## Tuesday, 9 July 2013

### What is Critical Complexity?

 What is critical complexity? Let's start with the basics. Information can be arranged into sets of rules. When these rules are related to each other they may be organized into graphs or maps, such as the one illustrated below. Each of the red dots represents a relationship between two parameters (nodes). An example of rule (from the above map, see top): "if UNEMPLOYMENT increases then NEW HOUSE CONSTRUCTION decreases". This is an example of a fuzzy rule - no numbers just a global trend. Rules can be more or less fuzzy, like in the example below, where two rules are represented by scatter plots - a collection of data samples (pairs) which ultimately produce the rule. On the left you can see a fairly crisp rule, while on the right a more fuzzy one. You can of course increase the fuzziness of a rule until it becomes so fuzzy that it no longer provides any useful information. Suppose in fact that in the above map all the rules are made so fuzzy that they are all about to break up. At that point, compute the complexity of the system - the value which you obtain is that of critical complexity. This is what OntoSpace allows you to do. What makes information fuzzy and less precise is noise and, in general, uncertainty. A great way to illustrate the concept is by analyzing, for example, a simple phrase, such as this: This is an example of a simple phrase which is used to illustrate the concept of critical complexity. Let’s introduce a few spelling mistakes: Thos is a n exrmple of a simpcle phrqse whih  I s us ed to illuxtrate the concyept of critizal com plexiuy. Let us introduce more errors – with some imagination the phrase is still readable (especially if you happen to know the original phrase): Tais xs a n exreple  zf a sempcle phrqee waih I s vs ed eo illuxtkate the concyevt of crstrzal ctm plexihuy. An even more: Taiq xs a n exrepye  zf d semicle pcrqee raih I s vs ed eo ilnuxtkare the cmncyevt tf crstrzaf ctm plsxihuy. This last phrase is unreadable. All of the original information has been lost. We could say that the phrase before this last one was critically complex - adding a small dose of uncertainty (spelling mistakes) would destroy its structure. Systems which are on the verge of losing their structure simply because one sprinkles a little bit of noise or uncertainty on top are fragile - they collapse with no early warning. This is precisely why in the case of very large or critical systems or infrastructures, such as multi-national corporations, markets, systems of banks or telecommunication and traffic networks, it is paramount to know how complex they are and how close to their own critical complexity they happen to function. If you do know how complex your business is, and how far from criticality it finds itself functioning, you have a great early-warning system.Today it is easy to know if a business functions close to its own critical complexity and if it is fragile. You may do this on-line here.