Complexity Explorables

Visualizing complexity

Ecologies and AI

Co-Creation: Systems Thinking Beyond the Machine

Complexity thinking is all the rage — in the arts and sciences. Yet, there are two different strands of thinking about complexity, which are often confounded. The first comes from cybernetics, focussing on control in complex situations. The second is ecological, aiming at sustainable participation in a reality beyond control. Their difference rests on a fundamental distinction: is complexity rooted in feedback regulation or collective co-creation? While feedback remains mechanistic, co-creation generates new spaces of possibilities. We need it to understand life and its evolution. And it empowers us to rewrite our future, to escape our mechanistic cage without abandoning scientific rigor. In this paper, we illustrate how we implement these powerful yet abstract principles through our artistic and philosophical practice.

Software in the natural world: A computational approach to hierarchical emergence

Understanding the functional architecture of complex systems is crucial to illuminate their inner workings and enable effective methods for their prediction and control. Recent advances have introduced tools to characterise emergent macroscopic levels; however, while these approaches are successful in identifying when emergence takes place, they are limited in the extent they can determine how it does. Here we address this limitation by developing a computational approach to emergence, which characterises macroscopic processes in terms of their computational capabilities. Concretely, we articulate a view on emergence based on how software works, which is rooted on a mathematical formalism that articulates how macroscopic processes can express self-contained informational, interventional, and computational properties. This framework establishes a hierarchy of nested self-contained processes that determines what computations take place at what level, which in turn delineates the functional architecture of a complex system. This approach is illustrated on paradigmatic models from the statistical physics and computational neuroscience literature, which are shown to exhibit macroscopic processes that are akin to software in human-engineered systems. Overall, this framework enables a deeper understanding of the multi-level structure of complex systems, revealing specific ways in which they can be efficiently simulated, predicted, and controlled.

The lost art of mathematical modelling

We provide a critique of mathematical biology in light of rapid developments in modern machine learning. We argue that out of the three modelling activities – (1) formulating models; (2) analysing models; and (3) fitting or comparing models to data – inherent to mathematical biology, researchers currently focus too much on activity (2) at the cost of (1). This trend, we propose, can be reversed by realising that any given biological phenomenon can be modelled in an infinite number of different ways, through the adoption of a pluralistic approach, where we view a system from multiple, different points of view. We explain this pluralistic approach using fish locomotion as a case study and illustrate some of the pitfalls – universalism, creating models of models, etc. – that hinder mathematical biology. We then ask how we might rediscover a lost art: that of creative mathematical modelling.

Self-Organization in Biological Systems

The synchronized flashing of fireflies at night. The spiraling patterns of an aggregating slime mold. The anastomosing network of army-ant trails. The coordinated movements of a school of fish. Researchers are finding in such patterns—phenomena that have fascinated naturalists for centuries—a fertile new approach to understanding biological systems: the study of self-organization. This book, a primer on self-organization in biological systems for students and other enthusiasts, introduces readers to the basic concepts and tools for studying self-organization and then examines numerous examples of self-organization in the natural world. Self-organization refers to diverse pattern formation processes in the physical and biological world, from sand grains assembling into rippled dunes to cells combining to create highly structured tissues to individual insects working to create sophisticated societies. What these diverse systems hold in common is the proximate means by which they acquire order and structure. In self-organizing systems, pattern at the global level emerges solely from interactions among lower-level components. Remarkably, even very complex structures result from the iteration of surprisingly simple behaviors performed by individuals relying on only local information. This striking conclusion suggests important lines of inquiry: To what degree is environmental rather than individual complexity responsible for group complexity? To what extent have widely differing organisms adopted similar, convergent strategies of pattern formation? How, specifically, has natural selection determined the rules governing interactions within biological systems? Broad in scope, thorough yet accessible, this book is a self-contained introduction to self-organization and complexity in biology—a field of study at the forefront of life sciences research.

The Compendium

A compendium of insights about complexity structured as inter-linked cards by Alex Komoroske

Hyperproblems: New Ways of Doing and Communicating Science - Hyperproblems

Hyperproblems: Hyperproblems are scientific challenges whose scale, complexity, novelty and interdependence overwhelm traditional research models, requiring…

EPISTEMIC STIGMERGY: NATURAL VS. ARTIFICIAL INTELLIGENCE

The article\(^{1}\) defends the thesis that intelligent behavior might require not internal complexity but complex interaction. This is demonstrated by the various forms of stigmergy that can be observed both in social insects and in humans. The exposition is structured as follows: (§0) explains how the term “intelligence” is interpreted in the following text; (§1) clarifies the relation between intelligence and complexity; (§2) shows that intelligent behavior does not require internal complexity; (§3) introduces the concept of stigmergy; (§4) presents the mechanisms that give rise to this phenomenon; (§5) distinguishes several types of stigmergic interaction; (§6) briefly discusses the evolutionary mechanisms that could have produced them; (§7) sketches the possible ways in which the concept of stigmergy is used outside biology; (§8) examines collaborative stigmergy in humans; (§9) points to its epistemic projections; (§10) outlines some conclusions concerning the role of artificial intelligence systems and their place in human society.

Why embracing complexity is the real challenge in software today

In the midst of industry discussions about productivity and automation, it’s all too easy to overlook the importance of properly reckoning with complexity.

All you need is data and functions

It's really easy to tend towards complexity as engineers. I think on some level, we love complexity. There are obviously bad types of complexity, but I think there are other types of it that we seek out, because there's something satisfying about wrapping your head around it; and I think a lot of that kind of complexity ends up in our programming languages.

Making Sense of Chaos

From a pioneer in the field of complexity science and chaos theory, a plan for solving the world’s most pressing problems  “Farmer convincingly argues t...

Agentic systems are adept at solving well-scoped, verifiable problems in computational biology

We introduce CompBioBench, a benchmark of 100 diverse tasks for evaluating agentic systems in computational biology. Unlike mathematics and programming, which more readily admit systematic verification, biological data are inherently noisy and open to interpretation.

The Fractal Organisation Manual: How to diagnose & design organisations using the Viable System Model | SCiO - Systems and Complexity in Organisation

RRP: £12.99; Paperback: ‎ 192 pp; Publisher: ‎ SCiO; ISBN 979-8250847018

Illusions of Understanding in the Sciences

Scientists seek to understand the causes of observed phenomena. Beliefs that they have succeeded are based on understanding that is rarely or possibly never complete, and varies in depth and quality. Most often scientists believe they understand more than they do, making their belief an illusion. This illusion then persists in explanations scientists provide in print, in talks, or in discussions. The illusion that a scientist has a valid and complete explanation tends to be magnified when the data are well described by mathematical and computer simulation models due to the precision of such models and their ability to predict well; prediction does not imply causality, but gives the illusion that it does. The first part of this essay supports the case for the universality of partial and incomplete levels of understanding by showing the difficulty of reaching a deep level of understanding for even a simple analysis and model that most scientists use and believe they understand: linear regression. The second part highlights some implications of the existence of many levels of understanding and explanation, and their use by scientists for design, testing, analysis, and theory development. It discusses the way that deduction and induction depend on the levels of understanding and the implications of the illusion that a scientist’s understanding is deep. It makes a case that the many incomplete levels of understanding affect, often unwittingly, the ways scientists design experiments, test theories, comprehend, communicate, and teach.