Complexity Uncategorized

How Structure Leads to Information

The importance of structure in physics and other branches of science cannot be overstated. Stucture is knowledge, structure is understanding. By structure we intend a map, or a graph, which reflects how information travels within a given system. In other words, we looking at the topology of all the interdependencies between the various actors, agents, or simply data channels, which compose or describe a system. Without structure, information cannot flow.

An example of structure is shown below. It has the form of a map. The squares represent agents (or data channels) while the black dots represent the said interdependencies. In general, the map’s structure changes in time as the underlying system evolves.


In the above map there are 29 variables which describe the system in question. If the veriables weren’t interdependent (i.e. there would be no map), the total amount of information contained in the 29 variables would simply be the sum of all the information carried by each variable and given by Shannon’s equation:

Now, complexity, defined as C=f(S; E), not only captures and quantifies the intensity of the dynamic interactions between Structure and Entropy, it also measures the amount of information that is the result of structure. In fact, entropy – the ‘E’ in the complexity equation – is already a measure of information. However, the ‘S’ holds additional information which is ‘contained’ in the structure of the interdependency map. In other words, S encodes additional information to that provided by the Shannon equation. In the example in 29 dimensions shown above the information breakdown is as follows:

  • Shannon’s information (in all 29 channels) = 60.25 bits
  • Information due to structure = 284.80 bits
  • Total information = 345.05 bits

In this example, structure furnishes nearly five times more information than the sum of the information content of each dimension. For higher dimensions the ratio can be significantly higher.

Complexity, therefore, is not just a measure of how intricate, or sophisticated, something is. It has a deeper significance in that it defines the topology of information flow and, therefore, of the processes which make Nature work. In addition, it quantifies the total amount of information within a system, in particular that emanating from the presence of structure.

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!

1 comment on “How Structure Leads to Information

  1. Reblogged this on Calculus of Decay .


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