Reflections on Science and Complexity
Note: This was originally written in response to an assignment for my course on the Collective Dynamics of Complex Systems at Binghamton University.
Warren Weaver's Science and Complexity is one of my favorite papers that I've read during my time in Binghamton's Systems Science program.1 Written in 1948, it feels as if Weaver is speaking directly to one of the core reasons I've become so enamored with systems — we need new scientific paradigms in order to effectively study social phenomena.
Weaver’s Framework
His core insight is that we can usefully distinguish between three eras of modern science, each concerned with separate classes of phenomena.
In the 17th century humanity started developing methods for dealing with problems of simplicity. These are problems where identifying the causal relationship between two or a few variables allows us to make meaningful and reliable predictions about physical phenomena. The physics and classical dynamics of the 19th century laid the foundations for technological developments from the telephone to the airplane.
During the 20th century we developed methods for dealing with problems of disorganized complexity. These are problems where we are dealing with a large number of variables, each of which has individually random behavior. However, using statistical techniques we can identify certain orderly and analyzable average properties of the system as a whole.
These methods allowed large telephone exchanges to make predictions about the average frequency of calls, and life insurance companies to maintain financial stability with their knowledge of the average frequency with which deaths occur.
However, in the mid-20th century scientists became increasingly aware of a third class of problem that doesn't neatly fall into either of the previous two categories. The second World War made it clear that we needed to develop reliable methods for dealing with problems of organized complexity. These are problems in which there are many variables involved, but they are interrelated in complex, non-random fashion. They show the essential feature of organization.
How is it that simply re-arranging the organization of atoms in a molecule can turn a substance from being harmless into a poison?
How exactly are the prices of commodities like wheat or gold determined?
How can countries win wars, or secure global peace?
The methods of physics and statistics have not proven sufficient for answering these types of questions, ones that the modern biological and social sciences are most concerned with addressing.
Applications in Systems Science
Re-reading Weaver's paper for a second time, I'm inspired to reflect on some of the theories and techniques I've been exposed to for making sense of systems which demonstrate the feature of organized complexity.
Information theory, originally developed by Claude Shannon in 1948 to improve the efficiency and reliability of communication systems, such as telephones and telegraphs, laid the theoretical and technical foundations which allowed us to build the modern Internet and World Wide Web.
Information theory has been identified as a useful framework for quantifying levels of self-organization within complex systems.2 While I've explored how these concepts might be usefully applied to the study of blockchain systems, I still feel like I have many more questions than answers.
Set theory and graph theory were identified by Ludwig von Bertalanffy in 1968 as being promising frameworks for, respectively, axiomatizing the general formal properties of systems and elaborating the relational structures within systems so we can deal with their structural properties rather than just quantitative relations.
Today, set theory serves as the foundation for modern database design while network science, grounded firmly in graph theory, is thriving as a field for formally studying the organization of complex systems.3 I've enjoyed exploring the fundamentals of set theory during my independent study in discrete mathematics and exploring the rich academic literature that applies graph theoretical techniques to the analysis of blockchain systems.4
I appreciated the opportunity to re-read this paper and feel excited about exploring some of these concepts through computer modeling and simulation.
Weaver, W. (1948). Science and Complexity. American Scientist, 36(4), 536–544. https://www.jstor.org/stable/27826254
Gershenson, C. (2023). Emergence in Artificial Life. Artificial Life, 29(2), 153–167. https://doi.org/10.1162/artl_a_00397
A Relational Model of Data for Large Shared Data Banks | SpringerLink. (1970). https://link.springer.com/chapter/10.1007/978-3-642-48354-7_4
Khan, A. (2022). Graph Analysis of the Ethereum Blockchain Data: A Survey of Datasets, Methods, and Future Work. 2022 IEEE International Conference on Blockchain (Blockchain), 250–257. https://doi.org/10.1109/Blockchain55522.2022.00042