Goethe had to
pay a price for choosing a true German university professor as the tragic hero almost for the first time in the history of German theater.
pay a price for choosing a true German university professor as the tragic hero almost for the first time in the history of German theater.
Kittler-Drunken
?
?
Man as a Drunken Town-Musician
Author(s): Friedrich Kittler
Source: MLN, Vol. 118, No. 3, German Issue (Apr. , 2003), pp. 637-652 Published by: The Johns Hopkins University Press
Stable URL: http://www. jstor. org/stable/3251939
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? Man as a Drunken Town-musician Friedrich Kittler
The sciences are on stage again. 1This self-referential assertion is less trivial and less timeless than it sounds.
Not knowledge, but science could certainly only have existed since the Greek vowel-alphabet connected an alternating interface be- tween the elements of letters and the elements of nature. AsJesper Svenbro has shown, what for the ionian philosophers of nature arose out of itself in fact only arose from writing. Therefore, everything which can be called science must be able to appear as text. The elements, whether Heraclitus' or Mendeljew's, are first given only in the sign of their names, and thus in Latin they have become 'data. '
Yet this basic relation between knowledge and writing has been so
deep-seated that it has scarcely reappeared. Almost in the same historical moment when Galileo directed all modern physics to the
reading of that book which Nature was supposed to have written
herself in geometric or, subsequently, algebraic signs, the modern novel and modern theater stepped in as evidence that modern
readers and spectators enjoy the effects of those fictions most of all when they are altogether free of science. Not only the age of Goethe, but first and foremost the one to whom this age owes its name bears eloquent witness to that effect, despite his love for mother nature and her open secrets. Goethe claimed that the intuition of nature could only take place however as far or as much as fortunate eyes were able to intuit and to see. Still, that elementary technique of culture
1What follows is the revised version of a lecture given at the Freie UniversitaitBerlin in the series of lectures StagesofKnowledgein theSciencesorganized by Helmar Schramm in 2000/2001.
MLN 118 (2003): 637-652 ? 2003 by TheJohns Hopkins University Press
? 638 FRIEDRICH KITTLER
common to all sciences, called mathematical codification, remained forbidden.
When, in 1826, Karl Friedrich Naumann, one of the founders of
modern crystallography, sent his latest publication from Leipzig to Goethe, one of the most ambivalent thank-you notes ever written was
drafted in Weimar: "the important document sent to me by Your
Honor," wrote the aged Goethe with the usual bureaucratic cer-
emony, "arrivedat a good moment, and I immediately read it with
great pleasure repeatedly up through page forty-five. At this point, however, I am standing at the limit which God and nature wish to
define for me as an individual. I am dependent upon word, language
and image in the truest sense, and completely incapable, to act in any way whatsoever through signs and numbers, with which the most talented spirits make themselves easily understood. "2
On that January day in 1826, the aged Goethe did not read any
further for reasons which Francesca and Paolo, or Lotte and Werther
could never have dreamed of. At the first mathematical symbol, the
first "quanitity,"as it is later called in the letter to Naumann, his
reading came to a halt. Through "signsand numbers," as they do not
belong to alphabetical language, the reader saw himself robbed of all
"qualities" with which "God and nature" were supposed to have
endowed his "individuality":"Word,language and image in the truest
sense. " This is how German poetry, when it called out its own three
media by their proper names, completely forgot the fact that it too
was alwaysalready over its designated limit. A "page 45," together with
the printed page number, is not only part of Naumann's crystallogra- phy, it can also be found in Goethe's Faust. It therefore does not help
very much to privilege the operations of literature over those opera- tions due to which the sciences are not only able to codify their own methods, but also their results and thus parts of the so-called nature.
Concepts of the text that stress a pure alphabetics while discarding its numerics (to take up Derrida's attack upon a supposedly europe-
wide phonocentrism and reformulate it somewhat more technically), have revenged themselves bitterly on their authors. Goethe had to
pay a price for choosing a true German university professor as the tragic hero almost for the first time in the history of German theater.
In addition to that, and according to his very personal model, he had
2 The letter from Goethe to Friedrich Naumann dates from January 24th, 1826, in Briefeund Tagebiichervol2. (Leipzig: Insel-Verlag n. d. ) 441.
? M LN 639
to pay an even higher price for granting this Doctor or rather Magister Faust with a passion for the innermost secrets of nature, a nature which punished loathsome measurings or even numeration of her exterior with contempt. This is precisely why Emil Du Bois-
Reymond, a leading physiologist at the Friedrich Wilhelm University in Berlin,3appeared before the admiring academic public with all the gold and taffeta of his new rectorship in order to demand the immediate end of the age of Goethe in a lecture antiphrastically titled "Goethe und kein Ende": "Goethe and No End. " Science as such therefore staged a court where-in a neat reversal of Galileo's trial- it threatened its enemies with excommunication and inquisition. Goethe's "Theoryof Colors,"which Du Bois-Reymond claimed to be a failure in the field of physics, did not retard scientific process in Germany any less than Faust's intuition of nature did, bereft as this intuition was of all mathematics. It is high time to check whether the so-called naturalists, the immediate contemporaries of Du Bois- Reymond and Claude Bernard, did not in fact write his tirade or mandate into literary deeds without further ado. In any event, the
great physiologist himself did not do so; instead, Du Bois-Reymond, after he bid farewell to Goethe's "Word"and "Language"in the name
of science, turned to the realm of the imaginary, which Goethe had celebrated as the "image in the truest sense. " In 1890, a small written piece on "Natural Science and Fine Art" ("Naturwissenschaft und bildende Kunst") issued forth from the pen of the Berlin Emeritus.
If there is ever to be something like a history of media studies, Du
Bois-Reymond's almost forgotten writing should appear in the canon of its holy texts next to Ernst Kapp's "Principle Characteristics of a
Philosophy of Technique. " Du Bois-Reymond's text writes the history of art from a perspective which has only recently been occupied again
by Samuel Edgerton or Jonathan Crary. The phenomenality of appearances, as it occurs in canvasses and statues, in painting and
plastic art, is everything but an unmediated beginning. In order for
styles and works of art to even appear, epistemological knowledge must first have established the field of their colors and forms. Du
Bois-Reymond cuts across, however provisionally it may be, the history of specific sciences in order to couple fifteenth-century geometry with the possibility of paintings in linear perspective, or to
3 The Friedrich Wilhelm University was renamed as the Humboldt University in 1949.
? 640 FRIEDRICHKITTLER
couple sixteenth-century anatomy with the possibility of muscle's becoming marble, and finally, the physical theories of color from Newton through Helmholtz with the history of painterly coloritoas a whole. At the end of his essay, however, this course of a history of science, not yet curbed by any modern artistic impulse, makes the transition from static to moving pictures, which is a brand-new idea in 1890. Five years before the Lumi&re brothers will raise Edison's
playful peep-box theater to the status of a mass-image medium, Du Bois-Reymond presents, if you will, the very first history of film. This
history has the unique feature of not describing moving pictures as animation or the surpassing of Daguerre's half-hour exposure times, as has become commonplace and self-evident since Hugo Miinster-
berg's scarcely less-forgotten psychotechnique of film. Du Bois-
Reymond's history does not begin at all with diorama painters or magic lantern players, but rather on a really elementary threshhold:
with the scientific history of moving. In the process of elaborating the thesis that without modern geometry there would have been no
paintings in linear perspective, Du Bois-Reymond's brief history of art ends with the statement that there would be no moving pictures
without the analysis of modern mathematics.
Today, one could make just the reverse statement: one could say
that without moving scientists there would be no modern analysis.
Geometry first became analytic, and that means cinematic, when an
officer on leave, who happened to be a burgeoning philosopher, first dreamed of movement as such in his winter quarters on the Donau.
"Larvatusprodeo"-masked, I go forth-remained Descartes' device, even when he no longer wore the uniform. But what has hindered
empirical movements from achieving mathematical and philosophi- cal honor in the same way seems to be precisely the steady motion of
Descartes' subject which he conceived of as a geometrical point and which analytic geometry since Descartes transposed into the ceaseless movement of a curve-defining point in a field of coordinates. Furthermore, empirical movements remained a domain of dance- instructors and their choreographies, or of the drills of officers educated in Hessen-Nassau and Hessen-Orange to whom the young
Descartes owed his drilling- and fencing-skills. 4Mathematical analysis, on the other hand, moved those dimensionless points, to which the
4 See Wolfgang Schaffner, "K6rperim Takt. Zur Geschichte symbolischer Maschinen im 16. und 17. Jahrhundert" in Kaleidoskopien3 (2000), 188-205.
? MLN 641
swinging pendulum or flying granades were reduced for the sake of simplicity, through every possible adventure of maxima and minima,
of turning points and null-points, of velocity moments and forces of acceleration. Only in the truly novelesque case of that lying baron,
who had the privilege of performing the analysis with his own body, did a cartesian subject ride along on the parable of a granade's trajectory. Once again the text of the novel, in Miinchhausen's case as
in Descartes', relied upon the certainty-unshakeable because imag- ined in the Donau winter quarters-that dreamed motion or faked
flying remained as inescapably true as only the Cogitoitself otherwise could be.
