Scheduled post no.4:

• What is complexity?

In the year 2016, the World Economic Forum released a comparative chart of the 10 topmost skills of 2015 and 2020: https://www.researchgate.net/figure/Top-10-Skills-in-2015-2020-Source-World-Economic-Forum_fig1_323994818

While there is some shuffling of the rank number of some skills ( critical thinking has moved from no.4 in 2015 to no.2 in 2020, and creativity has shot up from no.10 in 2015 to no.3 in 2020, and some new skills are listed for 2020, in both the lists at the top we have “ complex problem solving”. If we want to be future ready or future fit as the Prime Minister exhorted in his convocation address at IIT Guwahati, acquiring the skill of complex problem solving may be the most important one.

It is well accepted that solvable problems may be classified into four distinct types: Simple, Complicated, Complex, and Chaotic. It turns out that you can neatly put almost every problem we face into one of these types, and each type requires quite a different strategy.

Simple problems are solved just by following the rules — there’s only one solution and it’s well known. Complicated domains are ones where the rules are known and predictable — but the rules are significant and cannot be instinctively understood without some training. Complex domains, though, are ones that cross multiple domains and one can’t predict whether a change in one part might affect another. And finally, chaotic domains are where, even when witnessing a change, one can’t be certain of cause and effect. They are often also referred to as ‘wicked problems’. Because of the complex interdependence the effort to solve one aspect of a wicked problem may reveal or create other problems.

Complex systems research is now becoming more important in both the natural and social sciences. It is commonly implied that there is such a thing as a complex system, different examples of which are studied across many disciplines.

Complexity science was invented in the post-nuclear age when different scientists and social scientists came together during the Los Alamos experiment to invent the nuclear bomb. Having discovered that it was fun working with people outside their own narrow disciplines, a group created the Santa Fe Institute, the first think tank dedicated to complex, multidisciplinary thinking.

To deal with Complex Problems we have to agree on its definition to make any progress. The linked article (too long) explain the challenges in defining this field but starts with a definition which is:

“Complex Problem Solving tasks are situations that are: (1) *dynamic* because early actions determine the environment in which subsequent decision must be made, and features of the task environment may change independently of the solver’s actions; (2) *time- dependent* because decisions must be made at the correct moment in relation to environmental demands; and (3) *complex*, in the sense that most variables are not related to each other in a one-to-one manner. In these situations, the problem requires not one decision, but a long series, in which early decisions condition later ones.” http://lsa.colorado.edu/papers/manuscriptTIES.3.9.postReview.pdf

Complexity characterises the behaviour of a system or model whose components  interact in multiple ways and follow local rules, meaning there is no reasonable higher instruction to define the various possible interactions.

The term is generally used to characterize something with many parts where those parts interact with each other in multiple ways, culminating in a higher order of “emergence” which is greater than the sum of its parts. An example of emergence is the act of walking on 2 legs. On ne leg alone, we can just hop. But walking on 2 legs is more than just hopping with 2 legs. And a dance form has a greater elegance than robots performing similar motions. The study of these complex linkages at various scales is the main goal of complexity theory. 

The present situation is that “even among scientists, there is no agreement on a unique definition of complexity – and the scientific notion has traditionally been conveyed using particular examples…” Ultimately a generally accepted  definition of “complexity science” is “the study of the phenomena which emerge from a collection of interacting objects”.

Link to the Wikipedia article: https://en.wikipedia.org/wiki/Complexity

Complexity in computation : 

In computer science, the computational complexity or simply complexity of an  algorithm is the amount of resources required to run it. Particular focus is given to time and memory requirements. 

The study of the complexity of explicitly given algorithms is called analysis of algorithms, while the study of the complexity of problems is called computational complexity theory. Both areas are highly related, as the complexity of an algorithm is always an an upper bound on the complexity of the problem solved by this algorithm.

       The field of complexity can be considered to have the following domains as its main constituents: 

• Self organisation and emergence 
• Non-linear systems and chaos theory
• Network Theory 
• Complex Adaptive Systems

Here is a short video (11 minutes) that provides an overview and briefly and simply describes the above 4 elements: https://youtu.be/i-ladOjo1QA

Here is another slightly longer video that relates complexity theory  to educational change (15 minutes)  : https://youtu.be/vk2s7gumXMY

Here is another 8 minute video explaining ‘emergence’ and systems thinking : https://youtu.be/KN6SaRmF_8c