This is an extract from LEIB-CHR.DOC. Characteristica Universalis is abbreviated as CU .

Abbreviations for often used Terms

AC: Ars Characteristica

AL: Adamic Language

CS: Character System or Characteristica

CU: Characteristica Universalis

FCS: Formal Character System or Symbolic Machine

UL: Universal Language

UT: Universal Thinker or Universal Thinking

ST: Specialist or Scientific or Expert Thinker or Thinking

The terms Character and Symbol will be used as synonymous in the following discussion. This implies, for example, that the picture of a man can be used as a symbol in a script, and it can represent a character of a CS. Thus a CS can also be called a Symbol System.

Abbreviations for often used Bibliographic entries

A: LEIB-A

LEIB-BB

BLW: LEIB-BLW

C: LEIB-COUTURAT

ES: LEIB-ES

FS: LEIB-FS

GP: LEIB-GP

HA: HAARMANN-SCHRIFT

K88: KRÄMER-SYMB

K91: KRÄMER-VERNUNFT

K94: KRÄMER-GEIST

This is an extract from LEIB-CHR.DOC. Characteristica Universalis is abbreviated as CU .

Abbreviations for often used Terms

AC: Ars Characteristica

AL: Adamic Language

CS: Character System or Characteristica

CU: Characteristica Universalis

FCS: Formal Character System or Symbolic Machine

UL: Universal Language

UT: Universal Thinker or Universal Thinking

ST: Specialist or Scientific or Expert Thinker or Thinking

The terms Character and Symbol will be used as synonymous in the following discussion. This implies, for example, that the picture of a man can be used as a symbol in a script, and it can represent a character of a CS. Thus a CS can also be called a Symbol System.

Abbreviations for often used Bibliographic entries

A: LEIB-A

LEIB-BB

BLW: LEIB-BLW

C: LEIB-COUTURAT

ES: LEIB-ES

FS: LEIB-FS

GP: LEIB-GP

HA: HAARMANN-SCHRIFT

K88: KRÄMER-SYMB

K91: KRÄMER-VERNUNFT

K94: KRÄMER-GEIST

In 1677 Leibniz states the main objectives of his search for the CU, which he had entertained since his youth:

Leibniz saw the CU as a means to amplify the human mental system. He had said that his CU would improve the performance of the mind as did the telescope and the microscope for the eye. Much as the microscope can show the innards of nature, the CU would not only show the superficial features of objects (their surfaces), but the interior forms. One the many passages in his voluminous correspondence where he expressed this is cited here.

This metaphor is worth exploring a little bit. Just shortly before Leibniz wrote this, in 1670, Leeuvenhoek had constructed the first microscope [105]. This had caused a lot of stir in the scholarly world. It had also kindled a lot of imagination, because here worlds became visible that had been very hard to even imagine a generation before. This was a totally different impression than the development of the telescope which only made the observation of stars, that were well known since antiquity, more accurate.

In 1609 Galileo [106] had constructed a telescope and he pushed the revolution of astronomy with his invention. His observations of the sunspots and the satellites of Jupiter gave definite empirical evidence of the new copernican ideas invalidating the ptolemean and aristotelic views. Reading the book of Copernicus was one thing, looking through the telescope and actually seeing the sunspots wander across the sun or seeing the satellites circling Jupiter like a miniature solar system is an entirely different matter.

Today, we experience the rapid development of new mental tools . These are all connected with the computer, but calling them "computer-based xyz" is misleading, because the computer just serves as a base material, just like wood serves as a base material for a wooden desk. The character of the desk is not determined by the character of the wood. The new mental tools are characterized by a combination of visual and graphical display, equally powerful input technologies, and the data processing capability of the computer. Therefore we call the resulting tool no more a computer but a symbolator . We want to show here that there is a direct connection between Leibniz's thoughts on the CU and the symbolator as it is now coming into technological reach. This development has just started, since about ten years. We may call Alan Kay' s ideas of the Dynabook the first roots, and the Macintosh computer the first attempt at real-life implementation of the device. The road of development will continue to go on for about twenty more years, until we can expect the data transmission rates for networks and the data input/output rates for the graphical devices adequate. And, of course, research will have to be done for the right kind of Character for the Mind or Ars Characteristica , as Leibniz called it, to develop. The paper presented here is also an outline for a possible program of work to continue in the next twenty years.

. Leibniz inherited two thousand years of thought. He really did inherit more of the varied thoughts of his predecessors than any man before of since. His interests ranged from mathematics to divinity, and from divinity to political philosophy, and from political philosophy to physical science. These interests were backed by profound learning. There is a book to be written, and its title should be, The mind of Leibniz

(WHITEHEAD-MODE , p.3)

There have been many books written on Leibniz. One more book will not do. The mind of Leibniz cannot be mapped in a book, and the only adequate medium would be something written in his Characteristica. Since that is not yet available we might look if a hypermedia project on the mind of Leibniz might be more adequate than a book.

Documenting Leibniz' work on the CU would be an ideal subject for a hypertext project. This is because all the remarks and notes of Leibniz on the CU reside in thousands of locations distributed evenly through his voluminous works and they relate at the same time to two distinct domains: 1) the direct context where he had made the remark, and 2) to his overarching idea of the CU. Excerpting all the remarks in a separate text on the CU, as must of necessity be done in a book specializing in the subject, will destroy the equally vital context connection. This can only be preserved by directly hyper-linking into the original text. From there, the researcher may then browse into the context of the remark himself instead of going to the library and trying to get the original text as is nowadays necessary with the book medium.

Leibniz was by no means the first nor the only one to have worked on a universal language (UL) or character system (CS). Indeed, it could be said that the project of a UL was the craze of the day in 17th century proto-scientist circles (K88, 96). This quest can (somewhat arbitrarily, ANM:ADAM [107]) be originated with Jacob Böhme (1575-1624) who had called for the re-discovery of the Adamic Language (or AL) , the original language humans were supposed to have spoken before the events that were expressed in the biblical myth of the building of the Tower of Babel . Francis Bacon (1561-1626) proposed a set of universal characters in "The Advancement of Learning" and "De Augmentis Scientiarum" in 1623. The development was carried on. The list includes: Marin Mersenne 1636, John Wilkins 1641, Francis Lodwick 1647, Thomas Urquaart 1653, Cave Beck 1657, George Dalgarno 1661, Johann Joachim Becher 1661, Isaak Newton 1661, Athanasius Kircher 1663, Johann Amos Comenius 1668, Johann Sturm 1676, De Vienne Plancy 1681. (K91, p. 242; K88, 95-97). Leibniz was well aware of the approaches at UL and AL of his forerunners. Considerable influence in his thoughts had the combinatorical scheme of the Ars Magna of Raimundus Lullus (1233-1315) which he cites in "De Arte Combinatoria " of 1660. Lullus' system was not a language system but it played considerable importance in Leibniz' logical work on the CU.

