In the book, the ‘Laws of Form’ first published in 1969 George Spencer Brown creates a connection between the act of drawing a distinction and the creation of form. Any distinction creates three sides, the marked, the unmarked as well as the boundary between the two. Distinctions occur within a space which allows and conditions the distinction. The result of this process is the creation of form. While this notion of the form goes against most western philosophical ideas from Platon, Aristotle, Leibniz, Kant to Husserl (Krämer, 1998) form becomes something that is not timeless, universal or eternal anymore. Rather something that is created by someone at some point from a specific viewpoint. Form is never given but always created. For the form to exist there always needs to be someone who creates the distinction. Form is observation. Creating form is observing, and the four elements are the constitutions of any observation. For this reason, the first sentence of the second chapter in the Laws of Form is an instruction:
“Draw a distinction.”
G. S. Brown, Laws of Form, 1969, p.3
Someone always draws the form of distinction. Without an acting observer, there is no form. The observer creates the boundary, and she chooses the marked and unmarked state. It is always a political act, or as Spencer Brown writes:
“There can be no distinction without motive and there can be no motive unless contents are seen to differ in value.”
G. S. Brown, Laws of Form, 1969, p.1
Two things constitute any distinction. First, there needs to be something to distinguish, some differentiation the observer can make. And secondly a motive by the observer to differentiate in that specific way. For Niklas Luhmann, our environment holds an infinite number of possible differentiation. The number of connectable elements is so vast and allows for so many variations that it is a question of motive how one distinguishes. Any observer continually reduces the complexity of the system by drawing distinctions.
“Erfassung und Reduktion von Komplexität. Sie dienen der Vermittlung zwischen der äußeren Komplexität der Welt und der sehr geringen, aus anthropologischen Gründen kaum veränderbaren Fähigkeit des Menschen zu bewußter Erlebnisverarbeitung.”
Niklas Luhmann, Soziologische Aufklärung 1, 1970, p. 116
For example the word and the object ‘chair’. We reduce each observable object with a seat, back and most probably four legs into the meta-concept of ‘chair’ but in the world, there are only the individual items. We are drawing this distinction around a certain group of common objects. If we include objects without a back or an object with three legs is up to us. Rather than naming each item we draw distinctions by grouping and through this reducing complexity. Each chair itself is also a reduction of complexity as it might consist of wood, metal, screws, textiles, plastic and much more. Each of the named parts of a chair again is a reduction of complexity. This reduction of complexity is the drawing of distinctions, the creation of form. It is an act by an observer, driven by a motive.
This notion of the form connects to Alfred Korzybski’s map-territory relation:
“A map is not the territory it represents, but, if correct, it has a similar structure to the territory, which accounts for its usefulness.”
Alfred Korzybski, Science and Sanity, 1958, p. 58
Any map reduces the complexity of the actual system it represents. But while Korzybski is pledging for usefulness, Spencer Brown is asking for a motive.
Some artists explored this map-territory relationship. For example, Belgian surrealist artist René Magritte conceptualized the distinction throughout a number of paintings most famously in ‘La trahison des images’ (‘The Treachery of Images’). The artwork shows a pipe, below the pipe, Magritte wrote:
“Ceci n’est pas une pipe.”
“This is not a pipe.”
An image of a pipe is not a pipe.
“How people reproached me for it! And yet, could you stuff my pipe? No, it’s just a representation, is it not? So if I had written on my picture ‘This is a pipe’, I’d have been lying!”
Torczyner, Harry. Magritte: Ideas and Images, 1977 p. 71
Within the map/territory logic, we could say the image of the pipe is a map. The text below the picture is a map too. The territory is the real pipe, the stuffable, smokable pipe. The calculus of distinctions would argue all of these are distinctions. ‘Pipes’ are just one categorization one drawn distinction we make. The pipe can refer to briar, calabash, corncob, chibouk, chillum, hookah, kiseru, midwakh or sebsi. Each of these again refers to regional, or specific usages. Pipes are just what we distinguish as a pipe. Is a hookah the territory of Magritte’s pipe? Or are these two distinctions we draw? There is no direct territory to the image of the pipe Magritte drew. It is us differentiating what is included by the word ‘pipe’ and by the image Magritte drew.
