public was first introduced to Charles Babbage’s difference engine. Later on, this article will bring Scheutz to the creation of his famous differential engine.

In seeking to spread knowledge about science and technology, Scheutz published not only magazines and newspapers but also quite a number of technical handbooks. This began in 1819 with Handbok för så wäl enklare som mera konstig Blekning, and between then and 1832, he published some twelve handbooks in all, which were collected in a series entitled “Library for Art, Handicrafts and Applied Science”. Later on, Scheutz continued to publish technical handbooks, translated and edited by himself.

The creative side to Scheutz’s nature was not content simply to read and write about technical matters. The technical problems he encountered at his press, led him to make improvements and it was there that he was to make his own first inventions. Around the end of 1819, he applied for a twenty-year patent for a number of improvements connected with printing. In 1823 he submitted a new patent application. This time the foot-operated machine was equipped with a cylinder. Scheutz made inventions in other fields as well. Around 1835 Scheutz invented a safety valve for steam engines, which was manufactured and successfully used in at least one factory in Stockholm. Five years later he applied for a ten-year patent on “using steam to bring about a rotary motion” in other words, for a simple type of steam turbine. Another of his inventions was an optical instrument used for copying called “Portfeuille Iconografique” for which he sought a patent in 1841. The following year, Scheutz applied for a patent for a drawing instrument which he called ”Sinus-delare” (Sine divider), and in 1850 he applied for a patent for “metod att bränna Tak-och Murtegel” (method of baking tiles and bricks).

Scheutz was also one of the skillful Swedish translators from the first half of the 19^th century. In 1816 appeared Scheutz’s translation into Swedish Shakespeare’s Julius Caesar. It was the first translation into Swedish of this particular work and only the second of any Shakespearean work. Later on, he will translate and publish La Motte-Fouque, Werner, Kotzebue, and Boccaccio, classical works of Aristophanes and Xenophon, native literature such as the historic plays of Per Henrik Ling, and language readers for learning Latin or Italian.

Pehr Georg Scheutz was engaged to Anna Margaretha Schaumann and on 3 September 1821, in Stockholm was born their son—Edvard Georg Raphael (see the nearby photo). Anna Schaumann died on 16 March 1823, from breast fever after having given birth to a daughter. The child lived for only one day.

Edvard began his studies at the New Elementary School but was forced to discontinue on account of a leg injury. In 1835 he entered the Technological Institute and remained there until 1841. Little is known about Edvard Scheutz’s interests outside the field of mechanical technology. It seems clear, however, that he worked closely with his father. He even wrote a comedy published by the Scheutz publishing firm in 1836, when Edvard was only 15! Joining his father’s efforts to create a differential engine in 1837, till the end of his life in 1881, Edvard devoted almost all his life to the production, promotion, and efforts to sell the machine.

At the end of the 1870s, Edvard established himself as a civil engineer. He ran the printing establishment for two years after his father’s retirement, but he is best known as the inventor of a steam engine, patented in 1859, that proved useful in steamboat construction.

Pehr Georg Scheutz died in Stockholm on 22 May 1873. Edvard Scheutz died in Stockholm on 28 January 1881.

In establishing Scheutzes’ place in the history of computation, we must credit Georg and his son Edvard not only with the first working differential engine but with the first complete construction of a printing calculator.

The French Mathematician and Cybernetics pioneer Louis Pierre Couffignal (1902-1966) was a pupil of the prominent French mathematician and engineer Philbert Maurice d’Ocagne (1862-1938), who instilled in him his passion for calculating machines.