The end of the middle ages saw the decline of Latin as the standard language of savants in Europe. The printing press had given considerable impetus to this development. The new technology made mass distribution of books at lower prices feasible, but the mass market was in the native language speakers and readers. In England, France, and Italy, the native tongues were progressively used in publications of the academic circles. Germany lagged behind by about 100 years but finally followed. The loss of the universal communication medium of Latin was quickly felt. The european overseas discoveries showed the need for communication in international trade and politics for which an international language would be the answer.

Although after Leibniz, the activity at CU projects largely subsided, the interest in UL remained. 1765, in the Encyclopedie of Diderot and D'Alembert , Faiguet , the treasurer of France, published an article titled "Nouvelle Language " which anticipated and outdistanced proposals of more than a hundred years later. At that time, the late 19th century, came a veritable surge of activities arose toward constructing international languages. They were not intended as logical languages (often they were quite illogical). In 1880 Johann Martin Schleyer invented Volapük . It had some grave defects and created ardent following as well as heated controversies and arguments, wich resulted in a number of descendant or alternative projects. The best one known and still used today by an interest group is Esperanto invented in 1887 by Ludwig Lazarus Zamenhof . The emerging science of linguistics was not too interested in those international language planning projects, but some individual well known linguists actively participated in the work. One of them was Couturat , who had done important work on Leibniz's scriptures. Later linguist Rene de Saussure invented Esperantido . In 1903, the mathematician Giuseppe Peano created Interlingua , a version of Latin which had a very simplified grammar. He also referred in his work to Leibniz. Since most european languages are either direct descendants of Latin or have a large number of Latin loan words (like English), almost every well-educated European can read Interlingua at first sight. An example paragraph will demonstrate this:

(BODMER85 , 476)

The great Danish linguist Jespersen invented Novial in 1928. The English linguist Ogden recognized the fact that there is an almost-universal language spoken already all over the earth: English . English grammar is simpler than any other indogermanic language coming close to Chinese and Japanese which is one of the reasons of its large following (its spelling is instead much more difficult than most). Ogden re-worked the language to a more simplified form and called it Basic English . Since he wanted to keep the English "touch and feel" he could not remove the spelling difficulties because this would have involved forming a new vocabulary. (The varied, and sometimes strange fates of the inter-language projects and their inventors is amply described in BODMER85 , 448-518, also COUTURAT-LANG ).

Modern computing has brought another wave in the construction of Interlanguages . Machine translation of natural languages is a subject that is not completely solved and may not be solvable at all. Even if there is a measure of success for specialized applications, the computing costs are very high because the ambiguous sentence substructures have to be analysed with a high degree of content orientation, forcing the use of vast knowledge based systems that consume an enormous computing power aside from being extremely labor-intensive to develop.

Machine translation forces the research into intermediate structures that serve as common links between national languages - such structures could be called bridge-languages . The ability to unambiguously parse a language by computer has become the most important consideration in these projects. It was discovered some time ago that the South American language Aymara had a grammatical structure that allowed it to be parsed unambiguously. Thus it can serve as a bridge-language.

The project of Lingua Logica Leibnitiana or L³ goes a somewhat different path. It aims at creating an interlanguage structure, not a whole new language. (BIB-AG:LEIB-SYM.DOC, Appendix: "L^{3 -} Leibniz Logical Language ", ->::LEIB-LANG ). Its main point is that it is sufficient to create a universal unambiguous syntactic structure wich is computer parsable. It makes explicit use of the substructures of language in form of a phrase structure grammar . This way, the syntactical and referential structure of a sentence is explicit, not implicit as in a natural language and can be parsed unambiguously.

The main obstacle of any interlanguage is the problem of overcoming the economic barrier of the man-years involved when a community of users has learn a new language. This has never been solved by past interlanguage projects. The tradeoff is the simplification of communication versus the investment in time and effort any person wanting to use the language has to make. If she has to learn only a syntactical rule set, it is easier than learning that and a new vocabulary on top. And if the computer gives ample help for the syntactic rules there is still less investment to make. That is the main reason why today, interlanguages have a better chance than in yesteryears. There is now a wide possibility of computer support for constructing sentences by interactive support software. The initial effort invested to learn the new structure is much smaller than it would be for a whole new interlanguage. The user can essentially keep his whole native or specialist vocabulary which can be automatically translated with very little computing effort making real time translation with the computer power of a modern desktop PC economically feasible.

The various approaches of philosophical languages centered around the assumption derived from the idea of AL that it is essentially possible to assign a characteristic name for any and every thing existing. This was the model of "real characters" which Bacon formulated and Dalgarno and Wilkins elaborated upon. Wilkins' work was the most ambitious and extensive of these efforts. The base of his work was the classification of all the knowledge he knew at his time. He constructed a hierarchy of forty different classes, such as plants, animals, spiritual actions, physical actions, motions, possessions, matters naval, matters ecclesiastical etc. Wilkins' idea of categorizing all existant knowledge in forty categories was along the line of Raimundus Lullus ' combinatorics of basic principles. The system Wilkins created was ideographic, with a type of mark for each of the forty classes such that each concept could be constructed from a combination of these forty elements. Compared to the only other existing ideographic system, the Chinese script , this was a definite breakthrough in ideographic CS design. The Chinese script has about 240 radicals wich are assembled in any other way than logical, making the up to 10,000 resulting composita completely new conceptual units to be memorized as a whole. The validity of his effort has to be compared to the language structures existant at his time. Whereas a single Greek verb can have over two hundred different appearances due to flexion , conjugation and concord , and Latin about one hundred, Wilkins ' grammatical system had only forty different appearances which were uniform throughout the system (orthogonal). Although the principle itself was good, its execution suffered from the procrustean nature of the category system he applied.

Bodmer describes his classification as:

(BODMER85 , 452, 454-5).

An outlook on the mental and the psychological climate of the 17th century is appropriate. As Toulmin and other researchers have shown, the time of the origin of modern science, the time of Descartes , Leibniz and Newton was anything else than an optimistic, bright, prosperous, and enlightened age. To the contrary, it was a time of extreme cultural agony, fear, disorientation, and doubt. This was the time of one of the greatest human desasters and cultural breakdowns that had devastated central Europe , namely Germany and Bohemia : the 30 year war . (->: DESASTERS ) (See also: TOULMIN-KOSMO , BERMAN83 p. 25-61, PIETSCHMANN83 , ZINN89 )

In all this uncertainty, fear and doubt was born Leibniz who was all too painfully aware of the cultural desertification that had befallen german scholarship in the wake of the great war. It was for this desertification that he was virtually isolated in his lonesome intellectual outpost at Hannover yearning for the mental companionship of the intellectual circles in the great and prospering cities Paris , London , and Vienna , where he had, alas, not been able to find permanent employment by the local ruling elite. On the contrary, he had come to some bitter conflicts with the english savants, partly because he had a priority conflict with Newton over who had invented the first infinitesimal calculus but the rift was a deeper one. The mental culture of the english intelligenzia had developed into a direction which Leibniz considered deeply problematic and he tried to explicate that at the end of his life in the Leibniz-Clarke dispute .