This blessed time of the founding fathers in which consciousness
and analysis, thinking and differential calculus were one and the
same ended bitterly. The reason was simple: not all trajectories of
motion in physical empiricism were permitted to be ascribed to the
cinematics of a single point. What Huygens had achieved in the case
of the swinging pendulum already failed in the case of a vibrating
string whose innumerable points are elastically coupled and thus, in other words, enjoy uncountable degrees of liberty. Not even cartesian
subjects would have been in a position of being or thinking all points of the string at the same time in order to discover the secret of a
single tone from the violin. All that remained was for mathematical analysis to bestow this secret unto a new, no less mysterious theory: to the partial differential equations in brazen opposition to the usual ones. Newton's usual differential equations still sufficed for solar systems, since the stars which were part of those systems do not enjoy a single degree of freedom; but not everything that moves is as simple as in astronomy. In the case of violin strings and bell tones, drumskins and water surfaces, and even windstorms and electromagnetic vibra-
tions, only partial differential equations successfully modelled the countless parts moved in all their dimensions.
Thus the course of modern science finally arrived at physiological, day-to-daymotion. In 1836, a monograph from Wilhelm and Eduard Weber appeared which was almost without precedent: the "Mechan-
ics of the Human Walking Apparatus. An Anatomical-Physiological
dermenschlichen Eine anatomisch- Investigation" (Mechanik Gehwerkzeuge.
physiologischeUntersuchung). E5duardWeberhadatthattimejustbeen
5Weber, Wilhelm and Eduard, UberdieMechanikdermenschlichenGehwerkzeugen,ebst
der eines Versuchsiiberdas des aus der im Beschreibung Herausfallen Schenkelkopfes Pfanne
? 642 FRIEDRICHKITTLER
summoned to the University of Leipzig as professor of medicine; his brother Wilhelm, on the other hand, was already a professor of physics in G6ttingen since 1831, where he had just two years later, together with none other than GauB,made the first electric telegraph run. That alone suggests that the medical subtitle of their joint book is pure understatement. All the anatomical and physiological findings
concerning knees, hips, leg muscles and joints gathered in the first
part only serve the higher purpose of founding a mathematical physics of legs in just as strict a sense as Newton had demanded for
the physics of celestial bodies.
At least the anatomical and physiological investigations-or in
other words, the experiments both on corpses' legs in Leipzig and on
living legs in G6ttingen-make it clear from the startwhat the degree of freedom is, which a system of hips, knees and heels enjoys. Every
joint, as writers of computer animations would formulate it, or rather,
program it today, is a three-dimensional transformative-matrixwhose
rotations in turn transform the next subordinate joint. At the end of
the day, however, the matrix-product from all these turns and
displacements produces such variable values, or leg positions, that one is threatened by the appearance of sheer incalculability. "Itcan
perhaps be questioned," so the Weber brothers admit, "whether a
theory of walking and running can be provided at all since we are not walking machines, and these movements are altered in many waysby our free will. "6That merely appears to be the case, however. In 1836, no cartesian subject inhabits the curves or functions of his own limbs. On the contrary, "man binds his movements to certain rules even if he cannot express these rules in words. These rules are based totally on the structure of his body and on the given external conditions. They thus can be deduced from both structure and external conditions. "7
All the preliminary anatomical-physiological investigations have the single goal of reconstructing a per definitionem "unconscious"
walking machine first of all through measures and series of tests on the body, before the triumphant end to the book can go and present
luftverdiinntenRaume,in Wilhelm Weber's Werkee,d. Friedrich Merkel und Otto Fischer (Berlin: Konigliche Gesellschaft der Wissenschaften in Gottingen 1894), 322 [transl. by Maquet, Paul and Ronald Furlong, Mechanicsof theHuman WalkingApparatus(Berlin, Heidelberg, NewYorketc. :Springer-Verlag1992), 226].
6 Ibid. , 3 [VI]. 7 Ibid. [VII].
? MLN 643
the mathematical theory of walking and running. Everything rests on the fact that legs can provide for their own account, so that in the end
they can be in the books as a differential system. In 1836, long before Marey and Muybridge, the attainment of the differential system was at
first possible only in stasis, as if Daguerre's long-term exposures had found a scientifically parallel maneuver. In order to make agility at
least visible as latent motion, however, the brothers cut up the corpses' hips at the precise location where "the balls of the upper-legs lie in their sockets. " Just as in the drawing of a steam engine which
would explain the interplay of parts in the moment of explosion, admiring readers can glimpse the interplay between the ball of the
thigh bone and the socket of the joint.
The femoral head or so-called sphere was sawn perpendicularly from in front backwards and the section was printed on the paper. The curvature of the the two parts here cannot be altered by the drawer. The picture is indeed the imprint of the object itself. The bone thus divided can be used
as a wood-engraving for print. 8
Plate IX
Pelvis
? Fig. 1.
8Ibid. , 14 Fn. [10].
Femur
? 644 FRIEDRICHKITTLER
The work of the Weber brothers makes anatomy leave its proud old amphitheaters, where the dissection resulted in findings that made their way to woodcuts only belatedly. Instead, just as Henry Fox
Talbot's heliography did four years later, they were put onto the printed page as nature's imprint of itself. 9Thus the free will of human drawing-hands in scientific visualization remains just as excluded as it is in the mechanics of human legs. On this worldly scene of all religions and dances of the dead, the skeleton appears on the stage of
knowledge and points no longer to allegories of death, but rather to nothing more than its own animation.
In order to transpose the latent movements that occur around leg
joints, or degrees of freedom, into actual movements, the Weber brothers introduce two simple axioms. First of all, the individual
bones whose interplay comprises a step should swing according to the
law of the pendulum. The differential equation of every partial movement can thus already be accounted for by falling back on
Christian Huygens and his pendulum clock equation from 1656.
Secondly, however, the usual human gait should be a periodically
iterated interplay of all these partial movements, whereby a period is
clearly only counted after a completed pair of steps. '0 In any event, a summation of partial differential equations only appears as total
movement according, first of all, to the three dimensions of space,
and secondly, according to time. Having made these assumptions, the Weber brothers simply go ahead and copy the formula which
Poisson's Traite de mechaniquein the second, recently published edition from 1838 anticipated for such cases. ll With this fact, the misfortune which occupies all of our computer monitors today has come into existence: instead of "word, language and image in the truest sense," "symbol and number" have taken over human gait. Cinematics in the French sense of the word, which as of 1830, and at Ampere's instigation, calculates transversal and rotational move- ments of steam engines, becomes cinematics in the modern sense: it calculates virtual movements in virtual, that is, visualizable spaces.
For the sake of their animation, however, both the leg and Poisson's "general"differential system must make a few sacrifices. "To
9 See also Susanne Holl, "Ob oculos. Andreas Vesals 'De humani corporis fabrica' und der Buchdruck" in Kaleidoskopien3 (2000), 334-357.
0Weber, 191 [128]. " Ibid. , 217 [152].
? M LN 645
simplify the problem we imagine that: 1) Instead of the path there are
only some fixed points (similar to stones laid on the path) along a horizontal line placed as far apart as the length of a step. [. . . ] 2) The
leg is replaced by a straight solid line standing with its lower extremity on one of these points and is retained there by friction. 3) Instead of
being distributed over the entire length of the leg, the mass of the leg is concentrated in one middle point of the solid line. 4) The body is replaced by a mass concentrated in the upper point of this solid line.
This mass flies horizontally at an even velocity. "12In place of the legs and their three joints, a single center of mass around the knee
appears in order to swing henceforth perpetually around a dimen- sionless point which for mathematical reasons has formed itself "instead of the body. "As Christian Morgenstern correctly remarks: "A knee alone goes through the world. A knee alone, and nothing else. "
In fact: this 'nothing' is comprised of pure trigonometric functions. Sine and cosine are the two angle functions which cause this nothing
to step forward; g as gravitation and p as the measure of the circle are the two constants which maintain the steps forward into a period. With knee, g6nu, early Greek mathematics indicated the word for angle;'3 from the angle, gonia, arabic and modern mathematics indicated their trigonometric and thus periodic functions. At the end of this short story of sine and cosine stands the lapidary sentence:
The equation
d2X g sin X=- rl-
of Ch. 128 is replaced by an approximation,as occurs in analysingthe pendulum:
14 d8x
s = - rld ~_rldu2
The freedom of mathematical penstrokes thus finally conquers trigonometry itself. Because neither legs nor pendula are true wheels, that is, they simply do not create angles of any size, the periodic term
12Ibid. , 217 [152].
3JohannesLohmann, Musikeund Logos. Aufsdtzezur griechischePnhilosophiuend
MusiktheorieA,nastasios Giannaras,ed. (Stuttgart:MusikwissenschaftlicherVerlag 1970), 20.
14Weber,223 [159].
? 646 FRIEDRICH KITTLER
for a differential equation can be transposed into a linear one. If need be, the sine of c isjust c itself. For the sake of simplicity,15the Weber brothers only need to posit three further variables of their
general leg-swinging equation as constants of one or zero, and paragraph 128, the "Introduction to the Illustration of Walking
Figures," almost writes itself. Before computers with their explicit purpose of crunching systems of differential equations-at least
numerically-have
come into existence, scientific visualization can
only occupy itself with mercilessly simplified formula.
In its own progress, the "Establishment of a theory of walking and
running" achieves its goal when "the position of both legs" can be
constructed "at the various phases of each step" and "according to
these laws" or equations in order to enable "the artist" to judge
"whether he sees this representation corresponding to the actual
attitude of the legs during walking. ""6The new graph-producing science thus appears to subject itself to the judgement of a visual art.
It ends with an oppulant appendix of tables and figures which portray two lonely legs or knees in all individual phases of walking, running and jumping in order truly to resynthesize the unity of a pair of steps.
? Table XV
Fig. X
~k . ' ; ''
~ . . . i . 2
Fig.
Goethe had to
pay a price for choosing a true German university professor as the tragic hero almost for the first time in the history of German theater.
