Werner Künzel

The Birth of the MACHINE: Raymundus Lullus and His Invention

1. A Strange Invention

When, in about 1275, Raymundus Lullus invented his logical machine, the Mediterranean Sea was a kind of interface for three expanded cultural streams. Spain in general, and specifically the island of Mallorca, was at that time, one could say, a melting pot for the three religions which have determined the history of the world until the present. There was an encounter of the Christian religion with the culture of the Muslims, as well as a very important trace of the Jewish tradition. Raymundus Lullus began his work just a short time after the successful "reconquista" of Spain, which would not conclude until 1492. It is therefore necessary to regard his invention as embedded within a special situation, i.e., embedded in a deep crisis of communication.

With the "Ars combinatoria" of Raymundus Lullus, a real revolution of formalistic thinking was born, as this was the first known text-machine which was able to produce true (and, needless to say, false) declarations in a strange mechanical manner. At its apex, the discussion focused on Aristotle and his works included all the problems and conflicts of the Catholic Church with the Muslim tradition of the Greek philosopher (the German philosopher Ernst Bloch has written a beautiful essay on the subject, called "Avicenna, or the Aristotelian left wing"). With that dramatic culmination of scholastic reflection on questions of logic, Raymundus Lullus alone set out on a completely new path. He singularly founded the concept of a new method, a new organisation of thinking; one might say, a new hardware and a new software! It may be that there were indeed some traces of Cabbalistic, or even Arabic thinking; we may consider the phrase "ex oriente lux."

But what was at the heart of this invention, what is the nucleus of this partly forgotten revolution? The radical innovation Lullus introduced in the realm of logic is, in fact, the construction and the use of a paper-machine to combine elements of thinking, which means of course, elements of language! With the help of connected geometrical figures, following a precisely defined framework of rules, Lullus tried to produce all the possible declarations of which the human mind could think. These declarations or statements were nevertheless represented only by a series of signs, chains of letters.

Thus, his great invention was the idea of producing the totality of human wisdom by a mechanical method of combining a strictly limited quantity of signs. Armed with this method, Lullus had the proper intention to demonstrate all the truth of the Catholic church. For this reason, his first and highest task was, of course, the mission! His machine should deliver the transparence and the proof of the Catholic doctrine. The direction of his project was clear: to persuade the Muslims and the Jewish population who remained in Spain and on the coast of northern Africa.

Totality of wisdom, transparence of truth and the necessary opening of a dialogue by his machine are the three principles to be kept in mind. In observing the blueprint and the circuits of the lullistic machine 1, with its archaic yet surprising design, one finds all the information about the hardware of this machine - built of paper! A triple-circle arrangement is, as we would say nowadays, the central processing-unit of this machine. Three circular paper disks are fixed on an axis on which they can be turned. The paper disks contain the limited stock of letters, a special lullistic alphabet. When the circles are turned step by step, all the series of all possible combinations of these letters are produced, which is no small feat.

Just reading chains of letters, one may say. Then what is the use of that strange machine? Giordano Bruno, Athanasius Kircher, Gottfried Wilhelm Leibniz, Stephan Mallarmé, Jorge Luis Borges and Antoni Trpies have all valued this use, and you will understand the reason for their admiration with the following description. Regarding the next original design 2, we come a little bit closer to the trick of this machine: every single letter, from B to K, represents far from merely itself -- not only one meaning, but several strictly defined and placed meanings! Every single letter - a fantastic invention - every letter is a kind of an interface! Writing the letters from B to K as key-terms heading a table, series of different words can be easily constructed. For example, B=Bonitas, C=Magnitudo, D=Duratio, E=Potestas, F=Sapientia, G=Voluntas, H=Virtus, I=Veritas and K=Gloria. This is, initially, the paper-circle called the Prima Figura. The next strictly defined table of words can be produced on the next circle, perhaps as seen on the Secunda Figura 3, where we find categories and relations of thinking.

Hence the machine allows all the words to be combined by turning the circles step by step. In this manner, it is possible to connect every word with every other word, placed in a position of a table, depending only on the construction of the individual tables! Imagine the strategic play of Lullus, bearing in mind the notated words of the Prima Figura. These nine words are none other than the attributes of God. Combined with a table of nine questions, it is possible to construct the skeleton of the so-called Proofs of God. The machine shows all possible statements and declarations on this subject - but naturally, only the artist using this machine is able to decide which statement is true and which is false. The machine independently produces both: the universe of truth and the universe of the false, step by step. A double play, containing a source of problems, like Pandora's box!