Louis Couffignal published several articles and sent several notes regarding calculating machines to the French Academy of Science. The first note was in 1930 and devoted to a new calculating machine. In 1932, Couffignal organized at the Collège de France a conference on the “calculating machines, their principle, and their future”. In 1933 he published a monograph for calculating machines. In 1936 appears his decisive note on “the use of the binary notation in the calculating machine”. In 1938, Couffignal published an article, important for cybernetics, where it defines the machines as “a whole of inanimate or partially animated beings or even exceptionally animated able to replace the man” and further: “Since the machine is made for the man, it is field of the mechanical analysis to acquire an overall picture of the various activities where the man was or could be replaced by the machine, and to establish laws of substitutions”. In the same 1938, Couffignal becomes Ph. D. thanks to his thesis “The mechanical analysis, application to the calculating machines and the celestial mechanics”, which poses the principles of the electromechanical binary all-purpose computer. In his thesis, he described two calculating machines: a decimal calculator, and a binary electromechanical program-controlled calculator. There is also another Frenchman, who devised a binary-based calculating machine even before Couffignal—Raymond Valtat, and Couffignal mentioned him in his 1936 note  (Valtat filed several patents in the early 1930s for a mechanical calculator founded on the conversion of decimal input into binary before calculation).

Nearby you can see a diagram of the binary machine assembly (from the translation of Couffignal’s thesis in the book of Brian Randell The Origins of Digital Computers, Birkhäuser, 1982).

Look what wrote in the conclusion of the description of his machine Couffignal:
Without entering into very great detail, we believe we have shown that it is possible to construct a calculating machine, able, without any intervention by an operator, to execute a sequence of calculations, to store the intermediate results, to read mechanically a function table and to print all the numbers, recorded in its registers; we think that in view of its capacity the machine may be considered to be of great simplicity.
It is worth noting, that the connections between different parts of the machine are all electrical; the arrangement of the latter does not clash with any of the geometric or kinematics constraints that one meets with in a purely mechanical device, where all movements are caused or guided by physical contact: the number of each different type of component is therefore theoretically unlimited and in practice very high.

In the late 1930s, Couffignal was appointed director of the laboratory for calculation and mechanics in the Institut Poincaré, where he found himself alongside laboratories in which there was a certain amount of calculating machinery and some computing staff. In December 1939 the French Army suggested to Couffignal that he should turn his laboratory into a center for artillery calculations and should equip it with a powerful machine. At that time Couffignal had arranged a contract (worth FF 80000) for the construction of an electromechanical linking of a Sanders-Octoplex 10-column accounting machine to a Monroe A-1-213 calculating machine. This link was to enable any number produced by either machine to be transferred to the keyboard of the other, and all operations would be controlled automatically using a perforated tape.

Couffignal was to find his plans held up by the start of the war and the occupation of France. After the war, however, in 1947, Couffignal obtained the grants he needed for the building of his machine. He designed and the French computer manufacturer Logabax manufactured in 1952 the first French electronic digital computer. This universal computing machine (see the nearby image) contained 2000 tubes, but in fact, the machine was never finished and put into production.

Biography of Louis Couffignal

Louis Pierre Couffignal was born in Monflanquin, Fâcheries, in south-western France, on 16 March 1902, in a humble family: his father Guillaume Couffignal (born 1858), was a chief cantonnier, and his mother, Marie Deroux-Couffignal (born 1870), was a tailor.

After attending a primary school at Monflanquin, in 1913 Louis enrolled in the Collège et au Lycée de Villeneuve sur Lot, where in 1920 he received a bachelor’s degree in Latin, sciences, and mathematics. After graduation, he remained in the college as a part-time lecturer, and later on, continued his work as a lecturer in other colleges in the southwest of Brittany, then at the naval academy in Brest and, eventually, at the Buffon School (1938-1939) in Paris. Couffignal was more than 20 years (1938-1960) director of Laboratoire de Calcul Mecanique at the Institut Blaise Pascal. He was a good violinist.

Louis Couffignal died on 4 July 1966.

In 1893 the eminent Spanish engineer and inventor Leonardo Torres y Quevedo (1852-1936) presented his first paper to the Spanish Royal Academy of Sciences. It was devoted to an algebraic machine, able to calculate the roots of an any-grade equation. The paper was accompanied by a working prototype of the device. That was the first automatic calculator, designed by Leonardo Torres in a long list of them.

Quevedo’s major motivation in all his work in the field of automatic machines (besides calculating machines and chess automatons, he built also an automatic weighting machine and a machine for playing a game, similar to Nim) appears to have been exploiting, to the full, the new facilities that electromechanical techniques offered, and to challenge accepted thinking as to the limitations of machines, but not to create a workable general-purpose electromechanical computer, or some else great. Torres certainly had the knowledge and potential to manufacture such a machine, but it was too early, the need for large scale fully-automatic calculating machines appeared as late as the 1940s.

