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April 10, 2026
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"Hilberts Doktor-Vater Ferdinand Lindemann nannte diesen Existenzbeweis âunheimlichâ und Paul Gordan meinte (zitiert nach Otto Blumenthal â Lebensgeschichteâ in Hilberts âGesammelten Abhandlungenâ, Band 3 (Berlin 1935), S. 388â429, dort S. 394): âDas ist keine Mathematik; das ist Theologie.â Etwas später milderte Gordan seinen Ausspruch etwas ab und meinte: âIch habe mich davon Ăźberzeugt, daĂ die Theologie auch nĂźtzlich sein kannâ. Aber es gab auch viele Mathematiker, die sich nicht Ăźberzeugen lieĂen. Oskar Becker (1889â1964) beispielsweise reagierte sehr heftig und bezeichnete den Hilbertâschen Beweis des Basis-Satzes als âSchleichweg einer Schein-Konstruktionâ (O. Becker in: âMathematische Existenzâ, 1927, op. cit., S. 471)."
"Das ist keine Mathematik; das ist Theologie."
"The proof of this theorem of Hilbert's and of others is very abstract, but in itself quite simple and hence logically compelling. And for just this reason this work of Hilbert's ushered in a new epoch of algebraic geometry. But application to invariant theory is just as simple, but I can analyze it here even less. The whole question of the finiteness of the invariants, which Gordan had been able to solve for binary forms only by means of comprehensive calculations (see p. 290), is here solved, with one stroke, for forms with arbitrarily many variables. Because of its uniqueness, this work was first received with very diverse reactions. I had then resolved to draw Hilbert to Goettingen at the earliest opportunity. Gordan at first declined, saying, "It is not mathematics, it is theology" But later he said: "I have convinced myself that even theology has its merits". In fact, Gordan himself later on much simplified Hilbert's basic theorem (Muenchener Naturforscherversammlung 1899)."
"Since the discovery of the Indus civilization ⌠it has been almost universally accepted that the Sumerians immigrated from the east.... this immigration could have succeeded entirely by land if the Sumerians immigrated from somewhere in northern India... the westward migration of the Sumerian groups, whose language may have been related to the Dravidian languages of India."
"Gordan, eine in sich geschlossene Individualität, war kräftig und einheitlich im Leben und in der Arbeit. Kein Neuerer in der Wissenschaft: er griff nur an, was seiner Art gemäà war; aber was er angriff, fßhrte er nnermßdlich durch bis zu Ende. Aus dem Stoffe selbst heraus neue kombinatorische Methoden zu schaffen und seine Instrumente kräftig zu handhaben, das war sein mächtiges KÜnnen: er war Algorithmiker."
"Von Soden observes that âsince the discovery of the Indus civilization ⌠it has been almost universally accepted that the Sumerians immigrated from the east.â The immigrants are regarded as having arrived in lower Mesopotamia either at the beginning of the Ubaid period (c. 5000 B.C.) or at the beginning of the Uruk period (perhaps c. 3500 B.C., but perhaps as late as 3250). In either case, the Sumerians seem to have fitted easily into an advanced Chalcolithic culture where writing was already in the early stages of development. Therefore, the implication is that they must have been from another advanced culture, and that points to the East. Bottero agrees that âthe Sumerians must have arrived in Mesopotamia during the fourth millennium, apparently from the southeast.â Von Soden further observes that âthis immigration could have succeeded entirely by land if the Sumerians immigrated from somewhere in northern India,â and refers suggestively to âthe westward migration of the Sumerian groups, whose language may have been related to the Dravidian languages of India.â"
"Gordan - anfänglich diesen begrifflichen Deduktionen gegenĂźber mehr ablehnend: âdas ist keine Mathematik, das ist Theologie!" - ist dann zweimal (53), (69) dem diesem Beweise zugrunde liegenden Hilbertschen Endlichkeitssatze nähergetreten, indem er die gegebenen Formen F nach verschiedenen Kriterien in eine Reihe anordnete, die das Bilden eines endlichen Moduls aus ihnen deutlich machte; das erstemal in komplizierterer Weise speziell fĂźr die Invariantenformen, das zweitemal allgemein und einfach."
