31 Dec 2010

The Function of Disjunction: Rube Goldberg's Machines Under Deleuze's Differential Mechanics

by Corry Shores
Search Blog Here. Index-tags are found on the bottom of the left column.]

[Central Entry Directory]
[Deleuze Entry Directory]
The Function of Disjunction:
Rube Goldberg's Machines Under Deleuze's Differential Mechanics

What do the mechanical disjunctive functions of Rube Goldberg's inventions got to do with you?

Much in our life and the world around us seems to be mechanically related. But consider our more profound mechanical responses. At the death of a loved one, we might be moved to create something beautiful. The pain of our grieving triggers our making something that gives us joy to behold. Often times, the mechanisms in our lives pair together very different things, and in fact, that is what gives them their mechanical power; they take one thing and make it into something very different. The workings of our life, in a sense, could be seen as the contra-operations of many different mechanisms, all functioning on the basis of differences being mechanically connected. Given that they are based on differences, they are more disjunctions than conjunctions. Yet the whole assembly of differential machines that make up our lives somehow despite each other function to make us and our world.

Brief Summary

Rube Goldberg designed complex machines that do ordinary things but by means of relations between parts that are odd to one another. It is on the basis of the differences between the parts that they work together mechanically.

Points Relative to Deleuze
[Under Ongoing Revision]

Deleuze in a sense is a mechanical engineer. One way we might understand Deleuze's mechanics is by analyzing the workings of Rube Goldberg's machines (Deleuze & Guattari print two Goldberg machines in the appendix to the French edition of Anti-Oedipus, when describing desiring machines). What we note from the machines is how comically unrelated are the conjoined parts. They are more like disjunctions than conjunctions, but they are mechanical, because they affect one another; or we might say the resulting transformations are always implied yet never coherent. What we see is the production of differences on the basis of differences.

Simple Machine Differentials

Our main idea will be that Deleuze's mechanics is a science of difference and that this sort of mechanics pervades all aspects of our lives, including our behavior and the way we relate to other people and the world around us. At times Deleuze refers us to Rube Goldberg's machines. These we will understand in terms of differential relations of parts functioning by means of their disjunction. Before that discussion, we will look first at simple machines to see how in a basic way they are based on differential relations of a simpler sort than concerns us here.

Consider for example the lever.

Differential Lever Motion
lever arrow motion up down
(Thanks fi.edu/Science of Gears)

Pushing down on the lever lifts the rock upward. So the upward motion is the direct result of the downward one. This is a transfer of motion, in this case, an inversion of direction of linear motion. In a sense, up is implied in down. We might say that this is what gives the device its mechanical quality. It converts motion. Something goes in; something different comes out. It's like a black box, in a sense, except we can see the working inside.

Marvin Minsky's Black Box Machine
Marvin Minsky. black box. Computation Finite and Infinite Machines
(From Marvin Minsky. Computation Finite and Infinite Machines)

We might also think of it like Edwards & Penney's Function Machine. Some given value goes in, and another value, assigned to the first, invariably comes out.

Edwards & Penney's Function Machine
Function machine
(Thanks, from Edwards & Penney's Calculus)

Consider also a pulley. A downward motion on one side implies upward on the other.

Differential Pulley Motions

(Made with OpenOffice Draw and GIMP)

And finally, consider when two gears mesh together, with one rotating the other. Here the basis of the mechanism would seem to be the compatibility of the parts, and not their difference. But do not forget that one gear meshes with the other because there is a space where the other has a tooth. And the clockwise motion of the one implies the counterclockwise motion of the other.

The Counter-Motions of Rotating Gears
Gears moving opposite directions clockwise counterclockwise arrows rotating gears moving
(Thanks Imagination Factory) (Thanks Science Buddies. Credited as public domain.)

So the point is that these parts relate to one another differentially. In fact, this differential relation is the basis for their being mechanical. Mechanics, in way, is a science of the effective production of difference by means of difference, for example, the production of a different direction of motion by means of the physical differences allowing one gear's teeth to mesh where the other one has gaps. We might say that the gears are conjoined. But this concept of conjunction does not seem to apply when we consider the place where the motion transfers, like the lever's fulcrum. The precise center of the fulcrum would seem to be a place where the motion moves neither up nor down, and perhaps in fact it moves both directions at the same time. The fulcrum in a way is the place where up and down are forced immediately upon one another, smashed together. Up and down are disjunctively crushed up upon one another. This is a precise point, so we cannot say that any space separates the up from the down motion at the exact fulcrum point. Nothing extends between the two, but there is a pure intensity, a pure degree of difference at a point where the mechanical power explodes outward into its extensive expressions.

