Uexküll (3.4) Theoretical Biology, “The Mark-Signs”, summary

 

by Corry Shores

 

[Search Blog Here. Index tabs are found at the bottom of the left column.]

 

[Central Entry Directory]

[Jakob von Uexküll, entry directory]

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[The following is summary. All boldface and bracketed commentary is my own. Proofreading is incomplete, so please forgive my typos. Page citations refer to the 1928 German edition first and to the 1926 English edition second.]

 

 

 

 

Summary of

 

Jakob von Uexküll

 

Theoretical Biology

[Theoretische Biologie]

 

Ch.3 The Content-Qualities

[Die Inhaltsqualitäten]

 

3.4 The Mark-Signs

[Die Merkzeichen]

 

 

 

Brief summary:

Each threshold in our awareness of variation presents a “mark-sign”. The ability to discern mark signs varies for the person or creature, depending on their level of sensitivity to that sort of qualitative variation. There are two kinds of mark-signs. {1} Qualitative  mark-signs: these distinguish qualitatively-different things, and they are represented by angles in our diagrams. {2} Intensive mark-signs: these are found along a continuum of variation; they are determined by thresholds of variation-awareness; and they are represented in our diagrams by the lines between the qualitative mark-sign angles.

 

 

 

Summary

 

§383

[A “mark-sign” corresponds to a threshold in our attention. So a mark-sign is found at each of the smallest discernible objective changes in a stimulus. (It is an “alteration in the content that is just perceptible to the attention”.)]

 

[In the prior section we discussed a method of determining thresholds, based on Weber’s technique. The idea is that a continuously varying objective intensity in a stimulus is perceived in steps. The objective stimulus can increase continuously without our sensing it, but when it crosses a certain threshold in our awareness, we notice a change. We can think of these thresholds as moments when our attention changes or “turns”. Uexküll will now define his notion of the mark-sign in terms of these thresholds where our attention changes.] “By employing the method of determination of threshold, and developing the same principle, we arrive at the concept of the mark-sign” (65 / 76). [Uexküll describes a method for finding the thresholds or mark-signs in a color continuum. It seems the procedure finds the smallest objective variations that we can discern as distinguishable. Apparently, we keep magnifying the constituent parts of the continuum until we find a part where we are unable to discern a difference. The number of all the smallest discernible parts is the number of mark-signs in the continuum.]

We divide up the whole colour-band between two turning-points into tiny segments lying alongside one another, and make them so small that at least two adjacent parts, considered by themselves, are indistinguishable by the eye. Now let us magnify the individual parts until every two adjacent ones become just distinguishable from one another. Then the number of individual parts gives the number of mark-signs that the colour-band holds for us. Interpreted in this way, the mark-sign means the alteration in the content that is just perceptible to the attention.

(65-66 / 76)

 

 

§384

[The capacitiy to discern mark-signs varies with abilities and handicaps, like between a trained musician and a tone-deaf person.]

 

Certain people are more sensitive to color variations, and thus they experience more mark-signs in the same color continuum. “The number of mark-signs for colour increases with the skill of the individual observer in distinguishing colours; it gives us a clue to the amount of colour in his appearance-world [Erscheinungswelt]” (66 / 76, bracketed insertion mine). Color-blind people have fewer color mark-signs. While those with normal sight can think of the color-blind person’s appearance world by subtracting colors, the color-blind person is unable to imagine what it is like to have those color mark-signs. The same holds for those with tone-deafness (66 / 76).

 

§385

[There are two kinds of mark-signs: {1} qualitative  mark-signs, which distinguish qualitatively-different things and which are represented by angles in our diagrams, and {2} intensive mark-signs, which are found along a continuum, are determined by thresholds of variation-awareness, and are represented in our diagrams by the lines between the qualitative mark-sign angles.]

 

Uexküll then distinguishes two sorts of mark-signs: {1} mark-signs of qualitative difference, and {2} mark-signs of intensive difference. Qualitative differences are always ones involving definite qualities, and we represented them using angles in our spatial diagrams. But other less qualitatively definite qualities appear as intensive variations between definite qualities. They are distinguished by the thresholds.  [Recall the color example from section 3.2.

Here we see the two different sorts of mark-signs. Red, yellow, green, and blue are qualitative mark-signs, and the variations between them contain a series of intensive mark-signs.] When assessing intensive mark-signs, it is arbitrary where we start and which direction we go (66 / 76-77).

 

 

 

 

 

Works cited (in this order):

 

Uexküll, Jakob von. 1928. Theoretische Biologie, 2. gänzlich neu bearbeitete Auflage. Berlin: Springer.

 

Uexküll, Jakob von. 1926. Theoretical Biology. Translated by Doris Livingston MacKinnon. London: Kegan Paul, Trench, Trubner & Co. / New York: Harcourt, Brace & Company. PDF available at:

http://www.archive.org/details/theoreticalbiolo00uexk

 

 

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Uexküll (3.3) Theoretical Biology, “The Principle of Comparison”, summary

 

by Corry Shores

 

[Search Blog Here. Index tabs are found at the bottom of the left column.]

 

[Central Entry Directory]

[Jakob von Uexküll, entry directory]

[Uexküll, Theoretical Biology, entry directory]

 

[The following is summary. All boldface and bracketed commentary is my own. Proofreading is incomplete, so please forgive my typos. Page citations refer to the 1928 German edition first and to the 1926 English edition second.]

 

 

 

 

Summary of

 

Jakob von Uexküll

 

Theoretical Biology

[Theoretische Biologie]

 

Ch.3 The Content-Qualities

[Die Inhaltsqualitäten]

 

3.3 The Principle of Comparison

[Das Prinzip der Vergleichung]

 

 

 

Brief summary:

We have been using geometrical shape-diagrams to represent the experience of non-spatial sorts of continuous variations, like experiences of color. The “common denominator” between these experiences and the diagram shapes are marked changes, which in experience are changes in attention, and in the shapes, are changes in the direction of the lines.

 

 

 

Summary

 

§376

[We want to know more about how to spatially represent certain qualitative variations that are not experienced spatially or quantitatively, like the changes between qualitatively distinct colors along a continuous spectrum of color variation.]

 

[In the prior section we examined intensive quality circles, particularly the color circle. Here we drew a square, which showed relations between four colors that stood out in the spectrum, namely, red, yellow, blue and green.