In addition to that, and according to his very personal model, he had
2 The letter from Goethe to Friedrich Naumann dates from January 24th, 1826, in Briefeund Tagebiichervol2. (Leipzig: Insel-Verlag n. d. ) 441.
? M LN 639
to pay an even higher price for granting this Doctor or rather Magister Faust with a passion for the innermost secrets of nature, a nature which punished loathsome measurings or even numeration of her exterior with contempt. This is precisely why Emil Du Bois-
Reymond, a leading physiologist at the Friedrich Wilhelm University in Berlin,3appeared before the admiring academic public with all the gold and taffeta of his new rectorship in order to demand the immediate end of the age of Goethe in a lecture antiphrastically titled "Goethe und kein Ende": "Goethe and No End. " Science as such therefore staged a court where-in a neat reversal of Galileo's trial- it threatened its enemies with excommunication and inquisition. Goethe's "Theoryof Colors,"which Du Bois-Reymond claimed to be a failure in the field of physics, did not retard scientific process in Germany any less than Faust's intuition of nature did, bereft as this intuition was of all mathematics. It is high time to check whether the so-called naturalists, the immediate contemporaries of Du Bois- Reymond and Claude Bernard, did not in fact write his tirade or mandate into literary deeds without further ado. In any event, the
great physiologist himself did not do so; instead, Du Bois-Reymond, after he bid farewell to Goethe's "Word"and "Language"in the name
of science, turned to the realm of the imaginary, which Goethe had celebrated as the "image in the truest sense. " In 1890, a small written piece on "Natural Science and Fine Art" ("Naturwissenschaft und bildende Kunst") issued forth from the pen of the Berlin Emeritus.
If there is ever to be something like a history of media studies, Du
Bois-Reymond's almost forgotten writing should appear in the canon of its holy texts next to Ernst Kapp's "Principle Characteristics of a
Philosophy of Technique. " Du Bois-Reymond's text writes the history of art from a perspective which has only recently been occupied again
by Samuel Edgerton or Jonathan Crary. The phenomenality of appearances, as it occurs in canvasses and statues, in painting and
plastic art, is everything but an unmediated beginning. In order for
styles and works of art to even appear, epistemological knowledge must first have established the field of their colors and forms. Du
Bois-Reymond cuts across, however provisionally it may be, the history of specific sciences in order to couple fifteenth-century geometry with the possibility of paintings in linear perspective, or to
3 The Friedrich Wilhelm University was renamed as the Humboldt University in 1949.
? 640 FRIEDRICHKITTLER
couple sixteenth-century anatomy with the possibility of muscle's becoming marble, and finally, the physical theories of color from Newton through Helmholtz with the history of painterly coloritoas a whole. At the end of his essay, however, this course of a history of science, not yet curbed by any modern artistic impulse, makes the transition from static to moving pictures, which is a brand-new idea in 1890. Five years before the Lumi&re brothers will raise Edison's
playful peep-box theater to the status of a mass-image medium, Du Bois-Reymond presents, if you will, the very first history of film. This
history has the unique feature of not describing moving pictures as animation or the surpassing of Daguerre's half-hour exposure times, as has become commonplace and self-evident since Hugo Miinster-
berg's scarcely less-forgotten psychotechnique of film. Du Bois-
Reymond's history does not begin at all with diorama painters or magic lantern players, but rather on a really elementary threshhold:
with the scientific history of moving. In the process of elaborating the thesis that without modern geometry there would have been no
paintings in linear perspective, Du Bois-Reymond's brief history of art ends with the statement that there would be no moving pictures
without the analysis of modern mathematics.
Today, one could make just the reverse statement: one could say
that without moving scientists there would be no modern analysis.
Geometry first became analytic, and that means cinematic, when an
officer on leave, who happened to be a burgeoning philosopher, first dreamed of movement as such in his winter quarters on the Donau.
"Larvatusprodeo"-masked, I go forth-remained Descartes' device, even when he no longer wore the uniform. But what has hindered
empirical movements from achieving mathematical and philosophi- cal honor in the same way seems to be precisely the steady motion of
Descartes' subject which he conceived of as a geometrical point and which analytic geometry since Descartes transposed into the ceaseless movement of a curve-defining point in a field of coordinates. Furthermore, empirical movements remained a domain of dance- instructors and their choreographies, or of the drills of officers educated in Hessen-Nassau and Hessen-Orange to whom the young
Descartes owed his drilling- and fencing-skills. 4Mathematical analysis, on the other hand, moved those dimensionless points, to which the
4 See Wolfgang Schaffner, "K6rperim Takt. Zur Geschichte symbolischer Maschinen im 16. und 17. Jahrhundert" in Kaleidoskopien3 (2000), 188-205.
? MLN 641
swinging pendulum or flying granades were reduced for the sake of simplicity, through every possible adventure of maxima and minima,
of turning points and null-points, of velocity moments and forces of acceleration. Only in the truly novelesque case of that lying baron,
who had the privilege of performing the analysis with his own body, did a cartesian subject ride along on the parable of a granade's trajectory. Once again the text of the novel, in Miinchhausen's case as
in Descartes', relied upon the certainty-unshakeable because imag- ined in the Donau winter quarters-that dreamed motion or faked
flying remained as inescapably true as only the Cogitoitself otherwise could be.
This blessed time of the founding fathers in which consciousness
and analysis, thinking and differential calculus were one and the
same ended bitterly. The reason was simple: not all trajectories of
motion in physical empiricism were permitted to be ascribed to the
cinematics of a single point. What Huygens had achieved in the case
of the swinging pendulum already failed in the case of a vibrating
string whose innumerable points are elastically coupled and thus, in other words, enjoy uncountable degrees of liberty. Not even cartesian
subjects would have been in a position of being or thinking all points of the string at the same time in order to discover the secret of a
single tone from the violin. All that remained was for mathematical analysis to bestow this secret unto a new, no less mysterious theory: to the partial differential equations in brazen opposition to the usual ones. Newton's usual differential equations still sufficed for solar systems, since the stars which were part of those systems do not enjoy a single degree of freedom; but not everything that moves is as simple as in astronomy. In the case of violin strings and bell tones, drumskins and water surfaces, and even windstorms and electromagnetic vibra-
tions, only partial differential equations successfully modelled the countless parts moved in all their dimensions.
Thus the course of modern science finally arrived at physiological, day-to-daymotion. In 1836, a monograph from Wilhelm and Eduard Weber appeared which was almost without precedent: the "Mechan-
ics of the Human Walking Apparatus. An Anatomical-Physiological
dermenschlichen Eine anatomisch- Investigation" (Mechanik Gehwerkzeuge.
physiologischeUntersuchung). E5duardWeberhadatthattimejustbeen
5Weber, Wilhelm and Eduard, UberdieMechanikdermenschlichenGehwerkzeugen,ebst
der eines Versuchsiiberdas des aus der im Beschreibung Herausfallen Schenkelkopfes Pfanne
? 642 FRIEDRICHKITTLER
summoned to the University of Leipzig as professor of medicine; his brother Wilhelm, on the other hand, was already a professor of physics in G6ttingen since 1831, where he had just two years later, together with none other than GauB,made the first electric telegraph run. That alone suggests that the medical subtitle of their joint book is pure understatement. All the anatomical and physiological findings
concerning knees, hips, leg muscles and joints gathered in the first
part only serve the higher purpose of founding a mathematical physics of legs in just as strict a sense as Newton had demanded for
the physics of celestial bodies.
At least the anatomical and physiological investigations-or in
other words, the experiments both on corpses' legs in Leipzig and on
living legs in G6ttingen-make it clear from the startwhat the degree of freedom is, which a system of hips, knees and heels enjoys. Every
joint, as writers of computer animations would formulate it, or rather,
program it today, is a three-dimensional transformative-matrixwhose
rotations in turn transform the next subordinate joint. At the end of
the day, however, the matrix-product from all these turns and
displacements produces such variable values, or leg positions, that one is threatened by the appearance of sheer incalculability. "Itcan
perhaps be questioned," so the Weber brothers admit, "whether a
theory of walking and running can be provided at all since we are not walking machines, and these movements are altered in many waysby our free will. "6That merely appears to be the case, however. In 1836, no cartesian subject inhabits the curves or functions of his own limbs. On the contrary, "man binds his movements to certain rules even if he cannot express these rules in words. These rules are based totally on the structure of his body and on the given external conditions. They thus can be deduced from both structure and external conditions. "7
All the preliminary anatomical-physiological investigations have the single goal of reconstructing a per definitionem "unconscious"
walking machine first of all through measures and series of tests on the body, before the triumphant end to the book can go and present
luftverdiinntenRaume,in Wilhelm Weber's Werkee,d. Friedrich Merkel und Otto Fischer (Berlin: Konigliche Gesellschaft der Wissenschaften in Gottingen 1894), 322 [transl. by Maquet, Paul and Ronald Furlong, Mechanicsof theHuman WalkingApparatus(Berlin, Heidelberg, NewYorketc. :Springer-Verlag1992), 226].
6 Ibid. , 3 [VI]. 7 Ibid. [VII].
? MLN 643
the mathematical theory of walking and running. Everything rests on the fact that legs can provide for their own account, so that in the end
they can be in the books as a differential system. In 1836, long before Marey and Muybridge, the attainment of the differential system was at
first possible only in stasis, as if Daguerre's long-term exposures had found a scientifically parallel maneuver. In order to make agility at
least visible as latent motion, however, the brothers cut up the corpses' hips at the precise location where "the balls of the upper-legs lie in their sockets. " Just as in the drawing of a steam engine which
would explain the interplay of parts in the moment of explosion, admiring readers can glimpse the interplay between the ball of the
thigh bone and the socket of the joint.
