Theoretical analysis of what emergent behavior is.
In the previous article, I provided a variety of concrete examples of emergent behavior to demonstrate that it is ubiquitous. In this article, we will analyze what emergent behavior is and why it is a fascinating concept. I will do this by examining a set of premises that have been proposed by people from various disciplines.
The image the emergent I has of reality is an emergent interpretation of an emergent mind in an emergent universe.
1. Definition of emergent behavior
To start let's define emergent behavior:
Emergent behavior refers to the phenomenon in which a higher-level system [1] or property emerges as a result of the interactions and organization of its lower-level components or subsystems.
A system is a group of interacting or interrelated elements / components / properties, that act according to a set of rules to form a unified whole.
Emergent behavior is a conceptual phenomenon that is intertwined with many other concepts, including causality, reductionism, infinite regress, computational irreducibility, and determinism. It is relevant to a wide range of fields, if not all, including complexity science, biology, computer science, physics, and mathematical modeling. Let's look at some properties of an emergent system.
2. Properties of emergent behavior
Mark Bedau (Bedau, Mark A. (1997), Weak Emergence) puts it as:
- Emergent phenomena are somehow constituted by and generated from, underlying processes.
- Emergent phenomena can somehow be autonomous from underlying processes.
Further, people like Mark Badau, Stephen Wolfram, John H. Holland, Steven Johnson, John Conway, Stuart Kauffman, Murray Gell-Mann, etc. came up with various properties of emergent systems generally classified as:
- Emergent behavior can be robust. This means that it can persist even when the individual parts of the system are changed.
- Emergent behavior is often self-organizing. This means that the system itself is able to organize its parts in a way that produces emergent behavior.
- Emergent behavior is often unpredictable. This is because it is not possible to predict the behavior of a complex system simply by knowing the behavior of its individual parts.
- Emergent behavior is a fundamental property of complex systems. This means that it is not something that is added to a system from the outside, but rather something that arises from the interactions of the parts of the system.
- Emergent properties are collective: In the sense that they are properties of the system as a whole. This means that the emergent property cannot be attributed to any individual part of the system.
There seem to be two categories philosophers (e.g. Badeau) draw in emergent behavior, weak and strong behavior.
Weak emergent behavior
Refers to the appearance of predictable and explainable patterns or properties in a complex system arising from the interactions of its simpler components.
Weak emergent behavior is, for example, a flock of birds or a school of fish, the game ‘the game of life’. Those higher-level systems are not defined by programmatic rules but emerge out of lower-level rules that result in higher-level emergent behavior.
Strong emergent behavior
Refers to the appearance of unpredictable and irreducible patterns or properties in a complex system that cannot be fully explained by understanding the interactions of its individual components alone. It may involve novel principles or higher-level organizational structures that go beyond the sum of its parts.
Strong emergent behavior is, for example, the consciousness in the brain, Social and Economic Systems, Neural Networks, wheater, and swarm intelligence. Or simply said, it is a behavior that is hard to split into individual causations and it is unclear what exactly causes what.
The question of strong emergent behavior hinges on the interplay between reductionism and non-reductionism, calling for both detailed scrutiny of the properties that give rise to it and a holistic analysis of the entire system. Reductionism is the belief that the behavior of a complex system can be explained by the behavior of its individual parts. Non-reductionism is the belief that the behavior of a complex system cannot be explained by the behavior of its individual parts. As the philosopher Bedeau aptly put it, strong emergent behavior is ‘logically possible, but uncomfortably like magic,’ as discerning causal links within emergent systems proves arduous or even impossible.
3. Emergent behavior can be robust
This means that it can persist even when the individual parts of the system are changed
The emergent behavior of a flock, swarm, traffic jam, or fluids is made up of individual parts that can change, be removed, or be added, but these changes do not necessarily change the system as a whole. For example, if five birds are hit by a windmill, the flock system will likely survive. Similarly, if some oxygen atoms escape from a boiling pot of water, the liquid will remain to exist up to a certain point. However, there are limits to how much change a system can tolerate before the emergent behavior breaks down. This is a fascinating part of a study in many fields, as it defines state transitions, conductivity transitions, and morphations of matter.
4. Emergent behavior is often self-organizing
This means that the system itself is able to organize its parts in a way that produces emergent behavior.