"A queer fellow, impulsive and one-sided. A great walker and talker - he liked that kind of walk to which frequent stops at a beer-garden or a cafe belong. Either with friends, and then accompanying his discussions with violent gesticulations, completely irrespective of his surroundings; or alone, and then murmuring to himself and pondering over mathematical problems; or if in an idler mood, carrying out long numerical calculations by heart. There always remained something of the eternal "Bursche" of the 1848 type about him â an air of dressing gown, beer and tobacco, relieved however by a keen sense of humor and a strong dash of wit. When he had to listen to others, in classrooms or at meetings, he was always half asleep."
"38 Jahre von 1874 an hat Gordan in Erlangen verbracht. Sie sind fĂźr ihn gleichmäĂig verlaufen: täglich Vorlesungen, Arbeit, und die unentbehrlichen Spaziergänge entweder mit Mitarbeitern ⌠in drastisch lebhaften Zwiegesprächen, unbekĂźmmert um alle Umgebung, oder allein in tiefem Nachdenken und seine Gedanken im Kopfe so fertig verarbeitend, dass er seine Rechnungen zuhause fast ohne Striche [Streichungen] ausfĂźhren konnte."
"His strength rested on the invention and calculative execution of formal processes. There exist papers of his where twenty pages of formulas are not interrupted by a single text word; it is told that in all his papers he himself wrote the formulas only, the text being added by his friends."
"Der Beweis des Hilbertschen Satzes und anderer Sätze ist sehr abstrakt, aber an sich ganz einfach und darum logisch zwingend. Eben darum leitet diese Arbeit von Hilbert eine neue Epoche der algebraischen Geometrie ein. Ebenso einfach ist dann auch die Anwendung auf die Invariantentheorie, die ich hier noch weniger zergliedern kann. Die ganze Frage der Endlichkeit der Invarianten, welche Gordan seinerzeit nur mit umfangreichen Rechnungen fĂźr binäre Formen hatte erledigen kĂśnnen (vgl. oben S. 308), wird hier mit einem Schlage fĂźr Formen mit beliebig vielen Veränderlichen gelĂśst. Ihrer Eigenart entsprechend wurde diese Arbeit zunächst mit sehr verschiedener Stimmung aufgenommen. Mich hat sie damals bestimmt, Hilbert bei nächster Gelegenheit nach GĂśttingen zu ziehen. Gordan war anfangs ablehnend: âDas ist nicht Mathematik, das ist Theologie.â Später sagte er dann wohl: âIch habe mich Ăźberzeugt, daĂ auch die Theologie ihre VorzĂźge hat.â In der Tat hat er den Beweis des Hilbertschen Grundtheorems selbst später sehr vereinfacht (MĂźnchener Naturforscherversammlung 1899)."
"In seiner eigenen Wissenschaft war es weniger ein Vertiefen in fremde Arbeiten -- denn solche las er sehr wenig -, als ein Ăberblick Ăźber die inneren Zusammenhänge und ein instinktives GefĂźhl fĂźr die Wege und Ziele der mathematischen Bestrebungen, was ihn schon aus kleinen Andeutungen Wertvolles von Minderem scheiden lieb. Aber den auf die Grundlagen gehenden Begriffsentwicklungen ist Gordan nie gerecht geworden: auch in seinen Vorlesungen hat er alle Grunddefinitionen begrifflicher Art, selbst die der Grenze, vollständig gemieden. Sein Vorlesungsprogramm hat sich nur auf die Vorlesungen allgemeiner Art, gelegentlich auch auf binäre Formentheorie, erstreckt; die Ăbungen waren mit Vorliebe der Algebra entnommen. Ăber Jacobisches, so Ăźber Funktionaldeterminanten, trug er gern vor, nie Ăźber Funktionentheoretisches, hĂśhere Geometrie oder Mechanik; auch lieĂ er keine Seminarvorträge halten. Die Vorlesungen wirkten wesentlich durch die Lebhaftigkeit der Ausdrucksweise und durch eine zum Selbststudium anregende Kraft, eher als durch Systematik und Strenge."