Therefore, in contemplating the next design, the Tabula Generalis 4, it is clear that this is not a game of letters established and designed in a mixed manner of Gothic and Renaissance elements. It is rather like the pure listing of a computer printer, which prints out the results of a certain program, with a little graphic gambling, like everything today! Behind these series and chains of letters are the hidden words of the utilised tables. These columns of letters very precisely represent the totality of human wisdom; far from a poor reduction, the letters of the lullistic alphabet contain a rich potential of meanings. The connection to a certain site in each table allows each letter to represent unlimited words of unlimited fields.

Lullus established tables incorporating the subjects of all areas of human wisdom, material from theology at first, but later, material of the philosophical tradition, the natural sciences, and so on. Thus, when the machine was ready and the tables were chosen, it was very easy to read and write down all the combinations produced by turning the paper disks step by step.

In my essays and books, I have described the function and the rules of the machine in every detail. Here I can only highlight the most important points, as I outline the traces of this invention in the history of science and the history of philosophy.

One thing should be kept in mind: the artist had always to examine every single combination, and only he could tell which combination was right or wrong from this context. One can imagine that Lullus had a certain idea for the use of his machine and for teaching the use of it; all his various tracts dealing with the problems of this machine contain a certain chapter for the strict information of possible users! His books became, in the full sense of the word, the prototype for real manuals! In Latin, Vademecum, for users.

Thus with this special "art of invention," the "Ars Combinatoria," at first sight a very simple machine, connecting paper disks and tables, combining letters and words, Lullus created the fundamentals of computer culture! The Lullus-Machine was indeed the ancestor of the very famous Turing-Machine; Lullus had invented a logic-machine, producing results, statements - output of data in general - by a clearly defined mechanical algorithm! Since 1987, I have programmed this first beautiful algorithm of the history of philosophy into the computer languages COBOL, Assembler and C. When I published my programs, there was always a very interesting reaction from the public: some angry people in the areas of theology and philosophy, but many fascinated readers in all areas of the computer sciences.

Perhaps for some so-called intellectuals, it is difficult to accept that even philosophers have been involved in the process of technical development, that they are the inventors not only of brain-machines, but also of calculating-machines. They include Lullus, Leibniz, Babbage and Pascal, for example. I am still waiting for a new computer-language to be named after Raymundus Lullus.

But what happened to his great plans? What of his mission? Lullus had the idea of using his machine to demonstrate the truth of the Catholic belief. He wished to show all the truth of the Church by means of a dialogue, step by step, like a riddle of consequent statements, of questions and answers. He wanted to convince via open communication, with the machine as a transparent tool. Face-to-face communication, a dialogue - "inter faces!"

It is known that Lullus travelled around on his mission for more than 40 years. He was often in Barcelona, or other parts of Spain, and in Paris he presented his new method at the famous Sorbonne, where all the hot discussions of the scholastic scientists took place. He was in France and other places several times, and in the dangerous parts of North Africa, he went by ship to Cyprus and even to the coast of Turkey! He travelled through Italy, visiting Rome, Sicily and Naples, among other cities. A plan for a new crusade was in his mind, but without a chance of realisation. He dreamt of going with a fictive army to conquer Alexandria, where the library with the thesaurus of all the wisdom of ancient times was buried in the sea.

Once he was shipwrecked some miles off the coast of Pisa. Lullus was one of the very few survivors, at that time more than 60 years old. What did he do when he was rescued on the site of a monastery at Pisa? He commenced building a new machine, a very simple one, from paper, because he did not want to lose any time. He wanted to show his new method everywhere, from Paris to Pisa, from Mallorca to North Africa; the interface of the Mediterranean Sea was the interface of his machine, of his Ars Combinatoria, of his art of invention. A new method - a new dialogue - a new form of communication was born.