What we take special note of here is the fact that the colors are not spatially arranged in this way in experience. The right angles that turn from one color to another represent more how we experience the colors as veering qualitatively from continua of variation.] Uexküll now asks how we transfer relationships like that between colors in our experience to the spatial realm of our diagrammatic representations. We are especially concerned with how “while our eye ran along the band of the spectrum, we noticed at certain points that a new colour-mixture appeared. This turning-point in the color sequence we transformed into the turning-point in a line in space” (64-65 / 75). [In other words, we want to understand better how it is that we determine points where in our minds a qualitative variation reaches a “turn” when objectively speaking it would still be seen as undergoing a linear variation, like the light waves increasing or decreasing quantitatively while we perceive qualitatively distinct colors that do not seem to be more and less of something. Blue does not seem more or less of a common variable found in red.]

 

 

§377

[Along the continua of variation we experience turning points, like the different distinct and “pure” colors along the color spectrum.]

 

[In this prior section, one of the first things we noted was that the four colors (red, yellow, green, blue) stood out as distinct and pure colors.

So objectively speaking there is a continuum of variation that privileges no point along the change. But in our experiences, as our eyes move down the line, it is as if we cross through privileged points. So there is another layer of the motion, which is not linear and continuous. It is as if these privileged points were like pivot points swinging us toward another privileged point. We represented that in our diagram by having the lines turn at an angle.

]

Our attention, at first focussed on the red-yellow colour- mixture, was suddenly compelled to turn to the mixture of yellow with green. Even in ordinary speech we speak of our attention, “taking a new direction.” By drawing a line which suddenly takes a new direction, we give a concrete form to the expression.

(65 / 75)

 

 

§378

[As our eyes move between the pure colors, we experience a change in our attention that we can represent spatially by means of angles that turn the continuum of variation. These attention changes are the “common denominator” between a non-spatial color experience a spatial representation of it.]

 

[The next idea references some ideas from prior sections. See chapter 2 on moment-signs. Time is not space, but we can measure its flow by finding a pulse (46 / 54). And we can then represent that pulse by placing line markings in a row (47 / 55). This means that we have sound recurring at intervals (represented perhaps by muscle movements like taps) and a visual phenomenon recurring at intervals, like the lines or tick-marks written out in a row to represent the temporal repetition. Uexküll then asks what is the common basis between these two different dimensions of representation or experience that allows the two sorts of representation to be interchangeable? What is common, he says, is that both sorts of markings designate changes that appear to our apperception (47-48 / 56-57). We can also think of them as each marking a “change in the attention” (48 / 57). Since they are transposable in both temporal and spatial experience and representation, we can think of such attention changes as a common denominator. Now, there are certain quantitative variations that objectively are continuous but whose continuity of variation we cannot measure well by means of our own senses alone. Consider for example if we hold a bucket into which a slow and steady flow of water fills it gradually. We feel that the weight is increasing over time, but we have difficulty measuring that increase, because it is not like we have in our minds a dial with numerical markings telling us each time we go up an objective standard unit of weight. Uexküll refers us to Weber’s solution (see this entry and its initial links for more). Weber introduces the notion of a threshold of our perception. (Uexküll defines threshold in the following way: “Threshold means the just perceptible difference between two intensities of a quality.” (52 / 63).) The objective increase in weight will vary continuously, and if it is slow enough, it will go unnoticed, until we cross a threshold when we notice the difference. At lower weights, we are more sensitive to changes, and thus the thresholds correspond to smaller increases in the objective weight of the bucket. But as it fills heavier, we become less sensitive, as the thresholds correspond to greater intervals of weight-change (49 / 58-59). (This bracketed summarization of ideas found in prior sections holds for this and the following paragraphs, which will be quoted).]

In both instances, a change occurs in the process of attention. This yields us the common denominator that permits us to reproduce in the form of an event familiar to the eye one that is of quite another kind.

(65 / 75)

 

§379

[We made a similar spatial transposition when marking time-beats with strokes drawn side-by-side.]

 

[See the summary in the above section.]

 

We were employing the same method when we converted time-beats into a series of strokes set side by side, and thereby transformed time into space. Our attention was able to keep the change of content quite separate from the nature of the content, and to give this change a concrete expression by transference into spatial relations.

(65 / 75)

 

 

§380

[With this in mind, we could represent musical tones with a seven-sided pillar where the angles mark notes (with the variations between them on the intervening lines), but they are arranged so that each octave takes another horizontal layer of the pillar, placing all of the equivalent notes in vertical alignment.]

 

We can also spatially represent other sorts of non-spatial qualitative experiences. For example, “In order to reproduce in concrete form the relationship-form of musical sounds, we shall employ a seven-sided pillar, and on its edges we shall arrange all the sounds in a spiral, so that those that differ by an octave lie below one another. On the faces we shall place the transitional half-tones and quarter-tones” (65 / 75).

 

§381

[Other shapes can be used for other sorts of content-qualities.]

 

Henning suggests a prism to represent the “relationship-form” of olfactory qualities, but the other content-qualities could be represented using a two-dimensional plane shape (65 /75).

 

 

§382

[In all our diagrams, the turning-points in our attention correspond with angles in the shape.]

 

But even though we use different shapes, we maintain the same organizing principle, namely, that we demarcate the turning-points in our attention with changes of angles in the diagram shape (65 / 75-76).

The particular procedure in every case depends on the same principle: the turning-points at which our attention acquires a new direction are fixed concretely by the angles or edges of a spatial figure.

(65 / 75-76)

 

 

 

 

 

Works cited (in this order):

 

Uexküll, Jakob von. 1928. Theoretische Biologie, 2. gänzlich neu bearbeitete Auflage. Berlin: Springer.

 

Uexküll, Jakob von. 1926. Theoretical Biology. Translated by Doris Livingston MacKinnon. London: Kegan Paul, Trench, Trubner & Co. / New York: Harcourt, Brace & Company. PDF available at:

http://www.archive.org/details/theoreticalbiolo00uexk

 

 

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Uexküll (3.2) Theoretical Biology, “The Form of the Quality-Circles”, summary

by Corry Shores

[Search Blog Here. Index tabs are found at the bottom of the left column.]