This climate was the ground which bred Leibniz' idea of CU. He had intended it to be the means by which to decide philosophical questions. He had stated: "Whenever we have a philosophical question to decide, we will turn to the CU and calculate the answer." Now we may ask what is the outcome for someone to want to decide a question when he gets into a dispute with someone else? Deciding something means one party wins and the other party loses. It is in the terminology of game theory "a zero-sum game". This is not exactly the best way "to win friends and influence people" as Dale Carnegie has stated some time ago.

We don't know whether Leibniz was aware of this when he formulated his project of CU. But it fits well within the intellectual climate of his time and, unfortunately, also the following 300 years. Our modern scientific and technological age has become an age of decision . Our modern time is a time battles: disputes are not settled, but battled out in the courts and if that fails, on the battle fields. Warfare has become the solution after politics have failed. (War is the continuation of politics by other means). There is an unbroken chain of wars that devastated Europe up to and including the megaspectres of the first and second world war which all hinge with unflinching logical and consequential deadliness on this one ever-recurring theme: "let us decide, Sir". This may not be what Leibniz had intended.

What the european mind has lost in the shuffle is arbitration . Toulmin has made the point that in the age of Renaissance Humanism before the 17th century, there was an atmosphere of higher level of tolerance for ambiguity and dissension than our cherished preconceptions of medieval history make us think (TOULMIN-KOSMO, p. 11-13, 48-59).

The words decision and computation have the etymological root of cutting : putare , cadere . In the german language, entscheiden means: pulling the sword out of the scabbard. The words entscheiden (decide) and schiedlich machen (arbitrate) still share the same root in German. Leibniz was deeply involved in re-uniting the divided churches of christianity, in solving the fundamental conflicts which had caused the 30 year war, and he failed. He also had failed to make the right friends and influence the right people at the courts of the european rulers to find a position where he could influence european politics better and pursue his intellectual interests in a more fruitful way instead of having to collect the tedious bits of data that were necessary for the completion of the history of the house of Hanover which he had at one time promised and which had grown into a millstone around his neck keeping him from more productive work. Was his method to decide questions maybe not the right approach? Would it not have been better to intend the CU as a device to arbitrate questions instead of trying to decide them?

Descartes had in his own work on the subject of UL stated the main and principal problem one would have in constructing one:

Descartes to Mersenne 11-20,1629, DESCARTES-WORK , 1.81

Leibniz saw the problem equally well but true to his intrinsically optimistical nature he had an answer to that:

LEIB-COUTURAT , 28

Leibniz was proposing what the computer industry nowadays would call a bootstrap . The metaphor means lifting oneself by his own boot-straps. (Sometimes it is a trap also, as the word unwittingly implies). This laudable technique was popularized by the Baron von Münchhausen who didn't find as short a term for it but a much more interesting mode of operation: He called it "pulling yourself out of the swamp by your own pigtail". Now this is somewhat ambiguous because here it refers to the pigtail fashion of wearing the hair tied together that was popular from the time of Frederick the Great up to about the Napoleonic wars which was the time when Münchhausen lived. Although this was mostly regarded as a good joke of the great lie-telling baron, there is a deeper significance that we may hint at. The Indian Brahmin rule of hair dress consists in shaving all the hair of the head, leaving only a little pig-tail just where Münchhausen had his pig-tail. In Brahmin wisdom, this part of the head is where the soul enters and leaves the body. Lifting yourself by the pigtail has a quite special meaning, looking from this perspective. Leibniz may or may not have been aware of such a connotation but he surely was capable of it.

Sybille Krämer has summed up the logical reasons why Leibniz had to fail in his project of CU. The CU is a petitio prinicpii, i.e. it presupposes what it tries to achieve (K88, 107). The situation is not devoid of a certain paradoxical irony: Leibniz has himself laid the logical foundation for later logicians to prove that his aims for the CU were logically untenable. Goedel has proved that no formal system is complete (K88, 146-153). That would have to be the case if a CU were feasible (K88, 153).

Leibniz had given the CU the most far-reaching and deep-searching treatment of all researchers before and after him. He introduced scientific linguistic and logical methods in his project that after him grew into independent sciences. "In Leibniz's work converge the tendencies of language-theory (linguistics ) and language construction of his time like a collimating lens" (K88, 95). He worked to unite two entirely different objectives in his CU, namely that of Universal Language (UL) and that of Ars Charcteristica (AC). The idea of UL is derived from Jacob Böhme 's vision of the one Adamic Language (AL) that all of humanity was supposed to have spoken before the babylonian dispersion . From Böhme , the approach taken by Leibniz' forerunners was still strongly centered around the assumptions derived from the mythical cultural programming of biblical origin. The UL is mythical, the AC is logical. The problem of AC is to find a logically coherent operational system of truth as an instrument of scientific thought.

We will loosely follow the structure of Leibniz' research, not focussing too much on what he had researched but how he had gone about the task. As was said before ( ->: LEIB-SPIRIT and ->: LEIB-HORIZON ), the details of his work have been superseded by more modern data. His universal way of working though, has never been superseded, nor even successfully emulated.

The thematic centers of the CU can be classified in the areas grammato-logical, linguistic, and noetic.

This term is constructed from grammato- and logos . The term logos is one of the oldest and deepest terms of greek philosophy. Its etymologic derivation is from lego meaning: "to collect". Heraklit has given it its current philosophical content. For him the logos is the principle of the all-there-is . There is a considerable overlap with nous . While nous has more a connotation of recognizing and cognition (cog-nous) , logos has a connotation of manipulation. Its semantic field is wide.

A few meanings are:

Reason, thought, speech, the spoken word, insight, understanding, to compute, to calculate, law (engl.: legal), scientific enquiry, logic.

The affix grammato- denotes that the main focus of Leibniz' work was centered on written systems. The greek roots gra- for gramma and graphe denote things written, etched, chiseled, marked, scratched, inscribed which was the original greek method for writing (as opposed to chinese, which was painted with a brush). The word grammata denotes the letters of the alphabet. In the word grammatike appears a later derivation as the english word grammar. The grammatikos was the expert on writing, later the writing teacher.

The root graph- derives from the instrument used for writing, the stylus. Its use is almost synonymous with the former.

As will be expanded further in the chapter on Logocentrism , one main problem deeply affecting the CU is the matter of phonetic or graphic orientation. In greek thought, logos was intimately connected with the spoken word, and its inscription was thought secondary and inferior. Plato 's comment on writing in Phaidros exemplifies this attitude. Leibniz was one of the first workers assuming the independence of the gramma, or graphe, the inscription, from the phone , i.e. (the transcription of) the sound of the word. Leibniz' work on the CU centered around forming an independent graphic system.