2. The Use - or the Abuse - of the Lullistic Machine

The publication of the "Ars Magna Sciendi," the Great Art of Science, by Athanasius Kircher in 1669 was not a simple act of plagiarism. Kircher did not even attempt to hide his source of thinking and writing. The complete title of the third chapter 5 includes not only the name of Lullus, but some further very interesting information. First, there is no doubt that Kircher wanted to present the lullistic method of combination again as a new one - 400 years after the invention. In an appendix to the main title of the whole tract, he refers to it as a "new and universal" method! Second, Kircher seems to be convinced that the lullistic art of combination is a secret and mystical matter - a kind of esoteric doctrine! I would like to emphasise both of these points.

To understand these positions, which the Jesuit Kircher announces frankly to every reader of his book, it is necessary to know something about his personal background. Born in Fulda (Germany) in 1602, to a middle-class family, not especially wealthy nor noble people, Kircher was a child of the so-called Thirty Years' War. While attending a monastery school at the age of 16, as an extremely gifted pupil, the Great War broke out. Thanks only to a certain fortuitous protection, Kircher was sent to Rome a couple of years later to give lessons in mathematics and some other subjects. But there - in the eternal city of Rome - he very soon became a real shooting star, a wizard of all sciences!

While nearly all of Germany was drawn into this tremendous war, Kircher took advantage of his unique chance. The philosopher was very much in the right place at the right time! He was able to carry on his studies in every direction, without any obstacle, and he consequently took every opportunity to publish the results of his work. One must admit that Kircher occupied a decisive position on the battlefield of the sciences of his time. With all the treasures of the libraries and the archives of this singular city, the famous Jesuit could utilise every source of knowledge, every book and manuscript.

Following this introduction, I would like to present a certain element of Kircher's art of combination. The circle-figure at the beginning of Section 3. is a simple copy, a pure quotation of the original lullistic figure with the divine attributes. But the alphabet which Kircher proposes as material for his combination-machine reveals the difference to Lullus' at first sight. 6It is not the signification in correlation with the position in the table, because all nine places in each table are filled with the same significations we find in the lullistic tables. It is the notation which creates the big difference!

Whatever he was combining, Lullus used Latin words, words with clearly defined significations. But Kircher broke with this law; he began filling the tables with signs and symbols of a different kind. With this modification, he worked out the concept for a radical new application of the lullistic machine. Kircher attempted to solve problems other than the demonstration of the truth, which the Catholic Church had claimed.

It is important to be aware that Kircher's main task at the time was, in a certain sense, a far more mathematical and philological one, dealing with the graphical representation of limited quantities of signs, letters and symbols. 7This design should clearly be an aid for the memory of the reader and the user, belonging to the old tradition of "ars memoria." Kircher produced a series of graphics to demonstrate the relation between the elements of the combination-machine, the next design a fantastic example. 8 Apropos, Umberto Eco published this figure some years ago in his reknowned second novel, "Foucault's Pendulum."

In this context, Kircher tried to calculate the possible combinations of all limited alphabets (not only graphical, but also mathematical). For a contemporary mathematician, a quite typical problem, one would think. Whereas for Kircher, this was a vital question as he was becoming a specialist in the process of encoding and decoding. Regarding his tabula generalis 9, the more mathematical way of thinking created the great difference between Lullus and Kircher, who was already at that time the grand master of decipherment.

In a word, Kircher pretended to be the only one who could completely understand and decipher the Egyptian hieroglyphic language, and thus the first translator of that ancient system of signs. Although there had been a long tradition of scientists and charlatans working on that infamous riddle, no one had succeeded; until Kircher, there was no accepted solution. In this open situation, Kircher saw an opportunity of winning all. When he had arrived in Rome, some of the rich and mighty families, whose aims were always to provide the next Pope, demonstrated their power by erecting an obelisk of their own (even today, you can see several of them in Rome).

I will not describe the difficulties of procuring an obelisk, of organising the transport, and all the necessary work invested in such a project. Clearly, the erection of an obelisk in the heart of the city was a very important public event. It was always prepared with a translation of the hieroglyphic texts, engraved on all four sides of the desired object. Now Kircher's role in this game becomes clear. He had written numerous translations of hieroglyphic texts, and with the help and the money of the possessor of the obelisk, he published every single translation. As the glory of the possessor increased, so did the glory of the translator, with each obelisk, step by step, book by book (most of them printed in the Netherlands, and some in Rome).