The femoral head or so-called sphere was sawn perpendicularly from in front backwards and the section was printed on the paper. The curvature of the the two parts here cannot be altered by the drawer. The picture is indeed the imprint of the object itself. The bone thus divided can be used
as a wood-engraving for print. 8
Plate IX
Pelvis
? Fig. 1.
8Ibid. , 14 Fn. [10].
Femur
? 644 FRIEDRICHKITTLER
The work of the Weber brothers makes anatomy leave its proud old amphitheaters, where the dissection resulted in findings that made their way to woodcuts only belatedly. Instead, just as Henry Fox
Talbot's heliography did four years later, they were put onto the printed page as nature's imprint of itself. 9Thus the free will of human drawing-hands in scientific visualization remains just as excluded as it is in the mechanics of human legs. On this worldly scene of all religions and dances of the dead, the skeleton appears on the stage of
knowledge and points no longer to allegories of death, but rather to nothing more than its own animation.
In order to transpose the latent movements that occur around leg
joints, or degrees of freedom, into actual movements, the Weber brothers introduce two simple axioms. First of all, the individual
bones whose interplay comprises a step should swing according to the
law of the pendulum. The differential equation of every partial movement can thus already be accounted for by falling back on
Christian Huygens and his pendulum clock equation from 1656.
Secondly, however, the usual human gait should be a periodically
iterated interplay of all these partial movements, whereby a period is
clearly only counted after a completed pair of steps. '0 In any event, a summation of partial differential equations only appears as total
movement according, first of all, to the three dimensions of space,
and secondly, according to time. Having made these assumptions, the Weber brothers simply go ahead and copy the formula which
Poisson's Traite de mechaniquein the second, recently published edition from 1838 anticipated for such cases. ll With this fact, the misfortune which occupies all of our computer monitors today has come into existence: instead of "word, language and image in the truest sense," "symbol and number" have taken over human gait. Cinematics in the French sense of the word, which as of 1830, and at Ampere's instigation, calculates transversal and rotational move- ments of steam engines, becomes cinematics in the modern sense: it calculates virtual movements in virtual, that is, visualizable spaces.
For the sake of their animation, however, both the leg and Poisson's "general"differential system must make a few sacrifices. "To
9 See also Susanne Holl, "Ob oculos. Andreas Vesals 'De humani corporis fabrica' und der Buchdruck" in Kaleidoskopien3 (2000), 334-357.
0Weber, 191 [128]. " Ibid. , 217 [152].
? M LN 645
simplify the problem we imagine that: 1) Instead of the path there are
only some fixed points (similar to stones laid on the path) along a horizontal line placed as far apart as the length of a step. [. . . ] 2) The
leg is replaced by a straight solid line standing with its lower extremity on one of these points and is retained there by friction. 3) Instead of
being distributed over the entire length of the leg, the mass of the leg is concentrated in one middle point of the solid line. 4) The body is replaced by a mass concentrated in the upper point of this solid line.
This mass flies horizontally at an even velocity. "12In place of the legs and their three joints, a single center of mass around the knee
appears in order to swing henceforth perpetually around a dimen- sionless point which for mathematical reasons has formed itself "instead of the body. "As Christian Morgenstern correctly remarks: "A knee alone goes through the world. A knee alone, and nothing else. "
In fact: this 'nothing' is comprised of pure trigonometric functions. Sine and cosine are the two angle functions which cause this nothing
to step forward; g as gravitation and p as the measure of the circle are the two constants which maintain the steps forward into a period. With knee, g6nu, early Greek mathematics indicated the word for angle;'3 from the angle, gonia, arabic and modern mathematics indicated their trigonometric and thus periodic functions. At the end of this short story of sine and cosine stands the lapidary sentence:
The equation
d2X g sin X=- rl-
of Ch. 128 is replaced by an approximation,as occurs in analysingthe pendulum:
14 d8x
s = - rld ~_rldu2
The freedom of mathematical penstrokes thus finally conquers trigonometry itself. Because neither legs nor pendula are true wheels, that is, they simply do not create angles of any size, the periodic term
12Ibid. , 217 [152].
3JohannesLohmann, Musikeund Logos. Aufsdtzezur griechischePnhilosophiuend
MusiktheorieA,nastasios Giannaras,ed. (Stuttgart:MusikwissenschaftlicherVerlag 1970), 20.
14Weber,223 [159].
? 646 FRIEDRICH KITTLER
for a differential equation can be transposed into a linear one. If need be, the sine of c isjust c itself. For the sake of simplicity,15the Weber brothers only need to posit three further variables of their
general leg-swinging equation as constants of one or zero, and paragraph 128, the "Introduction to the Illustration of Walking
Figures," almost writes itself. Before computers with their explicit purpose of crunching systems of differential equations-at least
numerically-have
come into existence, scientific visualization can
only occupy itself with mercilessly simplified formula.
In its own progress, the "Establishment of a theory of walking and
running" achieves its goal when "the position of both legs" can be
constructed "at the various phases of each step" and "according to
these laws" or equations in order to enable "the artist" to judge
"whether he sees this representation corresponding to the actual
attitude of the legs during walking. ""6The new graph-producing science thus appears to subject itself to the judgement of a visual art.
It ends with an oppulant appendix of tables and figures which portray two lonely legs or knees in all individual phases of walking, running and jumping in order truly to resynthesize the unity of a pair of steps.
? Table XV
Fig. X
~k . ' ; ''
~ . . . i . 2
Fig. 2
5Ibid. , 238 [172]. 16Ibid. , 209 [147].
? Fig. 3
p-t).
! (i<
M LN
647
? Table XVI
? Tables XV and XVI from Weber and Weber, Mechanicsof theHuman Walking Apparatus.
However, what is and remains decisive as regards scientific visualiza- tion is the fact that it is no longer subordinate to the pronounced judgments of traditional arts. The Weber brothers have three good
reasons that claim as much. First of all, their entire pride rests on the
achievement of having constructed "the various ways of walking" "in
the various positions of every step according to theory and without
drawing upon experience. " Already, the fact that a movement cap- tured in differential equations dictates those laws of movement
already elevates such a theory discernably over the belatedness of
literary descriptions or painterly representations. Secondly, cinemat- ics and painting relate to each other no differently than early modern geometry and linear perspective once did. Having said as much, the Weber brothers had already brought forth Du Bois-Reymond's argu- ments, even in a more polite fashion.
? 648 FRIEDRICH KITTLER
The positions of the different parts of the body change too quickly during
walking and running to be completely imprinted on the senses and in the memory instantaneously. To capture them one needs certain instruments
and indirect methods which are not available to the artist. [. . . ] It is the same as for the science of perspectives which is so helpful to the artistwhen dealing with architectural pictures. One should not assert that the inner feeling of the artist is sufficient. In perspective this is never the case. [. . . ]
During walking and running one obtains no clear sensory perception of the simultaneous positions of the trunk and limbs because they pass so
rapidly. Therefore, the most capable artist lacks the means directly to perceive in Nature, without any help from science, the true circumstances
as they actually take place. Using perspective gives us the appearance of the truth by representing the distances in space and the positions of the
body. Similarly, study of walking and running brings to our pictures the appearance of the truth in the movements of life which are depicted. 17
Thirdly, it is decisive that artists, not to mention people in general, cannot perceive the mechanics of the human legs at all. This fact distinguishes cinematics since 1836 from linear perspective, which
has been promoted to the very principle of phenomenality and thus of visibility at the latest in the work of Johann Heinrich Lambert. 18
Like the vibrations of the violin's string, the phase pictures of walking
pass by too quickly to fall into perceptual times. What people can no longer see or hear, however, calls for technical media. Only "the
application of the theory of walking and running," the use therefore of"certain instruments and indirect methods," "can bring the appear-
ance of truth from the portrayed living movement into our images. "
Thus let it be-for the second time after Emil Du Bois-Reymond-
solemnly pronounced: it was Wilhelm and Eduard Weber, and neither Marey nor Muybridge, neither Edison, nor the Lumiere
brothers, who programmed the program which goes by the name of
film. In "Poggendorffs Annalen der Physik"-in 1836, global physics could still be found in German technical periodicals-both of them,
or perhaps really just Wilhelm Weber alone, stumbled on a "known technical device" of Faraday, which for a change did not have
anything to do with their common field of research, electro-magnetic induction. Instead, it has to do with "stroboscopic disks" as they had been "used by Joseph] Stampfer" in order to display "these draw-
17Ibid. , 6 [3].
18For further information on Lambert, see Friedrich Kittler, Phdnomen, Perspektive,
Medium. VonJ. H. Lambertzu G. W E Hegel(forthcoming).
? MLN 649
ings" before one's eyes "in such a succession that they gave the
impression of a figure walking quite normally. "'9In other words: that "certain instrument," which "brings the appearance of the truth of
the copied living movement into our images" is quite simply called a
stroboscope. To the great delight of Emil Du Bois-Reymond, the "mechanics of human legs" ends with how-to instructions that go far
beyond the state of affairs which scientific books and their attached tables could achieve. The how-to directions of Wilhelm and Eduard Weber are designed-for the first time in the history of science, as far as I can tell, for the visualization of partial differential equations.
It is interesting to illustrate the space and time data determined
absolutely according to the theory, by building and drawing the position of the limbs at each moment of walking and running
regularly. There is a means of convincing oneself that this construc-
tion matches experience as well as possible despite the imperfect measurement of the body on which one must rely. This means consists
of drawing a number of pictures representing the man in his successive positions during two steps. The internal surface of a
cylinder or of a drum is divided into as many facets as there are pictures plus one. The succesive pictures are glued one on each facet in proper order so that each picture on its facet appears as more displaced forwards than the previous one.