Noos or nous is also one of the oldest and deepest terms of greek philosophy. Its meaning is as deep as logos. Anaxagoras used it for the principle, the archae of the all-there-is . Connected with the similar but not identical meaning of logos and nous are subtly different schools of philosophy.

The word roots gnomae - and gnos - belong to the same meaning-field. The verb noeo means: to realize, to understand, to think. The English verb "to know " is a direct derivation of the greek word.

(From LEIB-CHR.DOC)

Between ca. 600 and 1500, the heart of cultural development west of the Oxus was in the Arabic countries. Notably the centers of Bhagdad and mauric Spain. There, a profound science of writing and language developed of which the Cabbala is just one branch. Jewish savants were prominent collaborators working side by side with their north-african colleagues in the same spirit and to the same aim. What they produced was not natural science as it is known after Newton and Galileo. It was a science of different taste and metaphysics, but is was very highly evolved indeed. It didn't lead to the automobile and the computer, but it also didn't lead to the atomic bomb. The Cabbala just expresses one fundamental trait of this metaphysics. The semitic languages Hebrew and Arabic share the same Aleph-Bayt pattern in their Autiot or Othiot system and there is a similar science like Cabbala in Arabic. But here is neither the place nor the time to follow these threads. The limits we see are the limits of our eyes.

(Literature: FLUSSER-SCHRIFT , HUNKE60 , HUNKE79 , KABBALA-SCHULITZ , KABBALA-LOVE , KABBALA-WEINREB )

By modern natural scientific standards, the idea of an Adamic Language that was common to all mankind before the days of the Tower of Babel is just another biblical myth that has folklore value at best and is better left to the fundamentalists and new-born christians. But matters should not be taken so lightly. The bible is a genuine piece of original mythology. It is just not the only existing original mythology and it is not the one-and-only-true-one to the consequence that all other mythologies are works of the devil that have to be burnt at the stake together with their proponents. The bible happens to be our mythology, i.e. the one that was adopted by christian religion and therefore the christian culture of europe as standard belief system base for the last 2000 years. There has been a historical struggle to detach from the hypnosis of a mental and psychological mechanism that tried to chain human thinking to the biblical version as the only one to believe in. In this struggle it was rightly and necessarily the outcome that the detachment from our guiding, and blinding myth was fought through. Now we are in a better position to turn back and re-appraise what we have left behind. (See BIB:MYTH , CAMP72 , THOMPSON87 10-24, CASSIRER-MYT )

The meaning of the hebrew word adamah is: (made) of dust . There is a tale in the Midrashim , the jewish folklore version of biblical stories: When god had finished his creation with the first human being, Adam , on the last day, he ordered the angels to bow before his last and highest creation. One of them, Samael , of the highest order of angels, refused to bow and said: "Thou hast created us out of the splendor of thy glory. Why should we bow before a creature that is made of dust?" God replied that Adam, even though he was made of dust, was superior to Samael in wisdom and understanding. Samael was enraged about this and challenged god to prove this. So god lined up all the other creatures and told Samael to name them. Samael was not able to utter one word. Then it was the turn of Adam to name them. And god implanted wisdom in the heart of Adam and asked him about the name of each creature in such a way that the first letter of each question indicated its name. This way, Adam realized the true name of all-there-is . Samael howled with rage and rebelled against god. From then on he is also known as Satan. (GRAVES-GEN , p. 12).

The mythological importance of Adamic Language is that Adam gave the things and animals the true names. The true name means that the name was not just an arbitrary sound pattern that could be exchanged for any other sound pattern like "foo" for "poff". Using the true names for things and people was of great magical value. Because knowing the true name meant having power over the thing or the person. "Haec nominum impositio delatat imperium et potestatem primi hominis in animantes" (PEREYRA , 525). The magical power of the true name was even used in antique warfare. Spies were sent out to discover the true name of a city and when it was discovered, the city was helpless and fell prey to the enemies. The jewish tradition of Cabbala derives from this usage. The letter has not only the atomic function of encoding an otherwise meaningless sound, but it has meaning in itself. In commonly known forms of the Cabbala , this meaning is numerical, thus giving a pythagorean connection.

Knowing the true name of something means knowing its essential nature and properties. The quest for the essential nature is also expressed in the greek philosophical tradition: Plato described the current lingustic theories of his time in Cratylus . He called his version of the true name the idea of things. Aristoteles sought the ousia (Metaphysics). In scholastic philosophy, this became Substance and Accidence .

The quest of universal language was an attempt to return to the true names of Adamic language. Only when using the true names was it sensible to create a language that was useful for all mankind.

When (the right kind of) dust is mixed with water, in becomes clay. Apparently, the hebrew adamah serves a double semantic role of meaning both dust in dry form and clay in wet form. From this, Vilem Flusser has created the modern myth of in-formation. He had himself some original jewish mythology to refer to from his childhood days. (Insertions in square brackets [...] are by A.G. ):

. The issue is: to create in-formations, to communicate [transmit] them, and to store them durably (if possible: aere perennius). This way the free spirit of the subject and its wish for immortality is counteracting against the treacherous inertia of the object, its tendency for thermal death . Inscribing writing, the inscription, seen this way, is the expression of free will

FLUSSER-SCHRIFT , 14-17

The cabbala belongs to the thought universe of the Semitic language family. Today, the best known of these are Hebrew and Arabic . They share the same Aleph-Bayt pattern and the autiot or othiot system. The formation law of semitic words follows the segmental scheme of a group of consonants, mostly three, sometimes two or four (see also "Systematics of CS" further down, ->: SYS-CS ). Each semitic word is formed by such a consonant segment and the various meanings derived from this segment are formed by vowel variation. For example: the words muslim and islam have the same segmental root: -slm-. This scheme allows for a totally different combinatorical pattern of meaning formation than in the indo-aryan languages and this is the reason why arabic poetry is almost impossible to translate into european language, or why the q'ran doesn't really make the same sense when translated as in the Arabic original. It was therefore fully justified to categorically forbid its translation - and the islamic faith was ill served by the breach of this injunction.

Although it is mostly believed that the Cabbala is jewish only, this is not so. There is a similar science like Cabbala in Arabic which will be further discussed in the section on "The Language of Pattern" ->: LANG-PAT . The fact is that the similar thought structure of semitic languages leads to similar metaphysical systems. (Literature: KABBALA-LOVE , KABBALA-SCHULITZ , KABBALA-WEINREB , SUARES-SEPHER )

Scholarly opinion on the origin of the cabbala is divided: some think that it is a system originating in the Arab-Hebrew schools of Bhagdad and Granada , some believe it to be extremely old, antedating the Mosaic form of Judaism and the Torah . The best known and documented transmission goes via moorish Spain. The renaissance cabbalists like Pico della Mirandola (and following the line onward to Jakob Böhme and Leibniz ) had their materials from this source. For the other view, of the antique cabbala , there is hardly any direct documentary material available from B.C. times, but cross-cultural examinations and structural analysis yield ample clues that point to this view.