As we now know, Kircher's translations were rubbish - poetical trash. But during his lifetime, no one was able to prove that, and no one was in the position to argue with him because he was placed in the centre of power. In the city of Rome, where more and more wealthy families began to collect Egyptian antiques, Kircher had access to every elegant palace. Some of them were practically museums. Thus he was able to deliver the most important and most beautiful work on ancient Egyptian culture, published in the middle of the century, the famous "Oedipus Aegyptiacus," the solution to all the Egyptian riddles. Four voluminous books, filled with fine copperplates and descriptions of a vast number of pieces of Egyptian art. And filled with very strange and absurd fantasies, as well, which Kircher called translations. I would call it historical science fiction!

In spite of this, he attempted to deliver a whole systematic architecture of that partly forgotten - and without knowledge of the language, nearly inaccessible - culture. These four heavy, splendid books became a standard resource for every researcher dealing with Egyptian history, and nonetheless, very rare. Incidentally, Umberto Eco is a great collector of Kircher's works. Years ago, he said in an interview that he possesses copies of nearly all the books of that strange writer. Moreover, Jean-Francois Champollion, who really was able to translate the hieroglyphic language thanks to the analysis of the Rosetta Stone (found during the famous expedition of Napoleon, two centuries later), did not ridicule Kircher. His translations had been rubbish, and Champollion demonstrated that very clearly, but at the same time, he confirmed that Kircher was indeed the first one to estimate the importance of the old Coptic language as a missing link in the history of hieroglyphic signs! And Champollion, like many others, used the copperplates from Kircher's books to study some objects.

This little excursion to ancient Egypt has not taken us very far away from Raymundus Lullus and his original "Ars Combinatoria" because Kircher always asserted that it was precisely this machine which enabled him to produce his decoding work. Finally, we cannot condemn Kircher for his Egyptian adventure because the great value of his work is connected with several important achievements. Although he was not only the one who re-introduced the lullistic method to the scientific society of Europe, he also demonstrated a new diversity of applications of that combinatorial method, a real method of invention.

Kircher consequently published a book about the problems of encoding and decoding, and he even designed mechanical machines for the task. In addition, he himself collected machines and automata of different kinds: optical and acoustic machines, music boxes, hydraulic and astronomical machines, clockworks, tools and toys, mechanical puppets, and so on. The collection he put together and cared for became as famous as he himself. Many scientists visiting the city of Rome went to Kircher's fantastic cabinet, his encyclopaedic museum of machines.

At the same time, the other Kircher, the Jesuit philosopher, was still fascinated by every current query and studied the tradition of natural science. He published like a writing-machine, without interruption. Books on magnetism, on the activity of volcanoes and the theory of light, a treatise about the pestilence and one about musical machines of all kinds. Of course, he also wrote books concerning religious questions, but very strange books, written in his own special way, for example, a treatise dealing with the difficulties of the construction of the Tower of Babel and one on the precise population of Noah's Ark.

Finally, there remains another very important role, which he fulfilled together with other Jesuit scientists. Rome in the 17th century occupied the position of a kind of switchboard or control panel for the scientific news from all parts of the world! The Jesuit society was not only a secret service with a very powerful and efficient network! We cannot forget that the missionary activity of the Jesuits produced a large body of diverse knowledge. Letters and treatises of Jesuit missionaries and scientists from America and Asia were sent to Rome, and their knowledge was often printed and spread across Europe. The city was a centre of communication. The most significant example of the process of mass-media in the Baroque era was the so-called "invention" of binary calculating, which came originally from ancient China via Rome to Europe -- and especially to the philosopher to whom we turn now.

3. The Age of Calculators

Gottfried Wilhelm Leibniz was the next German philosopher who used the lullistic method of combination in his own way. I will outline some of his more important projects, all dealing with this method and its various consequences. These projects and plans are like paradigms, which can elucidate the fundamentals of the Baroque era. In analysing the extensive work of Leibniz, practically no idea, concept or plan is un-contaminated by a certain mathematical spirit. In the full sense, it may be said that Leibniz was a child of the century of the formula. Especially the second half of the 17th century was the age of the great calculators.