The algebraic machine of Leonardo Torres
The algebraic machine of Leonardo Torres was an analog computing device, featuring a mechanism based on a cone-shaped pulley with a helical groove around it. The algebraic machine was used for the resolution of equations like:
x⁹ + Ax⁸ = B
or
x⁹ + Ax⁷ = B.

Torres’ first automatic machine
Torres’ major written work on the subject of automatics was his fascinating Essays on Automatics, published in 1913, in which he devised the term Automatics. The paper provides us with the main link between Torres and Babbage. Torres gives a brief history of Babbage’s efforts at constructing a mechanical Difference Engine and Analytical Engine. He describes the Analytical Engine as exemplifying his theories as to the potential power of machines and takes the problem of designing such an engine as a challenge to his skills as an inventor of electromechanical devices. The paper in fact contains a complete design (albeit one that Torres regarded as theoretical rather than practical) for a machine capable of calculating completely automatically the value of the formula α=ax(y–z)², for a sequence of sets of values of the variables involved (see the lower drawing). It demonstrates cunning electromechanical gadgets (switches, electromagnets…) for storing decimal digits, performing arithmetic operations using built-in function tables, and for comparing the values of two quantities. The whole machine was to be controlled from a read-only program (complete with provisions for conditional branching), represented by a pattern of conducting areas mounted around the surface of a rotating drum. Incidentally, the paper also contains, almost casually, what is believed to be the first proposal of the idea of floating-point arithmetic!

Later on, Torres created a series of working prototypes of the above-mentioned machine. Possibly the first was a demonstration machine, capable of evaluating p x q–b (see the lower photo). How successful this was in practice we do not know.

In 1920 Torres must have removed any uncertainty about his potential and knowledge to build a workable electromechanical calculating machine, because he startled the attendees at a Paris conference, marking the centenary of the invention of the first really practical calculating machine of Thomas Colmar, with a demonstration of his electromechanical arithmometer (see the lower photo). This machine consisted of an arithmetic unit connected to a (possibly remote) typewriter, on which commands could be typed and the results printed automatically. Torres apparently had no thought of making such a machine commercially, viewing it instead as a means of demonstrating his ideas and techniques.

To use the system, the operator types at the typewriter, in the usual manner, the statement of the operation, which he wishes to have executed. Thus if he wants to multiply 532 by 257, he presses successively on the keys representing the digits 5, 3, 2, then on the space bar, on the key representing the multiplication sign, again on the space bar, and finally on the keys for the digits 2, 5, 7: the machine thus types the statement 532×257. That’s all!
When the calculation is finished, the machine commands the typewriter which prints, after the data typed by the calculator, an equals sign and the result of the operation. Finally, the typewriter advances a line and the carriage is brought back to the left ready to print and execute a new operation.
The calculating machine and the typewriter are connected by an electric cable, so by using a long cable they can be separated by a big distance.
According to Torres the method of performing division is a main characteristic of my machine. It compares automatically the divisor and the remainder and then if the divisor is smaller, subtracts it from the dividend; otherwise, it divides it by 10, displacing the carriage by one place to the right.
Let’s see the principle of division, using the drawing from the presentation of Torres from 1920 (Bulletin de la Société d’Encouragement pour l’Industrie Nationale), describing the machine (see the lower drawing):

The five drums D₁, D₂, D₃, D₄ and D₅ represent the dividend. The three cranks M₁, M_2, and M₃ represent the divisor. The three pointers Q₁, Q_2, and Q₃ represent the quotient. The operation of the machine is not automatic, however. In short, the operator knows that he must subtract the divisor (operate the crank S) if it is smaller than the remainder or move the carriage (operate the crank A) if it is larger; he will compare the two numbers after each operation to decide what the next action must be. When the operation is finished, he will press the button r to return to zero.
At the end of the article, however, Torres mentioned, that in summary, automation can take into account all the circumstances which one wishes in order to decide the maneuver to be done and it can have the means to manipulate the control levers. I therefore believe that we have grounds to say that we can automate any arbitrary mechanical operation.