The Mechanics of Difference:
Rube Goldberg's Machines

Now we will go one step further, and look at the mechanics of the machines Rube Goldberg invented. We will see that Goldberg's machines are based even more heavily on differential relations, and in a way, they might strike us as being more like the sorts of mechanics we experience in our lives. Here are some pictures of Goldberg.

Rube Goldberg, portrait 1
Rube Goldberg, portrait
(Thanks National Cartoonists Society)

Rube Goldberg, portrait 2
Rube Goldberg, portrait
(Thanks Buck Batard at Bad Attitudes)

Rube Goldberg, portrait 3
Rube Goldberg, portrait
(Thanks Book Calendar)

Rube Goldberg, portrait 4
Rube Goldberg, portrait
(Thanks Mercury at Philosophy of Science Portal)

Rube Goldberg, portrait 5
Rube Goldberg, portrait
(Thanks William Roberts at bancroft.berkeley.edu)

And let's look first at some animations of his machines. The first is the opening sequence to rubegoldberg.com.

rubegoldberg.com Intro Sequence

(Thanks rubegoldberg.com)

The next one has the appearance of a Goldberg machine. It is from Sesame Street. (For all I know, Goldberg might have made it, but it at least resembles Goldberg's style).

A Rube Goldberg Alphabet Machine from Sesame Street

(Thanks sawing14s)

So let's analyze one of Goldberg's machines, looking for the differential mechanics. [Click on image to enlarge]

Rube Goldberg Machine (2 in credits)

(Thanks Stephen Worth at ASIFA)

[And thanks again Stephen Worth at ASIFA for each image-part to follow.] Goldberg announces at the beginning that the invention is a fire extinguisher.

And at the end we see a fire being extinguished.

But what we find is that the invention is not just the device shooting the water, but all the differential disjunctions involved, one implying the next, and all leading up the the extinction of the fire.

Note how it starts. The machine begins with an Eskimo. The fire makes him feel warm. As an Eskimo, he's not used to the heat, so he needs to take off his fur coat. Our first functional disjunction is Eskimo & heat.

He places the fur coat on an elk's antlers, which again seems to be a ridiculous disjunction.

Now we have the mechanical lever move a pair of scissors, which are also a lever, with its mechanical disjunction of motion. But what is more disjunctive is the oddly matched parts of an elk and a scissors.

The scissors releases a spring.

The spring triggers a lever with a hand on it, flipping a coin. Here the conjunction of lever and hand seems disjunctive, as if forced together while being incompatible.

The coin distracts a waiter. Here the connection of motion is highly disjunctive, being based on the mechanisms of human reactions to money.

This causes the waiter to turn himself aside, moving his seltzer bottle away from the drink he was spritzing.

This causes the spritzer to be turned toward the fire and presumably put it out.

This final mechanism is highly disjunctive. It is ridiculous that the waiter did not notice the fire, and instead used the spritzer for the drink. But he does notice money. What should have been an evident mechanical implication for the waiter -- spritzer-water implies fire extinction -- was instead perverted into: money-distraction implies fire extinction. So that is the disjunction: the distraction of money is crushed together with the action of the spritzer, for the function of putting out the fire. This is the function of disjunction. It's funny in this case, but it is quite common in our everyday experiences. Our lives do not function on account of sensible harmonious conjunctions. They function on account of a monstrous assemblage of differential mechanical relations, like a giant infinitely complex Goldberg machine. Often times our strongest motivations to succeed come from functional disjunctions. The profound downward motion of a person discouraging us can produce an upward motion, an unbending determination to prove the discouraging person wrong. Also consider how we might in our lives have had creative moments while under the influence of one intoxicant or another. In these states, incompatible ideas in our mind might emerge seemingly by things which normally would not evoke them. And these ideas might collide with others, producing new ideas that never normally would have been borne from our minds. Here again we see the function of disjunctions. But even mundane mechanisms are disjunctive. When we see a red light while driving, we press the brake peddle. But red and stomping are not logically related. The one implies the other (while driving), but they are foreign to one another, when considered by themselves. Perhaps all function is disjunction. And maybe all machines are differential.