In the poem ‘The Hunting of the Snark’ by Lewis Carroll the party is navigating the sea by a map they can all understand. A map that reduced the complexity of the ‘conventional signs’ until it was ‘perfect and absolute blank.’
He had bought a large map representing the sea, Without the least vestige of land: And the crew were much pleased when they found it to be A map they could all understand.
“What’s the good of Mercator’s North Poles and Equators,Tropics, Zones, and Meridian Lines?” So the Bellman would cry: and the crew would reply “They are merely conventional signs!”
“Other maps are such shapes, with their islands and capes! But we’ve got our brave Captain to thank (So the crew would protest) “that he’s bought us the best—A perfect and absolute blank!”
Carroll’s poem is a parody of the reduction of complexity. Reducing the environment until there are no distinctions left. His maps end where the distinction of the form begins (This is not entirely correct as the map already marks directions and a scale outside the map.).
The empty space is where the instruction to draw a distinction starts. What is drawn into the map depends on the motive of the observer. Without drawing a distinction there is no form, without form there is no asymmetry within the space without asymmetry there is no knowledge (Brown, 1969, Lau, 2015). Carroll’s blank map might be a map all can understand as there is nothing to understand. Understanding only arises out of the act of drawing distinctions.
In the short story “Del rigor en laciencia” (“On Exactitude in Science”) Jorge Luis Borges makes the opposite point to Carroll:
“In that Empire, the Art of Cartography attained such Perfection that the map of a single Province occupied the entirety of a City, and the map of the Empire, the entirety of a Province.”
In Borges story, we can see the difference between the map/territory distinction and the notion of the form. The map is seen as an abstraction of the territory, something that is either very close or very reduced and abstracted from it. But there is a territory that the map is imitating abstractly to be useful for the observer. In Brown’s form, the map cannot become like the territory as there always needs to be an observer who draws the distinction which is then drawn on the map. There is no territory without an observer, without someone or something that draws a distinction.
There are even cases in which the territory imitates the map. Mapmakers sometimes add fictional places to their maps as copyright traps for their competition. In the 1930s mapmakers, Otto G. Lindberg and Ernest Alpers combined their initials and added the fictional village named ‘Agloe’ to one of their maps in the in Delaware Country. A few years later one main competitor published a map with an indication for the town Algoe. The mapmakers threatened to sue the competition, but they protested and argued that Agloe exists. The Agloe General Store opened after the intersection became frequently visited because of the map (Jacobs, F., 2014). The map created the territory. While this example is somewhat an extreme example of the map/territory relation, it questions to what extent our own making influences what we observe (‘observer effect’).
Something simple as measuring the length of a coastline shows how observation influences what is meant to be the territory. In the 1960s scientist, Lewis Fry Richardson set out to research the relationship between the length of a common border two countries have and the probability that these two nations go to war. In this process, he found substantial inconsistencies between various sources of international borders. These discrepancies arise out of the way of measurement. The shorter the ruler one uses to measure the longer the resulting coastline.
This first feels counterintuitive but the shorter each measuring unit is, the observer can acknowledge more features within the landscape. As a coastline has features on every scale, the more fine-grained our measures become, the longer the shoreline becomes. The method of observation defines the length of measurement. The fractal structure of something as a coastline means that the analysis determines the extent of it. Our distinctions assess our observations.
“As an explanation of how chance can arise in a world which he regarded as strictly deterministic, Henri Poincare drew attention to insignificant causes which produced very noticeable effects. Sea coasts provide an apt illustration.”
