The Finiteness of Algorithms
Friedrich Kittler's keynote from transmediale 2007, transcribed and translated for the first time
What is the relation between computational algorithms and creative production? Can the second be arrived at through use of the first? Is there historical specificity to their relationship due to recent advances in technology, or are there age-old connections between mathematical constraints and creative questioning of the universe?
In 2007 the eminent media theorist Friedrich Kittler (1943–2011) worked through these questions (and many others) in a lecture at transmediale. The lecture and following conversation, moderated by informatics professor Wolfgang Coy, is publicly presented as text and translated from the original German for the first time here.
Kittler took the premise of that year’s festival title, unfinish, to carve an arc through several of the topics central to his theoretical work throughout his life on indeterminacy and finiteness—both as mathematical concerns and as fundamental philosophical matters. While he speaks on contemporary media art, he also emphasizes that algorithmic constraints when it comes to artistic production are nothing new: “I believe that nothing in this world—not even the invention of media and computer art—can alter the task of art, which is to reveal the eternal in the finite.”
Good evening ladies and gentlemen. I’m glad to see so many have made it here and that Friedrich Kittler is here. We can start. My name is Wolfgang Coy. I’m a professor of Informatics at Humboldt University. Friedrich and I are both at the Helmholtz-Zentrum für Kulturtechnik, and I’d like to say a few words about our guest before he starts his lecture, even though it is hardly necessary in Berlin. Perhaps just a couple of things anyway.
Friedrich Kittler studied German, Romance Languages, and Philosophy at the Albert Ludwigs University of Freiburg from 1963 to 1972. He received a doctorate in literature from there in 1996.
1976, I think.
1976? Did I say 1996? That would be a performance boost, wouldn’t it? Work per unit of time would be substantially more. No, in 1976, of course. He then spent ten leisurely years there as an assistant and in 1984 earned his Habilitation—that was still important then—and then, in 1987 he took the logical next step of accepting a professorship in Bochum at Ruhr University, an “architectural highlight” of the university landscape. We have been fortunate enough to have him at Humboldt since 1993, where he holds the chair of Media Aesthetics and History. I believe it is almost a direct lineage from Hegel’s chair.
With about 150 academic publications, our guest is very, very prolific. I want to mention just a few of the titles that you’ll know: Discourse Networks (1985) and Gramophone Film Typewriter (1986), which is probably the best-known work by title. In 2000, an introduction to philosophy that I personally really love, Cultural History of Cultural Studies, and now, in 2005, the first volume of Music and Mathematics with the subtitle “Hellas: Aphrodite,” of which there are still most likely four volumes to come—but who knows how many there’ll be, it could be seven, I don’t think it’s been decided yet. He has co-authored many books, and written many, many essays; from the published works I’ll only mention Computer as Medium from Fink Verlag, Turing, the “non-mathematical writings,” I think the subtitle was—writings about the Turing machine and thoughts about the computer. And a very famous work, The Expulsion of the Spirit from the Humanities, a work that has not succeeded, so to speak. That demand has unfortunately not really been met, but Friedrich’s great achievement is surely that, in many ways, he reoriented the humanities and reopened the bridge to other sciences. The unfortunate closure of that bridge, which came from [Wilhelm] Dilthey and our university as well, and had disastrous effects, has been somewhat overcome. Looking more closely, you sometimes have to ask whether just the names have been switched, but for many people, doors have opened to make other work possible. Today it can be seen that the humanities comprise more than just spirit.
He has taken on a whole host of internal academic responsibilities. He was head of the DFG Research Group from 1986 to 1990, a geographically dispersed group of literature and media analysts—not only Kassel people, but anchored in Kassel. He co-founded the Helmholtz-Zentrums für Kulturtechnik in 2001 where he is also deputy director. In 1993, he was awarded the ZKM media art prize. He’s done residencies in California—in Berkeley, Stanford and Santa Barbara. In 1996, he tapped into the East Coast where he was a “distance caller” at Yale, and in 1997 a distinguished visiting professor at Columbia in New York. And I probably should say: the writers perceptible in his work time and again are Martin Heidegger, Thomas Pynchon, Homer, and Andreas Stiller.
Friedrich, over to you.
A very good evening, ladies and gentlemen, sweet Ladies, dear Gentlemen, but I’ll speak German. Thank you, Wolfgang Coy for the lovely introduction and, above all, for connecting the last two names, Homer and Andreas Schiller—I had to switch gears for a moment until I realized that Andreas Stiller is, of course, the founding editor of c’t at Heise Verlag in Hannover.
With thanks to transmediale I am happy to comply with the request to talk about the finiteness of algorithms. It is difficult, so whether it is successful or not, we shall see in the discussion, which could well be longer than the lecture.
Finiteness… I will begin with finiteness and move on to algorithms and try, in the end, in the second part, to say something about algorithms and artworks.