We will find Deleuze illustrating Goldberg machines with Buster Keaton's contraptions. Some of them are sequences of events. Here is one from The High Sign, which is a machine. But note the influence of the cat, and how the cat sends waves of differential relations into the machine.

Buster Keaton's Dog-Gun Rube Goldberg Machine in The High Sign

The following are a number of other machines by Rube Goldberg. I am so very grateful to the sources. [click to enlarge]

Rube Goldberg machine, 1

(Thanks Stephen Worth at ASIFA)

Rube Goldberg machine, 2

(Thanks Stephen Worth at ASIFA)

Rube Goldberg machine, 3

(Thanks Stephen Worth at ASIFA)

Rube Goldberg machine, 4

(Thanks Stephen Worth at ASIFA)

Rube Goldberg machine, 5

(Thanks Stephen Worth at ASIFA)

Rube Goldberg machine, 6

(Thanks Stephen Worth at ASIFA)

Rube Goldberg machine, 7

(Thanks Red Yak)

Rube Goldberg machine, 8

(Thanks Bent at The Atlantic Community)

Rube Goldberg machine, 9

(Thanks thenonist.com)

Rube Goldberg machine, 10

(Thanks National Cartoonists Society)

Rube Goldberg machine, 11
Rube goldberg machine color
(Thanks wiki)

Rube Goldberg machine, 12
Rube goldberg machine self operating napkin
(Thanks libertylive.org)

Rube Goldberg 13

(Thanks counternotions.com)

Rube Goldberg machine, 14
Rube goldberg machine moth killer
(Thanks mousetrapcontraptions.com)

Rube Goldberg machine, 15
Rube goldberg machine cut hair
(Thanks William Roberts at bancroft.berkeley.edu)

Rube Goldberg machine, 17
Rube goldberg open egg machine invention
(Thanks Simple Machines Inventions Webquest)

Rube Goldberg machine, 18

(Thanks Simple Machines Inventions Webquest)

Rube Goldberg machine, 19
Rube Goldberg machine. wife letter
(Thanks mousetrapcontraptions.com)

Rube Goldberg machine, 20
Rube goldberg machine invention door
(Thanks pomperaug.com)

Rube Goldberg machine, 22
Rube goldberg machine invention olive jar
(Thanks Argonne)

Rube Goldberg machine, 23

(Thanks SCHS)

Rube Goldberg machine, 24

(Thanks Argonne)

Image Credits

Machine Images:

Rube Goldberg 1-6
(Thanks Stephen Worth at ASIFA)

Rube Goldberg 7
(Thanks Red Yak)

Rube Goldberg 8
(Thanks Bent at The Atlantic Community)

Rube Goldberg 9
(Thanks thenonist.com)

Rube Goldberg 10
(Thanks National Cartoonists Society)

Rube Goldberg 11
(Thanks wiki)

Rube Goldberg 12
(Thanks libertylive.org)

Rube Goldberg 13
(Thanks counternotions.com)

Rube Goldberg 14
(Thanks mousetrapcontraptions.com)

Rube Goldberg 15-16
(Thanks William Roberts at bancroft.berkeley.edu)

Rube Goldberg 17
(Thanks Simple Machines Inventions Webquest)

Rube Goldberg 18
(Thanks Simple Machines Inventions Webquest)

Rube Goldberg 19
(Thanks mousetrapcontraptions.com)

Rube Goldberg 20
(Thanks pomperaug.com)

Rube Goldberg 22
(Thanks Argonne)

Rube Goldberg 23
(Thanks SCHS)

Rube Goldberg 24
(Thanks Argonne)

Rube Goldberg 25
(Thanks Lee L. Lowery & Sandeep Ghorawat)

Lever image:
(Thanks fi.edu/Science of Gears)

Gears image:
(Thanks Imagination Factory)

Rotating Gears animation:
(Thanks Science Buddies. Credited as public domain.)

