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Tautology: Not Always Bad

A common criticism made against general system principles is that they are tautologous. Tautology is a concept from the study of logic and refers to statements that are trivial or circular, such as 2 = 2. Such a formula is true and cannot be disproved, but it is useless.

Tautology is considered something bad, and when a logician or philosopher calls something tautologous, this is usually a devastating criticism. Some would say general system patterns are tautologous and therefore trivial.

To which I would say, tautologous, maybe; trivial, no.

Each general system principle expresses an inevitability. Most of the general system principles must be true, because they analyze a behavior of a system that can occur in no other way.

There can be no goal pursuit without negative feedback, no stability without equilibrium and equifinality, and so forth. What I have been calling general system principles are the patterns discovered to underlie those behaviors in systems.

For example, if we ask, "How does this system produce goal-directed beha­vior?" we have already observed a system moving toward a goal. No surprise, then, that the system has mechanisms to reduce deviations from a goal state.

An actively goal-seeking system must sense the goal, so it needs sensors. It must reduce the distance between the system's current state and the goal state, so it needs effectors.

It needs to pass information between sensors and effectors, so it needs feedback. Hence it is inevitable that sensors, effectors, and feedback to reduce deviations from a goal will all be found in a system showing goal-directed behavior.

However, this is not a trivial insight. It shows us how to build intelligent systems, such as guided missiles, or problem-solving algorithms, or computers.

Something similar can be said about all the general system principles. Each is expressing a tautology, or as I prefer to say, an inevitability.

The presence of deviation-reducing feedback in a system is not suggested by the existence of goal-pursuit, it is the same thing as goal pursuit. If negative feedback is not present, goal-pursuit cannot happen.

If you see creativity, look for the variation with selective retention pattern. It will always be there. But, as a famous Italian architect said, God is in the details.

An investigator must fill in the specifics for each particular system. In cases of creativity, the generative process (the process of generating variations) is different for every system. There is no general system principle that will tell you how variations are generated in a particular system.

You are still better off knowing that something must be producing variations somewhere, if the system is showing creativity. Similarly, there must be some process selecting which of those variants to keep or replicate or propagate.

Explaining creativity in any system will inevitably involve figuring out how combinations are produced and selected. Again, that is inevitable, if you analyze what we mean by creativity, but it is not a trivial insight.

Identifying a general system pattern does not end an inquiry; it begins an inquiry. It gives a template for analysis and/or repair or construction. As you can see from examples in this toolkit, contemporary science research can be quite complicated in how it interweaves system principles.

But that is inevitable, too. Anything easy and obvious has already been discov­ered. Of course examples appearing in science journals are challenging. Otherwise they would not merit publication.

The general system principles described in this toolkit seem easy and obvious to experts. No evolutionary biologist doubts that variation and selective retention is involved in the evolutionary history of organisms, nor do they spend time thinking about such an obvious point.

A beginning student is in a different position. He or she might find it eye-opening (for example) that all creative processes show the same underlying pattern.

The same is true of other general system principles. They are often a revelation to beginners because they illuminate how certain processes must take place, to produce certain effects. Got oscillations? Look for opposing forces (and so forth).

In effect, knowledge of general system principles is part of scientific literacy. Most scientists never study General Systems as such; they just learn the patterns in the process of studying about specific systems in their specialty areas.

Is there no end to general system principles?

I identified 21 of the most useful general system principles I could think of, in this toolkit, but you could argue that there is potentially no end to general system principles. In a sense, mathematics is the ultimate general systems approach, and there is no end to mathematical formulas.

Any mathematical equation expresses a pattern of relationships between ele­ments. If the same mathematics can be used to describe systems of different content, it can be treated like a general system principle, sometimes a very odd or specialized one.

One of my favorite examples was the cover story of the November, 2010 issue of Science. It was titled, "How cats lap: Water uptake by Felis Catus."

The authors (Reis, Jung, Aristoff, and Stocker, 2010) described how cats lap up liquids with the back of the tongue, forming a little column that seems to defy gravity. They add:

The lapping of F. catus is part of a wider class of problems in biology involving gravity and inertia, some­times referred to as Froude mechanisms. For example, the water-running ability of the Basilisk lizard depends on the gravity-driven collapse of the air cavity it creates upon slapping the surface of the water with its feet...