When Leibniz published his famous thesis "Dissertatio de Arte Combinatoria" in 1666 ,10 he was a young student of twenty, full of plans and new ideas. The connection with Lullus and Kircher is more than evident if we remember Kircher's "Ars Magna Sciendi" of 1669. But this was the work of an elder generation! Though the design Leibniz places at the front of his book appears to be a very simple and even trivial diagram - compared to the copperplates of Kircher's books - the entire text which follows speaks a new and different language. It is now the advanced mathematician who analyses the potential power and limits of the art of combination.

Leibniz was not at all interested in any esoteric applications of this method but rather in a way of reproducing the totality of the universe within one science. After reading his very famous treatise on the monads as a model for the art of combination, his new, radical perspective is at once comprehensible. But at this point we must proceed step by step, i.e., examine a more detailed view of the context of his work before we come to the highlights of the Baroque age.

With regard to the situation in Western Europe in the mid-17th century, one phenomenon is astonishing: just a few years following the conclusion of the Thirty Years' War (1648), we find an expanding society of scientists spread over the entire European continent, all of them discussing and debating the same problems and questions! There is a steady stream of communication between these scientists, and the young Leibniz is to take part in nearly every discussion. He keeps up contacts with a great number of people and institutions, always seeking out the frontline of the current investigations. Not only in the widening areas of the natural sciences, but also in the philosophical tradition, Leibniz works hard to become an intellectual who knows about the decisive developments of his century.

An archaeology of our own century of electronic communication reveals its tracks and traces in the Baroque era. There we find, with the experience and the background of the Thirty Years' War, a new beginning of a formalised logic of combination connected with a theory of communication, which is now based on artificial languages. That long war destroyed the trust in the so-called classical, humanistic discourse of the Renaissance! Commencing with that war, in each scientific discipline, a new law rules: the law of experiment! Take Descartes, with his famous concept of self-consciousness -- an experiment; Pascal, wagering on the existence of God; Newton's theory of gravitation; and finally, the technical system of the monads, the communication system constructed by Leibniz.

The spirit of experiment alone ruled the Baroque era - each science, theory and method demanding a new language of its own! Hence, a whole world of new languages, an expanding universe of artificial systems of signs, artificial notations and alphabets developed. This age of communication demanded from its very inception a new subject of writing, of reading and of speaking, and naturally, it demanded the essential integration of the subject within the field of the new languages. From that perspective, as I wrote years ago, the Baroque age was the first "electronic" age, as the indications of all the important fundamentals of computer culture were there: the experiment in permanence and the invention of artificial languages for communication, as a work in progress.

There was no longer a fixed system of knowledge, nor a fixed method of organisation for producing and distributing knowledge. Scientists from all disciplines, from the mathematician to the philosopher, played a new hand: the eternal order of the universe was at stake when they began to calculate new possible orders, when they experimented with new artificial languages. Latin and ancient Greek gradually became more peripheral. Although they were still in use by Descartes, Newton and even Leibniz, the new winning tools were the mathematical languages, the neutral language of formulas, of combination and formalised invention. Thinking was now becoming a kind of calculation, like the fundamental revolutionary process Martin Heidegger described in the 17th century.

And now we return directly to Lullus and Kircher. There is a letter written by Leibniz to Johann Friedrich, Duke of Hannover, in April 1679, which offers the whole ambitious programme of the philosopher. In that letter, we find initially a confession about the source of the method of combination. But then Leibniz starts to criticise Lullus and Kircher because in his view, they did not go far enough in using this art of combination. Regarding his own idea of its use he says:

"My invention contains the application of all reason, a judgement in each controversy, an analysis of all notions, a valuation of probability, a compass for navigating over the ocean of our experiences, an inventory of all things, a table of all thoughts, a microscope with which to prove the phenomena of the present and a telescope with which to preview those of the future, a general possibility to calculate everything. My invention is an innocent magic, a non-chimerical Cabbala, a writing, which everyone can read and which everyone can very easily learn..."

If we could believe this pathetic proclamation, Leibniz would have invented a general problem-solver, like those in the computer sciences have always dreamed of. But of course, the whole gigantic programme was not to be realised. Only some aspects of that proclamation were really transposed into useful applications. At first, Leibniz made a few essential steps toward the calculation of probability, which is obviously a very important problem for all so-called expert-systems, and artificial intelligence in general. He then attempted to transcribe the whole art of combination into a system of formulas because he wanted to calculate every little part of the process, each step and each result of an interval. Thus he used consequently his mathematical skills to produce a new kind of combination by transposing meanings into figures and values.