Concerning finiteness, perhaps it would be best to start with a poem that Jorge Luis Borges says he found, by a ninth-century Arabic poet. The poem reads: “Others died, but it happened in the past, the season (as all men know) most favorable for death. Is it possible that I, subject of Yaqub Al Mansur, must die as roses had to die and Aristotle?”
So, we know from the time we are about ten years old that we are finite beings and that life is a finite process,
a “being-towards-death” as it’s called in Being and Time. Or, conversely, whether the universe in which we live and its processes, in which we are included, is itself a finite or an infinite process, has proven, so far, to be incalculable, and the hypotheses vacillate between a finite, sine-shaped universe and an infinite, hyperbolic sine-shaped universe.
It has been so since time immemorial, but only for the last 50 or 60 years have we lived in a world where we set up high-tech processes by programming computers. These processes are, of course, algorithms, which I will explain next. Explanation is necessary because these algorithmic processes have a tendency—like nature in Heraclitus—to be hidden.
In car industry circles, you hear that drivers of German luxury cars are accompanied by something like 200 invisible computers that are calculating and accelerating and braking and sensing. Embedded controllers sounds like the embedded reporters of the Iraq War, that is, they must be unnoticed or they will not be successful.
Now, finiteness is—at least hopefully—what separates algorithms from mathematics in general. The word “algorithm” is a made-up Latin word that sounds Greek. In fact, it’s not even Latin, but a Latin corruption of the name Muḥammad ibn Mūsā al-Khwārizmī—a mathematician who, despite his Arabic-sounding name, was not Arabic. He was born around 8131 in an oasis region of the (former) Aral Sea in today’s Uzbekistan called Khwarezm, or at that time, Chorasmia, from which the name al-Khwārizmī came.
His writings were so influential—or one of his works was—because it demonstrated the simplest arithmetic rules with the decimal number system, which had been imported from India to Arabia and later to Europe. How to add, how to subtract, and so on. This work was transliterated or translated into Latin a number of times in the twelfth and thirteenth centuries; the most influential was surely via Fibonacci and his book Liber Abaci from 1202. But the term algorithm was already in use in earlier, anonymous Latin translations, one of which begins with the memorable words: “Dixit Algoritmi: laudes deo rectori nostro” — “Algoritmi has spoken: praise be to God, our Lord.” And that is actually the deepest question transmediale posed to me: Is God necessary for mathematics and algorithms or not? We can’t answer that. Descartes, as we know, feared a God who could be so deceptive as to tell him that two plus three do not equal five. Therefore, cogito ergo sum.
It seems to me that Leibniz introduced the modern concept of algorithms, something that, dubiously, the most authoritative history book of algorithms doubts. In 1684, Leibniz formally described the basic rules of calculus, differential calculus, and called it an “algorithm” instead of what Sir Isaac Newton had previously called it, a natural-philosophical pseudo explanation of derivation rules. And Leibniz’ formalized concept seems to be the one that is now significant in—if Wolfgang Coy doesn’t shake his head—informatics. Or perhaps better to call it computing, as you said just before, or even computer science.
Now, for those who’d like a bit more precision, I’m going to briefly outline what is required of an algorithm and why it is required. The first basic characteristic is determinacy. With identical starting conditions, every application of an algorithm delivers the same output. There are, of course, exceptions. For example, we can only stochastically model the weather for the next fifty years—or model climate change, like you see in all the papers these days—not deterministically.
The second characteristic: determinism. For every step at every point of processing an algorithm, one specific step always follows.
And, finally, the third feature likewise connected with the term: termination. For each input, an algorithm always stops after a finite number of steps. You open the word processor, write your love letter, you close it again. The exceptions are both inconspicuous and insidious—embedded controllers in cars that run as long as the car runs and operating systems with their maliciousness and built-in advertising mechanisms and costs.
Of these three criteria, the last is surely the most important: after a finite number of steps, an end, a holding state, is reached. The question is how long it takes and how to estimate a priori the magnitude of this end state as the complexity of input increases. Processes that are, for you computer scientists, good and well-behaved are called class P, which can be solved in any quadratic or cubic time. If [a route between] ten cities is to be worked out, the difficulty, as far as I’m concerned, is ten to the power of two, so 100 steps. If [a route between] 100 cities needs to be figured out, the task time is 1002, that would be 10,000 steps.
Sadly, not all known algorithms belong to this wonderfully sensible, well-behaved class. There are many things in mathematics and in reality that can only be solved in exponential time, or worse. The most famous example is the traveling merchant who has to find the shortest route between ten cities, then between a hundred cities, and then between a thousand cities.
It’s a task that has only ever been solved in exponential time on a computer. But it’s not impossible— computer science gives us some hope that a polynomial solution may appear. We are open to surprises in the realm of algorithms, albeit pessimistically after 60 years.
