Complexity and How Serious Science Starts When You Begin to Measure

Network with growing number of nodes, edges and complexity. Contemporary “complexity science” is unable to measure its complexity. Surprisingly it doesn’t even try.

Not everything that counts can be measured and not everything that can be measured counts. This variation of a quote by Einstein is often used as an excuse in order to confine things that may be quantified into the realm of the intangible. The act of measurement is not just laborious. It is also risky. The risk stemming from a measurement lies in responsability. The moment you put a number on the table you are being held accountable. This is why some people prefer to talk, chat, speculate, gossip or babble, avoiding concrete verifiable statements. There are certain fields of science in which this is particularly popular.

But beyond the issue of accountability and responsability, without a metric there also lies the faculty of being able to conjure up your own unverifiable “theories” on matters of science. In such a mindless context debating ideas and concepts is like disputing with someone the validity of horoscopes. This is because such “theories” cannot be validated. A theory is something that can be tested by means of an experiment. But without numbers it is difficult to set up an experiment. A theory often produces a theorem, an equation, a characteristic constant. Think of the theory of gravity by Newton. It allows one to measure the force of gravity exerted by a body on another. This means there is an equation. The theory hinges on the gravitational constant, G. The theories of relativity or electromagnetism make use of another known constant, c, the speed of light. There exist experiments which allow us to validate these theories. We could mention experiments by Cavendish, or Michelson-Morley. But when a “theory” does not have a theorem, an equation of some sort or a characteristic constant, it cannot be called a theory. The whole point of science is to build theories which can help understand and explain natural phenomena and this involves the acts of measurement and of classification (ranking). Without a metric, one cannot do serious science. Serious science starts when you begin to measure.

There is one more reason why people stray from a quantitative approach. Coming up with a metric, especially when it comes to new things, is not easy and many people simply have no clue as to how it can be done.

One good example of this new age pop-science is complexity or the so called “complexity science”. Every person I confront on complexity has his own definition – which, evidently, never includes a metric – and his own views on the wonderful properties of complexity. Some people equate complexity to entropy. Some to chaos. Others say complexity is uncertainty. There are those who say complexity is a process of spontaneous self-organization on the edge of chaos. Some even say that complexity cannot be measured. The list is endless. At the end of the day, no good definition, no metric. Clearly, a good definition hints a metric, so if the definition is wrong, you can say goodbye to any quantitative work.

Numerous complexity centers around the world claim to conduct research in complexity. In the majority of cases the research that is performed is, in reality, the investigation of a wide class of (interesting) physical phenomena, in particular those that entail some sort of self-organization, aggregations, or collective behaviour of systems of numerous autonomous agents that cannot be deduced from the properties of a single agent. It is claimed that a system which emerges spontaneously and which exhibits behaviour that cannot be extrapolated from the properties of a single agent, is a complex system. Thus, systems such as:

  • forests (formed of trees)
  • societies (formed of people)
  • markets (formed of companies)
  • galaxies (formed of stars)
  • oceans (formed of water molecules)
  • storms of starlings……

are said to be complex systems. However, if one studies nature (i.e. physics) one realizes that everything in the Universe, at all scales, forms spontaneously from numerous smaller building blocks and without any external choreography (except that of the laws of physics). Therefore, according to this “definition”, eveything in Nature is a complex system. What advantange emerges from adding a new name to classes of well known physical phenomena is unclear. It is like saying that zoology is the study of non-human animals. Yeah, sure, so what?

However, if by studying, for example, ants, storms of starlings or other ensembles of autonomous (or not so autonomous) agents one still wants to claim that he is doing “complexity science”, this is the way it could be done:

  • Measure the complexity of a single agent
  • See how this maps onto the complexity of the system of agents. This means measuring this complexity, of course.
  • Measure the critical (maximum) complexity of each agent and see how it maps onto the critical complexity of the system.
  • Establish a relationship between the complexity of a single agent, number of agents and the complexity of the system of agents.
  • Extract modes of functioning of the system. Establish the most likely modes of functioning and their complexity.
  • Measure the resilience of the systsme of agents as a function of the complexity of each agent.
  • etc.

These are the sorts of things we at Ontonix do with proteins, investment portfolios, computer chips, market sectors or software on a car. Do you?

When you measure you make a giant leap – from opinions to science.

By the way, our Quantitative Complexity Theory does have equations. One is this:

PS. If you have a real theory, i.e. one which can be verified (or falsified) on empirical grounds, it already is quantitative. This means that “Quantitative” in “Quantitative Complexity Theory” is redundant. The reason we call our theory quantitative is simply to separate ourselves from the “qualitative” mainstream “complexity science”.

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!

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