Author(s): Friedrich Kittler
Source: MLN, Vol. 118, No. 3, German Issue (Apr. , 2003), pp. 637-652 Published by: The Johns Hopkins University Press
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? Man as a Drunken Town-musician Friedrich Kittler
The sciences are on stage again. 1This self-referential assertion is less trivial and less timeless than it sounds.
Not knowledge, but science could certainly only have existed since the Greek vowel-alphabet connected an alternating interface be- tween the elements of letters and the elements of nature. AsJesper Svenbro has shown, what for the ionian philosophers of nature arose out of itself in fact only arose from writing. Therefore, everything which can be called science must be able to appear as text. The elements, whether Heraclitus' or Mendeljew's, are first given only in the sign of their names, and thus in Latin they have become 'data. '
Yet this basic relation between knowledge and writing has been so
deep-seated that it has scarcely reappeared. Almost in the same historical moment when Galileo directed all modern physics to the
reading of that book which Nature was supposed to have written
herself in geometric or, subsequently, algebraic signs, the modern novel and modern theater stepped in as evidence that modern
readers and spectators enjoy the effects of those fictions most of all when they are altogether free of science. Not only the age of Goethe, but first and foremost the one to whom this age owes its name bears eloquent witness to that effect, despite his love for mother nature and her open secrets. Goethe claimed that the intuition of nature could only take place however as far or as much as fortunate eyes were able to intuit and to see. Still, that elementary technique of culture
1What follows is the revised version of a lecture given at the Freie UniversitaitBerlin in the series of lectures StagesofKnowledgein theSciencesorganized by Helmar Schramm in 2000/2001.
MLN 118 (2003): 637-652 ? 2003 by TheJohns Hopkins University Press
? 638 FRIEDRICH KITTLER
common to all sciences, called mathematical codification, remained forbidden.
When, in 1826, Karl Friedrich Naumann, one of the founders of
modern crystallography, sent his latest publication from Leipzig to Goethe, one of the most ambivalent thank-you notes ever written was
drafted in Weimar: "the important document sent to me by Your
Honor," wrote the aged Goethe with the usual bureaucratic cer-
emony, "arrivedat a good moment, and I immediately read it with
great pleasure repeatedly up through page forty-five. At this point, however, I am standing at the limit which God and nature wish to
define for me as an individual. I am dependent upon word, language
and image in the truest sense, and completely incapable, to act in any way whatsoever through signs and numbers, with which the most talented spirits make themselves easily understood. "2
On that January day in 1826, the aged Goethe did not read any
further for reasons which Francesca and Paolo, or Lotte and Werther
could never have dreamed of. At the first mathematical symbol, the
first "quanitity,"as it is later called in the letter to Naumann, his
reading came to a halt. Through "signsand numbers," as they do not
belong to alphabetical language, the reader saw himself robbed of all
"qualities" with which "God and nature" were supposed to have
endowed his "individuality":"Word,language and image in the truest
sense. " This is how German poetry, when it called out its own three
media by their proper names, completely forgot the fact that it too
was alwaysalready over its designated limit. A "page 45," together with
the printed page number, is not only part of Naumann's crystallogra- phy, it can also be found in Goethe's Faust. It therefore does not help
very much to privilege the operations of literature over those opera- tions due to which the sciences are not only able to codify their own methods, but also their results and thus parts of the so-called nature.
Concepts of the text that stress a pure alphabetics while discarding its numerics (to take up Derrida's attack upon a supposedly europe-
wide phonocentrism and reformulate it somewhat more technically), have revenged themselves bitterly on their authors. Goethe had to
pay a price for choosing a true German university professor as the tragic hero almost for the first time in the history of German theater.
In addition to that, and according to his very personal model, he had
2 The letter from Goethe to Friedrich Naumann dates from January 24th, 1826, in Briefeund Tagebiichervol2. (Leipzig: Insel-Verlag n. d. ) 441.
? M LN 639
to pay an even higher price for granting this Doctor or rather Magister Faust with a passion for the innermost secrets of nature, a nature which punished loathsome measurings or even numeration of her exterior with contempt. This is precisely why Emil Du Bois-
Reymond, a leading physiologist at the Friedrich Wilhelm University in Berlin,3appeared before the admiring academic public with all the gold and taffeta of his new rectorship in order to demand the immediate end of the age of Goethe in a lecture antiphrastically titled "Goethe und kein Ende": "Goethe and No End. " Science as such therefore staged a court where-in a neat reversal of Galileo's trial- it threatened its enemies with excommunication and inquisition. Goethe's "Theoryof Colors,"which Du Bois-Reymond claimed to be a failure in the field of physics, did not retard scientific process in Germany any less than Faust's intuition of nature did, bereft as this intuition was of all mathematics. It is high time to check whether the so-called naturalists, the immediate contemporaries of Du Bois- Reymond and Claude Bernard, did not in fact write his tirade or mandate into literary deeds without further ado. In any event, the
great physiologist himself did not do so; instead, Du Bois-Reymond, after he bid farewell to Goethe's "Word"and "Language"in the name
of science, turned to the realm of the imaginary, which Goethe had celebrated as the "image in the truest sense. " In 1890, a small written piece on "Natural Science and Fine Art" ("Naturwissenschaft und bildende Kunst") issued forth from the pen of the Berlin Emeritus.
If there is ever to be something like a history of media studies, Du
Bois-Reymond's almost forgotten writing should appear in the canon of its holy texts next to Ernst Kapp's "Principle Characteristics of a
Philosophy of Technique. " Du Bois-Reymond's text writes the history of art from a perspective which has only recently been occupied again
by Samuel Edgerton or Jonathan Crary. The phenomenality of appearances, as it occurs in canvasses and statues, in painting and
plastic art, is everything but an unmediated beginning. In order for
styles and works of art to even appear, epistemological knowledge must first have established the field of their colors and forms. Du
Bois-Reymond cuts across, however provisionally it may be, the history of specific sciences in order to couple fifteenth-century geometry with the possibility of paintings in linear perspective, or to
3 The Friedrich Wilhelm University was renamed as the Humboldt University in 1949.
? 640 FRIEDRICHKITTLER
couple sixteenth-century anatomy with the possibility of muscle's becoming marble, and finally, the physical theories of color from Newton through Helmholtz with the history of painterly coloritoas a whole. At the end of his essay, however, this course of a history of science, not yet curbed by any modern artistic impulse, makes the transition from static to moving pictures, which is a brand-new idea in 1890. Five years before the Lumi&re brothers will raise Edison's
playful peep-box theater to the status of a mass-image medium, Du Bois-Reymond presents, if you will, the very first history of film. This
history has the unique feature of not describing moving pictures as animation or the surpassing of Daguerre's half-hour exposure times, as has become commonplace and self-evident since Hugo Miinster-
berg's scarcely less-forgotten psychotechnique of film. Du Bois-
Reymond's history does not begin at all with diorama painters or magic lantern players, but rather on a really elementary threshhold:
with the scientific history of moving. In the process of elaborating the thesis that without modern geometry there would have been no
paintings in linear perspective, Du Bois-Reymond's brief history of art ends with the statement that there would be no moving pictures
without the analysis of modern mathematics.
Today, one could make just the reverse statement: one could say
that without moving scientists there would be no modern analysis.
Geometry first became analytic, and that means cinematic, when an
officer on leave, who happened to be a burgeoning philosopher, first dreamed of movement as such in his winter quarters on the Donau.
"Larvatusprodeo"-masked, I go forth-remained Descartes' device, even when he no longer wore the uniform. But what has hindered
empirical movements from achieving mathematical and philosophi- cal honor in the same way seems to be precisely the steady motion of
Descartes' subject which he conceived of as a geometrical point and which analytic geometry since Descartes transposed into the ceaseless movement of a curve-defining point in a field of coordinates. Furthermore, empirical movements remained a domain of dance- instructors and their choreographies, or of the drills of officers educated in Hessen-Nassau and Hessen-Orange to whom the young
Descartes owed his drilling- and fencing-skills. 4Mathematical analysis, on the other hand, moved those dimensionless points, to which the
4 See Wolfgang Schaffner, "K6rperim Takt. Zur Geschichte symbolischer Maschinen im 16. und 17. Jahrhundert" in Kaleidoskopien3 (2000), 188-205.
? MLN 641
swinging pendulum or flying granades were reduced for the sake of simplicity, through every possible adventure of maxima and minima,
of turning points and null-points, of velocity moments and forces of acceleration. Only in the truly novelesque case of that lying baron,
who had the privilege of performing the analysis with his own body, did a cartesian subject ride along on the parable of a granade's trajectory. Once again the text of the novel, in Miinchhausen's case as
in Descartes', relied upon the certainty-unshakeable because imag- ined in the Donau winter quarters-that dreamed motion or faked
flying remained as inescapably true as only the Cogitoitself otherwise could be.
This blessed time of the founding fathers in which consciousness
and analysis, thinking and differential calculus were one and the
same ended bitterly. The reason was simple: not all trajectories of
motion in physical empiricism were permitted to be ascribed to the
cinematics of a single point. What Huygens had achieved in the case
of the swinging pendulum already failed in the case of a vibrating
string whose innumerable points are elastically coupled and thus, in other words, enjoy uncountable degrees of liberty. Not even cartesian
subjects would have been in a position of being or thinking all points of the string at the same time in order to discover the secret of a
single tone from the violin. All that remained was for mathematical analysis to bestow this secret unto a new, no less mysterious theory: to the partial differential equations in brazen opposition to the usual ones. Newton's usual differential equations still sufficed for solar systems, since the stars which were part of those systems do not enjoy a single degree of freedom; but not everything that moves is as simple as in astronomy. In the case of violin strings and bell tones, drumskins and water surfaces, and even windstorms and electromagnetic vibra-
tions, only partial differential equations successfully modelled the countless parts moved in all their dimensions.
