Entropy Order and Disorder

The Last Question Entropy Quote by Isaac Asimov


Arieh Ben-Naim, author of Discover Entropy and the Second Law of Thermodynamics, A Playful Way of Discovering a Law of Nature (2010), refers that entropy as a concept was born in the late 18th and 19th centuries with engineers like Nicolas Leonard Sadi Carnot (1796–1832), William Thomson (1824–1907) and Kelvin with the first ideas on the Second Law of thermodynamics.

These engineers studied efficiency in energy and concluded that energy couldn’t be fully converted into useful work. Rudolf Clausius (1822–1888) researched the flow of energy from” a colder to a hotter body”, introducing the term ‘Entropy’ and creating a new law of “the ever-increasing entropy, or the Second Law of thermodynamics” (p.5).

Arieh Ben-Naim refers that experiments with energy reveal that entropy can be seen, for instance in boiling water. Water when heated, multiplicates the interactions of atoms, creating chaos (p.5). This idea of Entropy, however, has been somehow always present throughout the human history and Art (p.2).

Heat transfer from hot to
 a cold body
Figure 1: Reconstruction of the figure 1.3 from the book Discover Entropy and the Second Law of Thermodynamics, A Playful Way of Discovering a Law of Nature (Arieh Ben-Naim, 2010, p.5) of spontaneous processes. (a) Heat transfer from hot to
a cold body. (b) Expansion of a gas. (c) Mixing of two gasses.

Entropy happens in constraints

Entropy happens in constraints that keep a system stable. Constraints or tension reduction, as Arnheim names it, the author of Entropy and Art, An Essay on Disorder and Order (1971, 2001), promote order in a structural theme where forces and interplay happen with destruction (entropy) of elements that don’t work or are unable to adapt. The result is “unity in variety” from a “less probable to a more probable distribution of matter” (pp.30-42).

It’s a balancing act of self-regulation until a maximum level of Entropy is achieved for a particular system of constraints or conditions. The result is a new shape that is stable in those conditions until the process starts again if the constraints change or any internal or external force puts pressure on that system. Arieh Ben-Naim agrees that temperature can increase indefinitely but also mentions an order of events that must take place giving the example of a glass of water that when added a few ice cubes gets colder and always occur in this order of events. So by knowing the initial conditions and forces acting at a particular stage we could “predict the outcome at any given time” (p.10).

Entropy in “order” and “disorder” and the most probable

Probability goes hands with entropy. The physicist, Ludwig Boltzmann (1844–1906) introduces this concept of probability to entropy, by explaining that a state is initially “ordered — therefore very improbable” but “when left to itself it rapidly proceeds to the disordered most probable state” (p.13).

The order is important because it is necessary for an understanding of any concept, layout, landscape, painting, and music, making it “possible to focus on what is alike and what is different, what belongs together and what is segregated” (p.1).

An order is important to make anything work since our own body can only work if it is at least assembled in a minimum physical order. “Order is a prerequisite of survival; therefore the impulse to produce orderly arrangements is inbred by evolution” (p.4).

Rudolf Arnheim gives the example of some experiments that demonstrate how the human mind can see more quickly a combination of square and circle than the three units of figure 2 by organising elements and creating the most simple structure possible. What we are referring here is the gestalt law of “simple structure in psychology” (p.5) that “approaches the importance
of the order.

Disorder and Order figures
Figure 2: Reconstruction of square and circle from figure 2.1 of the book Entropy and Art, An Essay on Disorder and Order (Rudolf Arnheim, 1971, 2001, p.5).

Randomness is order – less probable to a more probable state

This state of order, however, moves towards an ever-increasing state of maximal disorder (p.7). Energy can then be changed from one form to another but it is not created or destroyed. Rudolf Arnheim refers Max Planck for a “principle of increase of entropy” (p.7), but entropy is only possible without the disorder. Entropy needs order in the first place. So this is a paradox.

So Arnheim focusing in this paradox refers Lancelot L. Whyte that asked the following: “What is the relation of the two cosmic tendencies: towards mechanical disorder (entropy principle) and towards geometrical order (in crystals, molecules, organisms, etc.)?” (p.9).

The relation is an intentional one. Arnheim gives the example of the process of shuffling cards that have the intention of creating order (give players an ordered number of cards) from creating disorder in the first place (shuffling). Arnheim concludes that shuffling is another principle of entropy by creating an “equal distribution” that prevails from a “sequence” (p.12).

We can then conclude that it is possible to find order in disorder as an “improbable arrangement of elements” (p.13). Randomness is ordered. Arnheim clarifies this statement by adding that in the transmission of information we are inducing an order, and therefore the less predictable events will have more information because they live in chaos and we are unable to predict what will happen next due to an enormous amount of information. What we are seeing here is
a less probable to a more probable state, where entropy increases.

Entropy and the whole

Entropy theory is the first attempt to deal with global form and conditions by saying that any element will be affected by several conditions and forces and it meant, therefore “a break with the century-old procedure of accounting for a whole by establishing the relations among its smallest parts” (p.18). The parts are not static, but constantly interacting. So Entropy predicts a steady increase in closed systems since irregular ones are more frequent than regular ones, “shuffling will increase irregularity until it reaches its maximum” (p18). Arnheim gives the example of the work of Jackson Pollock’s paintings and Jean Arp to explain this chaos
and order working together.