Leonardo Torres’s chess-machine
Leonardo Torres was not the first man, who dreamed of creating a chess-playing machine. Several attempts have been made for such machines before, but all of them were based on a fraudulent concept. The fraudulent chess-playing machine of Baron Wolfgang von Kempelen (called The Turk), presented in 1769, had a remarkable success record in its travels around the world but actually has a cabinet of 4x2x3 feet, which hid a small person, who mechanically controlled the hand movements of the turban-wearing mannequin. Later chess automatons were The Ajeeb ( from 1868) of Charles A. Hopper and The Mephisto (1878) of Charles Gumpel, both based on the same fraudulent concept as The Turk.

By the beginning of 1910 Torres commenced his work to make a chess-playing automaton, to prove his theory that machines could do many things popularly classed as thought. The machine dubbed El Ajedrecista (Spanish for Chess-player), was designed for the end game of King and Rook against King. This chess player was fully automatic, using electromagnets under the board, thus using electrical sensing of the pieces on the board and what was in effect a mechanical arm to move its own pieces.

The machine (see the upper images for the front and back view, and the lower photo of the machine) could, in a totally unassisted and automated fashion, deliver mate with King and Rook against King. This was possible regardless of the initial position of the pieces on the board. For the sake of simplicity, the algorithm used to calculate the positions didn’t always deliver mate in the minimum amount of moves possible, but it did mate the opponent flawlessly every time.

El Ajedrecista made its public debut during the Paris World Fair of 1914, creating great excitement at the time. The machine was widely mentioned in the Scientific American magazine article of 6 November 1915, as “Torres and His Remarkable Automatic Devices”.

In an interview given to a Spanish journalist, Torres described briefly his machine as follows:
It is an apparatus, that plays chess with the king and the rook as if it were a person, knowing with absolute precision all moves that occur and always matting its opponent. Besides this, it warns its opponent, in a courteous manner, if any mistakes (i.e. illegal moves) are made by his opponent by means of light, and after its opponent has made 3 mistakes, it ceases playing, considering that its opponent is no match for it… This apparatus has no practical purpose, but it supports the basis of my thesis: that it is always possible to create an automaton the actions of which always depend on certain conditions and which obey certain rules that can be programmed when the automaton is being produced. Evidently, these rules will be such as to be self-sufficient to determine the performance of the automaton without any uncertainty and at any given moment.

In 1920 Torres and his son Gonzalo created and demonstrated a second chess automaton, which is similar to the first, but used magnets underneath the board, not a mechanical arm, to move the pieces. Like a number of his other inventions, both machines are still in working order and can be found in the Torres Quevedo Museum of the Technical University of Madrid. When in Madrid, chess enthusiasts should see these unique inventions for themselves. Players can show their love for the game by wearing chess board decorated wristbands or wristbands with the words “play chess” emblazoned on them.

A description of the machine was created by Professor Aranguren, from the Complutense University of Madrid:
Roughly speaking, the movement of white pieces depends on the movement of the black king. Each of the 64 squares of the chess board (8 rows x 8 columns) is formed by three metallic pieces separated from each other by an insulating material; the central piece is circular and is connected to the positive terminal whereas the side pieces are triangular and are respectively connected to two conductors, one horizontal and one vertical.
The black king has a silver mesh-base that connects the central piece of the square to the triangular ones, thus closing two electrical circuits that move two respective sliding bars, one horizontal and one vertical, until they reach two positions that determine the black king position on the chess board. Similarly, the positions of the white king and rook are defined by four sliding bars, two for each of the pieces. When the black king moves into a position, the corresponding sliding bars move and close, by means of suitable contacts, the electrical circuits which act in turn on the white pieces making them move according to the game strategy. The white pieces have a steel ball in their base and are driven by electromagnets, which are placed under the table and suitably activated for each black king position.
When a check situation occurs, a phonographic disc pronounces the sentence “check to the king”. When checkmate occurs, the disc pronounces the corresponding sentence, and a warning light indicating mate is turned on. In these cases, an electromagnet removes the tension from the board, thus ending the game. The automaton won. Although the chess automaton function was limited to particular chess end-games, Torres Quevedo proved that further advances in computer technology were possible at a time when the information about “artificial intelligence” was very limited. At the time of this invention, Torres Quevedo was President of the Academy of Sciences of Madrid, Spain.