To give a drastic example from the foundational crisis of mathematics in the 1920s: there are functions that have been so thoroughly worked out that they have led to, for example, the famous Ackermann function that gets results from tiny arguments about nothing. With two and four as inputs, the Ackerman function is already a number with almost 20,000 decimal places—while, as a nice comparison, the lifespan of the Earth expressed in seconds is only 1017. To come to grips with this explosive realm, which could be compared to Archimedes’ famous grains of sand, 23-year old English mathematician Alan Turing lay down in a meadow near Cambridge and unintentionally led us into the computer age, an event later immortalized in pop music by Pink Floyd with “Grantchester Meadows.” It seems it was there he dreamed up what has since defined our Age of Turing.
It’s impossible to compute everything that can be questioned with mathematics. But there is a sub-class of functions and real numbers that can be calculated because they can be described in a finite number of steps. An example of what is non-computable in real numbers would be a number line onto which a needle with an infinitely fine point is dropped. Nobody could come up with a rule to specify exactly where the needlepoint hits the number line. In contrast, there are numbers—even those with an infinite number of decimal places, which seem incomprehensible at first, not comprehensible for computers, regardless of structure—that are described as computable real numbers.
Now I want to talk about the most famous and the oldest of these transcendent numbers—because it’s so nice and should wrap up the mathematical section of my meditations—pi: 3.14159 and so on with no end and without any apparent regularity in the sequence of decimal digits. The dreamers among computer scientists say: all the works of Shakespeare, the Bible, and everything are coded in the decimal places of pi, somewhere in the infinite number of points.
This curious, miraculous number, which defines the ratio of a circle’s circumference to its diameter, has been described in a closed-form expression since 1674. If I had a blackboard I would write out the formula; instead, I’ll just have to say that the arctan of one, multiplied by four, gives the number pi. And, as Leibniz and later the seven-year-old public school student Alan Turing discovered, the arctan of one can be expressed as: one minus one-third, plus one-fifth, minus one-seventh plus one-ninth. That can be written more simply with a sigma or sum symbol, and then even the even the most blind can see that an infinitely long number can in fact be written or defined—in these infinitely many signs—sigma one divided by x to the n—and therefore the problem of real numbers, of being uncountable with a countable, quasi-whole number, is replaced with the description of this number. And this description can, of course, be fed into any computer.
Turing wrote in his dissertation in 1936, “According to my definition, a number is computable if its decimal can be written down by a machine.” That is all well and good, and it was a great lightbulb moment, not yet in silicon at that time, but in thought, for the whole world.
The only downside to this limitation on computable, real numbers is that unpredictability remains. Most importantly, there is no algorithm, no machine that can automatically state, in advance, whether an algorithm presented to it is either going to end, or run indefinitely in an infinite loop.
That’s why Hilbert’s program failed between 1931 and 1935, but it is also why we are now living in a world where you can say, at the very least, that computers have taken control, just as Turing predicted. And although in that wonderful year of 1936, two American mathematicians proposed effectively the same theory, with calculable numbers and functions, Turing, in England, was the only one who specified a machine for it. The machine has appointed us and the machine, not mathematics, is the reason we are here talking about media art in 2007.
But what does it mean that we no longer calculate pi by hand, as Ludolph did, but that machines relieve us of that need and that there are things in the world that imagine things of the world without us having done anything other than construct them and get them to think? What does it mean that logic, in a Heideggerian sense, has fallen to machines, and that logic professors are gradually becoming superfluous? Does it mean anything for the formalism and laws of logic and thought, or do such things as pi and its decimal places reveal something about the world we live in? The physical, the chemical, the biological world that we’re in?
The most recent novel Thomas Pynchon published, last December 2006, Against the Day, answers the question with: yes, numbers and functions do say something about the world. An example in Pynchon’s novel is the conjecture by Bernhard Riemann of Göttingen, which is still unproven after 150 years, that all non-trivial zeros of the zeta function have a real part of 0.1. In the novel, a beautiful young and horny Russian mathematician appears in the middle of a lecture and tells Hilbert that this fact reflects something about the mystery of prime numbers that reveal themselves, so to speak, in this function the way the circle reveals its nature in pi. And we can read that in the course of our mathematical and world history. We learn something.
That’s actually the oldest idea that came to the European philosophy of mathematics from Plato. In the secret Seventh Letter to the tyrant of Syracuse, which the tyrant was supposed to burn immediately, Plato wrote that “circle” is, firstly, merely a word, different in every language; secondly, a drawing that never fully corresponds to a circle and is always defective; thirdly, a definition—all points with an equal distance from the center; fourthly, a concept that from this definition arises from the soul; and fifth, the circle is, in contrast to and distinct from the concept, something that is not only in our soul but simultaneously in the heavens. Not distorted like a drawing of a circle in the sand, but an eternally radiant truth. I think you have to be a bit of a Platonist to make this evening lecture a bit of fun for us all. The Aristotelian counter-assumption would immediately silence me.