[Central Entry Directory]
[Jakob von Uexküll, entry directory]
[Uexküll, Theoretical Biology, entry directory]

[The following is summary. All boldface and bracketed commentary is my own. Proofreading is incomplete, so please forgive my typos. Page citations refer to the 1928 German edition first and to the 1926 English edition second. Note for this section: I do not yet have the original 1920 German first edition on which the translation seems to have been based. So some references to prior sections will refer just to the English edition for now.]

Summary of

Jakob von Uexküll

Theoretical Biology

[Theoretische Biologie]

Ch.3 The Content-Qualities

[Die Inhaltsqualitäten]

3.2 The Form of the Quality-Circles

[Die Form der Qualitätskreise]

Brief summary:

We obtain sense data from various nerves, along with local signs telling us the spatial location of the stimulus and as well moment-signs telling us the temporal location. For each location there can only be one quality datum, or “content-quality”, and thus there cannot be contradictory qualities in the same location. The perceived space around us forms spheres of larger sizes, with us at the center. So we can think of there being content-qualities occupying spatial locations along a spatial circle haloing around us. But qualities can also take on circular relations of intensity. This is evident with the quality circle for color. As we move from red to yellow, there is between them a continuum of color mixture. From yellow we go to green, but since green is qualitatively very different from the red-yellow spectrum, we can think of the yellow-green continuum as moving in another direction. We turn yet another direction to go from green to blue. What comes after blue in the color spectrum is violet, which is a mixture of red and blue. Thus we turn from blue back toward red to complete our circle.

Summary

§369

[In chapter 1 we noted that the animal’s perception of space is like a series of larger and larger spheres centered on the creature.]

[The first couple paragraphs of this section will summarize some ideas from prior sections. Not all of the prior sections correspond between this English translation and the German edition I am using, presumably because the English edition is based on the German first edition, which I do not currently have access to. As such, I will refer to the English pages primarily to summarize these points. Uexküll begins this section by saying that in order to investigate the appearance-worlds [Erscheinungswelten] of others, we need to have an exact knowledge of our own (62 / 72). He then refers to an idea from the first chapter on space. One notion from the section “The Space of Animals / Die Räume der Tiere” (36 / 40) is that we can think of animals having a sphere of space surrounding them that is “like an invisible soap-bubble” (62 / 72). In this earlier section, he addresses the question, ‘What does space look like that surrounds animals?’ (??? / 40). We first need to create a diagram for human space, and then we modify it “according to the faculties of the animal under investigation” (??? / 40). To do this we should first note the idea of local signs. The basic idea is that our nerve endings give us qualities, like touch sensations. But they also tell us where on the body the sensation is coming from. These spatial indicators are called local signs [Lokalzeichen] (5 / 2). (See their description by Lotze here. The basic idea in that context is that the sense data coming from the nerves is not enough to provide spatial relations between the data. And thus we would not know how to spatially arrange the data in our minds. What is also needed are the local signs which give us those spatialized relations between impulse sources.) I am not certain, but I get the sense that the local signs are indicative not simply of the bodily location of the nervous stimulus but as well can be indicative of spatial features of the stimulus source out in the world. So perhaps for example there are local signs to tell us when a visual stimulus comes more from the distance, but I am not sure. “Direction-signs” involve the relation between local signs. “The sensation of direction comes in only when one local sign strikes up while the others most nearly related to it have not yet quite died away [...]. [...] what we call ‘motion’ is only that change in quality which is connected with the quality of direction.” (7 / 6) “I call that which connects local signs a direction sign” (???{cf.11} / 6). (In other words, if a tactile stimulus moves from one nerve on our skin to another located somewhere else on our skin, the relation between the local sign for the beginning place and that of the ending place gives us a direction of the movement of the stimulus). We return now to the space of animals and humans. Uexküll has us consider there being three circular pieces of cardboard, and we intersect them along the three planes of direction (??? /40-41). (I suppose we have one lying flat horizontally. The other two will stand upright vertically. So the second of the three circles will be vertical facing forward, while the third will be vertical at a right angle to the second, with all three of them sharing the same center-point. The three circles give us the main directions: forward-backward, up-down, and right-left.) We then place spheres of increasing size emanating from the center-point. There will be small spheres near the center that are placed close to one another. As we move outward to larger spheres, the distance between them increases. This distance between the spheres represents the discernible layers of depth. We are most sensitive to the distances in front of us, so we can differentiate the layers more precisely. This is why the spheres nearest us are closer together. But as we go further away, we are less able to make such precise determinations of distance. And, “Each sphere has just as many places on it as there are local signs available. Hence there are much fewer to the same surface of the larger and more distant spheres than there are on the smaller ones close at hand” (??? / 41). (The idea here might be that since the only way we have to differentiate spatial properties of the stimuli is by means of local signs, then there are just as many locations in the sphere as there are local signs for distinguishing them. Now if we consider geometrically how the rays of an angle grow further apart as they move into the distance, then we can imagine that the locations on the more distant spheres are also spaced further apart. “Place” is like all the locations on each spherical surface along one ray, standing one behind the other. “Position” is the location upon one such sphere. Position might instead just be like a designation of the sphere itself, which makes a coordinate with the place, or it might be that coordinate itself. I am not sure. The next idea might be that we can also transpose the places in our perception with places of the world understood according to more of a homogeneously metrical, decentralized understanding of space, as it is understood objectively in physics.) But space as we experience it, or “intuited space,” is what concerns us in biology (??? / 42). Humans have the three planes of direction (the three cardboard circles), but other animals may have just two or one. They may even have none and instead work only with the line of the horizon. For humans the larger and larger spheres are related also to our motor behaviors and thus we can use them to think of steps-into-distance. When studying other animals we should also look at their capacities for making steps-into-distance with respect to their spatial perception. We also must learn the number and distribution of the places in the animals space. (??? / 42). The next idea in this earlier section takes us to the notion of the soap bubble which is relevant to the current section we are examining. The idea seems to be that there is something like an a priori sort of representation of space in animals in the sense that the creature has a certain outer limit to their perception of space, but they assume there is more space beyond that boundary and that it will become apparent upon moving toward it. In this way, we can think of each animal being surrounded by a “soap-bubble” into which parts of the world enter as it moves its bubble around.

