5 Jan 2017

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


by Corry Shores


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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]


3.3 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.







[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.]




[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)




[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)



[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)




[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).



[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).




[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:





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