Indeed, you have to wonder how people got this number at all, the mystery of the circle and its irrational, transcendental number, which reveals itself as an algorithm and a historic process.
In the first Book of Kings, chapter 7, verse 23, pi put Solomon, King of Jerusalem, in such an awkward position that a king and a master builder named Hiram of Syros was brought from Phoenicia to build the first round basin in a Jerusalem temple. In the Bible, it says that the diameter was ten cubits and the circumference consequently thirty. I am unaware of any larger error in the calculation of pi. It’s a whole-number estimate or a rounding off. In the Rhind Papyrus, which is certainly older than the first Book of Kings—being an Egyptian papyrus—the approximation is much, much better: sixteen divided by nine, in brackets, squared. Archimedes went to the trouble of drawing, in the sand in Syracuse, a 96-sided polygon around a circle, and another 96-sided polygon within the circle to reached the wonderful estimate that 300/17 is smaller than pi is smaller than 22 over seven.
And in 1766, a Japanese person, God knows who, Amaterasu, helped him, gave the fraction, the fractional approximation of pi as 5,491,351 over 1,725,033. We call that Zen Buddhism.
But none of these approximations are generative forms that allow us to grow pi, so to say, like a tree, like an apple on a tree. And that’s the main point of this long mathematical world history. To find a closed form from which a principally unlimited number of processes can result.
This transition is extremely hard; you’ll have to think with me while I stammer a bit. I think that in this function of revelation, of deprivation, which then comes to an end, to completion, to a finished work, that algorithms have an inherent relationship with art. It’s probably only been noticeable since we’ve been surrounded by computers and algorithms and we’re no longer dazzled by masterpieces in museums and galleries the way we were in the nineteenth and early twentieth centuries, but where, in a series of images — surely the most difficult example—a process, a generative process, appears to us behind these images. I have to confess that I find Johannes Vermeer van Delft better than all media art, and when I’m standing in front of those miraculous panels, most of which show one and the same room populated by various beautiful people, the most exciting thing is to see that Vermeer apparently painted all these images with the help of a camera obscura.
There are different perspectives in this room, always from the same door, but at different distances from door and room. This was only discovered in the 1950s as interest in pictorial processes caught up with, but did not overtake, interest in pictorial content. So, we can see the process in which Vermeer, in hours, or days, or weeks of work, painted an image in oils: it was a machine-generated camera obscura image actually created from one window and the sunlight coming through that window. As we know, for a finished image the sun needs just fractions of fractions of seconds; the camera obscura also reveals an image in fractions of fractions of seconds. Vermeer took days or weeks. And when computer graphics in the 60s and 70s dared to imitate this effect of incidental light through a window and its reflections of reflections, my 386 computer in Bochum, in the 1990s, was calculating the algorithm, called Radiosity, for the whole night.
Now, an approximation can be done in an hour. The complexity of Radiosity relates to the complexity of the algorithm, to what is happening, and to what is, arguably, the task of all art. Such infinitely fast and infinitely continuous and infinitely exciting processes are captured in works of art and in algorithms, both of which are finite by definition! A perhaps more beautiful example for the computer enthusiasts among you might be the famous optical illusion woodcuts by M. C. Escher where a staircase around a brick square seems to go endlessly upwards, which is physically impossible. Or the corresponding waterfall, endlessly cascading, closing in on itself over and over again, and not just in our imagination, but really, in a strange limbo between painted-state and imaginary-state. Of course, Douglas Hofstadter has already said everything necessary about that in Gödel, Escher, Bach.
So, moving towards our goal, we have algorithms and processes on one side, and artworks on the other side, and between them things like the camera obscura, the Turing machine, computers, and more basic things: palettes, painting tools, and musical instruments. Things within which knowledge, often thousands of years of knowledge, have accumulated, knowledge that is, however, different from that which is in artworks; instruments and machines collect knowledge in order to create works and processes.
The best and most algorithmic way to end is definitely with musical processes, because the concept of this next step is highly difficult. Computer science doesn’t seem to have such drastic complexity as painting, where so many follow-on steps seem at least possible. This year’s transmediale is called unfinish, and it refers to the fact that a composer can write a score as an algorithm, as Mahler did. The instruments, the orchestras and their instruments are then machines that reproduce different instances of the Mahler score; you could also do the entire thing without instruments, and today it would be possible to approximate all the instruments of a big orchestra on a computer with physical modeling.