Every spatial animal world, however limited as regards places and steps-into-distance, and even though it be without planes of direction, is nevertheless surrounded by the pure extended, which, as necessary form, precedes all space-creating. The extended lies immediately behind the last step-into-distance. So the space peculiar to each animal, wherever that animal may be, can be compared to a soap-bubble which completely surrounds the creature at a greater or less distance. The soap-bubble of the extended constitutes for the animal the limit of what for it is finite, and therewith the limit of its world; what lies behind that is hidden in infinity.

(??? / 42)

So returning again to the current section, Uexküll says that we can describe the space around an animal as being like an invisible soap-bubble [Seifenblase] (62 / 72). After reminding us of a few features of animal space, he notes that “The laws of the content-qualities of our mind are as changeless as the spatial laws of our appearance-world [Erscheinungswelt]” (63 / 72, bracketed insertion mine. See pages 22-23 / 14-16).]

A preliminary condition for the investigation of the appearance-worlds of others is an exact knowledge of our own. In the first chapter, which dealt with the spatial qualities, we succeeded in forming an idea of space that permitted us to describe around every animal a space like an invisible soap-bubble, within which all its activities were carried on. A number of fixed places give support for its sense-organs, and a definite number of direction-steps give the measurement of the magnitudes, and determine the movement of its limbs. The direction of movement is fixed, in many cases, by immutable direction-planes. The laws of the content-qualities of our mind are as changeless as the spatial laws of our appearance-world [Erscheinungswelt].

(62-63 / 72, bracketed insertion mine)

§370

[We will study the ways that the content-qualities work in our minds by seeing them in action.]

Uexküll, again referring to past sections, says that we cannot simply learn the laws that regulate our own mind, because “The activity of our qualities consists in constructing our appearance-world [Erscheinungswelt]” (63 / 72, bracketed insertion mine). [The idea seems to be that the laws of the organization of the qualities given to our senses only come to light when we see that organizational process. Let me quote.] “Considered by themselves, all our qualities seem just a confused heap of building-materials, all more or less alike. The laws are revealed only when the work of construction is in progress” (63 / 72).

§371

[Content-qualities are found at particular locations by means of local signs. The same place cannot have contradictory content-qualities.]

[The next idea seems to be that the content-qualities coordinate with spatial locations by means of the local signs. Perhaps we might consider looking at a painting. Different spatial locations (corresponding perhaps somehow to different optical nerve locations) give us different color qualities. What is important to emphasize here is that for each location there can only be one content-quality for each sense modality. In other words, one location cannot have contradictory qualities.]

When the content-qualities are fitted into the local signs, fixed places appear, having definite properties. And now the outline of a fundamental law is revealed. The “circles” of relationship, which were but faintly indicated in the original material, can be de-limited one from another. Each place, that is to say, can receive only one property from each quality-circle. A certain place may be blue-green, but never blue | and green. It may be of medium hardness, but never both hard and soft; it may be lukewarm, but never both hot and cold at the same time.

(63 / 72-73)

[I am not sure I understand the idea of the quality-circles. Given that they are related to local sigs, perhaps they would be like qualities located on one spatial sphere. Or perhaps the circle is meant simply to give a non-spatial sort of indication of relations. I am not certain.]

§372

[Given that there can only be one content-quality per place, that means you cannot have two different related qualities in the same place.]

[The next idea seems to reinforce the prior one regarding there being just one content-quality per place. Now the notion emphasizes that the appearance of a quality at one place prevents there being a related quality at the same place. Let me quote to be sure:]

This circumstance (i.e. that at each place properties from all the relationship circles may be assembled, but never more than one single quality from each) shows that the qualities of each circle are connected together by law in such a way that the appearance of one quality excludes the simultaneous appearance of a related quality at the same place.

(63/73)

§373

[We can consider the content-qualities extensively as occupying spatially a place in an extensive quality-circle, or we can think of content-qualities occupying an intensive quality-circle.]

[The next idea seems to be the following, but since I am uncertain, please consult the quotation to follow. We so far have considered the extensive spatial relations between the quality contents, as their spatial relations are given by means of the local signs. There is also the matter of intensive differences between the content qualities. We will now form intensive quality-circles so to study their laws. Let me quote, as there is more to this that I am missing:]

As soon as it enters into activity, the material of our mental qualities reveals a form governed by law, which form may enter into appearance along with space and time, or must especially be sought out for the content-qualities. Since only the form of the extensive quality-circles of the local signs and direction-signs is given by intuition, we must try to include within that extensive form the intensive quality-circles, in order to arrive at a clear idea of the laws governing them. To admit of comparison between the extensive qualities themselves, we have already expressed in spatial terms the form of the moment-signs, which is not intuited; and so we shall now attempt to represent in terms of space the other quality-circles likewise.

(63 / 73)

§374

[We can arrange the relations between colors as being on a spectrum but one that wraps around upon itself. The color mixtures can take a hexagonal form.]

Uexküll has us consider if we view a color spectrum. [Let us consider this manner of presenting one:

] Uexküll says when we look at it, “four fixed points immediately strike our eye, at which certain colours emerge pure from the mixture,” namely, pure yellow, red, green, and blue. But between every two points of pure color there is a continuum of color mixture. So we begin with two, the red and the yellow. We will now make our own diagram for these color quality relations. We have fixed yellow and red as points of pure color.

And we can draw a straight line between them to represent the continuum of mixture between them (with a color-band added in the diagram below).

[The next observation is interesting. Uexküll seems to be saying that the difference between these two color points varies continuously and linearly. But as we go to a third color, it is not on that same continuum of variation. He does not explain why, but it seems that it has something to do with the qualitative difference that defies quantitative variations of more and less. In other words, we can say that between yellow and red is a range of variations of yellow-red mixtures, but when we move further to green, there is not a continuation that carries forward a larger range of red-green mixtures (As I understand, if you mix red and green light, you get yellow. But maybe the idea here is that we do not perceive yellow as somehow being between green and red, although we perceive orange as being between yellow and red, because it seems to have qualities of both). Rather, we are starting a new mixture sequence, and for this reason he depicts the variations as taking a right turn.]

We cannot carry the straight line from the red any further, for here we are dealing no longer with red-yellow colours, but with colours that are a mixture of yellow and green. To express the difference, we must give the line a new direction. So we shall place the green point below the yellow and connect these two by means of a line representing the colours that are a mixture of yellow and green.

(64 / 74)

This holds again for the next sequence between green and blue.