"Ich habe mich davon Ăźberzeugt, daĂ die Theologie auch nĂźtzlich sein kann."
"How will he be judged in the long run? I do not know, but it will not be fair. In the Weinberger interview Kittler claims that every fifth sentence in McLuhan can be proved wrong. Speaking as a Kittler translator who has spent many an afternoon hunting down factual errors, faulty page references, and bungled quotations, I doubt whether his stats are much better. ... clairvoyance seems to be composed of shameless simplifications (Kittler), the statistically inevitable result of scattershot predictions (McLuhan), and provocations churned out on an industrial scale (both)."
"If one compares the fate and acceptance of Johannes Hertel's "Aryan research" with what was said above about Zimmer and Schroeder, one can hardly find a better illustration of the complicated situation that an Indologist who was interested in Aryan antiquity could get into with the gradual institutionalization of the National Socialist idea and the seizure of political power by the NSDAP. While Heinrich Zimmer's scientific work is still highly valued today and Leopold von Schroeder is also respected as a Veda researcher, the judgment on Johannes Hertel with regard to his "Aryan research" is, to put it mildly, somewhat uncertain."
"The key role played by Lassen in the development of modern ideas of race is not a matter of dispute, but what is less often noted is the central role the MahÄbhÄrata played in his reconstructions of ancient Indian history. If the racism of Gobineau is unimaginable without Lassenâs researches, it is equally true that Lassenâs researches are unimaginable without the MahÄbhÄrata."
"Many controversial aspects of his workâincluding war, women, and a strange continental provincialism that increased with ageâwere already apparent back then. Kittler was ahead of his time, but he invested considerable energy into informing others that they were behind. He was an inspiring teacher, yet he was prone to seek out the danger zone where instruction turns into seduction, education becomes a form of contamination, and the pedagogue takes on the trappings of the demagogue."
"... collapse of traditional edifices of meaning accompanied by the corresponding emergence of hitherto obscured materialities of communication and inscription. I certainly did not grasp the finer points, but I came to understand that taking apart my Saba VS2160 amplifier or intently listening to scratches on old Yes or Tubes LPs constituted a genuine act of theory."
"In spite of his copious studies on the MahÄbhÄrata, however, Lassenâs work was not especially innovative: once laid down, his basic views on the epic remained unchanged for nearly a quarter century. Later studies amplified and provided additional âethnographicâ evidence for views he had already articulated in his 1837 article, but they did not in any way question or otherwise critically illuminate the basis for these views. Regardless, Lassenâs pedantic, self-assured tone and the confidence with which he put forth speculative assertions about ancient India as established fact greatly impressed a generation of scholars. Albrecht Weber, Theodor GoldstĂźcker, and Adolf Holtzmann Jr. all accepted his reconstructions of ancient Indian history and ethnography."
"The comprehensive picture of ancient Indian civilization that he was able to give meant that the Indians were now finally and "fully accepted" into the circle of ancient cultural peoples that were significant for the history of mankind and, as such, could be included in historical comparisons. The expansion of the historical-geographical horizon that Lassen's four volumes made possible was a very important step in the process of overcoming the old biblical view of history - after all, just twenty years earlier, like for Peter von Bohlen in his History of the Ancient World, only the old biblically relevant cultures of Egypt, Israel, Persia, Greece and Rome had been considered the roots of human culture."
"The end of media is a situation in which the computer subsumes all other media. The machine subject appears as a sort of minimalist inhuman subjectivity wrought by recursion. It operates beyond or below the phenomenological capacities of humans, does not employ natural language, and does not think in terms of meaning. Myriad machine subjects are networked to form a loop of absolute knowledge. This loop excludes humanity which is functionally unable to participate therein. Within the loop, the machines cognize somehow in an asemantic logic and antagonistically evolve away from any semblance of humanity."