At some point, Mahler finishes the composition. He gets it printed. When it’s played, it lasts 120 minutes and then comes to an end—totally different to Plato’s imaginary Music of the Spheres, which we supposedly don’t hear because it’s been playing since the beginning of the world, since before we were born and will continue after we die. And at some point, very in keeping with unfinish, Mahler decides to rework the piece, despite the completed, printed score, to change the instrumentation, to add a few notes and, especially, to take some out, to make the composition tighter—that’s the style of late Mahler as opposed to mid-career Mahler. And I wonder, I really openly ask the question: could it be that just as the zeta function betrays something about the otherwise totally chaotic prime numbers and their coding, and as pi reveals something about the essence of the circle, that Mahler, when he takes up the composition for the second time and changes it, and makes the work into a process again—could it be that when Mahler changes something in the image he has made of the Earth, that the Earth in reality sounds different?
If you ask yourself this as I have, then perhaps you‘ll understand why Mahler used German translation of ancient Chinese poetry for all the songs in Das Lied von der Erde but wrote the last six lines himself, even though he was a composer and not a poet. These last six lines, which of course shouldn’t be read out here but rather “heard,” are not entirely accidental and seem to me to describe the relationship between infinity, processuality, artworks, finiteness—I quote: “Beloved Earth, everywhere, blooms in spring and flourishes anew everywhere and eternal blue light in the distance, eternal, eternal, eternal, eternal,” Pianissimo, end.
I believe that nothing in this world—not even the invention of media and computer art—can alter the task of art, which is to reveal the eternal in the finite.
Yes, thank you so much. If anyone wants to step out, you can do it now. And for those remaining there is an opportunity to ask questions; we have microphones in the hall. I don’t know what it’s like in the back, it might be a bit difficult, but we’ll just start. So we have about forty minutes to talk about this topic. Would anyone like to ask a question or make a comment? Or is everyone so completely satisfied that we—I think, over there—was there somebody? Yes. I thought it was somebody wanting to ask, but people aren’t out yet.
And what does this do...? Hello?
I don’t know.
Audience member [in English]
Hi, I’m Jaromil. I’m a programmer. Thank you for your keynote, it was fascinating and I’d like to pose a question: you basically focus on the relationship of humans and machines, and I’d like to ask you, how do you see the relationship between humans nowadays concerning algorithms? I’ll give an example: I like to depict programmers—or whoever writes algorithms—as alchemists, for instance, from the eighteenth century. They were really jealous about their ingredients—in fact, the ingredients couldn’t be copied, they were finite, and so it was very difficult to exchange recipes, and I think the situation has radically changed nowadays, since it's possible to copy, to reproduce very easily all those recipes. Plus, as you mentioned, computers are a really powerful extension of the human mind, so basically we can tell that straw can be converted into gold. An example is Second Life and the crossover between reality and metaverse. In all this, do you see any change in the relationship between humans also regarding algorithms, so what changed in creating algorithms in this sense?
I didn’t quite get the first part of the question unfortunately, because of the technical issues.
I mean, is it only that machines brought an extension to humans to execute the algorithms? But if we consider the fact that we can exchange algorithms much more freely nowadays and basically they grow out of what Pierre Lévy or other philosophers define as collective intelligence—de Kerckhove and so on—what do you see that has changed in the history of algorithms? And what is changed and—this is pretty recent, no? —is the way, really, to exchange the ingredients? I’m not really a historian of mathematics as you are, so I’m pretty curious about your vision compared to the Abbasid dynasty once when Muḥammad al-Khwārizmī was forging those algorithms and now passing through all the various stages of human developments in terms of science.
Yes, yes, yes. I’ve got it now.
I felt it was important, as I said at first, that the algorithm is, as you also confirmed, much older than computer science, and that you can’t say whether it is a divine gift or enlightenment or a human construction. We must, I believe, accept the history of algorithms in their contingency, in their randomness. Of course, sometimes reasons—historical, media-historical signs—can be offered for why this algorithm appeared at this time—with Leibniz, for instance. But what was most important to me was the escalation, the bottleneck that occurred the moment algorithms were no longer created with paper and pencil, but were entered into operable machines with operating systems that solve the whole lot much, in most cases a hundred thousand times, faster than humans.
And in contrast to Mr Lévy, Monsieur Lévy, I won’t see it as the result of an average, internationally distributed, global, collective intelligence, but as the performance of people who have found, for example, this highly efficient prime number algorithm, and have therefore earned the Fields Medal they have been awarded.
Whether the rest of humankind is anything other than passive is a question better addressed to Wolfgang Coy than to me.
I mean, if no one has a question at the moment, I would like to respond. The exciting thing is, yes, on one hand the machine confronts us as our own product, but one that engulfs us, and in many respects reveals us faster than we can see ourselves in the mirror. But, on the other hand, this is how I understood the question—we experience the networking of machines as a communicative system simultaneously. So the special status of the machine, its becoming independent, which you emphasized, has nevertheless been weakened in a new development where this communication can be unbelievably more diversified than we’ve ever experienced in traditional machine communication. Is that a shift? Have we experienced a change in the last ten years or is it just “more of the same”? Is this ultimately just the self-sufficiency of the system?