At this point Uexküll makes another interesting observation, namely, that as we go further from blue in the linear spectrum, we move into violet, which is a mixture of blue and red. This brings us then back to red.

As we can see from this wheel portrayal, the spectrum can be understood as circular.

Uexküll describes further modifications:

So we may bring back the line from the blue point straight to the red. In this way we get a square, on which we may set equilateral pyramids, one above and one below; this gives a hexagon. The apex of the upper pyramid shall be white and that of the lower one black. While all the angles of the hexagon carry pure colours, on each of the edges will lie colours arising from a mixture of two. The faces of the hexagon, on the other hand, will display colours formed by mixture of three colours, which radiate outwards, in diminishing strength, from the three angles surrounding each face. If we make a transverse section through a face, we can always tell at what level the single colours lie above one another, in order to produce in this way all possible mixed colours.

(64 / 74)

[I can imagine combining two pyramids with a square base to them, placing them base-to-base, so to form an eight-sided diamond-like figure. But I do not know how to obtain a hexagon from that. Perhaps the “equilateral pyramids” are triangular on all faces, and perhaps furthermore they are placed together offset so that their bases taken together create the six points of a hexagon. So it might perhaps resemble something along the lines of this diagram.

(And possibly furthermore we are to think of the top pyramid having pure tones at its base, but tapering continuously to white at the apex, and the bottom one tapering to black. I am not sure however why they would converge at a point. Maybe the top pyramid represents the combination of colors as light and the bottom as the combination of colors as pigments. If it were just to show light and dark variations of each color hue, I would think they would not converge at a center but rather rise up and down like in a cylinder.) But in that case of combining pyramids with triangular bases, I am not sure how to situate them in relation to the original square we drew. So I am not certain about the shape Uexküll is forming.]

§375

[This hexagonal arrangement provides a visualization of the laws of the color-quality circle.]

This color hexagon depicts the laws in the circle of the color-qualities (64 / 74). [The laws seem to be the laws of color relations, including those of mixing.]

Works cited (in this order):

Uexküll, Jakob von. 1928. Theoretische Biologie, 2. gänzlich neu bearbeitete Auflage. Berlin: Springer.

Uexküll, Jakob von. 1926. Theoretical Biology. Translated by Doris Livingston MacKinnon. London: Kegan Paul, Trench, Trubner & Co. / New York: Harcourt, Brace & Company. PDF available at:
http://www.archive.org/details/theoreticalbiolo00uexk


Other image sources:

Visible color spectrum, linear:
SOHO (Solar and Helospheric Observatory). “Making your cerealbox spectroscope.” https://soho.nascom.nasa.gov/classroom/spectroscope.html

Color spectrum wheel:
Programming Design Systems. “Computational Color”. http://printingcode.runemadsen.com/lecture-color/

Color wheel with hexagon:
Artfactory.com. “Color Terms for Art and Design, I”.
http://www.artyfactory.com/color_theory/color_terms_1.htm



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Breath of Color: Merleau-Ponty on Painting and Cézanne in Eye and Mind and Cézanne's Doubt

by Corry Shores
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[Note: all boldfaces in quotations are my own modifications. Quoted citations come from PDF translations on the internet (see works cited). Page citations give PDF number, then 'see ...' for the printed text page citation.]

Breath of Color:

Merleau-Ponty on Painting and Cézanne
in Eye and Mind
and Cézanne's Doubt

(Thanks awesome-art.com)

What does the phenomenology of painting go to do with you?

Painters are sensitive to the way things appear to us. But what if things appeared to us because we were completely meshed with the world, rather than it be the case that we stand before the world and the objects around us stand over against us? Then the painter could tell us more about how we are inherently mixed-in with the world we perceive.

Brief Summary

Our senses integrate us with a world that is integrated within itself. Painters like Cézanne have insights into how this integration works.

Points relative to Deleuze:

Deleuze also thinks that painters can teach us about phenomena. However, Deleuze thinks we learn much different lessons. Painters show us that our contact with the world is not one of integration, but of us facing a world of difference that is itself different from us. [See this entry for more.]

Merleau-Ponty:

From Eye and Mind

Our bodies are integrated into the fabric of the world and into what gives it meaning [see this entry on horizonal integration as meaning, from Phenomenology of Perception]. Painters are able to live purely in this enmeshment with the world and express it visually in their works. This is their 'secret science' (Merleau-Ponty, Eye and Mind, 2c, see 161d).

We first note how our vision and movement in the world indicates our integration with it. We move about the world by means of our vision. Because we see the world, we can interact with it, relate to it, move around through it. (see 162b.c)

Now, we are not just able to sense the things in the world around us. We can also sense our selves. But there is more. We can notice that we are seeing something. In other words, we can see our selves seeing. (see 162d)

So we move through the world in an integrated way with it. The fact that we are moving around it tells us we are somehow apart from it, but the fact we are always integrated indicates that we are also somehow a part of it. [See this entry from the Phenomenology of Perception for more on our integration with the world. There is the famous example of the walking stick. A stick from a tree might seem like a part of the world that is not a part of us. But when a blind person learns to walk with a stick, she soon begins to be able to actually feel the world with the stick, as if her nerve endings extended through the wood to the farthest side that does the feeling. So in a way, parts the world are parts of us.] [And also note the sympathy our sense organs have with the world. Parts of our ears for example vibrate at the same frequency of the sound wave they are receiving. So we profoundly get in touch with the world around us, and it becomes ambiguous who is the sensor and who is the sensed.]

Visible and mobile, my body is a thing among things; it is one of them. It is caught in the fabric of the world, and its cohesion is that of a thing. But because it moves itself and sees, it holds things in a circle around itself. Things are an annex or prolongation of itself; they are incrusted in its flesh, they are part of its full definition; the world is made of the very stuff of the body. (3c, see 163b)
The body's animation is not the assemblage or juxtaposition of its parts. Nor is it a question of a mind or spirit coming down from somewhere else into an automation— which would still imply that the body itself is without an inside and without a "self." A human body is present when, between the see-er and the visible, between touching and touched, between one eye and the other, between hand and hand a kind of crossover occurs. (4a, see 163d)
Our organs are not instruments; on the contrary, our instruments are added-on organs. Space is not what it was in the Dioptrics, a network of relations between objects such as would be seen by a third party, witnessing my vision, or by a geometer looking over it and reconstructing it from outside. It is, rather, a space reckoned starting from me as the null point or degree zero of spatiality. I do not see it according to its exterior envelope; I live it from the inside; I am immersed in it. (12c, see 178ab)

We in a way are integrated with the things around us by means of our vision. Our body has a certain affinity for them which allows us to see them. They have a sort of 'secret visibility' within us. Painting is faced with the task of depicting this inner secret visibility of the external world, based on our bodily affinity and integration with it.