The Sepher Yetsira (from now on: SY ) is the fundamental text on the Cabbala . The interpretation given here follows Carlo Suarès' work (SUARES-SEPHER ).

The second chapter of the SY describes in six verses the Autiot scheme.

See also ILL:K1-K5 .

SUARES-SEPHER, p. 23

The interpretation of the cabbala as given by Suarès follows a thought pattern that we will find again in the chapter on "Symbolic Machines" or "Formal Character Systems". (See: ->: SYM-MACH , ->: ARS-CHAR ) On page 38 to 40, Suarès describes the cabbala of the SY in terms recognizable as an approximation to the Ars Characteristica aspect of Leibniz' Characteristica Universalis .

SUARES-SEPHER, p. 39

The terms used by Suarès are somewhat on the poetic side, but we can recognize the universal, combinatoric structure of a formal CS as Leibniz also had intended. Whether this interpretation can be worked through, or operated, cannot be determined here since that would require a thorough understanding of hebrew.

The cabbala is in this view an Ars Characteristica that has only been confused and confounded with (mostly theological) meanings by mystics first and later by rational theologists like Gerson Scholem.

SUARES-SEPHER, p. 20

The simple premise for this is that any meaning a human mind can give to the primordial (archae -ic) calculus of the cabbala will be a limiting meaning. The human mind must go about working through the cabbala the same way a computer must go working through a formal algorithm: mindlessly, simply following the pattern. Any meaning that arises will detract from the path and must be eliminated.

Suarès gives one striking example of how to go about to eliminate meaning. He cites a theistic interpreter of the cabbala , and then adds his own comment:

SUARES-SEPHER, p. 19-20

We can see in this quotation how the theistic thought universe extending from Moses via St. Paul , Augustinus , Mohammed , Thomas Aquinas , Cusanus up to Leibniz is with one stroke quietly wrapped up and discarded. We may even refer back to a well known injunction of the Bible itself: "Thou shalt not make an image of Me." This has been deeply misunderstood by jews, christians, and muslims. Image making does not stop at pictures and idols. Any meaning is a mental image . Not even that is allowed.

It might be instructive to compare the exact wording used by Leibniz concerning his metaphysical interpretation of the binary system as stated in his letter to Bouvet (LEIB-BOUVET ) and in LEIB-SIEMENS , p. 31-60.

Leibniz' letter to Pater Bouvet, Braunschweig, 15. 02. 1701:

A further discussion of the cabbala requires a thorough understanding of Hebrew, which we cannot supply here. What we can do, is look at the formal aspects of the cabbalistic system. An important observation is the tree structure of the autiot characters. Since the name of each character can be expanded in a manner of context free grammars , each character or aut gives rise to an endlessly repeating tree structure.

ALEPH is constructed of

ALEPH LAMMED PHAY

LAMMED is constructed of

LAMMED MEM DALLET

MEM--MEM--MEM

DALLET is constructed of

DALLET LAMMED TAV

and so on.

Now this in itself may be nice but there is nothing new to it. We can do the same with the Greek Alpha-Beta system and form a tree, or in whatever language where the letters have full names. But we have a start that we will come back to. In the chapter on fractal character systems we will show a way to make good use of a nested character structure. Its system is somewhat different but it is following the same line of thought.

A very interesting possibility should ensue when we can find a systematic means of changing the tree hidden under a character as influenced by its neighbor characters. This has not been envisioned by the cabbalists who had nothing but their unaided brains to do their symbol processing for them. (ANM:LIFE [108]) Such exploits are better done with the symbolator.

The matter is so important because here we are hung on a subject which Leibniz couldn't solve in his CU: how to find basic atomic primitives for the characters of the CU from which to construct the aggregates. This may be unsolvable because there may not be any basic primitives to combine just as we found out in particle physics (ANM:PARTICLES [109] ).

The hermeneutic circle means that in order to know the meaning of a word, we first must know the meaning of its context. And from the combined meanings of all the words in a sentence or a paragraph we construct the meaning of the sentence or the paragraph thusly ending up again in the context.

SUARES-SEPHER, p. 19

We now make a little jump to ancient Greece: The fundamental cabbalistic thesis is concordant with Plato 's statement in Timaios :

TIMAIOS, 30b-c

(From LEIB-CHR.DOC)

Sybille Krämer has elaborated the grammato-logical approach taken by Leibniz with the Ars Characteristica (AC ) aspect of his work on the CU (K88, K91). AC means a formal , operational CS or FCS as it is called below (ANM:ARS [110]). A CS may be any liberally chosen system that only has to satisfy the condition that its symbols are unambiguous and give the means of adequately mapping the target domain (i.e. we have to have the means to form words, or thought-pictures, for all the things we want to describe and refer to). To fulfil the condition of operationality or formalization, we must be able to perform logical operations with the system.

Sybille Krämer has introduced the term Symbolic Machine (K88, 2) for a formal CS (from now: FCS ). The FCS is a symbolical device to transform character strings. The FCS depend on three conditions:

1) Typographical fixation .

It is necessary to be able to produce and re-produce unambiguous characters in definite order.

2) Schematization

A formal description of the manipulation must be given such that it can be reproduced

3) Interpretive Transparency

The Operation of the Characters used must not depend on any meaning

K88, 1-2

Every process that can be formally described can be described as operation of a symbolical machine. Computer s are devices that can imitate any symbolic machine . The idea of formalization in the form as it appears in modern western science was condensed and formulated by Leibniz. Its beginnings can be traced far back in the history of arithmetic and algebraic symbols . (K88, 3-4)

Counting and counting marks are as old or older than the oldest ideographic traces of writing. A wolf bone age 30,000 years shows groups of grooves in groups of five, giving an indication of counting use (K88, 9). Clay tokens found in Mesopotamia of -9000 show a widespread use of token counting systems. (K88, 8; see also: "About Character Systems" and "The Origins of Symbol Systems" ->: ORIG-SYMB .) The evolution of counting systems brought a successive abstraction and separation of the things counted from the result determined by the counting: the number . This separation was not always clear: In primitive languages and in some modern examples we find one word for an item, alone and a different word for the same item, in greater number. E.g. 10 cocoa nuts means koro, 1000 cocoa nuts mean saloro in the Fiji language. (K88, 5-7)

The first step toward calculation came with the representation of numbers by auxiliary or representative sets - this is also called the analogical method (K88, 8). The first objects that were used for representative sets were the fingers (digites). For this reason most number systems used by humans are decimal. "Calculare " is the latin word for the ubiquitous calculation device of antiquity up through the middle ages to the 14th and 15th centuries. Calculare means using little stones to represent the numbers and move them on a board to sum and subtract. In greek, these are called psephoi . The word psephyzein means the same as calculare. The "calculation" techniques do not use numbers but quantities . (K88, 28-33).