Black Box:
Minsky, Marvin.
Computation: Finite and Infinite Machines. London: Prentice-Hall International, Inc., 1972

Edwards & Penney's function machine:
Edwards & Penney: Calculus. New Jersey: Prentice Hall, 2002.

First animation from:
(Thanks rubegoldberg.com)

Sesame Street alphabet Rube Goldberg machine from
(Thanks sawing14s)

Rube Goldberg portrait images:

Rube Goldberg portrait, 1
(Thanks National Cartoonists Society)

Rube Goldberg portrait, 2
(Thanks Buck Batard at Bad Attitudes)

Rube Goldberg portrait, 3
(Thanks Book Calendar)

Rube Goldberg portrait, 4
(Thanks Mercury at Philosophy of Science Portal)

Rube Goldberg portrait, 5
(Thanks William Roberts at bancroft.berkeley.edu)

30 Dec 2010

Broken Open to the World. Merleau-Ponty and Opennes to the World, 1

by Corry Shores
[Search Blog Here. Index-tags are found on the bottom of the left column.]

[Central Entry Directory]

[Other entries in the Merleau-Ponty phenomenology series.]

[May I sincerely thank the source of the image
Credits are given below the image and at the end.]

Broken Open to the World

(Thanks themasterteacher.tv)

Merleau Ponty: Openness to the World, 1

What does phenomenological openness to the world go to do with you?

The world appears before us. In a way, it is given to us. But the world receives us just as much as we receive it. So just as the world is given to us, so are we given to the world. We might say that we are open to the world. Yet perhaps it is not that we are open to it. Perhaps we are cracked open before it. Maybe there is a crack between us and it, because we are cracked from within. Perhaps then we are exposed to the world, vulnerable to it, because we are fundamentally different from it. We are in a differential relation to the world; and this is the basis for our being able to relate to it in the first place. So we are not integrated with the world; rather, we are continually different from it.

Summary of the main idea in this passage:

We are in an integrated relation with the world.

Points relative to Deleuze
[Under ongoing revision]

For Deleuze, we relate to the world only differentially. We are 'open' to it in the sense of our being cracked open and abruptly exposed to it. We 'communicate' with it in the sense that we and the world cause one another to resonate from our differences, like two magnets forced together same-to-same pole.

Quotation from Phénoménologie de la perception / Phenomenology of Perception:

The world is not what I think, but what I live through. I am open to the | world, I have no doubt that I am in communication with it, but I do not possess it; it is inexhaustible. (xviii-xix)

Le monde est non pas ce que je pense, mais ce que je vis, je suis ouvert au monde, je communique indubitablement avec lui, mais je ne le possède pas, il est inépuisable. (17c)

Merleau-Ponty, Maurice. Phenomenology of Perception. Transl. Colin Smith. London/New York: Routledge, 1958.

Merleau-Ponty, Maurice. Phénoménologie de la perception. Paris: Éditions Gallimard, 1945.

Image obtained gratefully from:
(Thanks themasterteacher.tv)

9 Dec 2010

Deleuze Cinema Update: Hideous Passion. Buster Keaton. Battling Butler

Corry Shores
[Search Blog Here. Index-tags are found on the bottom of the left column.]

There is a new Deleuze Cinema Project entry. Click on the title below.

Buster Keaton Battling Butler

Variations on a Line: Wilhelm Worringer's Northern Line (Gothic Line)

Corry Shores
[Search Blog Here. Index-tags are found on the bottom of the left column.]

[Central Entry Directory]
[Deleuze on Bacon Entry Directory]

Variations on a Line:
Wilhelm Worringer's Northern Line (Gothic Line)

What does Gothic got to do with you?