Once this strange system of exchanges is given, we find before us all the problems of painting. These problems illustrate the enigma of the body, which enigma in turn legitimates them. Since things and my body are made of the same stuff, vision must somehow come about in them; or yet again, their manifest visibility must be repeated in the body by a secret visibility. "Nature is on the inside," says Cézanne. Quality, light, color, depth, which are there before us, are there only because they awaken an echo in our bodies and because the body welcomes them. (4a, see 164a)

When we see things, we take them into us, in a sense. And painters must be very sensitive to how our vision takes in the world. We might even say that it is a matter of letting the world see us, that is, to penetrate us the way our gaze penetrates it. It is like our inhalations are the worlds exhalations [we discussed this metaphor in this entry from Phenomenology of Sensation].

We speak of "inspiration," and the word should be taken literally. There really is inspiration and expiration of Being, respiration in Being, action and passion so slightly discernible that it becomes impossible to distinguish between who sees and who is seen, who paints and what is painted. We say that a human being is born the moment when something that was only virtually visible within the mother's body becomes at once visible for us and for itself. The painter's vision is an ongoing birth. (6c, see 167d)

Mirrors help us see the "metaphysical structure" of our our entwinement with the world. We see an image of ourself. We also sympathize with it. It is as if we doubly feel what we are feeling and what the image is feeling. And the image of us will be seen by others. They too might sympathize with what they see. In this way it is as if we and the world share the same flesh. (see 168a.c)

Let's also note how when we see something, we see a world that is integrated with itself. He offers two excellent examples. The first is Rembrandt's Nightwatch.

The hand pointing toward us in The Nightwatch is truly there only when we see that its shadow on the captain's body presents it simultaneously in profile. The spatiality of the captain lies at the intersection of the two perspectives which are incompossible and yet together. (6a, see 167a)

We might use this example to illustrate another point he made in Phenomenology of Perception about the integration of the parts of the world, how to see the front of an object is also to have on the horizon of our awareness the way that things behind it would be seeing the back side. The Nightwatch example also shows us how when we see something from one perceptive, we see it from all the others, because the way it looks from all the other perspectives influences the way we see it from our own point of view.

Rembrandt. De Nachtwacht (The Night Watch) 1642

(Thanks www.students.sbc.edu)

We see the shadow of the pointing-man's hand cast upon the captain's body. On the one hand, we see what his hand looks like from the front.

Rembrandt. De Nachtwacht (The Night Watch), detail

(Thanks russianpaintings.net)

So far, we might regard the images before us two-dimensionally. However, the shadow shows us the profile of the arm, as if we were at the same time viewing it from the side.

Rembrandt. De Nachtwacht (The Night Watch), detail

(Again, thanks russianpaintings.net)

So we also see how his hand looks from objects standing to his right, all while we look at him from the front. The parts of our world are all coherently interwoven. Another great example is seeing the bottom of a pool. We might think that we are seeing the bottom, even though the water is obscuring it. But in fact, the water is the very reason we can see it. The water is what is letting the light waves through. And when we look to the trees above the pool, we see a reflection of the ripples. The tree has it appearance only because it is integrated with the water motion.

When through the water's thickness I see the tiled bottom of the pool, I do not see it despite the water and the reflections; I see it through them and because of them. If there were no distortions, no ripples of sunlight, if it were without that flesh that I saw the geometry of the tiles, then I would cease to see it as it is and where it is—which is to say, beyond any identical, specific place. I cannot say that the water itself—the aqueous power, the syrupy and shimmering element—is in space; all this is not somewhere else either, but it is not in the pool. It inhabits it, is materialized there, yet it is not contained there; and if I lift my eyes toward the screen of cypresses where the web of reflections plays, I must recognize that the water visits it as well, or at least sends out to it its active, living essence. This inner animation, this radiation of the visible, is what the painter seeks beneath, the words depth, space, and color. (13-14; see 182a.b)

There is something else we noted before in Phenomenology of Perception. Each sense senses things differently. But what they sense is always analogous between the different senses. Our vision has a sense of space. So too does our vision. They are not the same, but the two mesh together in one act of space-perception. Merleau-Ponty in Eye and Mind says something similar. He notes how painters also make good sculptures, for example. This is because what we gain in knowledge of sight translates into knowledge of analogous things in the other senses.

Anyone who thinks about the matter finds it astonishing that very often a good painter can also produce good drawings or good sculpture. Since neither the means of expression nor the creative gestures are comparable, this is proof that there is a system of equivalences, a Logos of lines, of lighting, of colors, of reliefs, of masses—a nonconceptual presentation of universal Being. (15b; see 182c)

So our vision allows us to see things from all perspectives, or at least to have all these other perspectives on the horizon of our awareness. He has us also consider when we look straight down a set of train tracks. They converge on the horizon. But it is only because they converge that we know they remained parallel even at the furthest extent we see. In a way, we are indirectly seeing their being parallel down there by viewing them as convergent from here. So in a sense, when we see the train tracks, we see also something invisible from our perspective, which is their remaining parallel throughout. An invisible absence is given in the visual presence. But we might say there is another sort of invisibility that is given to us. That would be our entwinement with the world, our already being a part of it and enmeshed with it as one flesh.