The next step comes with the development of special number symbols denoting quantities of one, ten, hundred, thousand and so on. The use of such symbols coincides with the evolution of writing. (K88, 8-11) Most earlier such systems proved cumbersume for actual calculation, like the roman numerals, so the calculi method was still prevalently used.

In order to efficiently calculate in a symbolic system, one has to have a place value system . These systems started in ancient Babylon and China. The modern decimal place value system with its use of the Zero derives from India. It came to Europe via the Arabian countries in about 1400-1500.

In the egyptian Papyrus Rhind we can find the first use of a word for variable: aha, or heap (K88, 20). It was used to denote the unknown in an equation to be solved. Variables are another step toward formalization, but in the egyptian case, as well as in the whole world of antiquity, no formal algebra was developed. Egyptian and Babylonian mathematics was a know-how system, or a system of how-to-do recipes, a techné (K88, 25-26), and not an epistemé.

The greeks developed the first system of mathematical proof , the mathéma and effected the transformation from techné to epistémé (K88,26-27). But the Euclidean greek system of proof was geometrical, and it lost whatever algebraical methdods and possibilities the Babylonian proto-algebra could offer (K88, 34-35). The Pythagorean mathematical techniques depended largely on the calculi or pséphoi (K88, 28-30).

Only in Alexandrinian times (+250) did Diophant apply the Babylonian technique (K88, 36-39). Here we find the first applications of algebraic techniques that were later made popular by the Arabic scholar Al-Hwarizmi . From the arabic use, the words "Aljabr " and "Almukabala ". These denote the basic algebraic techniques of moving and eliminating terms in an equation. Aljabr is the root word of Algebra. al-Hwarizmi's name stands for the essential concept of Algorithm in modern FCS . Although Diophant found and used symbols for the variables in an equation, the Alexandrinian algebra was lost to Europe in the turbulences of the breakdown of the Roman Empire only to be re-introduced to Europe thousand years later via the Arabic world. The process of formalization was not complete with Diophant since his variable symbols still stood for a definite, if as yet unknown number. There was no use of symbol for its symbol value only.

The chinese culture offers many riddles for the western mind. Many inventions were made here and not "exploited" only to diffuse later to the West leading there to its technological dominance: Paper , the compass , gunpowder . Chinese mathematics was highly evolved with a concentration on algorithmics. The Chinese first used negative numbers and their calculating technique was based on the calculating tablet. (K88, 40-45) They also used the Abacus . Joseph Needham gives a Chinese example of the solution of the Pythagorean theorem which is so obvious, easy, and intuitive that Euclid's proof appears unnecessarily circuitous compared with it. (NEEDHAM-CHIN , Vol. 3, p 22-23, 95-97) Schopenhauer had described it as "a proof walking on stilts, nay, a mean, underhand proof" (SCHOPENHAUER , I.15).

The indian number system finally developed all the characteristics for symbolic calculation. These are:

1) A basic set of symbols to denote the small numbers. These are the numbers 1 to 9 of the Brahmi set .

2) The multiplicative principle . The position of a digit in a number is a multiplicative form of representation where its position itself represents one factor.

3) The Place Value System . The Indian Number System uses the potencies of ten for place values.

4) The Symbol for Zero . This symbol indicates that at a specific place a vacuity exists, i.e. no powers of ten are present.

In Seleucid Babylon of -200, it was already possible to mark the vacuity in a number representation. They lacked the possibility to calculate with a Zero symbol. (K88, 45-48). The Sanskrit word for Zero is Shunya . As has been noted in BIB-AG:SHUNYA.DOC , there is a remarkable connection between the concept of Shunyata as used in the buddhist philosophy , namely of Nagarjuna , and the mathematical use of Shunya for Zero . Buddhist philosophy applies the essential tenets of FCS to human worldly life itself: Whereas the condition for FCS is its use regardless of meaning, Buddhism states explicitly that the condition of human worldly life itself is void (shunya) of meaning, making it a kind of formal system.

The Arabic translation of shunya is as-sifr . From here derive the European words cipher , ciphering , chiffre , Ziffer .

The ability to operate with the symbol for emptiness itself proved the sufficient condition to formalization . Before this, humanity simply seemed not to have been able to make the mental jump of explicitly assigning "no-meaning " to a symbol. Before this, any symbol just had to have a meaning for which it stood. From this point on, algebraics as it is known today evolved.

The Arabic use of Aljabr is traced back to Al-Hwarizmi , about 780-850. (K88, 50-53) His books was copied again and again in the European centers of learning and several copies survive to this day. Arabic Algebra seems to have fallen behind its Indian standard because if doesn't use any symbolic expressions. Everything, even numbers, is given in full text. This use indicates that Al-Hwarizmi did not make direct use of the Indian sources but has made a compendium of Near-Eastern mathematics as it had derived from Alexandrine (Diophant ) and the Indian sources.

Calculation with the Indian number system entered Europe slowly. (K88, 55) Gerbert of Aurillac at the end of the first millennium made use of indian (arabic) numbers without the Zero symbol on a calculating tablet . This was only a halfway success of the decimal system. The writings of Al-Hwarizmi appear in Europe from about 1200. In 1202 appears the book "Liber abaci " by Leonardo Fibonacci . Fibonacci was closely connected to the commerical circles of his time and here, his technique found immediate interest. Still, it took about 200 years until the indian decimal system had penetrated Europe. In 1494, all the account books of the Medici use it. (K88, 57)

After the use of the decimal system was established in Europe, occured the next step toward formalization. François Viète (1540-1603) introduced letter symbols not only for the unknown terms of an equation, but for known ones. (K88, 61-63) He denotes the change in method when he talks about the calculation with numbers as logistica numerosa , his new method of calculating with symbols as logistica speciosa . Here the step was made toward formalization as transformation of meaningless symbol strings. Descartes (1596-1650) introduced the algebraical methods to Geometry, thereby forming Analytical Geometry (K88, 64-67).

In the work of Leibniz (1646-1716) the development toward formalization comes to completion (K88, 68-72). Leibniz introduces the Infinitesimal Calculus and its notation as it is still used today. Leibniz formulated the requirements of the FCS as it was given above.

(From LEIB-CHR.DOC)

Much more is known today than at the time of Leibniz about the different Character Systems (from now on abbreviated CS) that have been used by humans throughout history. The known universe of one-time, present, and possible human symbol use has considerably expanded since the days of Leibniz .

