Concrete examples to show how common emergent behavior is and why it's worth learning about.
Emergent behavior is literally everywhere around you and occurs in every field of study. In this article, I will be highlighting various examples to show it's worth learning more about in my next article on the theory of emergent behavior.
The article is structured in a way from low-level emergent systems to high-level emergent systems.
Emergent Behavior in Formal Systems
Axiomatic systems are formal systems that are based on a set of axioms. Theorems can be derived from axioms using inference rules. The set of theorems that can be derived from a given set of axioms is called the theory of the axiomatic system.
In geometry, complex geometric theorems and properties can be derived from a small set of axioms, such as Euclid’s axioms. This is an example of how axiomatic systems can be used to build complex theories.
Axiomatic systems are also used in logic. Propositional logic and predicate logic are two examples of axiomatic systems in logic. These systems provide a foundation for reasoning and deduction. Complex logical proofs and theorems can be derived from the axioms and inference rules of these systems. These theorems represent emergent properties of the system.
Emergent Behavior in Quantum Physics
According to string theory, ‘assuming’ it as starting point, vibrating strings form subatomic particles, such as quarks and neutrinos. These particles then combine to create the nucleus of an atom. Atoms are the basic building blocks of matter, and they cannot be broken down any further without losing their essential properties. They are the foundation of the material world, and they serve as the basis for the next section when talking about Newtonian physics and biology.
Emergent Behavior in Newtonian Physics (reference GPT model)
A fascinating example is the relationship between Newtonian physics and quantum physics. Newtonian physics can be seen as an emergent property of the more fundamental theory of quantum physics. Despite their different operational principles, modern physicists are actively working towards a unified “theory of everything” that bridges the gap between these two frameworks. In this pursuit, emergent behavior may play a significant role, but the precise details of such emergent phenomena are yet to be fully understood and discovered.
Phase transitions in condensed matter physics exemplify emergent behavior. During a phase transition, the interactions between constituent particles, such as atoms, molecules, or ions, do not change fundamentally. The basic forces governing the behavior of individual particles remain consistent before, during, and after the phase transition. However, emergent properties, like magnetism or superfluidity, arise at the macroscopic scale due to the collective behavior and interactions of these particles. These emergent phenomena are not reducible to the interactions of individual constituents but manifest as global behaviors of the material.
Superconductivity is a striking example of emergent behavior in certain materials at very low temperatures. These materials exhibit the loss of electrical resistance when cooled below a critical temperature. This emergent phenomenon stems from the collective behavior of paired electrons, known as Cooper pairs. The interactions between these pairs lead to a coherent quantum state that enables the flow of electric current without resistance. This macroscopic property emerges from the cooperative behavior of a vast number of electrons, which is not apparent in individual electron interactions.
In the field of quantum chromodynamics, which governs the strong interactions between quarks and gluons, an essential emergent behavior is quark confinement. Quarks are never observed in isolation but are always confined within composite particles like protons and neutrons. This confinement arises from the strong force interactions between quarks, making it impossible to observe them individually due to the increasing energy required to separate them as they move apart. As a result, quarks remain permanently bound, forming color-neutral composite particles, and this confinement emerges from the intricate dynamics of the strong force at the quantum level.
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. Wheater in general is an emergent property of an unknown amount of complexity of factors.
Emergent Behavior in Biology
Atoms combine to form molecules. Chains of molecules form amino acids and nucleic acids, which then combine to form proteins. Proteins form enzymes, which are responsible for metabolism. Enzymes allow cells to form, and cells form tissues. Tissues form organs, organs form organ systems, and organ systems form organisms. Evolution is a beautiful theory that builds on top of this idea of emergence with simple rules.
Swarming is a complex behavior found in many species in nature, from swarms of grasshoppers to flocks of birds. In flocks of birds, simple rules, such as maintaining a distance from each other, aligning their movements, and following the leader, are applied to each individual bird. These rules give rise to the complex behavior of the flock as a whole.
Traffic flow behaviors, such as congestion waves, emerge from the interactions of many individual drivers. Social behaviors, such as the spread of news, political ideas, and religious beliefs, also emerge from the interactions of individuals. Ant colonies, which build complex cave systems and hills without a central leader, are another example of emergent behavior.
Recursive behavior can emerge from simple rule sets and base states. When certain rules are applied repeatedly, this can lead to the formation of complex systems. For example, snowflakes, broccoli, pinecone scales, trees, lightning, and even your fingers and toes all exhibit fractal-like growth patterns. These patterns are inspired by the laws of physics, such as quantum mechanics. Recursive structures can be found in many other areas of life as well. For example, any type of language is also an emergent property of the human species that became self-conscious.
Emergence in Computer Science
The emergence of humans led to the emergence of science and mathematics. The emergence of that led to controlling electrical signals as fundamental on/off states used for transmitting and processing information in electronic circuits. By switching or amplifying electrical signals, transistors enable the creation of more complex conditions and operations. Through the utilization of transistors and other components, arithmetic operations such as addition, subtraction, and more can be performed. Groups of transistors and other components form arithmetic logical units (ALUs), which execute arithmetic and logical operations. Integration of multiple ALUs results in computational units (CUs), allowing for more intricate computations and data processing. The CPU comprises multiple CUs, memory management units, and control units. It executes various operations and machine instructions. Machine Instructions (MIs) are predefined statements understood and directly executed by the CPU. Encoded in binary format, they represent basic operations. Assembly language (ASL) provides a human-readable representation of MIs, utilizing mnemonics to simplify programming and enhance comprehension. Many ASL instructions can build a program that parses sequences of input text to a sequence of MI’s, also called compilers. Once a compiler is built and those input text achieve Turing completeness they can build a compiler but in their own notation. Once a language can compile itself we can have the same feedback loop but for higher-level programming languages like C++. After that its an explosion of functional, system-languages, object-oriented programming languages. After that, we get scripting languages to even very high-level configuration languages and node graphs or other similar visual languages.
Those languages help us to give rise to evolutionary algorithms and self-organizing algorithms that have the ability to recognize patterns and learn on their selves using logical, linear regression, neural networks. Neural networks give rise to intelligent systems which may give rise to self-aware systems. Intelligent systems will give rise to incredible emergent systems beyond human emergent systems.
For some fields, my emergent mind used the emergent technology, a GPT -model, to validate/refine some of my statements on emergent behavior.
Emergent Behavior in Music
Sound is a complex phenomenon that can be represented as a series of sinusoidal waves. Each musical instrument produces its own unique set of waves, which vary in frequency, amplitude, and duration. These waves can be combined to create harmonic progressions, which are the building blocks of music. Rhythm is created by the regular repetition of different frequencies, and harmony is created by the combination of different frequencies. Orchestration is the art of combining different instruments to create a cohesive musical piece. Improvisation is the art of creating music spontaneously, and it arises from the mind of the musician. The mind is an emergent system, which means that it is a complex system that arises from the interactions of simpler components.
I started off thinking about emergence as a concrete thing but after this article, I realized it’s more a description of abstract phenomena that is not implemented in one specific way. That's why I wrote a second article going more depth into the theory of emergent systems.