By looking within ourselves, we might discover a force of freedom thriving within us. It is not exactly that part of us which is like self-defiance, an element in our personalities that causes us to act in a self-sabotaging way against our best interests, or to recklessly act without thinking. However, it is very similar, and might best be described by considering first certain elements of this more readily conceivable careless freedom. For, unlike the reckless freedom, the other more freer freedom is not a reaction. It does not react against ourselves or against things, people and events in our lives. So consider for example that force in us that might drive us to spontaneously go on a drinking binge after just losing a job. It cannot be this other freer freedom, because it reacts against an unfavorable event, an unfair boss, or a self-pitying and self-despising self. Yet it is a sort of defiance. And maybe the freer freedom is defiance without there first being something that we are defying against. Of course we are born into power structures, but our actions can have the spirit of pure, non-reactive defiance. Perhaps this is what we see in the moments of great artistic creation, a sort of joyful defiance, a continual denying that there ever was a restriction in the first place. Now imagine we try to express this force in the act of drawing a line. But also consider if we first drew a curve with supreme control over our hand, to make it as perfect as possible. And also imagine that we at another time were violently impulsive, and drew an erratic line. But the third case is a line inspired by the freer freedom. Like the nicely-drawn curve, the free line would not be a messy chaos. But also, the free line will not be as regularized. And like the erratic impulsive line, the free line will be liberated from the expectations set by how the line was being previously rendered. In a sense it lives at the tiny infinitely small point of the absolute present moment, never fully bound to the immediate or passing past. But unlike the erratic line, the free line will not be defiant in an artificial or reactive way.

So in one sense the free line is drawn in the infinitely small present moment. But in every such infinitely small moment, the line is tending toward extending into infinity. That is because at no moment does it suggest or move toward an organic completion. How is this so? Consider lines that make a labyrinthine pattern.
interlace ornament Morovingian Worringer. Form Problems of the Gothic. plate 8a
Such labyrinthine patterns make us think that there is no beginning or end. Another example is a Gothic cathedral.
Salisburry Cathedral. Worringer. Form Problems of the Gothic. plate 22
Only the vertical lines are emphasized, which gives us an impression of going up to infinity.

Worringer calls the free line the "Northern line." If we drew our lives as a northern line, we would not be bound to our pasts, or adjust our actions so that they properly react to something else. We would live in the present not in a thoughtless or careless way, but in the sense of making this moment the seed of an infinite future of continued freedom. Such a 'northern life' is powerfully creative.

Brief Summary:

Worringer discusses certain styles that cultures have developed throughout history. There is a trend, called the Gothic, which ornaments its works with a liberated line, termed the "Northern Line". This line is continually undetermined and it strives for infinity.

Points relative to Deleuze
[Under continual revision]:

One of the places Deleuze refers to the northern line is in his Francis Bacon: The Logic of Sensation book. One element that is central to his notion of sensation is continual variation. So consider a part of a painting that we might characterize as being northern or Gothic; it would have lines that are in continuous variation. Visually speaking, this line will act on the other elements of the painting. But because it is in continual variation, then it expresses either explicitly or implicitly self-difference at every point. Thus there is an infinity of different influences it has on the rest of the painting. This prevents our eyes from ever satisfying their effort to make visual sense of what they see. There will never be an organic coherence, because the artwork will be infinitely fertile in the ways its parts can re-relate. This continual defiance to our efforts of recognizing or mentally representing what we see causes our impressions to be in continual variation. We have a sensation when we are confronted with an irreducible difference that forces itself upon us. Thus the northern or Gothic line can be an element of a painting which allows the artwork to continually affect us with its constant variation.

Selective Summary, from:

Wilhelm Worringer

Form Problems of the Gothic

Latent Gothic of Early Northern Ornament

Worringer will speak of "three principal stages in the process of adjustment of man to outer world" (43). He will focus on the Gothic stage, which he says does not correspond with the Gothic historical age. Rather, he examines the Gothic in terms of a "psychology of style" (43b). All the Western World is Gothic in this sense, so long as it is not immediately influenced by the antique Mediterranean culture. Thus Gothic refers to present times as well (44a).

Worringer begins by describing the art of the Northern European peoples at the fall of the Roman Empire. (45d) The art does not represent nature. It is purely ornamental. There is a "purely geometrical play of line" (although he will later clarify this sort of playfulness). (46ab)

They begin to develop their own language of the line, their own "linear fantasy called intertwining band ornament or braid ornament" (46bc).