"Kittler wanted to establish a real computer literacy. And our group was both the justifying nucleus of this demand and his evidence of possibility."
"Brilliant, controversial and cantankerous. In his penetrating examination of our increasingly militarised and 'mediatised' existence that, he argued, replaced human agency, Kittler outlined with great energy the post-human historical condition. Perhaps his greatest academic transgression was to have such an emphatic sense of technology's triumph over the delusions of human agency, articulated in his writings on war and speed, mathematics and cryptography, in addition to the style of his claims, sculpted like a series of steps of military escalation, in imitative performance of the computerised world of total militarisation and technologisation that he portrayed."
"Here was someone who â at last! â had charted the genealogy, or transmission lines, of writingâs interface with bodies, from Sade to Kafka, Marinetti to Pynchon. Most exciting of all, he lucidly and irrefutably articulated something Iâd been trying ineptly to persuade people of for years: that Dracula is a book about the Dictaphone."
"For Kittler, [Geisteswissenschaften, "humanities", but more literally "spirit sciences"] to be taken to its hard core: sciences stand at the centre of arts and humanities in the age of technical media... media are not only the mass media of television, newspapers and such, but a technical constellation that at its core is based on scientific principles of coding, channeling and decoding of signals... Man is a temporary solution, a crossroad in the complex practices and epistemologies of knowledge that might (has?) proved to be not so useful anymore when media can communicated to each other without human intervention. Ask your plugged-in Ethernet cable, it knows the amount of data that goes through it without you pushing even a single key."
"Kittler's speciality is the creatively enhanced misquotation... all the ameliorative sloppiness that Kittler the analyst attributes to authors of the âDiscourse Network 1800â such as Goethe and Hegel, who kept bungling their quotations in highly creative self-serving ways."
"There is little doubt that Lassen was one of the foremost theoreticians of race of the nineteenth century, responsible in large part for supplying the âhistoricalâ data that led to the creation of the âÄryanâ race concept. This makes the present-day enthusiasm for him even more puzzling."
"It was already in the middle of the former century that Christian Lassen qualified the opposition of arya and dasyu or dasa as a contrast between different religions expressed by the age-old symbolism of black opposed to white and not as a contrast of darkcomplexioned to white coloured men."
"Riding together in a taxi from some airport Kittler tried to explain to Luhmann that in contrast to social systems, switching circuits cannot exist without input and output. "Herr Kittler, it was like that already in Babylonia. A messenger rides through the city gate. Some [like me] ask, what kind of message he brings. Others [like you] ask what kind of horse he rides.""
"When meanings come down to sentences, sentences to words, and words to letters, there is no software at all... the so-called philosophy of the computer community tends to systematically obscure hardware by software, electronic signifiers by interfaces between formal and everyday languages... This ongoing triumph of software is a strange reversal of Turing's proof that there can be no mathematically computable problem a simple machine would not solve. ... software successfully occupied the empty place and profited from its obscurity. The ever-growing hierarchy of high-level programming languages works exactly the same way as one-way functions in recent mathematical cryptography."
"Kittler's project was to trace "not the triumphal emergence of humanity into freedom, but our exit from the fulsome enjoyment of our taste for ourselves that assigns humanity a place to which it has no right"."
"I have some problems with Christianity, but in favor of the fact that every living being, be it plant or animal, has been begotten by the lovely union of female and male. ... like many Germans before me, including Friedrich II, Nietzsche, and to a certain extent Heidegger, I am after love that is fundamentally anti-Christian."
"The only kind of politics I am interested in is military politics, to begin with. In fact, this is the only thing I can think of when one says politics."
"Storing information and transmitting information without having to employ such obscure instances as the human âspiritâ or âsoulâ: such is the very definition of media."