However, the decisive point in his proclamation was the idea of calculating itself: Leibniz constructed not only the famous calculating engine, with a radical new type of cylinder with which to carry the ten in the case of overflow, a machine with all four fundamental operations, working by a handle. He was also the first one to realise the importance of the binary system. In two clear and lucid treatises 11, Leibniz analysed the possibilities of that system and, demonstrating its four fundamental operations of calculation - addition and subtraction, multiplication and division - he expressed the conviction that one day in future the machines would use this system.

Though hard to believe, in his first treatise, as may be seen in the illustrated page of the manuscript, he even describes a calculating machine which works via the binary system: a machine without wheels or cylinders -- just using balls, holes, sticks and canals for the transport of the balls! Leibniz was indeed the great inventor - in spite of not realising his dream of inventing the general problem-solver. In a note, written late in his life, when he was reflecting on his works, he remembered the old programme of the universal art of combination:

"I thought again about my early plan of a new language or writing-system of reason, which could serve as a communication tool for all different nations... If we had such an universal tool, we could discuss the problems of the metaphysical or the questions of ethics in the same way as the problems and questions of mathematics or geometry. That was my aim: Every misunderstanding should be nothing more than a miscalculation (...), easily corrected by the grammatical laws of that new language. Thus, in the case of a controversial discussion, two philosophers could sit down at a table and just calculating, like two mathematicians, they could say, 'Let us check it up ...'"

Finally, we have again the situation Lullus had already prescribed: two partners are communicating by means of a new type of a machine, and they are solving their problems with the help of a transparent tool, a calculating tool. There is no question about it: they are using a type of interfering media, which is indeed changing the whole situation - which is changing even the basic idea of communication itself! The very origin of the diversity of our modern black-boxes is transparent, without any mystical effects.

At this point on our long way from Raymundus Lullus to Charles Babbage, we should consider a special factor. As I have explained, Lullus had established his new discourse of the "ars combinatoria" in the region of the Mediterranean Sea. Hence his new logic of communication was concentrated on that geographical interface between the different cultures. On my map 12, the immense extension of that space, which I call the network of the Mediterranean Sea, is perceptible. It was his space for travelling and, of course, the space for his mission. From Mallorca to the eastern part of that sea, Lullus left out nearly no important site.

But in the 17th century, the entire situation of Europe had changed. Especially with regard to the organisation of the different sciences, it was another discourse that was the determining factor: the great era of the Gutenberg-galaxy had commenced, and one must admit that the network of the new and revolutionary sciences was spread between the mighty academies and universities of Northern Europe. 13 Books, letters and printed matter of all kinds were now circulating relatively fast within that network of Northern Europe.

Leibniz, an excellent paradigmatic example of the Baroque age, concentrated on the scientific developments at the "Royal Society" in London and the "Academie des Sciences" in Paris. This shifting of the scientific network from the Mediterranean to northern Europe becomes very clear when we note that Leibniz wanted to continue the work of Lullus - in his own way and method - exactly in the middle of Germany. His aim was to construct a triangle of communication between Paris, London and his new location. Situated in a region called Harz, he planned to establish a school-centre to teach his new art of combination, dreaming of the famous school of Athens in ancient times. A very interesting idea; however, it was not to be realised.

I find one of the most inspiring and humourous books about that character of the Baroque age in the novel "The Crying of Lot 49," written by Thomas Pynchon. One may find all the elements of that fascinating century: the open and the secret networks, the different systems of signs and symbols, a short history of the post in old Europe -- all wrapped within a dramatic play. The protagonist is a woman called Oedipa, not "Oedipus Aegyptiacus" - but rather an Oedipa-America, the riddle of America.

4. Modern times - Charles Babbage and his mechanical computer

When Charles Babbage, in about 1822, began to construct the first mechanical computer, he was the philosopher who looked after the heritage of Leibniz. We can find his roots in a deep and fertile accord with the German inventor. Especially in the area of mathematical problems, Babbage even defended the positions of Leibniz against the successors of Newton. But with the first calculating engine Babbage was planning, he had already entered and revealed another dimension of machines. This famous precedent, the "Difference Engine," was a fantastic revolution compared with the machines of Leibniz and Pascal.