Thus the course of modern science finally arrived at physiological, day-to-daymotion. In 1836, a monograph from Wilhelm and Eduard Weber appeared which was almost without precedent: the "Mechan-
ics of the Human Walking Apparatus. An Anatomical-Physiological
dermenschlichen Eine anatomisch- Investigation" (Mechanik Gehwerkzeuge.
physiologischeUntersuchung). E5duardWeberhadatthattimejustbeen
5Weber, Wilhelm and Eduard, UberdieMechanikdermenschlichenGehwerkzeugen,ebst
der eines Versuchsiiberdas des aus der im Beschreibung Herausfallen Schenkelkopfes Pfanne
? 642 FRIEDRICHKITTLER
summoned to the University of Leipzig as professor of medicine; his brother Wilhelm, on the other hand, was already a professor of physics in G6ttingen since 1831, where he had just two years later, together with none other than GauB,made the first electric telegraph run. That alone suggests that the medical subtitle of their joint book is pure understatement. All the anatomical and physiological findings
concerning knees, hips, leg muscles and joints gathered in the first
part only serve the higher purpose of founding a mathematical physics of legs in just as strict a sense as Newton had demanded for
the physics of celestial bodies.
At least the anatomical and physiological investigations-or in
other words, the experiments both on corpses' legs in Leipzig and on
living legs in G6ttingen-make it clear from the startwhat the degree of freedom is, which a system of hips, knees and heels enjoys. Every
joint, as writers of computer animations would formulate it, or rather,
program it today, is a three-dimensional transformative-matrixwhose
rotations in turn transform the next subordinate joint. At the end of
the day, however, the matrix-product from all these turns and
displacements produces such variable values, or leg positions, that one is threatened by the appearance of sheer incalculability. "Itcan
perhaps be questioned," so the Weber brothers admit, "whether a
theory of walking and running can be provided at all since we are not walking machines, and these movements are altered in many waysby our free will. "6That merely appears to be the case, however. In 1836, no cartesian subject inhabits the curves or functions of his own limbs. On the contrary, "man binds his movements to certain rules even if he cannot express these rules in words. These rules are based totally on the structure of his body and on the given external conditions. They thus can be deduced from both structure and external conditions. "7
All the preliminary anatomical-physiological investigations have the single goal of reconstructing a per definitionem "unconscious"
walking machine first of all through measures and series of tests on the body, before the triumphant end to the book can go and present
luftverdiinntenRaume,in Wilhelm Weber's Werkee,d. Friedrich Merkel und Otto Fischer (Berlin: Konigliche Gesellschaft der Wissenschaften in Gottingen 1894), 322 [transl. by Maquet, Paul and Ronald Furlong, Mechanicsof theHuman WalkingApparatus(Berlin, Heidelberg, NewYorketc. :Springer-Verlag1992), 226].
6 Ibid. , 3 [VI]. 7 Ibid. [VII].
? MLN 643
the mathematical theory of walking and running. Everything rests on the fact that legs can provide for their own account, so that in the end
they can be in the books as a differential system. In 1836, long before Marey and Muybridge, the attainment of the differential system was at
first possible only in stasis, as if Daguerre's long-term exposures had found a scientifically parallel maneuver. In order to make agility at
least visible as latent motion, however, the brothers cut up the corpses' hips at the precise location where "the balls of the upper-legs lie in their sockets. " Just as in the drawing of a steam engine which
would explain the interplay of parts in the moment of explosion, admiring readers can glimpse the interplay between the ball of the
thigh bone and the socket of the joint.
The femoral head or so-called sphere was sawn perpendicularly from in front backwards and the section was printed on the paper. The curvature of the the two parts here cannot be altered by the drawer. The picture is indeed the imprint of the object itself. The bone thus divided can be used
as a wood-engraving for print. 8
Plate IX
Pelvis
? Fig. 1.
8Ibid. , 14 Fn. [10].
Femur
? 644 FRIEDRICHKITTLER
The work of the Weber brothers makes anatomy leave its proud old amphitheaters, where the dissection resulted in findings that made their way to woodcuts only belatedly. Instead, just as Henry Fox
Talbot's heliography did four years later, they were put onto the printed page as nature's imprint of itself. 9Thus the free will of human drawing-hands in scientific visualization remains just as excluded as it is in the mechanics of human legs. On this worldly scene of all religions and dances of the dead, the skeleton appears on the stage of
knowledge and points no longer to allegories of death, but rather to nothing more than its own animation.
In order to transpose the latent movements that occur around leg
joints, or degrees of freedom, into actual movements, the Weber brothers introduce two simple axioms. First of all, the individual
bones whose interplay comprises a step should swing according to the
law of the pendulum. The differential equation of every partial movement can thus already be accounted for by falling back on
Christian Huygens and his pendulum clock equation from 1656.
Secondly, however, the usual human gait should be a periodically
iterated interplay of all these partial movements, whereby a period is
clearly only counted after a completed pair of steps. '0 In any event, a summation of partial differential equations only appears as total
movement according, first of all, to the three dimensions of space,
and secondly, according to time. Having made these assumptions, the Weber brothers simply go ahead and copy the formula which
Poisson's Traite de mechaniquein the second, recently published edition from 1838 anticipated for such cases. ll With this fact, the misfortune which occupies all of our computer monitors today has come into existence: instead of "word, language and image in the truest sense," "symbol and number" have taken over human gait. Cinematics in the French sense of the word, which as of 1830, and at Ampere's instigation, calculates transversal and rotational move- ments of steam engines, becomes cinematics in the modern sense: it calculates virtual movements in virtual, that is, visualizable spaces.
For the sake of their animation, however, both the leg and Poisson's "general"differential system must make a few sacrifices. "To
9 See also Susanne Holl, "Ob oculos. Andreas Vesals 'De humani corporis fabrica' und der Buchdruck" in Kaleidoskopien3 (2000), 334-357.
0Weber, 191 [128]. " Ibid. , 217 [152].
? M LN 645
simplify the problem we imagine that: 1) Instead of the path there are
only some fixed points (similar to stones laid on the path) along a horizontal line placed as far apart as the length of a step. [. . . ] 2) The
leg is replaced by a straight solid line standing with its lower extremity on one of these points and is retained there by friction. 3) Instead of
being distributed over the entire length of the leg, the mass of the leg is concentrated in one middle point of the solid line. 4) The body is replaced by a mass concentrated in the upper point of this solid line.
This mass flies horizontally at an even velocity. "12In place of the legs and their three joints, a single center of mass around the knee
appears in order to swing henceforth perpetually around a dimen- sionless point which for mathematical reasons has formed itself "instead of the body. "As Christian Morgenstern correctly remarks: "A knee alone goes through the world. A knee alone, and nothing else. "
In fact: this 'nothing' is comprised of pure trigonometric functions. Sine and cosine are the two angle functions which cause this nothing
to step forward; g as gravitation and p as the measure of the circle are the two constants which maintain the steps forward into a period. With knee, g6nu, early Greek mathematics indicated the word for angle;'3 from the angle, gonia, arabic and modern mathematics indicated their trigonometric and thus periodic functions. At the end of this short story of sine and cosine stands the lapidary sentence:
The equation
d2X g sin X=- rl-
of Ch. 128 is replaced by an approximation,as occurs in analysingthe pendulum:
14 d8x
s = - rld ~_rldu2
The freedom of mathematical penstrokes thus finally conquers trigonometry itself. Because neither legs nor pendula are true wheels, that is, they simply do not create angles of any size, the periodic term
12Ibid. , 217 [152].
3JohannesLohmann, Musikeund Logos. Aufsdtzezur griechischePnhilosophiuend
MusiktheorieA,nastasios Giannaras,ed. (Stuttgart:MusikwissenschaftlicherVerlag 1970), 20.
14Weber,223 [159].
? 646 FRIEDRICH KITTLER
for a differential equation can be transposed into a linear one. If need be, the sine of c isjust c itself. For the sake of simplicity,15the Weber brothers only need to posit three further variables of their
general leg-swinging equation as constants of one or zero, and paragraph 128, the "Introduction to the Illustration of Walking
Figures," almost writes itself. Before computers with their explicit purpose of crunching systems of differential equations-at least
numerically-have
come into existence, scientific visualization can
only occupy itself with mercilessly simplified formula.
In its own progress, the "Establishment of a theory of walking and
running" achieves its goal when "the position of both legs" can be
constructed "at the various phases of each step" and "according to
these laws" or equations in order to enable "the artist" to judge
"whether he sees this representation corresponding to the actual
attitude of the legs during walking. ""6The new graph-producing science thus appears to subject itself to the judgement of a visual art.
It ends with an oppulant appendix of tables and figures which portray two lonely legs or knees in all individual phases of walking, running and jumping in order truly to resynthesize the unity of a pair of steps.
? Table XV
Fig. X
~k . ' ; ''
~ . . . i . 2
Fig.
Goethe had to
pay a price for choosing a true German university professor as the tragic hero almost for the first time in the history of German theater.
In addition to that, and according to his very personal model, he had
2 The letter from Goethe to Friedrich Naumann dates from January 24th, 1826, in Briefeund Tagebiichervol2. (Leipzig: Insel-Verlag n. d. ) 441.