We must take literally what vision teaches us: namely, that through it we touch the sun and the stars, that we are everywhere at once, and that even our power to imagine ourselves elsewhere—"I am in Petersburg in my bed, in Paris, my eyes see the sun"—or freely to envision real beings, wherever they are, borrows from vision and employs means we owe to it. Vision alone teaches us that beings that are different, "exterior," foreign to one another, are yet absolutely together, are "simultaneity"; which is a mystery psychologists handle the way a child handles explosives. Robert Delaunay says succinctly, "The railroad track is the image of succession which comes closest to the parallel: the parity of the rails." The rails converge and do not converge; they converge in order to remain equidistant farther away. The world is in accordance with my perspective in order to be independent of me, is for me in order to be without me, to be a world. The "visual quale" gives me, and is alone in doing so, the presence of what is not me, of what is simply and fully. It does so because, as a texture, it is the concretion of a universal visibility, of one sole Space that separates and reunites, that sustains every cohesion (and even that of past and future, since there would be no such cohesion if they were not essentially parts of the same space). Every visual something, as individual as it is, functions also as a dimension, because it is given as the result of a dehiscence of Being. What this ultimately means is that the hallmark of the visible is to have a lining of invisibility in the strict sense, which it makes present as a certain absence. (17-18b; see 187a.c)
There is that which reaches the eye head on, the frontal properties of the visible; but there is also that which reaches it from below—the profound postural latency whereby the body raises itself to see—and that which reaches vision from above like the phenomena of flight, of swimming, of movement, where it participates no longer in the heaviness of origins but in free | accomplishments. Through vision, then, the painter touches both extremities. In the immemorial depth of the visible, something has moved, caught fire, which engulfs his body; everything he paints is in answer to this incitement, and his hand is "nothing but the instrument of a distant will." Vision is the meeting, as at a crossroads, of all the aspects of Being. "A certain fire wills to live; it wakes. Working its way along the hand's conductor, it reaches the canvas and invades it; then, a leaping spark, it arcs the gap in the circle it was to trace: the return to the eye, and beyond." There is no break at all in this circuit; it is impossible to say that here nature ends and the human being or expression begins. It is, then, silent Being that itself comes to show forth its own meaning. (18c, see 187-188)

Merleau-Ponty:
Cézanne's Doubt

According to Merleau-Ponty, Cézanne painted things in a distorted way, but this is because he knew how our minds would reconfigure them to have the effect of seeming normal. When we look at something, it is not as though our eyes are photo cameras. Our eyes are constantly shifting. And contextual factors alter the way things look [see this entry for the example of the moon on the horizon.] In a sense, Cézanne paints what we really see and not just what we would see if our eyes were cameras.

This is the reason for his difficulties and for the distortions one finds in his pictures between 1870 and 1890. Cups and saucers on a table seen from the side should be elliptical, but Cezanne paints the two ends of the ellipse swollen and expanded. The work table in his portrait of Gustave Geffroy stretches, contrary to the laws of perspective, into the lower part of picture. In giving up the outline Cezanne was abandoning himself to chaos of sensation, which would upset the objects and constantly suggest illusions, as, for example, the illusion we have when we move our heads that objects themselves are moving—if our judgment did not constantly set these appearances straight. (2; see 13a)
Cezanne did not think he had to choose between feeling and thought, as if he were deciding between chaos and order. He did not want to separate the stable things which we see and the shifting way in which they appear. He wanted to depict matter as it takes on form, the birth of order through spontaneous organization. He makes a basic distinction not between "the senses" and "the understanding" but rather between the spontaneous organization of the things we perceive and the human organization of ideas and sciences. We see things; we agree about them; we are anchored in them; and it is with "nature" as our base that we construct our sciences. Cezanne wanted to paint this primordial world, and his pictures therefore seem to show nature pure, while photographs of the same landscapes suggest man's works, conveniences, and imminent presence. (4a, see 13c.14a)
By remaining faithful to the phenomena in his investigations of perspective, Cezanne discovered what recent psychologists have come to formulate: the lived perspective, that which we actually perceive, is not a geometric or photographic one. The objects we see close at hand appear smaller, those far away seem larger than they do in a photograph. (This is evident in films: an approaching train gets bigger much faster than a real train would under the same circumstances.) To say that a circle seen obliquely is seen as an ellipse is to substitute for our actual perception what we would see if we were cameras: in reality we see a form which oscillates around the ellipse without being an ellipse. In a portrait of Mme Cezanne, the border of the wallpaper on one side of her body does not form a straight line with that on the other: and indeed it is known that if a line passes beneath a wide strip of paper, the two visible segments appear dislocated. Gustave Geffroy's table stretches into the bottom of the picture, and indeed, when our eye runs over a large surface, the images it successively receives are taken from different points of view, and the whole surface is warped. It is true that I freeze these distortions in repainting them on the canvas; I stop the spontaneous movement in which they pile up in perception and tend toward the geometric perspective. (4b, see 14a.c)
Similarly, it is Cezanne's genius that when the overall composition of the picture is seen globally, perspectival distortions are no longer visible in their own right but rather contribute, as they do in natural vision, to impression of an emerging order, an object in the act of appearing, organizing itself before our eyes. In the same way, the contour of an object conceived as a line encircling the object belongs not to the visible we but to geometry. If one outlines the shape of an apple with a continuous line, one makes an object of the shape, whereas the contour is rather ideal limit toward which the sides of the apple recede in depth. Not to indicate any shape would be to deprive the objects of their identity. To trace just a single outline sacrifices depth—that is, the dimension in which the thing is presented not as spread out before us but as an inexhaustible reality full of reserves. That is why Cezanne follows the swell of the object in modulated colors and indicates several outlines in blue. Rebounding among these, one's glance captures a shape that emerges from among them all, just as it does in perception. (4d, see 14-15)
the world is a mass without gaps, a system of colors across which the receding perspective, the outlines, angles, and curves are inscribed like lines of force; the spatial structure vibrates as it is formed. (5a, see 15b)

Cézanne: Still Life with Apples (1890-94)

(Thanks dl.ket.org)

Cézanne. Still Life, Fruit and Pitcher on Table

(Thanks awesome-art.com)

Cézanne: Gustave Geoffrey


(Thanks en.easyart.com)

Cézanne: Portrait of a Woman in Green Hat (Mme Cézanne) (1894-95)


(Thanks www.dl.ket.org)

In other words, things appear to us as dynamically deformed. Just moving a little bit will change how the things in a scene before us appear. But that is how we look at things, by moving our eyes around it. But our mind is able to synthesize all the differences together into a perception of something more organized and seemingly stable. This is what a photograph presents to us, the finished product. But Cézanne's paintings give us the experience of seeing the actual things. He knows that even though they might look deformed when compared to a realistic rendition, they will appear natural. They will appear as if we had Cézanne's eyes while he was in the act of seeing the objects.

So all the different ways the object appears are synthesized coherently and holistically so that we properly perceive their visual features. But also, all our senses are together involved in the sensation. They begin already as integrated.