The Froude number is also relevant to swimming, for example, setting the maximum practical swimming speed in ducks... it is interesting to note that [in horses] the transition from trot to gallop obeys nearly the same scaling of a frequency with mass as lapping [and they give the function] (Reis, Jung, Aristoff, and Stocker, 2010, p.1234)

So: the same mathematical function captures unique systems-level behavior of (1) a cat lapping water, (2) the maximum swimming speed of ducks, (3) a horse transitioning from a trot to a gallop, and (4) how a Basilisk lizard runs over water.

Basilisk lizard running on water
A Basilisk lizard calculating Froude numbers.

Who would have thought four such diverse phenomena had an underlying similarity? Yet this pattern, the Froude number (or Froude mechanism) has a name and is apparently well known to research biologists, although new to me. How many more such patterns could exist in the world?

Is Everything Math?

Mathematical relationships are com­pletely abstract. They are not "about" any particular system. But they can be applied to any system if they fit.

That suggests that any mathematical formula, if it is useful or interesting, could be construed as a quote-unquote system principle. It unites the analysis of two or more systems that differ in their specifics.

Mathematical models are highly desir­able for analyzing a system, because they are clear and unambiguous. They allow specific predictions about the behavior of a system, making it possible to test a model scientifically.

Something like that happened with Clark Hull's theory in the study of motivational psychology. For a time Hull had the leading theory of motivation.

Hull's theory was respected in part because he used formulas to make non-trivial predictions within the context of a very limited experimental para­digm: running Norway rats through mazes. Hull was a role model for using a precise, falsifiable model.

His theory was falsified. The specific behavioral predictions it made were not confirmed. No amount of adjustment made the model work. By the late 1960s it was abandoned.

How tragic, you say. No, it was good, for the same reason replication failures are ultimately good for science. This was error-correction in action. Not all scientific theories are valid, and if they are specified with mathematical models, it is much easier to test them.

Every principle outlined in this toolkit is non-mathematical as presented, but math lurks right over the horizon. We discussed oscillation in a way that was non-mathematical, but particular oscillating systems are described precisely with equations.

The other side of the coin is that mathematical explanations of general system principles can be opaque compared to verbal explanations. Anatol Rapoport (2009) gave a mathematical version of Bertalanffy's equifinality concept that was just a list of differential equations.

Compare that to the clarity of a marble rolling to the bottom of a bowl, and you understand the superiority of verbal descriptions in certain situations. Rapoport's equations would not have succeeded in giving most students an understanding of equifinality or the ability to recognize the implications of equifinality in novel systems, but a simple verbal explanation can do that.

You could argue that verbal explanations of physical systems are opportunistically borrowing from our hard-earned knowledge of everyday physics, built up since babyhood by interacting with the world. I would say that is true, but it is a good form of opportunism. Call it "implicit math."

How do you express negative feedback or variation with selective retention in mathematics? I am sure it is possible with the right formalisms, but language is presently a better tool for explaining those concepts to beginners.

A Proliferation of Principles?

As an example of how system principles can proliferate, consider the Principia Cybernetica Project (Hoylighen, Joslyn & Turchin, 1991). This was conceived as a super network of systems experts communicating over the internet who would assemble a list of cybernetic principles very similar to the system principles in this toolkit.

The group received enthusiastic and approving comments from some of the luminaries mentioned here, such as Herbert Simon and Donald T. Campbell. The early PCP writings had a zealous and euphoric quality, as if the participants were looking forward to the construction of the Encyclopedia Galactica (a repository of all human knowledge, invented by science fiction writer Isaac Asimov for his Foundation Trilogy).

As it turned out, Wikipedia is the Encyclopedia Galactica. The Principia Cybernetica Project floundered. When I checked, their web page had not been updated since 2003.

They made a stab at listing all conceiv­able system principles, but many seemed useless. They came up with patterns like the "Law of Requisite Variety" which states that "The larger the variety of actions available to a control system, the larger the variety of perturb­ations it is able to compensate."