Actually, if I’m being honest, that I would prefer fewer people be connected through the internet and more machines to be connected.
I think that is an opinion, but there was just a question and I wanted to explain.
At least, I’m more interested in—the best network I’ve ever found is called “Farmen,” a gigantic “farm” of Linux computers, which are unused at night—because their users need to sleep sometimes, the freaks. The machines simply continue, and in the end, for films like Titanic, endless virtual images of sea storms have been generated that nobody has filmed and which have never existed; they were computed. That is the best high-performance computer networking, I think.
Well, I would rather they calculate more Zen prime numbers, but okay, please, they like to calculate the Titanic too.
I used that example specifically because it connects to art and media art. It’s not a made-up story, it’s true, and I would like for a second to throw out into this great hall the question of whether such anonymous, industrial— as far as I’m concerned even commercial—products of computer art do not deserve our respect?
Otherwise, the impression is that media or computer art is an extension of the individual artist with other, commercially available products.
I can’t see so well with the lights, was there a question? Yes.
Could you stand up so that the audience has a rough idea of where you are?
Audience member [in English]
In the last session, we had a discussion about media art and about how the word “media art” became less interesting. There was a citation from you in that session, saying that “media determine our situation.” And I was thinking: could you say, for example, that algorithms are defining our situation today, and I am thinking in a way of how the logic of the game, for example, is penetrating into the world of theater, into the world of art, so that in a way there are algorithms that are working inside artworks in different ways? So would this be a way of restating and updating your opening on your book from 1986?
Secondly, in that book you also predict the end to media, because the difference between different media is eroding—and also the end to the concept of the medium. Is it possible to ask you how you look upon those predictions now, 20 years later?
Yes, I would like to try to answer. Twenty-one years ago, when I wrote that sentence, I wasn’t really interested in theater and play and things like that, but in the fact that the cable telegraph played a key role in the war in 1870–1871, the early wireless radio in the First World War from 1914–18, and the battle between radio encoding machines and British computers (and their eventual victory) in the Second World War. That was the situation at that time. The fact that now every G.I. in the American army has their own laptop follows the logic of this progression.
That’s why the media that determine our position should still be on the lookout for the industrial, military, political complexes—and not so much through the small window that the art world offers us, it seems to me. The seriousness of the assumptions or hypotheses from that time have not changed much. I think it’s already been almost 20 years since the founding father and head of Intel predicted a battle for our attention between the computer monitor and the television screen. “Battle of the eyeball,” it was called. The television and film industries laughed themselves sick over yet another nonsensical prediction from one of these Intel company founders. And today, after the World Cup, we all have to face the fact that he was right. And it is exactly that point where the individual sense-fields of these connected media flow into this universal medium conceived by Alan Turing. Except the landline telephone—I think I’m the only user that still has one of those.
So, we of course have to admit that last week Bill Gates also thought the end of television was a possibility. So that’s probably settled it.
That means there is a job for the Helmholtz-Zentrum as well, when everything works in bits and bytes and zeros and ones—at least works acceptably to end-users. Then the question arises of whether there are actually any specific characteristics of different sense-fields and media. For example, whether you would have to try—which can’t possibly be imagined this evening—a kind of algorithmic minimal configuration of what a picture is, or what music is, and not just in the popular neurophysiological sense that is dominant in the press at the moment, but also in the sense of an assertion about a thing’s being. So, I still hope that Immanuel Kant is wrong that when it comes to beauty—for beauty at least, if not for the sublime—there are some things that can be mathematically analyzed in fields like music, images, sculpture, and architecture, as in the complexity-theory approaches attempted by Birkhoff and continued by Max Bense. Are you skeptical?
I am skeptical because I don’t see it, but Bense did write a wonderful foreword for his Informationsästhetik. The last sentence says something like, “It may be that none of what we say works, but if it were to save us from the dreadful drivel of the culture section in the papers, that would be a tremendous advance.” In that sense, I would agree.
Would anyone like to offer an opposing view on information aesthetics?
I would like to ask again briefly, in terms of understanding, and ask you about speculation from the area that you raised, which is difficult to respond to. You spoke at the end about Mahler and about the task of the artist, in order to demonstrate the eternal in the finite. In a way, Mahler still belongs to a succession of musicians who somehow failed at the end, who are unable to complete their tenth symphony as the pinnacle and conclusion of their work. And, you would know more about this, but a pupil of his, like Schönberg, said in the eulogy, “If Mahler had written the tenth, we would have heard something that would have changed our world much more fundamentally.” I’m wondering why now, on the topic of algorithms, you refer to this tradition of failure. Does something resonate with you in the fact that the Linux computer you brought up—which has to be connected before it can work—could have helped somebody like Mahler complete this intention in the tenth in a different way, whether he succeeded or not?