Let us call a CS any symbolic non-ephemeral (written, inked, etched, graphed, hewn, computer-coded, etc.) means of recording thoughts and concepts that is evolved enough to be useful (or has at one time been used) as a means of interpersonal communication. This excludes ad-hoc systems like the proverbial knot in the handkerchief, and more or less mindless scribbling, scratching or graffitying. What it includes is: All the known existing examples and remnants of human symbol use - starting with the highly evolved alphabetic systems used for transcribing the sounds of spoken languages, namely: latin, cyrillic, sanskrit, hebrew and arabic alphabets. The mathematical, professional and scientific notation systems. Pictograms and other symbol systems. Notation systems for dance and music. Then historical encoding systems for syllables and sound patterns: cuneiform and hieroglyphic writings. Ideographic writing systems like Chinese, pictorial writing like Aztec. Non-language encoding systems like the Inka Quipu. And finally patternings which we usually are inclined to call ornamental, like Navajo or Hopi weaving patterns, sand and body paintings and Shibipo pottery patterns, ornamental canons like arabesque patternings and architectonic decoration styles.

ORIG_SYMB

There is some measure of insecurity about what forms the most ancient Symbol Systems took. It is most widely assumed that pictorial representations are the oldest symbols used. This may be an artefact. It is by far easier for a modern researcher to recognize the picture of a bull or a bison as such than to make sense of a strange pattern of dots or a group of lines. How easy it is to "create" the most wonderful and phantastic pictures from a set of engravings on a stone is exemplified in the story of the Dighton Writing Rock near the Taunton River in Southeastern Massachusetts (TUFTE90 , p. 93). In the cave paintings of Lascaux and many other paleolithic sites appear strange dot patterns in between the animal paintings (HA 51-52). These patterns must have some meaning, but it is much harder to decode than the animals. Heated arguments are common to arise about the interpretation of such patterns. One of the most disputed objects of this kind is the "baton de command " found in Cueto de la Mina in the spanish province of Asturias, minimum age 12,000 years. One interpretation sees it as a codification of lunar phases (HA 54-57, ILL:W 55, 57 ).

Logographic

Pictographic

Ideographic

Grammatological: Abstract-Logographic, Ornamental, Geometric

Phonographic

Segmental Symbols for consonant patterns

Syllabic Symbols for syllables

Alphabetic Symbols for atomar sounds

(Adapted from: HA 147)

One Symbol is used for one concept or one word (HA 147). There is a question what exactly represents the base of concept. In the european tradition, it is the word (greek: logos ). It is a certain measure of presupposition to make the spoken word the base of concept formation. This has been often overlooked, especially when dealing with Symbol systems like the Inca quipu or American Indian weaving, pottery and body painting patterns.

Ancient Sumerian writing -3000 to -2550 (HA 152, ILL:W141-229)

Ancient Egyptian CS, ILL:W128-133

Aztec pictograms

These CS derive from pictorial representations, i.e. the picture of a hand is used as the symbol for the concept "hand" etc. A further development into abstraction and generalization occurs when the picture of a foot is used for the concept of "to walk, to go".

Chinese writing.

ILL:W109,143,175,178,179,180,181 (WIEGER-CHINES )

Chinese is also derived from pictorial representations. Chinese writing is not pure ideographic but has acquired a strong morphemic character through the hsing-sheng pattern. This character formation pattern makes for about 90% of all current chinese characters. It constructs a chinese character from two root symbols: the semantic Determinator and the phonetic Indicator.

Traditional, folklore:

Inca: quipu (HA 56)

Calendar and counting marks (HA 50-55)

Navajo or Hopi weaving patterns and sand paintings (ILL:D )

Bororo Indian body painting (Levi-Strauss, ILL:B-C )

Shibipo pottery Ornamental patterns

Ornamental canons: arabesque patternings (ILL:I and P )

Architectonic decoration styles

European:

Typographical symbols like "&", %, #, and @

Mathematical symbols

Dance notation systems

Musical notation

Professional and technical coding systems

Computer codes

There is still an ongoing process in research on this subject what is to be classified together with what. Many entries of the traditional subgroup are borderline cases. In the folklore systems is a wealth of material hidden that has been overlooked by the logocentric viewpoint. Due to the influence of logocentrism , european researchers were long not bound to consider traditional and folklore CS as Systems. It is of significance that the most prominent of these were developed on the american continent. Not without good cause did the christian priests seek to utterly destroy and eradicate from the cultural memory of mankind all those writing systems that had been produced by the American Indian cultures: Quipu, Maya and Aztec codices ILL:W 199,197,200,201 . For a phonetically oriented mind system, a system of totally different mental structure can only be considered devillish. To break down the self-identity of the Indian cultures, their CS and the accompanying culture-bearers (like quipu interpreters) were eradicated, forcing them into cultural amnesia and substituting the foreign and alien mental patterns of phonetical european CS on the Indians. (Quipu and Aztec was non-phonetic, Maya is syllabic.)

The grammatological area is today the most important area of cultural evolution. Computerization, or rather, the evolution of complex graphic display and manipulation devices is the driving force in the development of new CS.

Phonographic CS are encodings of sound structures. They are always descendants of older Logographic CS (HA 211). The best recorded instance of this development is in the history of mesopotamian CS.

Egyptian Hieroglyphics -3000 (HA 213+)

This CS encodes only consonant structures consisting of 1, 2, or 3 consonants. Since vowels are omitted these are called segments, to distinguish from syllables which are vowel-consonant patterns. There are numerous remnants of the older egyptian logographic structures (HA 218). The writing direction was variable. Hieroglyphs could be faced any of the four directions, so that the writing could mimic a dialogue between persons who faced each other - like speech bubbles in cartoons (HA 221, SCHLOTT89 , 162, 163)

Later Sumer cuneiform from -2400 (HA 223). Sumerian writing always kept a strong logographic component. The descendant Cuneiform writings Akkad (-2300), Babylon (-2000), Assur (-1500 to -700) evolved more and more into phonetic systems (HA 225+).

Maya writing is also a syllabic CS.

ILL:W 199,197,200,201

Ugarit uses Cuneiform with alphabetic manner around -1500 (HA 267, 380)

Nubian uses Hieroglyphics in alphabetic manner (HA 385)

Phoenician -1600 (HA 268 f).

ILL:W 276,277,279,286,287

Any influence of the Cretian writing systems Linear A and B on the Phoenician alphabet is a matter of debate. There is strong evidence of cross cultural influences between the Minoic civilization and the Phoenicians who took over the mediterranean trade from the Minoans after their civilization collapsed around -1400. Haarmann believes that old european CS of Vinca origin (located in the area of former Jugoslavia) influenced the Minoan CS which in turn influenced Phoenician (HA 70-94, 267, 283).