Another explanation and a drawing of El Ajedrecista can be found in the article Les automates: Le jouer d’checks automatique de M. Torres y Quevedo by Henri Vigneron from 1914 (see below):

The (defending) black King
is in the same zone as the (white) rook	is not in the same zone as the rook and the vertical distance between the black king and the rook is
	more than a square	one square, with the vertical distance between the two kings being
		more than two squares	two squares, with the number of squares representing their horizontal distance apart being
			odd	even	zero
The rook moves away horizontally	The rook moves down one square	The king moves down one square	The rook moves one square horizontally	The white king moves one square towards the black king	The rook moves down one square
1	2	3	4	5	6

If the opponent plays an illegal move, a light comes on and the robot refuses to make a move. Once three such illegal moves have been made, the robot ceases to play altogether. If, on the contrary, the robot will carry out one of six operations, depending upon the position of the (just moved) black king. In order to archive this, Mr Torres uses two zones on the chessboard: the one on the left consisting of the a-, b-, c-files, and the corresponding one on the right consisting of the h-, g-, and f-files. We then have six operations as shown in the above table:

Both versions of Torres’ chess automaton are still working and are on display at the Colegio de Ingenieros de Caminos, Canales y Puertos in Madrid.

Biography of Leonardo Torres

Leonardo Torres y Quevedo was born on 28 December 1852, on the Feast of the Holy Innocents, in a stone house in Santa Cruz de Iguña, a small village in the north of Spain, near Molledo (Cantabria), Santander.

From his mother, Valentina Quevedo de la Maza, who was also born in Santa Cruz de Iguña, Leonardo inherited the Castilian austerity and her love for the highlands. From his father, Luis Gonzaga María Torres Urquijo, AKA Luis Torres de Vildósola y Urquijo (1818-1891), a civil engineer from Bilbao, he inherited his scientific rigor and his love for mathematics, a passion very useful in his long career as an inventor.

Luis Torres and his wife Valentina were well-educated, very intelligent, and strict people, who tried to devote as much as possible time to their family but had to travel a lot. Besides Leonardo, they had a daughter, Joaquina Torres de Vildosola y Quevedo (born in 1851), and a younger son, Luis Torres Quevedo (born on 21 March 1855), who became a military officer and inventor with numerous patents in his name (e.g. the photographic machine from 1886).

As a little boy, Leonardo used to rummage about his father’s office, examining his engineering books, instruments, and drawings.

The family resided for the most part in Bilbao, where Luis Torres, a descendant of one of the most liberal families in Bilbao—Urquijo, worked as a railway engineer, although they also spent long periods in his mother’s family home in Santander’s mountains. In Bilbao, Leonardo studied a bachelor’s school program at the Instituto de Enseñanzas Medias, and later spent two years (1868-1870) at the College of Brothers of the Christian Doctrine, Paris, to complete his studies. In 1870, his father was transferred, bringing his family to Madrid. In 1871 Leonardo began his higher education at the Civil Engineering Faculty of Madrid, where his father was already a professor. He temporarily suspended his studies in 1873 to volunteer for the defense of Bilbao, which had been surrounded by Carlist troops during the third Carlist war. Returning to Madrid, he completed his studies in 1876, fourth in his graduating class.

In the same 1876, Leonardo began his career with the same train company for which his father had worked, but soon he decided to resign from the railways and dedicate himself to being a full-time inventor, concentrating on mechanical and electrical inventions. In fact, Leonardo was already a wealthy man, after receiving in the late 1860s a substantial inheritance from a distant relative, Pilar Barrenechea. As a teenager, still in Bilbao, Leonardo was taken care of by the unmarried Barrenechea sisters, relatives of his father, and one of them, Pilar, declared him an heir of his property, which facilitated his future independence (she was a very wealthy person, who left in the property and in money many millions of reals and bequeathed her entire fortune to Leonardo). Thus he immediately set out on a long trip through Europe to get to know the state of the art in technology. He traveled to France, Switzerland, and Italy, where he was mainly interested in everything related to electrical applications, e.g. in Paris he met some great scientists: Henry Poincare, Paul Appel, and Maurice d’Ocagne.