That is a difficult question—I’m not sure what you mean by “failed”? Failed as a musician? Failed as a husband and cuckold? Dying of a broken heart, as it were, because of that woman?
But still prominently immortalized in her biography, so…
Could you not answer that, from the first sketch of the first movement, it was almost finished, and the drafts for the other movements of Mahler’s tenth symphony, which so many good musicians tried to complete over the last 80 years since his death—that something like a structure emerges, which is not a failure, but calls for its completion? This is not something that every building, work, film, or piece of music does, but large fragments seem to be able to and would more likely be an indication that unfinished is a pain in which something is concealed, as Greek sculptors said of the veined marble in which Apollo was hidden. As far as beauty and art are concerned, I would at least try to maintain this semi-platonic perspective—that there are responsibilities there, which have already been written into Mahler’s fragments. There is just musical logic, a notion firmly held by no less than Adorno.
But when you mention marble, and go back to your lecture, then all completed music is within pi. We only have to reveal it.
So then let’s start looking now.
So, I’ll take that lovely example again from Against the Day, Pynchon’s last novel, because nobody actually knows it. The (sex-) heroine of the novel, this Russian mathematician, believes—more so than her teacher, David Hilbert in Göttingen—that information about prime numbers and their seeming chaos is so encoded in the Zeta function that we become acquainted, so to speak, with physical constants. So bold is the lady of the novel. And then the novel becomes—and this is not uninteresting in discussions of art and poetry—so recursive that it starts thinking about itself: “I am a historical novel. I am set before the First World War and describe what everything is like during the catastrophe of the First World War—and how, above all, the grandiose powers of European anarchism are destroyed between high-capitalism and Bolshevism. One-half of the world is capitalist and the other half is Bolshevist. I am a novel that knows and perceives more than just the coarsest features of history, not like the silly historical novels a là Gustav Freytag or Felix Dahn. I am a novel that does everything right. The taxis that drive armies to the Battle of the Marne, and so on.”
It’s all correct. You find no mistakes and you get the impression that Pynchon is trying to build a time machine in 1,085 pages. A time machine that goes back to being a conventional historical novel. Just as the heroine is able to report prime numbers from the Zeta function, Pynchon had the story given to him in order to almost—or not even almost—reactivate the power of this anarchism in 2006. In the novel he plays the same game that his heroine plays before she resigned—in mathematics, or between mathematics and physics. It seems a fascinating possibility to think that,—to go beyond the humble, undemanding scope of mere metaphor and comparison into realms where novels and systems of equations and algorithms are subject to the same conditions of seriousness. That may sound very poetic.
We’ll have to wait a bit until all 1,085 pages have been processed … but I think there is another question.
Hello, I have an educational question. You gave a very dense kind of introduction to the mathematical philosophy behind computation. How important is it, in your opinion, for an artist or media theorist dealing with computers, computer culture, and the effect that computers have on our perception, to have this kind of background, this kind of education? How deep does a computer artist, net artist or media artist need to go into mathematical theory, in order to be able to say something real or unreal about the way we are being affected?
Nice question. I don’t want to make rules for media and net artists, and I’d like first to be a bit critical of my profession or vocation. Professors of media history or media theory who have never used even a little Pascal algorithm or have never unscrewed the cover of their machine—I simply don’t trust them. And I can only offer a report on what it’s like for media artists. Ten years ago I was at a computer art exhibition in Chicago, at a cold lake in the Windy City—and it was depressing to see how many HTML applications were being presented as great computer art. That’s something that anyone could do now.
And after these dull screens on whatever kind of communication signs were spinning, paradoxical or meaningful, random or senseless, in Chicago I heard an electric guitar in the distance. And I followed this sound because I love electric guitar. I went into a room and there was a steel guitar lying on a steel block. It had steel guitar strings, and the strings were being played by a steel hand that was being controlled remotely by a computer. On another table there was a microphone, a Fourier analyzer and, as I discovered, a Kohonen network. I asked the programmer and builder, who was from Hamburg, how it had been programmed—and he said, “in plain C.” Respect.
What kind of device was it? And why was it so much more fascinating than the image and screen programs built in ignorance of computer music and mathematics? This guitar started playing by itself at seven o’clock every morning—completely random notes. But the Kohonen network that the designer had put into the feedback path was programmed to improve over the course of the day, to play like an electric guitar from Windy City Chicago Blues. At noon when I was there, the designer said it was playing the blues half right, still with mistakes. In the evening, when he turned it off, it would be the perfect Chicago blues guitar—although the drums and saxophone to go with it had unfortunately not gotten through US customs.