"Unlike Foucault, or indeed other leading media theorists such as Jean Baudrillard or Paul Virilio, Kittler steeped himself in physics, engineering, optics, the science of fibre-optic cables, and even wrote computer code â arguably gaining a more profound insight into media than his contemporaries."
"I do not believe that human beings are becoming cyborgs. Indeed, for me, the development of the Internet has much more to do with human beings becoming a reflection of their technologies, of reacting or responding to the demands of the machine. After all, it is we who adapt to the machine. The machine does not adapt to us... pursuing the cyborgian vision would have also meant that the incredible speed of Mooreâs Law, that computing power doubles every 18 months or so, would have been impossible to accomplish. So, in my view, the computing industry is less interested in the development of cyborgs than it is in the development of software."
"the real connection is not between people but between machines... the most remarkable thing about Linux for me is how other people just keep coming along to embellish Torvaldsâ source code, making it more and more powerful every day. And so as far as I am concerned the Internet is at its best when it is operating as a self-reflection of computer systems, when it furthers the evolution of technology."
"Computer technology is an alliance of hardware and software, of physics and logic, which has taken the place of the gods who have fled far away. Zeus, as you know, was at once the mighty brightness of the Greek sky and âthe lightning that guides everythingâ. Only gods and computers are in the position of predicting today whether blue skies or rainstorms will be the weather tomorrow."
"we are literally taught the alphabet through a sort of structural violence... How else would I have learned the alphabet? I certainly would not have learned it on my own accord. In fact, without being subject to this structural violence, I would still be a 5-year-old boy."
"quoted in Kittler and the Sirens|url=https://www.lrb.co.uk/blog/2011/november/kittler-and-the-sirens|access-date=2024-06-30|website=LRB Blog|language=en}}"
"Ever since IF-THEN commands ceased to be a privilege of the human being, all philosophical debates about the death of the subject have been settled, simply because weapons have become subjects themselves."
"0.1% of all telecommunications on this planet are absorbed by the NSAâs artificial intelligence. What then happens with them, no one knows. As a rule, orders for secrecy are lifted only after 30 years. Perhaps they will no longer be necessary at all three decades from now. The Word that was in the Beginning is vanishing into computer data banks anyway. When all that is said by the inhabitants of the earth has disintegrated into bits, Alan Turing's Universal Discrete Machine will be perfected."
"âDerrida of the digital ageâ whose vision combined the circuitry of Lacanâs models for the psyche, and Foucaultâs archaeological conception of all knowledge and its systems, with the material hardware of technological transcription and recording: typewriters, tape recorders, film projectors and their non-analogue offspring."
"Of Christian Lassen, it was said as early as 1890 [Oldenberg 1890:27] that âthe sagacity of philological thought is wanting in himâ. Need we say more?"
"a few far-seeing scientists say ... nature is not a computer ... the only rational hope I have that we have not arrived at the end of history. Because if the digital calculators did not have a kind of internal limitation, they would truly bring world history to an end, in all the aspects that you have mentioned: time would no longer be human time, space would no longer be human space, but merely a corridor within the circuits of these wonderful little machines."
"I cannot stand on American soil with much pleasure. In fact, my antipathy to America is one of the main reasons why I often avoid talking about the military-industrial complex since for me to talk about the devil is to talk with the devil. As a good friend of mine said to me lately, we in Germany should not say a word about Americaâs war on Iraq ... we should talk about love in Europe."
"From a 2002 interview. Quoted in Winkler, Robert A. ""Alle Apparate abschalten." Conceiving Love and Technology with Heidegger And Kittler." (2020)."
"there are no such things as thoughts. There are only words."
"whether or not we personally ever use the typewriter is not important. What is important is that all of us are thrown into the age of typewriting, whether we like it or not. Of course, Heidegger himself preferred to continue his work in his own handwriting."
"But why people - and I include myself here â would rather sit in front of a computer than do other things such as have a conversation is difficult to explain. Perhaps it is a fascination with power. For example, in earlier times, some people directed their love away from their wives and families and directed it instead towards an image of Jesus or Mary."