A system can act as an atomnous entity, where it does not strictly depend on higher or lower-level systems for input. There will always be dependencies, but take for example an ant colony, the ants compose grand complex networks of tunnels and communicate close by food sources without any help of a leader. Similarly, a more complex case is the human mind's ability to focus where it can arrange its attention to solve, and plan, problems. Tornadoes are self-organizing systems that form when warm, moist air rises and meets cold, dry air. The interactions between these two air masses create a vortex that can suck up debris and other objects. The tornado like our mind and ants, acts as an autonomous entity.
5. Emergent behavior is often unpredictable
This is because it is not possible to predict the behavior of a complex system simply by knowing the behavior of its individual parts.
I am a proponent of causality and the principle of sufficient reason (PSR). I believe that everything that exists has a reason for its existence and that everything that exists can be reduced to something else that caused or makes up its existence. This means that even if something is unpredictable due to its complex nature, there must still be a causal link in order for emergent behavior to not be magic. (more on the fundamental ground of reality later).
However, we should not disregard the holistic perspective. Strong emergent systems demonstrate that it can be difficult to define a system by its individual properties and determine the exact causes of its behavior. In these cases, the unpredictability is more or less a shadow of the complexity of the system.
Taking this into account, we can define emergent behavior as follows:
- Every high-level system is necessarily made up of a lower-level system.
- Every low-level system can be part of the high-level system.
- If a low-level system can combine with a higher-level system, there is no sufficient reason to stop it from happening, and therefore it might happen given the right context of a system.
Emergent behavior is a phenomenon that arises from the interactions of lower-level and higher-level systems. I like to think of it as a process in which system A gives rise to system B with new properties. If system B is stabilized, it can be defined by its unique characteristics that are not found in system A.
I envision emergent behavior as a directed acyclic graph (DAG), where each node represents a system and the edges represent interactions between systems. The leaves of the DAG represent the lowest-level systems, and the parents of a node represent higher-level systems. However, it is important to note that not all systems interact with each other. For example, subatomic particles only interact with other subatomic particles, and they do not interact with the concept of atoms, molecules, or enzymes. On the other hand, higher-level systems can interact with many other systems, and they can contribute to the emergence of many different behaviors. For example, carbon atoms can be part of many different molecules, and they can also be part of cells. Programming languages can be used to create many different types of software, and they can also be used to create artificial intelligence. Lego blocks give rise to countless possible structures. The DAG nature of emergent behavior makes it difficult to predict the type and number of parents a node has, as well as the type and number of children it has. This is especially true in complex systems, where the interactions between systems are not always simple observable casual interactions. As a result, it becomes nearly impossible to use a reductionist approach to understanding complex systems but requires both holistic and reductionistic approaches to understand emergent behavior.
6. Emergent behavior is a fundamental property of complex systems
This means that it is not something that is added to a system from the outside, but rather something that arises from the interactions of the parts of the system.
Psychology is not applied biology, nor is biology applied chemistry. We can now see that the whole becomes not merely more, but very different from the sum of its parts (Anderson, P.W. (1972)[19])
Andreson’s statements highlight the fascinating nature of emergent behavior. Higher-level systems that emerge from lower-level systems acquire unique characteristics that do not exist in lower-level systems. This implies that things have the potential to come into existence as long as they follow the laws of emergent behavior, even if they do not have a necessary definition in reality. What is the nature of those things that are emergent?
This is exactly what the evolution of species is about. If something can happen under certain conditions, it will happen under certain conditions. This happening is the process we described as emergent behavior. It's interesting that there is a potential for a species to develop, what does the future of species look like?
Emergent systems can exhibit both downward and upward causation. Downward causation is when higher-level systems influence lower-level systems. For example, the mind, as a higher-level system, can enact specific physical changes in the body through cognitive processes. Upward causation is when lower-level systems influence higher-level systems. For example, studies have shown that the mind can influence immune control and adrenaline control, and hormones are shown to change the state of mind. Despite both being physical systems, the mind functions at a higher level than the particles that make it up.
The above statement is truly mind-blowing! It demonstrates how system A can give rise to system B, and in turn, system B can influence or change system A. This can lead to feedback loops, where the emergent phenomenon influences and shapes the underlying rules or processes that brought it into existence. Not only can it change itself, but it can also change other systems that are not directly in its causal chain. For example, my mind is able to pick up a rock, or a tornado is able to interact with a flock of birds. Also, mental disorders are sometimes closely related to physical abnormalities. It requires work on both mind and body to enhance overall well-being.
Douglas Hofstadter’s books Gödel, Escher, Bach: An Eternal Golden Brain and Strange Loop explore self-referential systems and strange loops. Gödel’s incompleteness theorem states that any formal system that is powerful enough to talk about itself will inevitably contain statements that can be neither proved nor disproved within the system. This is because any such system will have to rely on axioms or basic assumptions, and these axioms will inevitably be self-referential. Hofstadter hypothesizes that the mind is a self-referential, emergent, strange loop. He believes that this is the foundation of what makes the mind “aware.”