From the very beginning, Babbage wanted to construct a real calculating automaton in the full sense of the word. Consequently, he dreamt of a calculating machine working with steam-power instead of a person's manual power via the turn of a handle. When we look at the drawing of that famous machine 14, we recognise that there is, however, still the good old handle for activating the calculating process. The computer as a steam-engine was not to be realised during Babbage's lifetime. Nonetheless, this "Difference Engine" was the first calculating automaton because it could calculate tables of numbers and figures and series of mathematical values of all kinds. The machine could automatically handle the differences between the solutions of a given formula. For example, the formula of square or cubic numbers, or of certain logarithms, and so on.

Babbage, furthermore, was interested not only in the fields of mathematics; he wanted to construct this machine as a support for the English traders and, of course, for solving the difficulties of navigation. England was already at that time ruling the sea. This "Difference Engine" could produce all the required endless listings, which until then were printed in books full of troublesome errors. So this was a question of application right from the beginning: a machine for calculating, a real mathematical tool!

There was another very important invention to follow. Babbage learned something of the machinery of the looms, and he took on that area, too. The loom illustrated here 15demonstrates a control of the processing by a series of connected punch-cards, while the man operates only the machine. The French industrialist Jacquard had made this invention for controlling the looms and producing different patterns. Babbage, on the other hand, grasped at first sight the hidden potential of those cards, as he dreamed of a new and more powerful machine:

"Every set of cards made for any formula will at any future time recalculate that formula with whatever constants may be required. Thus the "Analytical Engine" will possess a library of its own. Every set of cards once produced will then at any future time reproduce the calculations for which it was initially arranged." (Ch. Babbage, Passages from the Life of a Philosopher, p. 119.)

The idea of programming a calculating machine was born, and the name of that machine was "Analytical Engine" 16because it had a certain intelligence, a certain power of analysing a given problem in a mathematical manner. In other words, this machine could execute programs, written and notated on punch-cards. However, it was not merely the invention of this software that made the "Analytical Engine" a real revolution; it was also its hardware. This machine was designed with a structure that we still use today: there is a "mill," the modern CPU (Central Processing Unit), a "control unit" for all transports, then a "storage" and a "memory," the input-area for the punch-cards and a connected printer for all the calculated results! This architecture is, certainly, well-known to us. But it is not an invention of our century.

Charles Babbage himself formulated this description of the power and the principles of that machine:

"Now, it is obvious that no finite machine can include infinity. It is also certain that no question necessarily involving infinity can ever be converted into any other in which the idea of infinity in some form does not enter. It is impossible to construct machinery occupying unlimited space, but it is possible to construct finite machinery and to use it for an unlimited time. It is this substitution of the infinity of time for the infinity of space of which I have made use, in order to limit the size of the engine and yet to retain its unlimited power. (...) Thus it appears that all of the conditions which enable a finite machine to make calculations of unlimited extent are fulfilled in the "Analytical Engine." The means I have adopted are uniform. I have converted the infinity of space, which was required by the conditions of the problem, into the infinity of time."
(Ch. Babbage, Passages ... pp. 124 and 128.)

What Babbage had anticipated in the time of steam-power is nowadays the normal work of the computer, based on electronic principles. We should also note that even his pure and filigree mechanical machine was able to perform all the requisite work in the fields of mathematics. Programming this "Analytical Engine" was, nevertheless, not a simple nor trivial task, perhaps comparable with writing programs in the abstract modern computer-languages like Pascal, C or Assembler.

Incidentally, it was only Lady Ada Augusta Lovelace - the famous daughter of Lord Byron - who truly recognised the power and the limits of that machine and its programming. In 1843, she wrote the earliest critical prognosis on the development of artificial intelligence via her explanation of all the problems involved in programming the "Analytical Engine." It was her genius to comprehend the consequences of this revolution, which combined natural intelligence with the artificial intelligence of the calculating automata. There is a certain disappointment in that some people still do not know why the programming language is called ADA.