Lewis F. Richardson, “The problem of contiguity: An appendix to Statistic of Deadly Quarrels”, 1961
Within the operation of the form, there are only forms. There is no territory entity which we are trying to imitate in the most useful way. There are only forms drawn by the motives of the observer. In ‘Form, Substance, and Difference’ Gregory Bateson questions the notion of the territory by saying:
“We say the map is different from the territory. But what is the territory? Operationally, somebody went out with a retina or a measuring stick and made representations which were then put on paper. What is on the paper map is a representation of what was in the retinal representation of the man who made the map; and as you push the question back, what you find is an infinite regress, an infinite series of maps. The territory never gets in at all. […]Always, the process of representation will filter it out so that the mental world is only maps of maps, ad infinitum.”
Gregory Bateson, “Form, Substance and Difference,” Steps to an Ecology of Mind, 1972, p.429
Our retina, measuring sticks, sheets of paper are all medium/form relationships that draw distinctions. The map-territory relationship suggests an end, some ground truth at some level.The notion of the form always questions the observation and asks for the two assumptions: Which distinction has been drawn for this specific form and in what medium did this happen? The map is not the territory. There is no territory. There are only maps of maps of maps.
Knowledge, with its roots in ‘acknowledge’ or ‘recognize’ (German: Erkenntniss -> Erkennen) accounts for this. Knowledge always needs someone to recognize. It is an active act, not something given by the world some territory that holds the ground truth. That said Niklas Luhmann makes an important point in his writing ‘Erkenntnis als Konstruktion.’ The operation of the form does not imply that there is no environment (‘Umwelt’), it is just not reachable as there is always a construction of form necessary to create knowledge.
“Wir gehen davon aus, daß alle erkennenden Systeme reale Systeme in einer realen Umwelt sind, mit anderen Worten: daß es sie gibt. Das ist naiv, so wird oft eingewandt. Aber wie anders als naiv soll man anfangen?”
Niklas Luhmann, Erkenntnis als Konstruktion, Aufsätze und Reden, 1988, p.221
The environment does not know any distinctions; it is just what it is. But for us to recognize the environment we need forms to do so. Every observation needs to be done by someone. Without the observer’s distinction, there is no recognition and no knowledge. This means that there is no knowledge in the environment itself. Knowledge is a product of distinction.
But at the same time once we draw distinctions there is feedback from the environment. The environment is not arbitrary otherwise we could draw any distinctions within any medium. Without form, there is no knowledge. Without the environment, everything would be possible.
Bateson, G., 1972. Steps to an Ecology of Mind, University of Chicago Press.
Jacobs, F., 2014. Agloe: How a Completely Made Up New York Town Became Real. bigthink.com. Available at: http://bigthink.com/strange-maps/643-agloe-the-paper-town-stronger-than-fiction [Accessed December 16, 2017].
Korzybski, A., 1958. Science and Sanity, Institute of GS.
Krämer, S., 1998. Form als Vollzug oder: Was gewinnen wir mit Niklas Luhmanns Unterscheidung von Medium und Form? userpage.fu-berlin.de. Available at: http://userpage.fu-berlin.de/~sybkram/media/downloads/Aufsaetze/Form%20als%20Vollzug%201998%20(51).pdf [Accessed October 31, 2017].
Lau, F., 2015. Die Form der Paradoxie,
Luhmann, N., 1988. Erkenntnis als Konstruktion,
Luhmann, N., 1970. Soziologische Aufklärung. In Soziologische Aufklärung 1. Wiesbaden: VS Verlag für Sozialwissenschaften, Wiesbaden, pp. 66–91.
Magritte, R. & Torczyner, H., 1977. Magritte, ideas and images,
Richardson, L.F., Statistics of Deadly Quarrels, 1809-1949. ICPSR Data Holdings.
Spencer Brown, G., Laws of Form. manuelugarte.org. Available at: http://www.manuelugarte.org/modulos/biblioteca/b/G-Spencer-Brown-Laws-of-Form.pdf [Accessed November 15, 2017].