I had to think about that one for a while. An example, I suppose, would be the adaptability of a musician receiving requests for different types of music. The larger your repertoire of musical skills, the more likely you are to handle a challenge thrown at you, such as "Play the melody of Three Blind Mice in bebop jazz style."

Like all the system principles, it is tautologous or inevitably true. Of course a system with more "varieties of action" will do better in facing novel challenges.

That's like saying, "People who are more flexible can bend better." Whether the Law of Requisite Variety could prove useful is another matter.

How I Learned to Love the Law of Requisite Variety

That was where the matter stood with me, until I came across an article about resistance to pests in tropical jungles (Coley & Kursar, 2014). They explained that jungles are strange because, despite being relatively uniform ecosystems, they contain an astonishing diversity of plant species. (That constitutes a puzzle to be solved, for a scientist.)

"One hector of rainforest contains more species than all of Canada and the continental United States." Coley and Kursar were able to show that greater variety enables the jungle to withstand a larger variety of pests.

It is the law of requisite variety! In this case, the control system is the jungle ecosystem, and actions are different species, so it is like conceiving of the jungle as a system that promotes living things (a fair definition of an ecosystem).

The actions of this ecosystem are any changes in the environment or the behaviors of its living things. Parasites and predators are perturbations to that system, because they kill living things. Once you make those substitutions, the law of requisite variety applies to ecosystems.

Pondering that made me realize the same pattern occurs in genetics. The textbook explanation for biparental origins (having two parents rather than cloning) is the same as Coley and Kursar's explanation for species variety in the jungle. Having two parents increases genetic variability, and that increases resistance to parasites and diseases in a population.

With greater variability, at least a few members of a family or a group or a species are more likely to survive a disease epidemic or other attack from parasites or predators. Hence the property of having two parents is very widespread in the animal kingdom, with cloning used only by a few species in highly protected environments like caves.

Horticulturists know the dangers of monoculture (planting all the same species) because it creates vulnerability to disease. Widespread cultivation of cotton created an opportunity for the boll weevil in America. Over-dependence on one species of potato led to vulnerability to disease and famine in Ireland.

On the North American continent, elm trees and chestnut trees and now pine trees have fallen in large numbers to specialized predators, as each was (apparently) too abundant on the North American continent, with not enough genetic variation. This provided an opportunity for specialized pests.

Had there been a greater genetic variation, these epidemics (targeting particular tree species) would not have been so devastating. Again: variety is better for fighting off parasites and evading predators.

Then there is the human immune system. The dirty world hypothesis suggests that loading up with antigens (things that might provoke an immune response) creates a stronger and more resilient immune system.

That is the reason children who grow up on farms do not get asthma nearly as often as children who grow up in modern apartment buildings. The farm children are exposed to more immune chal­lenges, and their immune systems are able to deal with a greater variety of attacks without the damaging over-reactions called allergies.

Research into the microbiome, the bacterial population of the gut, is likely to reveal the same thing. It changes in response to diet, and (do you think?) researchers will probably find that a greater variety of gut bacteria promotes our ability to fight off parasites and diseases and miscellaneous gastro­intestinal problems.

Gradually the "law of requisite variety" has been transformed, in my mind at least, into a truly useful principle. All the examples I have cited are from biology, but the principle can also apply to non-biological systems.

If your computer has many ways to fight off threatening viruses and malware (quarantining it, deleting it, calling up the last functioning configuration after the computer crashes, restoring from a backup image) your computer is more likely to be restored to health after a malware or virus attack. It is the law of requisite variety again.

So the law of requisite variety is actually quite useful. I had not realized it because of the abstract and pedantic way the principle was presented on the Principia Cybernetica web site. They included no examples, when they should have included three.

Perhaps another general principle lurks here. "Do not judge the utility of a conceptual tool until you have learned to use it and practiced with it."


Rapoport, A. (2009) General Systems Theory. In Parra-Luna, F. (2009) Systems Science and Cybernetics, Volume 1. Oxford, UK: Eolss Publishers. pp.112-135.

Reis, Jung, Aristoff, and Stocker (2010) "How cat's lap: Water uptake by Felis Catus." Science, 26, 1231-1234. doi:10.1126/science.1195421

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