? M LN 639
to pay an even higher price for granting this Doctor or rather Magister Faust with a passion for the innermost secrets of nature, a nature which punished loathsome measurings or even numeration of her exterior with contempt. This is precisely why Emil Du Bois-
Reymond, a leading physiologist at the Friedrich Wilhelm University in Berlin,3appeared before the admiring academic public with all the gold and taffeta of his new rectorship in order to demand the immediate end of the age of Goethe in a lecture antiphrastically titled "Goethe und kein Ende": "Goethe and No End. " Science as such therefore staged a court where-in a neat reversal of Galileo's trial- it threatened its enemies with excommunication and inquisition. Goethe's "Theoryof Colors,"which Du Bois-Reymond claimed to be a failure in the field of physics, did not retard scientific process in Germany any less than Faust's intuition of nature did, bereft as this intuition was of all mathematics. It is high time to check whether the so-called naturalists, the immediate contemporaries of Du Bois- Reymond and Claude Bernard, did not in fact write his tirade or mandate into literary deeds without further ado. In any event, the
great physiologist himself did not do so; instead, Du Bois-Reymond, after he bid farewell to Goethe's "Word"and "Language"in the name
of science, turned to the realm of the imaginary, which Goethe had celebrated as the "image in the truest sense. " In 1890, a small written piece on "Natural Science and Fine Art" ("Naturwissenschaft und bildende Kunst") issued forth from the pen of the Berlin Emeritus.
If there is ever to be something like a history of media studies, Du
Bois-Reymond's almost forgotten writing should appear in the canon of its holy texts next to Ernst Kapp's "Principle Characteristics of a
Philosophy of Technique. " Du Bois-Reymond's text writes the history of art from a perspective which has only recently been occupied again
by Samuel Edgerton or Jonathan Crary. The phenomenality of appearances, as it occurs in canvasses and statues, in painting and
plastic art, is everything but an unmediated beginning. In order for
styles and works of art to even appear, epistemological knowledge must first have established the field of their colors and forms. Du
Bois-Reymond cuts across, however provisionally it may be, the history of specific sciences in order to couple fifteenth-century geometry with the possibility of paintings in linear perspective, or to
3 The Friedrich Wilhelm University was renamed as the Humboldt University in 1949.
? 640 FRIEDRICHKITTLER
couple sixteenth-century anatomy with the possibility of muscle's becoming marble, and finally, the physical theories of color from Newton through Helmholtz with the history of painterly coloritoas a whole. At the end of his essay, however, this course of a history of science, not yet curbed by any modern artistic impulse, makes the transition from static to moving pictures, which is a brand-new idea in 1890. Five years before the Lumi&re brothers will raise Edison's
playful peep-box theater to the status of a mass-image medium, Du Bois-Reymond presents, if you will, the very first history of film. This
history has the unique feature of not describing moving pictures as animation or the surpassing of Daguerre's half-hour exposure times, as has become commonplace and self-evident since Hugo Miinster-
berg's scarcely less-forgotten psychotechnique of film. Du Bois-
Reymond's history does not begin at all with diorama painters or magic lantern players, but rather on a really elementary threshhold:
with the scientific history of moving. In the process of elaborating the thesis that without modern geometry there would have been no
paintings in linear perspective, Du Bois-Reymond's brief history of art ends with the statement that there would be no moving pictures
without the analysis of modern mathematics.
Today, one could make just the reverse statement: one could say
that without moving scientists there would be no modern analysis.
Geometry first became analytic, and that means cinematic, when an
officer on leave, who happened to be a burgeoning philosopher, first dreamed of movement as such in his winter quarters on the Donau.
"Larvatusprodeo"-masked, I go forth-remained Descartes' device, even when he no longer wore the uniform. But what has hindered
empirical movements from achieving mathematical and philosophi- cal honor in the same way seems to be precisely the steady motion of
Descartes' subject which he conceived of as a geometrical point and which analytic geometry since Descartes transposed into the ceaseless movement of a curve-defining point in a field of coordinates. Furthermore, empirical movements remained a domain of dance- instructors and their choreographies, or of the drills of officers educated in Hessen-Nassau and Hessen-Orange to whom the young
Descartes owed his drilling- and fencing-skills. 4Mathematical analysis, on the other hand, moved those dimensionless points, to which the
4 See Wolfgang Schaffner, "K6rperim Takt. Zur Geschichte symbolischer Maschinen im 16. und 17. Jahrhundert" in Kaleidoskopien3 (2000), 188-205.
? MLN 641
swinging pendulum or flying granades were reduced for the sake of simplicity, through every possible adventure of maxima and minima,
of turning points and null-points, of velocity moments and forces of acceleration. Only in the truly novelesque case of that lying baron,
who had the privilege of performing the analysis with his own body, did a cartesian subject ride along on the parable of a granade's trajectory. Once again the text of the novel, in Miinchhausen's case as
in Descartes', relied upon the certainty-unshakeable because imag- ined in the Donau winter quarters-that dreamed motion or faked
flying remained as inescapably true as only the Cogitoitself otherwise could be.
This blessed time of the founding fathers in which consciousness
and analysis, thinking and differential calculus were one and the
same ended bitterly. The reason was simple: not all trajectories of
motion in physical empiricism were permitted to be ascribed to the
cinematics of a single point. What Huygens had achieved in the case
of the swinging pendulum already failed in the case of a vibrating
string whose innumerable points are elastically coupled and thus, in other words, enjoy uncountable degrees of liberty. Not even cartesian
subjects would have been in a position of being or thinking all points of the string at the same time in order to discover the secret of a
single tone from the violin. All that remained was for mathematical analysis to bestow this secret unto a new, no less mysterious theory: to the partial differential equations in brazen opposition to the usual ones. Newton's usual differential equations still sufficed for solar systems, since the stars which were part of those systems do not enjoy a single degree of freedom; but not everything that moves is as simple as in astronomy. In the case of violin strings and bell tones, drumskins and water surfaces, and even windstorms and electromagnetic vibra-
tions, only partial differential equations successfully modelled the countless parts moved in all their dimensions.
Thus the course of modern science finally arrived at physiological, day-to-daymotion. In 1836, a monograph from Wilhelm and Eduard Weber appeared which was almost without precedent: the "Mechan-
ics of the Human Walking Apparatus. An Anatomical-Physiological
dermenschlichen Eine anatomisch- Investigation" (Mechanik Gehwerkzeuge.
physiologischeUntersuchung). E5duardWeberhadatthattimejustbeen
5Weber, Wilhelm and Eduard, UberdieMechanikdermenschlichenGehwerkzeugen,ebst
der eines Versuchsiiberdas des aus der im Beschreibung Herausfallen Schenkelkopfes Pfanne
? 642 FRIEDRICHKITTLER
summoned to the University of Leipzig as professor of medicine; his brother Wilhelm, on the other hand, was already a professor of physics in G6ttingen since 1831, where he had just two years later, together with none other than GauB,made the first electric telegraph run. That alone suggests that the medical subtitle of their joint book is pure understatement. All the anatomical and physiological findings
concerning knees, hips, leg muscles and joints gathered in the first
part only serve the higher purpose of founding a mathematical physics of legs in just as strict a sense as Newton had demanded for
the physics of celestial bodies.
At least the anatomical and physiological investigations-or in
other words, the experiments both on corpses' legs in Leipzig and on
living legs in G6ttingen-make it clear from the startwhat the degree of freedom is, which a system of hips, knees and heels enjoys. Every
joint, as writers of computer animations would formulate it, or rather,
program it today, is a three-dimensional transformative-matrixwhose
rotations in turn transform the next subordinate joint. At the end of
the day, however, the matrix-product from all these turns and
displacements produces such variable values, or leg positions, that one is threatened by the appearance of sheer incalculability. "Itcan
perhaps be questioned," so the Weber brothers admit, "whether a
theory of walking and running can be provided at all since we are not walking machines, and these movements are altered in many waysby our free will. "6That merely appears to be the case, however. In 1836, no cartesian subject inhabits the curves or functions of his own limbs. On the contrary, "man binds his movements to certain rules even if he cannot express these rules in words. These rules are based totally on the structure of his body and on the given external conditions. They thus can be deduced from both structure and external conditions. "7
All the preliminary anatomical-physiological investigations have the single goal of reconstructing a per definitionem "unconscious"
walking machine first of all through measures and series of tests on the body, before the triumphant end to the book can go and present
luftverdiinntenRaume,in Wilhelm Weber's Werkee,d. Friedrich Merkel und Otto Fischer (Berlin: Konigliche Gesellschaft der Wissenschaften in Gottingen 1894), 322 [transl. by Maquet, Paul and Ronald Furlong, Mechanicsof theHuman WalkingApparatus(Berlin, Heidelberg, NewYorketc. :Springer-Verlag1992), 226].
6 Ibid. , 3 [VI]. 7 Ibid. [VII].
? MLN 643
the mathematical theory of walking and running. Everything rests on the fact that legs can provide for their own account, so that in the end
they can be in the books as a differential system. In 1836, long before Marey and Muybridge, the attainment of the differential system was at
first possible only in stasis, as if Daguerre's long-term exposures had found a scientifically parallel maneuver. In order to make agility at
least visible as latent motion, however, the brothers cut up the corpses' hips at the precise location where "the balls of the upper-legs lie in their sockets. " Just as in the drawing of a steam engine which
would explain the interplay of parts in the moment of explosion, admiring readers can glimpse the interplay between the ball of the
thigh bone and the socket of the joint.