I find this idea fascinating. It suggests that an emergent universe can give rise to emergent systems so complex that they are able to modify and study themselves. Our self-aware mind, seen as an emergent system, is a product of cosmic evolution. In this regard, our mind is not much different from an emergent AI system, other than that it is self-reflective.
7. Emergent properties are collective
In the sense that they are properties of the system as a whole. This means that the emergent property cannot be attributed to any individual part of the system.
The emergent properties of a system are not simply the sum of the properties of the individual parts (a resultant). Rather, they are something new that arises from the interactions between the parts. In the case of water, the emergent properties arise from the way that the hydrogen and oxygen atoms are arranged in the molecule. The specific arrangement of the atoms allows water to form hydrogen bonds, which are responsible for its liquid state and other properties. It is a fascinating example of how new properties can arise from the interactions between simple parts.
8. Advaita Vedanta Joined with Materialism
The philosophical topic of mind and matter I think are reconcilable and both views talk about the same thing but because there is a paradox at play they usually are seen as different interpretations. The paradox is that matter / emergent systems observe matter / emergent systems. It is a cyclic dependency with self-reference. The crucial part is to recognize emergent systems creating new properties and relying on lower-level properties.
Both Advaita Vedanta and Materialism perspectives suggest that the mind is not separate from the world, but rather an integral part of it. However, there are also some important nuances and differences between these perspectives.
Advaita Vedanta takes a holistic perspective, arguing that everything is the mind. We can motivate by stating that the mind is an emergent system that can retrospect back into the tree of lower-level systems. Materialism, on the other hand, takes a reductionistic approach, seeing the mind as the result of the process of neurons interacting with one another.
From the holistic perspective, the mind is seen as an interconnected system that is influenced by all of its parts. This means that the mind is not simply defined by its own properties, but also by the properties of the systems that it interacts with. In the reductionist perspective, the mind is seen as a product of the brain. This means that the mind is simply defined by the properties of the neurons in the brain.
The holistic perspective is more compatible with the view that the mind is an emergent system. This is because the emergent system is defined by the interactions of its parts, and these interactions cannot be fully understood by simply studying the parts themselves. The reductionistic perspective is less compatible with the view that the mind is an emergent system. This is because the reductionist perspective ignores the interactions between the parts, and it only focuses on the properties of the parts themselves.
The mind is a special kind of observing emergent system that builds up a representation of itself and other emergent systems in itself. From this article, it is clear emergent systems gain new properties that did not exist in the sum of the parts of that system. In other words, the properties of the mind (colors, tastes, spatial, emotional features, system interpretation, etc…) are unique to the system of the mind and are not located in other systems such as neurons or molecules.
From the perspective of Advaita one can claim, everything that we observe occurs in this mind system and that experience represents the universe as we know it. And that on a fundamental level, the lower-level systems, are part of the mind and not different. Advaita would say the mind is one with Brahman, the ultimate reality. Both materialism and Advaita would agree here that the mind is one and part of reality.
This is because all objects and emergent systems around us appear in our emergent experience. The body and brain are emergent systems, and the mind is an emergent system from the brain. Emergent systems can observe systems and have downward, upward, and perpendicular causal influences. The mind is a self-referential strange loop and can observe its own and other emergent systems. Therefore, the mind is able to observe the world around it, and this experience is the foundation of all reality.
9. Cleanups
The examples we have discussed make it clear that when two systems, A and B, interact, they form a link, connection, and interaction. If this interaction evolves over time, it can enact certain causation that we describe as emergent behavior from system A to system B.
Emergent behavior refers to the phenomenon in which a higher-level system [1] or property emerges as a result of the interactions and organization of its lower-level components or subsystems.
Although we know the properties of certain systems such as chemistry, quantum physics, and biology, the links between these fields are still an area of active research. This is because it is difficult to define how causal links work between these systems. However, it is a fascinating topic to think more deeply about, as we can see emergent behavior all around us. We ourselves are an emergent system of incredible complexity that evolved over a few billion years. The universe has entered a phase where it can now reflect on itself, and with the introduction of ML systems, this reflective capability is likely to become even more advanced. The process differences between us, an ML system, and a tornado are systematically not that different. We arose from the lower-level systems and became unique autonomous entities.
The image the emergent I has of reality is an emergent interpretation of an emergent mind.
