Tuesday, 2 July 2013

No Measurement No Science


Can there exist a science, any branch of science, that doesn't measure the object of its investigation? Imagine physics with no measurements. Imagine the laws of gravity or the laws of Newton without measuring the mass or acceleration of bodies. Imagine doctors trying to lower cholesterol without ever measuring it. The evolution of science is man's struggle to invent new ways of measuring and inventing metrics, to come up with ingenious means of squeezing more precision and accuracy. Recall the experiments of Cavendish or Michelson-Moreley which provided us with values of the Gravitational Constant and speed of light. What would modern cosmology be without Hubble's constant?

The act of measurement is not only an act of courage, it is also when science gets serious. The rational practice of measurement, classification and ranking of objects or phenomena constitute first step towards scientific activity. Science has the scope of establishing theories which can help explain natural phenomena and understand Nature. Measurements, provide ideas, insights, these in turn suggest conjectures which may end up one day as established theories (until a better theory is proposed).

But when can you actually call something a theory? People often use the expression "I have a theory" about this or that. However, from a strict and scientific point of view, a theory is something that can be verified (or falsified) via an appropriately designed and repeatable experiment that can be performed by an independent team of scientists. Once a theory has been established and accepted, it typically produces:

  • a law, or a fundamental theorem (or series of theorems)
  • a characteristic constant (G, h, c, etc.)
  • a basic equation (or equations)

Consider now the so-called "complexity science" which has been around now for a few decades. It has produced none of the above: no characteristic constant, no equations, no laws. What is most disconcerting, it has never produced a workable definition of complexity, not to mention a measure. Scientists engage in long disquisitions as to complexity and its mysterious properties, they even say that something is more complex than something else, and yet, without ever measuring complexity. How is that possible? Can we call this science? Certainly not.

One of the objects of "complexity science" are storms of birds, typically starlings, which every now and then get together by the thousands and offer elegant and breathtaking displays of their ability to avoid collisions and, at the same time, to give rise to beautiful and organized shapes. All this is done without a master choreographer, spontaneously. Complexity scientists say, in awe, "now that is a complex system". How they come to that conclusion is a bit of a mystery. The surprising thing is that they are never curious as to how complex that thing really is. Well, we are. We have measured the complexity of storms of starlings. In particular, we have analyzed four scenarios originating from the same storm. 

Scenario 1
Scenario 2
Scenario 3
Scenario 4

Here are the results, with the corresponding Complexity Maps. Your intuition may be challenged.

Scenario 1: Complexity = 121.5
Scenario 2: Complexity = 230.4
Scenario 3: Complexity = 269.1
Scenario 4: Complexity = 128.6

It may not be a result of any particular practical use. Today. However, the above is a small piece of modern complexity science.