And that is real computer art, in contrast to entertainment electronics. To sum it up: ordinary communication between average people is not something that justifies duplication. Every sunset and coral reef and guitar are a thousand times more beautiful. And to the earlier question you would probably have to say, “out of love for what exists, it is worth learning mathematics and physics.” The more we ourselves know about it and the less only web encyclopedias and professors know about it, the better, as the Greeks would say, life is. Fully Zen. The Japanese were so enthusiastic about tape recorders, when they were still made in Germany, that they said, “You know, we used it very differently from you. You record a whole Mahler on the tape, from beginning to end, or an entire Wagner, but we do something else. We get up at three in the morning, climb the holy mountain, Fujiyama, and record bird songs.”
So, if there are no more questions, I think this meditative element would make quite a nice conclusion. But if there are still any pressing questions, that I can’t see well from up here because the light is very—yes, there’s another question.
I still have one question. When I listen to you talk, I wonder why you seem to doubt the artist. Because, yes, that is very to the point, of course, but when you say that there was a blues guitar that learns to play perfect blues by the evening, and that behind Mahler’s composition there is nothing but an algorithm—if, with more powerful computers, this principle could be expanded or extrapolated, it could be possible to produce almost any kind of art with a machine. Are you telling these people that they’re going to be unemployed in a hundred years?
Could you say the last sentence again?
Are you telling these people here—well, these people will all probably be dead in a hundred years—but their children—that as artists they will be unemployed? Will art as a human endeavor no longer exist? It’s provocatively formulated, but I can’t help wondering.
I can’t help wondering either, but I would like to make a distinction between unpredictable conceptual discoveries in art, or even in mathematics, and the sort of applications that we are all capable of. A simple example: you can teach people to draw or paint pictures in correct perspective, but it took a certain brilliant Leon Battista Alberti to come up with the idea of geometric perspective construction in the first place, which then defined all the paintings in Europe for 400 years—until just before Picasso and George Braque. And I think this form of opening doors, “doors of perception” as Jim Morrison as others before him spoke of it, will still exist in a hundred years, because there is still so much to solve, also in computer graphics, for example.
In a way, that is as inventive and unpredictable as a new principle of painting or composing—Ligeti’s clusters, things like that—just as unpredictably. A new algorithm is suddenly found and can be used to finally calculate what is most trivial and optically beautiful in the Californian world. So far, to my mind, this remarkable David Hockney-esque dappled light on the bottom of sun-drenched swimming pools is only calculable if the concrete blocks are all perfectly flat—all five—and if it were a bathtub, for example, it couldn’t be calculated. There needs to be another leap in the progress of algorithms; someone has to invent something as ingenious as Alberti did, defining the essence of the image… then a whole flock of artists will follow. Perhaps I was mocking them a little tonight, because they are sometimes disturbingly similar to one another, like all those paintings of bellowing stags above sofas in the nineteenth century.
But you can still practice a bit? So that you can get there? I mean, there is a certain problem: I understand your desire for radical change and new ideas very well, but how do get into a position to do it? Is there a path leading there? And doesn’t this path possibly consist of digital stag paintings?
Didn’t you yourself recently—
No, no, no, you spoke positively about the fact that when quantum computers really work, that would be a quantum leap. It is not true, as far as I’m aware, that these quantum computers are simply the fruit of linear technical progress. They are the result of the explicit, theologically justified protest of Albert Einstein; they have had powerful enemies. That is a point that is probably also relevant as to why the great upheavals aren’t more frequent.
Yes, um, I’m not so good at math, so I won’t be able to formulate my remark as a question. Nevertheless, I have a tiny Johann Sebastian Bach machine inside me, and when I ride a bicycle I whistle melodies that are incalculable. I know the construction principles and, from the components and new improvisations, it whistles itself. As every bike ride ends, this game ends too. It goes on practically independently of me—like here, during the lecture, together with me. And if I didn’t know these famous final notes in the Art of the Fugue, during which, according to legend, the pen fell from Bach’s hand, the end of every bike ride and the corresponding stopping of this little Bach-whistling machine would be incredibly unsatisfactory.
And it is probably also here when we are talking about art, again, my desire is to reconnect with a satisfaction, or a beauty or a sadness of endless processes, that computers are not known for handling well. Finished processes that always remind us of something—if Glenn Gould hadn’t played those final notes so beautifully, and they weren’t so stuck in my head, the end of every bike ride while whistling would be so sad. I always find that is a great thing about art: to find models, so to speak, to deal with this finiteness. Thank you.
To that, I can only say, “Yes, yes, yes,” like Molly Bloom in the last sentence of a certain novel.
And because that is the last sentence of a certain novel, could we take that as an indication that it was perhaps also the last sentence of this event? Or is there still an urgent need to speak?
I could live with that very happily, if you can too.
Then, our thanks to Friedrich and the audience. We thank the audience for not going for blood, and I wish you a pleasant evening.
- 1. Editor's note: Muḥammad ibn Mūsā al-Khwārizmī is believed to have been born around 780.