Phoenician is the oldest alphabetic system which uses the name pattern of Aleph, Beth (Bayt), Ghimel etc. for its symbols. Phoenician is a non-vowel CS like Hebrew and Arabic and writes from right to left. The inclusion of vowels was done by the Greeks around -800 and the writing direction changed left to right (HA 282-288). The Greek alphabet was standardized in -403 by Archinos (HA 289). The Greek alphabet diffused in all directions and gave rise to the Roman alphabet by the bridge of Etruscian and Tyrrhenian alphabets (HA 290-294). Other important derivations from the Greek CS are Cyrillic and Armenian CS.

In the Middle East, Alphabets gave rise to a very diverse number of CS, the most important of these being Aramaic (-800 to -400), Hebrew (-500) and Arabic (+600) (HA 299-320). All these follow the Phoenician pattern of right to left writing and vowel omission (or later, dot notation).

[105]Leeuwenhoek, Antoni van, from SOFT-ENCYC

{lay'-vuhn-hook, ahn'-tohn-ee vahn}

Antoni van Leeuwenhoek, b. Oct. 24, 1632, d. Aug. 26, 1723, was a Dutch biologist and microscopist. He became interested in science when, as a Dutch businessman, he began grinding lenses and building simple microscopes as a hobby. Each microscope consisted of a flat brass or copper plate in which a small, single glass lens was mounted. The lens was held up to the eye, and the object to be studied was placed on the head of a movable pin just on the other side of the lens. Leeuwenhoek made over 400 microscopes, many of which still exist. The most powerful of these instruments can magnify objects about 275 times. Although future microscopes were to contain more than one lens (compound microscopes), Leeuwenhoek's single lens was ground to such perfection that he was able to make great advances and to draw attention to his field.

Leeuwenhoek was the first person to observe single-celled animals (protozoa) with a microscope. He described them in a letter to the Royal Society, which published his detailed pictures in 1683. Leeuwenhoek was also the first person, using a microscope, to observe clearly and to describe red blood cells in humans and other animals, as well as sperm cells. In addition, he studied the structure of plants, the compound eyes of insects, and the life cycles of fleas, aphids, and ants.

Reviewed by Louis Levine

Bibliography: De Kruif, Paul, Microbe Hunters (1926; repr. 1966); Dobell, Clifford, Antony van Leeuwenhoek and His "Little Animals", 2d ed. (1958); Ford, B. J., Single Lens (1985); Schierbeek, A., Measuring the Invisible World: The Life and Works of Antoni van Leeuwenhoek (1959)

[106]Galileo Galilei, from SOFT-ENCYC

{gal-i-lay'-oh gal-i-lay'-ee}

Galileo Galilei, a pioneer of modern physics and telescopic astronomy, was born near Pisa, Italy, on Feb. 15, 1564. In 1581 he entered the University of Pisa as a medical student, but he soon became interested in mathematics and left without a degree in 1585.

After teaching privately at Florence, Galileo was made professor of mathematics at Pisa in 1589. There he is said to have demonstrated from the Leaning Tower that Aristotelian physics was wrong in assuming that speed of fall was proportional to weight; he also wrote a treatise on motion, emphasizing mathematical arguments. In 1592, Galileo became professor of mathematics at the University of Padua, where he remained until 1610. He devised a mechanical calculating device now called the sector, worked out a mechanical explanation of the tides based on the Copernican motions of the earth, and wrote a treatise on mechanics showing that machines do not create power, but merely transform it.

In 1602 Galileo resumed his investigations of motion along inclined planes and began to study the motion of pendulums. By 1604 he had formulated the basic law of falling bodies, which he verified by careful measurements.

Late in 1604 a supernova appeared, and Galileo became involved in a dispute with philosophers who held (with Aristotle) that change could not occur in the heavens. Applying the mathematics of PARALLAX, Galileo found the star to be very distant, in the supposedly unchangeable regions of the cosmos, and he attacked Aristotelian qualitative principles in science. Returning to his studies of motion, he then established quantitatively a restricted inertial principle and determined that projectiles moved in parabolic paths. In 1609 he was writing a mathematical treatise on motion when news arrived of the newly invented Dutch telescope. He was so excited at the possible scientific applications of such an instrument that he put all other work aside and began to construct his own telescopes.

The Telescope and the Copernican Theory

By the end of 1609, Galileo had a 20-power telescope that enabled him to see the lunar mountains, the starry nature of the Milky Way, and previously unnoted "planets" revolving around Jupiter. He published these discoveries in The Starry Messenger (1610), which aroused great controversy until other scientists made telescopes capable of confirming his observations. The Grand Duke of Tuscany made him court mathematician at Florence, freeing him from teaching to pursue research. By the end of 1610, he had observed the phases of Venus and had become a firm believer in the Copernican HELIOCENTRIC WORLD SYSTEM. He was vigorously opposed in this belief, because the Bible was seen as supporting the opposite view of a stationary earth. Galileo argued for freedom of inquiry in his Letter to the Grand Duchess Christina (1615), but despite his argument that sensory evidence and mathematical proofs should not be subjected to doubtful scriptural interpretations, the Holy Office at Rome issued an edict against Copernicanism early in 1616.

Galileo died at Arcetri on Jan. 8, 1642.

Influence

Among Galileo's students was Benedetto Castelli, founder of the science of hydraulics and teacher of both Bonaventura Cavalieri and Evangelista Torricelli. Cavalieri formulated principles that were important to the development of the calculus, and Torricelli devised the barometer and explained phenomena of atmospheric pressure. Outside Italy, Galileo's influence was not great, except in making scientists conscious of the need for freedom of inquiry. As he had seen, not only religious but philosophical tradition had to yield to observation and measurement if science were to prosper.

Stillman Drake

Bibliography: Allan-Olney, Mary, The Private Life of Galileo (1970); Drake, Stillman, Discoveries and Opinions of Galileo (1957), Galileo Studies: Personality, Tradition and Revolution (1970); Galileo At Work--His Scientific Biography (1978); Geymonat, Ludovico, Galileo Galilei, A Biography (1965); Redondi, Pietro, Galileo: Heretic (1987); Santillana, Giorgio de, The Crime of Galileo (1955).

See also: ASTRONOMY, HISTORY OF; PHYSICS, HISTORY OF.

[107]ANM:ADAM

When seen from the eurocentric perspective. Böhme was deeply influenced by cabbalistic thought. See also the chapter on cabbala

[108]ANM:LIFE

Cabbala work was anyhow tantamount to a life sentence. The cabbalist became mentally entangled in a system that was of a higher order of magnitude than his own mind. Many could never mentally detach from the game and became enslaved to it.

W.I. Thompson has succinctly stated that atomic particles is what you get when you build an atomic accelerator. Otherwise they don't exist.

[110]ANM:ARS

This use of the term AC is somewhat at variance with Leibniz' use who used CU and AC as synonyms. It is used here in the specific sense because the meaning of ars in this context is essentially the operationality of the symbols.