Upon returning to Spain, on 16 April 1885, Leonardo Torres married in Portolín (Santander), to Maria Luz Niceta De Polanco y Navarro (1856-1954), a daughter of Miguel Polanco y Corvera (born 1818 in Santillana) and Julia Navarro y Trujillo (born 1833 in Madrid).

The couple had eight children (4 boys and 4 girls: Leonardo (born 1887, died 2 years old in 1889), Gonzalo Torres-Quevedo y Polanco (born 1889, died 9 March 1965), Luz, Valentina, Luisa, Julia (also died young), Leonardo, and Fernando). The couple moved to Moledo-Portolin, a small village close to Santa Cruz de Iguña, where they spent their first married years.

It was in the early 1880s when Leonardo Torres started with inventions. Soon after his marriage, on 9 September 1887, Torres received his first patent—in Germany, for a small funicular (so-called transbordador or ferry). Soon he received a patent in Spain (Nr. 7348) for “A multi-wire aerial cableway system”, and in 1888 he extended this patent to the United States, France, Italy, Canada, Great Britain, Prussia, Austria-Hungary, and Switzerland.

Later on, Torres (and according to his patents) designed several other funiculars (cableways), the most famous of which is the Whirlpool Aero Car over Niagara Falls in Ontario, Canada, which started in 1913 and finished in August 1916 (directed by Torres himself and his son Gonzalo on the place), and still working at present without having any problem in its over hundred years of working (see the lower photo). Other Torres’ funiculars have been installed successfully in Mount Ulia in the Basque Country, in Chamonix in the French Alps, and in Rio de Janeiro, Brazil.

In 1893 Torres presented his first paper to the Spanish Royal Academy of Sciences for an algebraic machine, able to calculate the roots of an any-grade equation and print the solutions. That was the first automatic calculator built by Torres in a long list of them. This machine however has not been manufactured.

In 1889 Torres moved to Madrid with the firm intention of carrying out the projects he had devised in previous years and became involved in that city’s cultural life. In 1890 he made a trip to Switzerland, presenting his ferry project, but without getting the expected support. From the work he carried out during these years, the Athenaeum created the Laboratory of Applied Mechanics of which he was named director. The Laboratory dedicated itself to the manufacture of scientific instruments. That same year, he entered the Royal Academy of Exact, Physical and Natural Sciences in Madrid, of which entity he was president in 1910.

Another field of interest for Torres was Aerostatics. He presented his first project for the airship to the Spanish and French Academies of Sciences in 1902, receiving immediate recognition (later on he would receive patents for his airship). In 1906 he built his first dirigible balloon and two years later built the second one with the partnership of the French constructor Astra, whose company bought the patent. During WWI both French and English armies used Torres dirigibles in order to counteract the German Zeppelins (in the nearby photo you can see the second airship of Torres—Torres Quevedo №2, demonstrated in Guadalajara in 1908).

Torres is also the inventor of an electronic device, widely used every day—remote control. The work on Aerostatics drove Torres to the invention of the so-called Telekine, as he wanted to control the flight of dirigible balloons from the ground, without risking human lives. He started work on this system in 1901 and in 1903 the Telekine was presented to the Academy of Sciences in Paris, in the same year, he obtained a patent in France, Spain, Great Britain, and the United States. In the patent he describes the Telekine so: It consists of a telegraph system, with or without wires, whose receiver sets the position of a switch, that switches on a servomotor, operating any mechanism. In 1906, in the presence of the Spanish king and before a great crowd, Torres successfully demonstrated the invention in the port of Bilbao, guiding a boat from the shore (see the nearby photo for the prototype of Telekine, from the Museum of Torres Quevedo in Madrid, source Antonio Yuste).