Figure 3: Jackson Pollock
Figure 4: Jackson Pollock She-Wolf 1943
Figure 5: The Crucified Walter Quirt 1943 Oil on Canvas 30×50 inches

In fact, the Abstract Expressionism work of Jackson Pollock’s paintings “of the late 1940’s, show a random distribution of sprinkled and splashed pigment controlled by the artist’s sense of visual order”. In the same way, Jean Arp experiments with the “laws of chance” by using shapes that fall on a surface and creates a set of wood reliefs in 1942, named Three Constellations of Same Forms, creating a visual interpretation of a chance effect.

But geometry and “perfect” objects, however, do not “give the visual effect of randomness” (p.21). Arnheim mentions that physicists know that an “increase of entropy often leads to a state of equilibrium” (p.21). But equilibrium is the opposite of disorder where the forces compensate each other, like a scale.

Figure 6: “Jean Arp. Three Constellations of Same Forms. Triptych”. Entropy and
Art, An Essay on Disorder and Order (Rudolf Arnheim, 1971, 2001, p.20)


Equilibrium implies standstill, no more action, expect if it comes from an external source and represents the simplest structure. When a particular system grows or changes its complexity will demand a new order and a process of transition where shape develops for the optimal function and the best “spatial solution for the given organisation”. During this transition, the incomplete elements create tensions to obtain a potential order as objective. This process of transition is ignored in Entropy since entropy only considers one state or the other.

One of them is the principle of tension reduction or of decreasing potential energy. Gestalt theory has this principle as a favourite, the tendency toward simplicity, symmetry, regularity or as Kohler has called it the Law of Dynamic Direction directed to obtain the maximum of orderliness under the given conditions of a system. This system, however, cannot function without the free interaction of forces and is therefore limited by the constraints of the system itself.

Figure 7: Reconstruction of figure 10.2 of the book Entropy and Art, An Essay on
Disorder and Order (Rudolf Arnheim, 1971, 2001).
“Entropy versus Structural (geometrical) Order” (p.30).

The destruction of shape – the catabolic effect

Arnheim gives the example of the water container that has two unequal portions of water that when taken out of the container are free to attain an equilibrium. Those constraints accordingly to Arnheim is the hand of man or natural elements like crumbling and rusting, erosion or friction. Any removal of constraints will broaden the range of its efficiency. But is this so? For instance, if we remove laws, culture even, religion, will we increase the probability of efficiency? Arnheim names this as the “destruction of shape the catabolic effect” (p.23).

The virtue of Constraints

Constraints “freeze the constellation and keep it stable” (p.25). Arnheim gives the example of an imperfect square that underdim light is still perceived as regular and insists that disorder can actually be perceived as order by being randomly homogeneous, but at a higher cost of loss of precious information. Like a Poussin painting that if blurred might bring out shapes in a more efficient process and with time economy and the use of fewer materials, actions, and energy but “its order will be at a lower, less valuable level” (p.26). So Arnheim concludes “that the tendency to tension reduction by simplication describes order incompletely. Tension reduction promotes orderliness; but orderliness is only one aspect of order” (p.27).

Anabolic tendency

Arnheim explains that anabolic tendency is the “shape-building cosmic principle” (p.27) or how thermodynamics refers negative entropy by being the structural a theme of a pattern, which creates order by interaction with the tendency to tension reduction.

Arnheim refers the Thomson’s experiment where small magnets in a bowl of oil play antagonistic forces, the structural theme, leading to the most simple and stable arrangement possible ( the best symmetric new shape possible), under the physical circumstances of a particular case. The atomic model, crystals and unicellular radiolaria are given as examples of this natural process.

Figure 8: Atomic orbitals of a neon atom
https://en.wikipedia.org/wiki/Atomic_theory, 17th June 2016, 22:25 p.m.
Figure 9: Unicellular radiolaria. The unicellular radiolaria in entropy really interested me and since then I started to research the possibility of printing a new object or creating digital art based on this research.
sets/kinematics/, 17th June 2016,
22:35 p.m.
process/, 17th June 2016, 22:43 p.m.

The Structural Theme

So the structural theme balances elements such as size, distance, direction, curvature, volume and each one as its own appropriate form. They react to each other and establish an order by using opponent forces but they are contained in each other and incapable or creating a change in the interrelation. They create a stable structure. They are a balancing act, a standstill of self-regulation. This balance means that the maximum level of entropy was reached for a particular system of constraints. Arnheim gives the example of Art, the body and the brain, society, and machine. They are self-regulatory, an ongoing play with forces, that the Artist himself is submitted to. In Art, this process is a purely mental process, an ongoing and active process of communication and mental reasoning with the material. Entropy is not the simply disorder, it moves towards order.

Arnheim concludes a relation between two tendencies, one towards a mechanical disorder (entropy) and another towards a geometrical order (in crystals, molecules, organisms, etc.). This order results from patterns of forces and the interplay of a structural theme, “brought about by the anabolic tendency” (p.30) which strives toward tension reduction and thereby attains the simplicity of orderliness. So with Arnheim, the entropy principle is not a full tendency towards disorder because of the catabolic process that moves from a “less probable to a more probable distribution of matter” (p.30). In fact, Arnheim agrees, by referring the Kohler’s Law of Entropy (Entropy and Art an Essay on Disorder and Order) or Dynamic Direction, entropy moves toward order by reducing tension and not by degrading energy. Entropy organizes energy according to the simplest, most balanced structure available to a system. So in fact what we are talking about, more than entropy is a Theory of Order.


Get in Touch

St.Ives, Cambridgeshire
07523134255 | estrelaestela@icloud.com

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