In my book about the machines of Charles Babbage, I have tried to present this context, especially the connection between Hegel and Babbage. It was in 1834 when Babbage designed his first sketch of the "Analytical Engine," nearly at the same time when the German philosopher published his important treatise on logic, which can be considered as a pure processing-logic. In other words, Hegel invented a logic-in-process, which can be transformed in a programmable machine to produce knowledge. Both Hegel and Babbage have thus constructed "Difference Engines," i.e., automata with the power of producing solutions to given problems and conditions. Even the famous "Turing-Machine" seems not to be a child of our century.

To understand the entire tradition of our modern computer culture, it may be useful to have a look at my final summary diagram 17, which shows the history of the inventions, as well as the long trajectory of my investigations. You can see that Hegel wrote his famous "Phänomenologie des Geistes," the birth of his dialectic method, when Charles Babbage was still a young boy, awaiting his initiation. His own memory of that specific situation, a key event of his early boyhood, follows:

"Taken to an exhibition of mechanism - Silver Ladies...
During my boyhood, my mother took me to several exhibitions of machinery. I remember one of them well, in Hanover Square, by a man who called himself Merlin. I was so greatly interested, that the exhibitor remarked the circumstance and, after explaining some of the objects to which the public had access, proposed to my mother to take me up to his workshop, where I should see still more wonderful automata. We accordingly ascended to the attic. There were two uncovered female figures of silver, about twelve inches high. One of these walked, or rather glided, along a space of about four feet, until she turned round and went back to her original place. She used an eyeglass occasionally, and bowed frequently, as if recognising her acquaintances. The motion of her limbs was singularly graceful. The other silver figure was an admirable danseuse, with a bird on the forefinger of her right hand, which wagged its tail, flapped its wings and opened its beak. This lady possessed a most fascinating attitude. Her eyes were full of imagination and irresistible. These silver figures were the chef-d`oeuvres of the artist; they had cost him years of tireless labour, and were not even then finished."
(Ch. Babbage, Passages..., p. 17f.)

About 50 years later, Babbage took part in the big World Fairs in London. Both expositions, in 1851 and 1862, were to demonstrate the power of British industry, the achievements of trade and, of course, also the level of scientific development. In 1862, even the new "Difference Engine" was presented in a special hall of machines. But these great exhibitions, linked up with the tradition of Kircher and Leibniz, presented not only new inventions and new machines. They established a new language and a new way of thinking. Very soon it became clear that the language of the calculating machines could be combined with other languages and other systems of order. Programming a machine is nothing other than using a certain grammatical order. The "ars combinatoria" Lullus had invented is not as far away from the language Assembler as some might believe.

I would like to close this essay with a deep and keen-sighted statement of some late followers of Raymundus Lullus. In my own opinion, language itself is the permanent source for all kinds of "butterfly effects." I believe that Laurie Anderson and William S. Burroughs are walking in the footsteps of the lullistic tradition when they say: "language is a virus from outer-space..."

1 Plate 1: The lullistic logical machine, taken from a manuscript of the Ars Combinatoria of 1305.
2 Plate 2: Prima Figura, taken from an edition of the Ars Brevis, Paris 1578.
3 Secunda Figura, taken from an edition of the Ars Brevis, Paris 1578.
4 Tabula Generalis, taken from an edition of the Ars Brevis, Paris 1578.
5 Ars Magna Sciendi, in XII Libros digesta, qua Nova & Universali Methodo... , Amsterdam 1669.
6 Alphabetum Artis Magnae, taken from Ars Magna Sciendi, Amsterdam 1669.
7 Principia memoriae, taken from Ars Magna Sciendi, Amsterdam 1669.
8 Epilogismus combinationis linearis, taken from Ars Magna Sciendi, Amsterdam 1669.
9 Tabula Generalis, taken from Ars Magna Sciendi, Amsterdam 1669.
10 Logical figure, taken from "Dissertatio de Arte Combina-toria," Leipzig 1666.
11 Second page of the original manuscript "De Progressione Dyadica," dated March 1679.
12 The network of the Mediterranean Sea at the time of Raymundus Lullus.
13 The network of Northern Europe at the time of Leibniz.
14 "Difference Engine," drawing of a part of the machine, which was shown at the exposition of the World Fair, London 1862.
15 Loom with punch-cards, about 1830.
16 Plan of the "Analytical Engine," ca. 1840.
17 History of the inventions in the fields of logic-theory, communication-machines, calculating-machines and computers.

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