The femoral head or so-called sphere was sawn perpendicularly from in front backwards and the section was printed on the paper. The curvature of the the two parts here cannot be altered by the drawer. The picture is indeed the imprint of the object itself. The bone thus divided can be used
as a wood-engraving for print. 8
Plate IX
Pelvis
? Fig. 1.
8Ibid. , 14 Fn. [10].
Femur
? 644 FRIEDRICHKITTLER
The work of the Weber brothers makes anatomy leave its proud old amphitheaters, where the dissection resulted in findings that made their way to woodcuts only belatedly. Instead, just as Henry Fox
Talbot's heliography did four years later, they were put onto the printed page as nature's imprint of itself. 9Thus the free will of human drawing-hands in scientific visualization remains just as excluded as it is in the mechanics of human legs. On this worldly scene of all religions and dances of the dead, the skeleton appears on the stage of
knowledge and points no longer to allegories of death, but rather to nothing more than its own animation.
In order to transpose the latent movements that occur around leg
joints, or degrees of freedom, into actual movements, the Weber brothers introduce two simple axioms. First of all, the individual
bones whose interplay comprises a step should swing according to the
law of the pendulum. The differential equation of every partial movement can thus already be accounted for by falling back on
Christian Huygens and his pendulum clock equation from 1656.
Secondly, however, the usual human gait should be a periodically
iterated interplay of all these partial movements, whereby a period is
clearly only counted after a completed pair of steps. '0 In any event, a summation of partial differential equations only appears as total
movement according, first of all, to the three dimensions of space,
and secondly, according to time. Having made these assumptions, the Weber brothers simply go ahead and copy the formula which
Poisson's Traite de mechaniquein the second, recently published edition from 1838 anticipated for such cases. ll With this fact, the misfortune which occupies all of our computer monitors today has come into existence: instead of "word, language and image in the truest sense," "symbol and number" have taken over human gait. Cinematics in the French sense of the word, which as of 1830, and at Ampere's instigation, calculates transversal and rotational move- ments of steam engines, becomes cinematics in the modern sense: it calculates virtual movements in virtual, that is, visualizable spaces.
For the sake of their animation, however, both the leg and Poisson's "general"differential system must make a few sacrifices. "To
9 See also Susanne Holl, "Ob oculos. Andreas Vesals 'De humani corporis fabrica' und der Buchdruck" in Kaleidoskopien3 (2000), 334-357.
0Weber, 191 [128]. " Ibid. , 217 [152].
? M LN 645
simplify the problem we imagine that: 1) Instead of the path there are
only some fixed points (similar to stones laid on the path) along a horizontal line placed as far apart as the length of a step. [. . . ] 2) The
leg is replaced by a straight solid line standing with its lower extremity on one of these points and is retained there by friction. 3) Instead of
being distributed over the entire length of the leg, the mass of the leg is concentrated in one middle point of the solid line. 4) The body is replaced by a mass concentrated in the upper point of this solid line.
This mass flies horizontally at an even velocity. "12In place of the legs and their three joints, a single center of mass around the knee
appears in order to swing henceforth perpetually around a dimen- sionless point which for mathematical reasons has formed itself "instead of the body. "As Christian Morgenstern correctly remarks: "A knee alone goes through the world. A knee alone, and nothing else. "
In fact: this 'nothing' is comprised of pure trigonometric functions. Sine and cosine are the two angle functions which cause this nothing
to step forward; g as gravitation and p as the measure of the circle are the two constants which maintain the steps forward into a period. With knee, g6nu, early Greek mathematics indicated the word for angle;'3 from the angle, gonia, arabic and modern mathematics indicated their trigonometric and thus periodic functions. At the end of this short story of sine and cosine stands the lapidary sentence:
The equation
d2X g sin X=- rl-
of Ch. 128 is replaced by an approximation,as occurs in analysingthe pendulum:
14 d8x
s = - rld ~_rldu2
The freedom of mathematical penstrokes thus finally conquers trigonometry itself. Because neither legs nor pendula are true wheels, that is, they simply do not create angles of any size, the periodic term
12Ibid. , 217 [152].
3JohannesLohmann, Musikeund Logos. Aufsdtzezur griechischePnhilosophiuend
MusiktheorieA,nastasios Giannaras,ed. (Stuttgart:MusikwissenschaftlicherVerlag 1970), 20.
14Weber,223 [159].
? 646 FRIEDRICH KITTLER
for a differential equation can be transposed into a linear one. If need be, the sine of c isjust c itself. For the sake of simplicity,15the Weber brothers only need to posit three further variables of their
general leg-swinging equation as constants of one or zero, and paragraph 128, the "Introduction to the Illustration of Walking
Figures," almost writes itself. Before computers with their explicit purpose of crunching systems of differential equations-at least
numerically-have
come into existence, scientific visualization can
only occupy itself with mercilessly simplified formula.
In its own progress, the "Establishment of a theory of walking and
running" achieves its goal when "the position of both legs" can be
constructed "at the various phases of each step" and "according to
these laws" or equations in order to enable "the artist" to judge
"whether he sees this representation corresponding to the actual
attitude of the legs during walking. ""6The new graph-producing science thus appears to subject itself to the judgement of a visual art.
It ends with an oppulant appendix of tables and figures which portray two lonely legs or knees in all individual phases of walking, running and jumping in order truly to resynthesize the unity of a pair of steps.
? Table XV
Fig. X
~k . ' ; ''
~ . . . i . 2
Fig. 2
5Ibid. , 238 [172]. 16Ibid. , 209 [147].
? Fig. 3
p-t).
! (i<
M LN
647
? Table XVI
? Tables XV and XVI from Weber and Weber, Mechanicsof theHuman Walking Apparatus.
However, what is and remains decisive as regards scientific visualiza- tion is the fact that it is no longer subordinate to the pronounced judgments of traditional arts. The Weber brothers have three good
reasons that claim as much. First of all, their entire pride rests on the
achievement of having constructed "the various ways of walking" "in
the various positions of every step according to theory and without
drawing upon experience. " Already, the fact that a movement cap- tured in differential equations dictates those laws of movement
already elevates such a theory discernably over the belatedness of
literary descriptions or painterly representations. Secondly, cinemat- ics and painting relate to each other no differently than early modern geometry and linear perspective once did. Having said as much, the Weber brothers had already brought forth Du Bois-Reymond's argu- ments, even in a more polite fashion.
? 648 FRIEDRICH KITTLER
The positions of the different parts of the body change too quickly during
walking and running to be completely imprinted on the senses and in the memory instantaneously. To capture them one needs certain instruments
and indirect methods which are not available to the artist. [. . . ] It is the same as for the science of perspectives which is so helpful to the artistwhen dealing with architectural pictures. One should not assert that the inner feeling of the artist is sufficient. In perspective this is never the case. [. . . ]
During walking and running one obtains no clear sensory perception of the simultaneous positions of the trunk and limbs because they pass so
rapidly. Therefore, the most capable artist lacks the means directly to perceive in Nature, without any help from science, the true circumstances
as they actually take place. Using perspective gives us the appearance of the truth by representing the distances in space and the positions of the
body. Similarly, study of walking and running brings to our pictures the appearance of the truth in the movements of life which are depicted. 17
Thirdly, it is decisive that artists, not to mention people in general, cannot perceive the mechanics of the human legs at all. This fact distinguishes cinematics since 1836 from linear perspective, which
has been promoted to the very principle of phenomenality and thus of visibility at the latest in the work of Johann Heinrich Lambert. 18
Like the vibrations of the violin's string, the phase pictures of walking
pass by too quickly to fall into perceptual times. What people can no longer see or hear, however, calls for technical media. Only "the
application of the theory of walking and running," the use therefore of"certain instruments and indirect methods," "can bring the appear-
ance of truth from the portrayed living movement into our images. "
Thus let it be-for the second time after Emil Du Bois-Reymond-
solemnly pronounced: it was Wilhelm and Eduard Weber, and neither Marey nor Muybridge, neither Edison, nor the Lumiere
brothers, who programmed the program which goes by the name of
film. In "Poggendorffs Annalen der Physik"-in 1836, global physics could still be found in German technical periodicals-both of them,
or perhaps really just Wilhelm Weber alone, stumbled on a "known technical device" of Faraday, which for a change did not have
anything to do with their common field of research, electro-magnetic induction. Instead, it has to do with "stroboscopic disks" as they had been "used by Joseph] Stampfer" in order to display "these draw-
17Ibid. , 6 [3].
18For further information on Lambert, see Friedrich Kittler, Phdnomen, Perspektive,
Medium. VonJ. H. Lambertzu G. W E Hegel(forthcoming).
? MLN 649
ings" before one's eyes "in such a succession that they gave the
impression of a figure walking quite normally. "'9In other words: that "certain instrument," which "brings the appearance of the truth of
the copied living movement into our images" is quite simply called a
stroboscope. To the great delight of Emil Du Bois-Reymond, the "mechanics of human legs" ends with how-to instructions that go far
beyond the state of affairs which scientific books and their attached tables could achieve. The how-to directions of Wilhelm and Eduard Weber are designed-for the first time in the history of science, as far as I can tell, for the visualization of partial differential equations.
It is interesting to illustrate the space and time data determined
absolutely according to the theory, by building and drawing the position of the limbs at each moment of walking and running
regularly. There is a means of convincing oneself that this construc-
tion matches experience as well as possible despite the imperfect measurement of the body on which one must rely. This means consists
of drawing a number of pictures representing the man in his successive positions during two steps. The internal surface of a
cylinder or of a drum is divided into as many facets as there are pictures plus one. The succesive pictures are glued one on each facet in proper order so that each picture on its facet appears as more displaced forwards than the previous one.