Worringer. Form Problems of the Gothic. plate 8a.jpg
The lines form various fantastic and intriguing arrangements. Early primitive lines are abstract and geometrical, without any organic interpretation. (47a) Nevertheless, they express an extreme liveliness. (47b) He says that this line style we see above is a clash between "the abstract character of primitive geometric ornament" and "the living character of Classical organically tinged ornament" (47b.d) These two other styles shown respectively.
Worringer. Form Problems of the Gothic. plate 2.jpg
Worringer. Form Problems of the Gothic. plate 5a.jpg
So, classical ornament has organic clearness and moderation, and it seems to spring "without restraint from our sense of vitality." And also, "It has no expression beyond that which we give it" (48b). But by contrast, northern ornament seems to take on a life all its own, and in fact seems to act upon us ourselves.
The expression of northern ornament, on the other hand, is not immediately dependent upon us; here we face, rather, a life that seems to be independent of us, that makes exactions upon us and forces upon us an activity that we submit to only against our will. In short, the northern line is not alive because of an impression that we voluntarily impute to it, but it seems to have an inherent expression which is stronger than our life. (48bc, boldface mine)
The elaborate his idea of the northern line, he illustrates with common experience. We are to pick up a pencil and draw a line.

What do we notice? Worringer suggests we sense two things. One is "the expression dependent upon us" and the other is the "expression of the line seemingly not dependent upon us" (48d). Perhaps in one way, we see that we drew it; we see that it is a line from our hand not that that of someone else. But perhaps in another way, we see a geometrical form that we were trying to render. The line, as a line, expresses something that is geometrically real even without such an attempted instantiation.

He also has us draw the line in "fine round curves". When we do so, we feel the movement of our wrist. But to that motion we also accompany to it our "inner feeling". We sense that the line grows spontaneously from the play of our wrist, and this gives us a pleasant sensation. "The movement we make is of an unobstructed facility; the impulse once given, movement goes on without effort." (48d). This pleasant feeling is a "freedom of creation," and we transfer it
involuntarily to the line itself, and what we have felt in executing it we ascribe to it as expression. In this case, then, we see in the line the expression of organic beauty just because the execution corresponded with our organic sense. (48-49)
But consider if we see a line made by someone else. We will still involuntarily feel inside us the impressions one has if drawing such a line. (49a)

Gothic lines may have this "organic expressive power", like we see in Classical ornament. But it has another such expressive power. Worringer has us imagine drawing a line more excitedly.
If we are filled with a strong inward excitement that we may express only on paper, the line scrawls will take an entirely different turn. The will of our wrist will not be consulted at all, but the pencil will travel wildly and impetuously over the paper, and instead of the beautiful, round, organically tempered curves, there will result a stiff, angular, repeatedly interrupted, jagged line of strongest expressive force. It is not the wrist that spontaneously creates the line; but it is our impetuous desire for expression which imperiously prescribes the wrist's movement. The impulse once given, the movement is not allowed to run its course along its natural direction, but it is again and again over whelmed by new impulses. When we become conscious of such an excited line, we inwardly follow out involuntarily the process of its execution, too. (49b.d, boldface mine)
But when we follow someone else's wild line, we do not feel pleasure. It seems more like "an outside dominant will coerced us" (49cd). What we feel seems like the forces of the ruptures in the line's incoherent discontinuity.
We are made aware of all the suppressions of natural movement. We feel at every point of rupture, at every change in direction, how the forces, suddenly checked in their natural course, are blocked, how after this moment of blockade they go over into a new direction of movement with a momentum augmented by the obstruction. The more frequent the breaks and the more obstructions thrown in, the more powerful becomes the seething at the individual interruptions, the more forceful becomes each time the surging in the new direction, the more mighty and irresistible becomes, in other words, the expression of the line. (49-50, boldface mine)
The line forces its expression upon us. Thus we feel it as something autonomous and independent of us. (50a)

