Complexity Engineering

How Complex are Formations of Starlings?


There is a tendency to regard the phrase “the whole is greater than the sum of the parts” as a (sort of) definition of “complex systems” by those who claim to “study complexity”. Curiously enough, the said “complexity scientists” engage in an exercise which, inexplicably, does not contemplate a measure of the object of their studies, namely complexity. Imagine a sprinter who doesn’t measure his 100 meters performance. Imagine a doctor who wants to lower a patient’s blood pressure but does not measure it. Imagine a weight loss expert who doesn’t resort to a scale. Well, contemporary “complexity scientists” study complexity by never measuring it. Unbelievably, they don’t even possess the curiosity to do it. Science and lack of curiosity don’t go hand in hand….

Once you develop a measure of complexity, and when you apply it to thousands of systems – natural or man made – you realize that in the Universe there exists systems which are very complex, moderately complex and not so complex. The same may be said of mass, energy, momentum, current, etc., etc. Things get interesting once you discover the existence of critical complexity – a physiological upper bound on the complexity any given system may attain. Then you realize that, just like most things in life, complexity is a relative measure.

Starlings are known to form beautiful patterns in the sky – known as starling murmurations – and “complexity scientists” claim that they form a “complex system” because the behavior of the entire formation cannot be deduced by studying a single starling. Amazingly, all things in nature are formed by smaller building blocks that don’t anticipate the dynamics of an agglomeration thereof – think of water, galaxies, societies, the human body, a car or a computer. So, according to this “definition” all things in the Universe are “complex systems”. A useless tautology. Pop science.

Since we believe that serious science starts when you begin to measure, we have measured the complexity of four starling formations. These are shown below.

In each case we have measured the complexity of each formation by computing the complexity of each image. The charts below represent the corresponding complexity maps, where one may find the said measure of complexity.

As may be observed, complexity ranges from 121 to nearly 270. It is curious to observe how no formation gets even close to its critical complexity, in which case the formation would be on the verge of breaking up.

PS. There are numerous systems which are lesser than the sum of the parts and these too can be pretty complex.

Established originally in 2005 in the USA, Ontonix is a technology company headquartered in Como, Italy. The unusual technology and solutions developed by Ontonix focus on countering what most threatens safety, advanced products, critical infrastructures, or IT network security - the rapid growth of complexity. In 2007 the company received recognition by being selected as Gartner's Cool Vendor. What makes Ontonix different from all those companies and research centers who claim to manage complexity is that we have a complexity metric. This means that we MEASURE complexity. We detect anomalies in complex defense systems without using Machine Learning for one very good reason: our clients don’t have the luxury of multiple examples of failures necessary to teach software to recognize them. We identify anomalies without having seen them before. Sometimes, you must get it right the first and only time!

2 comments on “How Complex are Formations of Starlings?

  1. Ajay Kumar

    Very good concept and explanation. But these formation of starlings are in 3D space. So complexity of a 2D image may not be the sufficient , to find out the complexity of the formation.

    Liked by 1 person

    • True, but the goal here was to show the difference between doing science having a metric or not having one at all. A 3D formation can be analyzed using two or more cameras, located in different positions, and then analyzing sequences od 2D images. we have software for that. It is called OntoView and there is a recent blog about it.


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