Cezanne does not try to use color to suggest the tactile sensations which would give shape and depth. These distinctions between touch and sight are unknown in primordial perception. It is only as a result of a science of the human body that we finally learn to distinguish between our senses. The lived object is not rediscovered or constructed on the basis of the contributions of the senses; rather, it presents itself to us from the start as the center from which these contributions radiate. We see the depth, the smoothness, softness, the hardness of objects; Cezanne even claimed that we see the odor. If the painter is to express the world, the arrangement of his colors must bear within this indivisible whole, or else his painting will only hint at things and will not give them in the imperious unity, the presence, insurpassable plenitude which is for us the definition of the real. (5a, see 15c, boldface mine)

Cézanne came before an indeterminate scene where its parts are given together, but in a way that allows us to ignore certain aspects in favor of others. So Cézanne tried to present these aspects as interwoven together. Cézanne called this phenomenally rich scene he painted his motif (we discuss Deleuze's interpretation of Cézanne's motif here.) The painter's job is to produce a recognizable image by means of the synthesis of the scene's parts.

He went to the Louvre every day when he was in Paris. He believed that one must learn how to paint and that the geometric study of planes and forms is a necessary part of this learning process. He inquired about the geological structure of his landscapes, convinced that these abstract relationships, expressed, however, in terms of the visible world, should affect the act of painting. The rules of anatomy and design are present in each stroke of his brush just as the rules of the game underlie each stroke of a tennis match. But what motivates the painter's movement can never be simply perspective or geometry or the laws governing the breakdown of color, or, for that matter, any particular knowledge. Motivating all the movements from which a picture gradually emerges there can be only one thing: the landscape in its totality and in its absolute fullness, precisely what Cezanne called a "motif." He would start by discovering the geological foundations of the landscape; then, according to Mme Cezanne, he would halt and look at everything with widened eyes, "germinating" with the countryside. The task before him was, first, to forget all he had ever learned from science and, second, through these sciences to recapture the structure of the landscape as an emerging organism. To do this, all the partial views one catches sight of must be welded together; all that the eye's versatility disperses must be reunited; one must, as Gasquet put it, "join the wandering hands of nature." "A minute of the world is going by which must be painted in its full reality." His meditation would suddenly be consummated: "I have a hold on my motif," Cezanne would say, and he would explain that the landscape had to be tackled neither too high nor too low, caught alive in a net which would let nothing escape. Then he began to paint all parts of the painting at the same time, using patches of color to surround his original charcoal sketch of the geological skeleton. The picture took on fullness and density; it grew in structure and balance; it came to maturity all at once. "The landscape thinks itself in me," he would say, "and I am its consciousness." Nothing could be farther from naturalism than this intuitive science. Art is not imitation, nor is it something manufactured according to the wishes of instinct or good taste. It is a process of expression. Just as the function of words is to name—that is, to grasp the nature of what appears to us in a confused way and to place it before us as a recognizable object—so it is up to the painter, said Gasquet, to "objectify," "project," and "arrest." [...]
We, forgetting the viscous, equivocal appearances, go through them straight to the things they present. The painter recaptures and converts | into visible objects what would, without him, remain walled up in the separate life of each consciousness: the vibration of appearances which is the cradle of things. (6a.c, see 17a.17d; 17-18)

Cézanne as a painter is sensitive to the way we are visually affected by the world, and his job is not so much to paint the world as much as it is to paint our relation with the world, the way it affects us.

Cezanne's difficulties are those of the first word. He thought himself powerless because he was not omnipotent, because he was not God and wanted nevertheless to portray the world, to change it completely into a spectacle, to make visible how the world touches us. (7d, see 19d)

Consider when we see a new painting that really impresses us. We need look at it in a way we have never looked at something before. It teaches us a new way to see the world. And we learn this new way of seeing through the process of our novel encounter with the work. It somehow simultaneously teaches how to 'read a new text' if you will, by means of the new language of that text which we still need to learn.

It is not enough for a painter like Cezanne, an artist, or a philosopher, to create and express an idea; they must also awaken the experiences which will make their idea take root in the consciousness of others. If a work is successful, it has the strange power of being self-teaching. The reader or spectator, by following the clues of the book or painting, by establishing the concurring points of internal evidence and being brought up short when straying | too far to the left or right, guided by the con-fused clarity of style, will in the end find what was intended to be communicated. The painter can do no more than construct an image; he must wait for this image to come to life for other people. When it does, the work of art will have united these separate lives; it will no longer exist in only one of them like a stubborn dream or a persistent delirium, nor will it exist only in space as a colored piece of canvas. It will dwell undivided in several minds, with a claim on every possible mind like a perennial acquisition. (8a, see 19d)

Merleau-Ponty. "The Eye and Mind." Transl. Carleton Dallery. in The Primacy of Perception and other Essays on Phenomenological Psychology, the Philosophy of Art, History, and Politics. Ed. James M. Edie. Evanston: Northwestern University Press, 1964.

Quotations come from the PDF, obtained very gratefully from Timothy Quigley's course page
http://homepage.newschool.edu/%7Equigleyt/vcs/em-text.pdf

Merleau-Ponty. "Cézanne's Doubt." Transl. Hubert L. Dryfus & Patricia Allen Dreyfus. In Sense and Non-Sense. Chicago: Illinois University Press, 1964.

Quotations from the PDF also obtained with all my gratitude from Robert Innis' course page:
http://faculty.uml.edu/rinnis/cezannedoubt.pdf

Images

Cézanne: Gustave Geoffrey
http://en.easyart.com/canvas-prints/Paul-Cezanne/Gustave-Geffroy-354053.htm

Cézanne: Still Life with Apples (1890-94)
http://www.dl.ket.org/webmuseum/wm/paint/auth/cezanne/sl/apples/index.htm

Cézanne. Still Life, Fruit and Pitcher on Table
http://www.awesome-art.com/awesome/shop/category.aspx?catid=44&page=1&sortby=
(Thanks awesome-art.com)

Cézanne: Portrait of a Woman in Green Hat (Mme Cézanne) (1894-95)
http://www.dl.ket.org/webmuseum/wm/paint/auth/cezanne/portraits/mme/index.htm

Rembrandt's Nightwatch
http://www.russianpaintings.net/doc.vphp?id=753