So consider when we were drawing the curved line. We felt physically a pleasure on account of there being no obstructions breaking the flow of our hand's movements. The parts of our wrist worked together to create a line that is self-consistent in its curving motion. With the erratic line, however, there seems to be unpredictable forces which break the flow, in fact prevent one from starting, and prevent any possibility of there being coherence in the motions or the line. Our hands drawing calmly seem to do so merely by means of our bodies acting automatically and with coordination among its parts. So when it is erratic, that suggests to us the forces causing the unpredictabilities do not come from the body, but rather from some psychic or spiritual source.
The essence of this inherent expression of the line is that it does not stand for sensuous and organic values, but for values of an unsensuous, that is, spiritual sort. No activity of organic will is expressed by it, but activity of psychical and spiritual will, which is still far from all union and agreement with the complexes of organic feeling. (50b, boldface mine)
Worringer clarifies that Gothic ornament and such a scrambled line made by an emotionally or mentally excited person are not at all the same things. However, Worringer will compare them to clarify what he means by the northern line. He says for example that the lines of northern cultures tell us that they were
longing to be absorbed in an unnatural intensified activity of a non-sensuous, spiritual sort one should remember in this connection the labyrinthic scholastic thinking in order to get free, in this exaltation, from the pressing sense of the constraint of actuality. (50d, boldface mine)
Worringer sees this supersensuous longing expressed in "fervent sublimity of the Gothic cathedral, that transcendentalism in stone" (51a). Such architecture exhibits "a complete degeometrization of the line for the sake of the same exigencies of spiritual expression" (51ab).

Pointing us to the left item in the image below, Worringer tells us that "primitive ornament is geometric, is dead and expressionless [Pl. III, C]. Its artistic significance rests simply and solely upon this absence of all life, rests simply and solely upon its thoroughly abstract character" (51b).
Egyptian pottery with geometrical designs. Worringer. Form Problems of the Gothic. plate 3c
Worringer then says that the original dualism between man and world weakened the geometrical character of the line. This degrading of the geometrical line can take two courses. One is toward "an organic vitality agreeable to the senses," as with classical ornament. (51bc)
Worringer. Form Problems of the Gothic. plate 5a.jpg
Or instead it can develop toward a "spiritual vitality, far transcending the senses," which we see in northern ornament (51c). Here we find the Gothic character.

Gothic interlace ornament. Tunc Book of Kells. Worringer. Form Problems of the Gothic. plate 8 image
He continues to claim that the Gothic has more expressive power.
And it is evident that the organically determined line contains beauty of expression, while power of expression is reserved for the Gothic line. This distinction between beauty of expression and power of expression is immediately applicable to the whole character of the two stylistic phenomena of Classic and Gothic art. (51cd, boldface mine)

The Infinite Melody of Northern Line

Worringer will further elaborate the distinction between Classical ornament and Gothic/northern ornament.

Classical ornament exhibits symmetry.
late gothic ornament. Worringer. Form Problems of the Gothic. plate 8a b
However Gothic does not. But instead of symmetry repetition is predominant. (52ab) Classical has repetition too, but like a mirroring. The repetitions have the "calm character of addition that never mars the symmetry" (52bc).
Worringer. Form Problems of the Gothic. plate 5a.jpg
Ludovisi Throne Worringer. Form Problems of the Gothic. plate 6c
Gothic repetition, however, is more like a repetition of difference striving to rise to the nth power.
In the case of northern ornament, on the other hand, the repetition does not have this quiet character of addition, but has, so to speak, the character of multiplication. No desire for organic moderation and rest intervenes here. A constantly increasing activity without pauses and accents arises, and the repetition has only the one intention of raising the given motive to the power of infinity. The infinite melody of line hovers before the vision of northern man in his ornament, that infinite line which does not delight but stupefies and compels us to yield to it without resistance. If we close our eyes after looking at northern ornament, there remains only the echoing impression of incorporeal endless activity. (52-53, boldface mine)

Worringer then cites work from Lamprecht where he describes the laberinthine nature of the Gothic lines.
Lamprecht speaks of the enigma of this northern intertwining band ornament, which one likes to puzzle over [PI. VIII]. But it is more than enigmatic; it is labyrinthic. It seems to have no beginning and no end, and especially no center; all those possibilities of orientation for organically adjusted feeling are lacking. We find no point where we can start in, no point where we can pause. Within this infinite activity every point is equivalent and all together are insignificant compared with the agitation reproduced by them. (53a.b, boldface mine)
Worringer. Form Problems of the Gothic. plate 8a.jpg
Worringer. Form Problems of the Gothic. plate 8c jpg. tunc book of kells
In Gothic architecture, "the impression of endless movement results from the exclusive accentuation of the vertical." (53c)
Salisburry Cathedral. Worringer. Form Problems of the Gothic. plate 22

Wilhelm Worringer. Form Problems of the Gothic. New York: G.E. Stechert, 1920.
PDF available online at: