Understanding Emergence

—Exploring the possible

Starlings flocking, a predator bird can be seen upper right

Introduction

Emergence, a phenomenon both awe-inspiring and enigmatic, lies at the heart of the intricate tapestry of the universe. It is the phenomenon through which simple components interacting on a local level give rise to complex and novel behaviors at higher levels of organization. This course delves into the concept of emergence, drawing examples from nature and society. We will explore the nuances of weak and strong emergence and delve into the role of emergence in the context of evolution.

Remarkably, everything in the universe emerged from the basic laws of physics. Quarks and electrons combine to form atoms which combine into molecules and form all materials. Air, water, rocks, and minerals emerge from various combinations of chemical elements.  Rain, wind, storms, lightening, and fire also emerged. Oceans formed, mountains rose, volcanos erupted, earthquakes shook, and eventually life emerged in the form of microorganisms, plants, and animals.

Each of these transformations are remarkable, yet although each is really new, there is nothing really new.

While reductionism tells us what there is, emergence helps us understand what there can be; what can be constructed.

Objectives

The objectives of this course are to help students:

1. Identify emergent phenomenon.
2. Explore the possibilities of emergence.
3. Understand the limitations of emergence.
4. Evaluate and understand claims of emergence.
5. Distinguish between a phase transition and emergence.
6. Analyze the implications of a claim such as “B emerged from A”.
7. Distinguish claims of weak emergence and strong emergence.
8. Augment scientific reduction.  

This course is part of the Applied Wisdom curriculum and of the Clear Thinking curriculum.

If you wish to contact the instructor, please click here to send me an email or leave a comment or question on the discussion page.

Characterizing Emergence

In everyday language the word emergent broadly refers to “the process of coming into being or becoming prominent”. However, in the context of philosophy or science, it refers more narrowly to  something that is “arising and existing only as a phenomenon of independent parts working together”. This course focuses on that second definition.

A property of a system is “emergent” if it is not part of a detailed “fundamental” description of the system, but it becomes useful or even inevitable when we look at the system more broadly.

As a simple example, recognize that a painting emerges from the artist’s brushstrokes. At a fine-grained level of analysis, the painting is nothing more than a collection of brush strokes on a canvas. At a course-grained level of analysis, the way in which we typically view a painting, it is a visual representation of some scene, person, or imagined object. Examining the brush strokes ever more closely will not reveal the artistry and aesthetic value of the painting.

The Mona Lisa can be described as a collection of brush strokes, or as an enigmatic portrait.

Each emergent phenomenon can be accurately and consistently analyzed and described at two scales, fine grained and coarse grained. The painting can be described at the fine-grained level by describing each individual brush stroke, or it can be described at the course-grained level by describing the scene that emerges from these brush strokes, and perhaps the mood that it evokes.

As another example, consider the air in the space surrounding you. The air can be described (at the course-grained or macroscopic level, perhaps by a meteorologist) as having a particular temperature, pressure, humidity, and density. It can also be described (at the fine-grained or microscopic level, perhaps by a physicist of chemist) as a collection of individual nitrogen, oxygen, and other atoms.

Note, in each case that the two different stories describing each system use very different vocabularies. When describing a painting we identify brush strokes at the microscopic level, and images at the macroscopic level. When describing air, we talk about molecules at the microscopic level, and temperature and pressure at the macroscopic level. Each story is correct and complete at its own level, but each of these the stories must remain at their respective levels.

Disappearances

As our understanding evolves, several substances thought to exist have evaporated as the illusion was explained. Here are some examples.

The phlogiston theory is a superseded scientific theory that postulated the existence of a fire-like element called phlogiston contained within combustible bodies and released during combustion.

Phlogiston theory stated that phlogisticated substances contain phlogiston and that they dephlogisticate when burned, releasing stored phlogiston which is absorbed by the air. Growing plants then absorb this phlogiston, which is why air does not spontaneously combust and also why plant matter burns as well as it does.

Work by  Antoine-Laurent de Lavoisier and others in the 1770s lead to the development of the modern oxygen theory of combustion.

Phlogiston was never found because it never existed, it was only an illusion.

As another example, the caloric theory is an obsolete scientific theory that heat consists of a self-repellent fluid called caloric that flows from hotter bodies to colder bodies. Caloric was also thought of as a weightless gas that could pass in and out of pores in solids and liquids. The "caloric theory" was superseded by the mid-19th century in favor of the mechanical theory of heat, but nevertheless persisted in some scientific literature—particularly in more popular treatments—until the end of the 19th century.

Caloric was never found because it never existed, it was only an illusion.

Luminiferous aether (luminiferous meaning 'light-bearing') was the postulated medium for the propagation of light. It was invoked to explain the ability of the apparently wave-based light to propagate through empty space (a vacuum), something that waves should not be able to do.

The negative outcome of the Michelson–Morley experiment (1887) suggested that the aether did not exist, a finding that was confirmed in subsequent experiments through the 1920s. This led to considerable theoretical work to explain the propagation of light without an aether. A major breakthrough was the theory of relativity, which explains why the experiment failed to see aether, but was more broadly interpreted to suggest that it was not needed.

Luminiferous aether was never found because it never existed, it was only an illusion.

Élan vital is a term coined by French philosopher Henri Bergson in his 1907 book Creative Evolution, in which he addresses the question of self-organization and spontaneous morphogenesis of things in an increasingly complex manner. Élan vital was translated in the English edition as "vital impetus” but is usually translated by his detractors as "vital force". It is a hypothetical explanation for evolution and development of organisms, which Bergson linked closely with consciousness – the intuitive perception of experience and the flow of inner time.

The existence of Élan vital, and the associated vitalism theories are superseded and discredited by the majority of modern scientists.

Élan vital was never found because it never existed, it was only an illusion.

In each of these examples, although the initial hypothesis turned out to be incorrect, the investigations inspired by that hypothesis were valuable and contributed to our better understanding of the universe. These are example of how understanding evolves.

Today the nature of consciousness and free will are debated. Mechanisms explaining consciousness are not yet identified. The actual existence of free will is seriously debated. Perhaps these are emergent phenomena, or perhaps consciousness requires discovery of some new substance. Free will may be an  illusion. We await the answers as our understanding evolves.

Distinct from Phase Transition

Emergence is distinct from a phase transition. A phase transition is a transformation that takes place over time. For example, when an ice cube melts, water transforms from the solid phase into the liquid phase. In contrast to a phase transition, emergence allows a single system to be described two very different ways, macroscopically and microscopically, at the same time. For example, a box of gas can be described macroscopically by temperature, pressure, humidity, and density. At the same time, it can be described microscopically by specifying the position and velocity of each molecule.

Several examples of each are listed in this table.

Phase Transition	Emergence
Melting ice Boiling water Evaporation Sublimation	Temperature Hurricane Swarms Fire A painting

Everything Emerged

We begin this course by examining, and eventually accepting the statement “everything in the universe emerged from the basic laws of physics” . This is a brief statement of naturalism philosophy, often considered equivalent to materialism. According to naturalism, the causes of all phenomena are to be found within the universe and not transcendental factors beyond it. Supernatural claims are dismissed in the absence of extraordinary evidence.

Everything emerges as the Big Bang continues to unfold.

The statement is true by definition, because the goal of physics is to understand how the universe behaves. The behavior of the universe is described by the laws of physics. Although these laws are not now fully known, our current understanding of the most fundamental laws of physics is the core theory of the standard model particle physics plus general relativity. The standard model identifies quarks, electrons, photons, electromagnetism, and other elementary particles and fundamental forces of the universe. General relativity describes gravity, the fourth known force in the universe. That is what there is. That is all there is.

Our current understanding is that the universe expanded from an initial state of high density and temperature in a process known as the big bang. Although this unfolding is described in detail, no one knows “what (if anything) banged”, or what, if anything, preceded the big bang. About one millionth of a second into the expansion, quarks and gluons combined to form baryons such as protons and neutrons. A few minutes into the expansion, neutrons combined with protons to form the universe's deuterium and helium nuclei in a process called Big Bang nucleosynthesis. Most protons remained uncombined as hydrogen nuclei.

Over a long period of time, the slightly denser regions of the (nearly) uniformly distributed matter gravitationally attracted nearby matter and thus grew even denser, forming gas clouds, stars, galaxies, and the other astronomical structures observable today. Eventually the chemical elements formed, atoms combined into molecules and our sun, solar system, and earth formed.

When we accept the premise that “everything emerged” what is special about the claim that some particular phenomenon emerged? Claiming that something emerged is the claim that the emergent phenomenon is qualitatively different from the components it emerged from. There is something new and different here. The image that emerges from a painting is qualitatively different from a collection of brush strokes. Although water is composed of only hydrogen and oxygen, water is very different than hydrogen or oxygen. Similarly, table salt is different from the sodium or chlorine elements it is composed of.

Claims of emergence are claims of novelty (also known as “autonomy”), referring to something new and different about the emergent object.

This justifies the first part of the claim “Although this is really new, there is really nothing new”.

Emerged From

Claiming that water emerged from hydrogen and oxygen is the claim that hydrogen and oxygen is the exhaustive list of all the constituent parts of water. The substance water is composed only of hydrogen and oxygen.

Similarly, the claim that fire emerges from combustible materials and oxygen after ignition, is the claim that fire is composed of only these components. No phlogiston is to be found; none is needed.

This justifies the second part of the claim “Although this is really new, there is really nothing new”.

Emerged How

Although the claim that water emerged from hydrogen and oxygen identifies the constituent parts, it does not explain how the transformation takes place. What mechanism works to transform hydrogen and oxygen into water? The causal factors must be identified and fully described. We now know that each water molecule contains one oxygen and two hydrogen atoms, connected chemically by covalent bonds, where electrons are shared among the atoms.

This emergence can be reversed because hydrogen and oxygen can be made to emerge from water through electrolysis. Here electricity provides the energy to break the chemical bonds and release elemental hydrogen and oxygen.

Furthermore, to support the claim of emergence, the mechanism described must be bottom-up rather than top-down. The mechanism must rely only on some organization or configuration of the laws of physics. No appeals to magic, supernatural phenomenon, or teleology is permitted.

Emerged Why

Finally, it is helpful to be able to identify why the new phenomena emerged. The answer is often that the emergent phenomena represent a more advantageous (lower) energy state. At the same time, entropy typically increases.

Free energy—energy available to perform work—provides the power that enables emergence. This free energy is often in the form of a naturally occurring gradient.

For example, combining hydrogen with oxygen to form water releases energy. In fact, so much energy is released that hydrogen is often combined with oxygen and used as rocket fuel. Fuel cells typically work by combining hydrogen and oxygen to produce electricity.

These ideas are explored more fully in the section Powered by free energy, below.

Four Claims

Claiming that “B emerged from A” makes the following four subsidiary claims:

1. The emergent phenomenon is novel. Novelty (also known as “autonomy”), describes what is new and different about the emergent object.
2. composition (also known as “dependency”) if we claim that B emerged from A then we are claiming that all the constituent components in B are already in A.
3. A transformation mechanism is identified, demonstrated, simulated, or suggested.  This explains (or at least describes) how the transformation occurred. The ability to describe the transformation mechanism is the difference between science and magic.
4. The energy source that powers the transformation is identified, explained, described, or suggested. This explainswhy the transformation happened.

For example, the statement that “life emerges from a chemical soup” makes two (ontological) claims that are almost contradictory. The first claim is that something new is created. This recognizes that life is qualitatively different from a chemical soup because it includes the biological processes of metabolism, reproduction, and growth along with the property of agency, if only as chemotropism. The second claim is that nothing new is required. The life that emerges does not contain any constituent parts that are not originally in the chemical soup.  Life is just a bag of chemicals.

Although this is really new, there is really nothing new.

While the claim that life has emerged from a chemical soup is often made, and thorough analysis and decomposition of living organisms have failed to identify any substances in life that are beyond chemistry, the claim remains speculative until a mechanism can be verified. The claim could be falsified by discovering something beyond chemistry, such as the Élan vital, that life requires.

Mechanisms for abiogenesis have been suggested, including the formation of a habitable planet, the prebiotic synthesis of organic molecules, molecular self-replication, self-assembly, autocatalysis, and the emergence of cell membranes. Many proposals have been made for different stages of the process. None of these are yet verified (for example by being duplicated in the lab) and none are yet falsified.

One hypothesis for the energy source that propelled abiogenesis are the chemical and thermal gradients present around hydrothermal vents. Other mechanisms have been proposed. Again, none of these are yet verified and none are yet falsified.

It only seems like Magic.

Stages in the origin of life range from the well-understood, such as the habitable Earth and the abiotic synthesis of simple molecules, to the largely unknown, like the derivation of the last universal common ancestor (LUCA) with its complex molecular functionalities.

Emergence is about science, not magic.

This course emphasizes that emergence is not magic. Throughout this course we maintain a naturalist worldview, the understanding that only natural laws and forces (as opposed to supernatural ones) operate in the universe. The only building blocks of the universe are those physicists have identified. None-the-less, remarkable structures emerge from these simple building blocks.

Not all emergent phenomena are currently understood and can be explained in terms of causal mechanisms. While it may be tempting to replace the phrase “B emerged from A” with, “There was A, and then a miracle happened and now B appeared”. That is not what we are saying or implying.

We recognize that there are many mysteries, but no magic.

The mechanisms that generate several of the phenomena studied here, including phase transitions, temperature, and pressure, are well understood. Mechanisms explaining other phenomena, including abiogenesis, include transformation and processes that are largely unknown and can only be suggested or hypothesized at this time.

When an emergence claim is made, yet the subsidiary four claims cannot be justified in detail, then the claim is speculative and may suggest hypothesis to be tested.

Examples

Consider these various emergence claims:

• Temperature emerges from the motion of gas particles and is an example of statistical dynamics.
• Ice melting is a phase transition.
• Smelting iron ore to obtain iron is an example of chemical transformation.
• When mountains, valleys, and volcanoes are formed by the movement of tectonic plates, that is an example of geological dynamics.
• Hurricanes emerge from warm waters as flow of warm, moist, rapidly rising air, starts to rotate cyclonically as it interacts with the rotation of the earth.
• When an oak tree grows from an acorn that is an example of development.
• When new species form, that is an example of speciation and  evolution.
• Swarms emerge from collective motion of a large number of self-propelled entities.
• Formation of culture is an example of social behavior.
• Building a chair from a felled tree is an example of manufacturing.
• The statue of David emerged from a block of marble and magnificent artistry.
• Appearance of roads, bridges, computers, and the internet are examples of engineering.
• Superconductivity emerges when certain materials are cooled below their characteristic critical temperature.
• Wikipedia emerged from volunteers and a governance system.

Assignment—Part 1

For each of the emergence claims listed above, identify each of the four claims: 1) novelty, 2) composition (from), 3) mechanism (how), and 4) energy source (why).

Assignment—Part 2

1. This general List of emergent phenomena illustrates a range of emergent phenomena that occur in nature.
2. Identify three examples from the list (or elsewhere) to study for this assignment.
3. Construct each of the four claims that define emergence, presented above.
4. Are each of the four claims viable? Is the phenomenon studied truly emergent? Why or why not?

Levels

Philosopher Auguste Comte described the hierarchy of the sciences. This table is a modern adaptation of his ideas:

Discipline	Holons	Catalogue
Sociology	People, interpersonal relationships, organizations, cultures, societies.	Outline of sociology
Psychology	Neurons, brain, nervous system	Connectome, DSM,
Biology	Proteins, RNA, DNA, cells, tissues, organs, organisms.	Biological taxonomy, anatomical descriptions
Chemistry	Atoms, molecules, compounds.	The periodic table of chemical elements.
Physics	Electrons, quarks, photons, gravity, and other elementary particles and forces.	Standard model of particle physics
Mathematics	Numbers, axioms, operators, theorems, formulas, points, lines, planes, sets, and other structures.	Mathematics subject classification

Chemistry emerges from physics because atoms, molecules, and compounds can be described as collections of electrons, quarks, and forces. Similarly, biology emerges from chemistry because proteins and other biological substances can be described as chemicals. Similar emergent relationships occur at each level of the hierarchy. Mathematics holds a special place in this hierarchy because it is fundamental and foundational making it useful at all levels.

As another example, we can describe, study, analyze, and enjoy a book at many different levels, shown in the table below.

Element	Attributes	Disciplines
Culture, society, shared knowledge	Tradition, arts, crafts, all social institutions, forms of expression, and modes of social interaction…	Cultural studies, Social studies, Information science
Library, bookstore	Number of volumes, scope, specialty, accessibility, organization, building design, location …	Library science
Genre	Category, structural elements, stories, instances, exemplars …	Genre studies
Book	Title, style, genre, creative contribution, action, character, dialogue, narration, pace, plot, point of view, setting, style, suspense, theme, tone, voice, accuracy, organization, intended audience, purpose, originality, clarity, vocabulary choice …	Comparative literature, literary criticism, creative writing
Chapter	Title, introduction, organization, unity, subheadings, conclusion, transition, length, references, illustrations, voice …	Writing style, book design
Paragraph	Topic sentence, unity, coherence, development, structure, transitions, length, clarity, consistency, concluding sentence, purpose, tone, target audience, focus …	Writing style
Sentence, clause, phrase	Length, purpose, tense, voice, mood, modifiers, punctuation …	Grammar
Words	Word choice, part of speech, vocabulary, idioms …	Spelling, vocabulary
Letters, symbols	Choice of alphabet, upper or lower case, typefaces, point size, line length, line spacing,  page layout,  …	Typography, graphic design

A printer, as differentiated from a reader or critic, may consider the type of ink, paper, trim size, cover materials, spine, and  binding style of the book.

A book emerges from letters, words, sentences, paragraphs, chapters, paper, and ink arranged by authors and printers. A book about typography spans several levels, as do books on grammar, writing style, and other literary elements. A printed book about typography is both an instance of typography, as well as a discussion of typography. It is self-referential.

Assignment

1. Study this emergence diagram.
2. Identify higher and lower levels and the associated holons for several items shown in the hierarchy of science diagram.

Mechanisms

Claims 1 (novelty) and 2 (composition) are relatively easy to verify (or falsify). Claim 3, describing a mechanism, often more difficult. In this section we begin by exploring several mechanisms that are well-understood, and then identify other mechanisms that are not as well understood.

Here are examples of emergence caused by specific, typically well-understood, mechanisms.

Phase Transitions

Phase transitions are a common example of changes over time, that occur in equilibrium systems.

In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma.

During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure. This can be a discontinuous change; for example, a liquid may become gas upon heating to its boiling point, resulting in an abrupt change in volume. The identification of the external conditions at which a transformation occurs defines the phase transition point.

Paradigm shifts are significant changes in the way people perceive, think, or understand certain concepts or phenomena. These are phase transitions occurring in our understanding that are analogous to phase transitions that occur in materials.

Although phase transitions result in substantial qualitative changes—ice is different from water—this is not an example of emergence, as described above in the section Distinct from Phase Transition.

Assignment:

1. Study these Examples of phase transitions.
2. Study these Examples of Paradigm Shifts.

The Kinetic Theory of Gases

The temperature of the ideal gas is proportional to the average kinetic energy of its particles.

Although we have a clear intuitive sense of temperature as a measure of our perceptions of hotness and coldness, we may not have a clear understanding of what temperature is and how it can be explained in terms of more fundamental constituents of nature.

Physicists now understand that temperature emerges from the motion of gas particles.

We begin our detailed study of emergence mechanisms with the kinetic theory of gases because it provides a well-established and readily understood explanation for the macroscopic properties of gasses such as volume, pressure, and temperature, as well as the transport properties such as viscosity and thermal conductivity.

Self-Organization, Slime Mold

Dictyostelium discoideum, commonly known as slime molds, represents a remarkable group of organisms. Initially, these creatures exist as solitary single-celled amoebas, nourishing themselves on the bacteria inhabiting decaying leaves within forest floors. However, when confronted with food scarcity, these numerous individual amoebas undergo a transformative process, coalescing into a singular entity.

Dictyostelium exhibiting chemotaxis through aggregation

Several questions naturally arise. What orchestrates this aggregation of individual organisms? What acts as the pacemaker, the central governing entity, dispatching chemical signals to summon this collective assembly? The key to this enigmatic phenomenon lies in the production of a chemical known as AMP by starving amoebas. When these individuals detect a concentration of AMP greater than their own output, they instinctively gravitate toward the source in a process known as chemotaxis. A few simple rules, followed by each single-celled amoeba, results in the emergence of the larger slime mold. No individual amoeba knows more that these simple rules, and each act as an autonomous agent.

This process seemingly mirrors the function of a pacemaker, even though a conventional pacemaker is absent. This confounded biologists, who questioned, "Where is the originator cell? Where is the pacemaker?" It left them with a sense of dissatisfaction. In fact, this pacemaker hypothesis persisted as the prevailing model for another decade until a series of experiments compellingly demonstrated that slime mold cells were self-organizing from the bottom up.

Until this juncture, it had been widely assumed that the universe adhered to a top-down structure, as exemplified by religion and teleology. However, as illustrated by this example, the natural world operates differently—there are no instances where change results from top-down, preconceived strategic designs or mandates issued by a solitary individual or authority figure. Nature adheres to a bottom-up paradigm.

Here are the fundamental principles governing slime molds:

• All low-level nodes are initially interchangeable.
• Each amoeba is indistinguishable from another.
• The emergent entity, the slime mold, emerges from these more basic constituents and possesses characteristics that are novel and irreducible compared to its individual components.
• The progression is from rudimentary rules at the lower level to increased complexity at higher levels.

These specific rules apply to interactions and network positioning:

• Produce AMP in response to food availability.
• When AMP reaches a certain threshold, move in its direction.
• Leave trails when experiencing "hunger" – depleted levels of AMP.
• Erase trails in the face of failure.
• Extend growth along successful trails.

A decentralized communication mechanism operates through chemical signals. While an individual amoeba constitutes a single organism, a threshold is reached wherein a slime mold emerges as the product of numerous interworking amoebas.

Slime molds emerge when many individual amoebas self-organize and coordinate to find food.  

Other examples of swarm intelligence in natural systems include ant colonies, bee colonies, bird flocking, hawks hunting, animal herding, bacterial growth, fish schooling and microbial intelligence.

In 1972 Nobel prize winning physicist Philip W. Anderson wrote an article called "More is Different" in which he emphasized the limitations of reductionism and the existence of hierarchical levels of science, each of which requires its own fundamental principles for advancement.

Dynamic Equilibrium

Dynamic equilibrium refers to a balanced state between an open system and an environment that is feeding it a steady supply of free energy.

A car travelling along a straight line at a constant velocity is a simple example of a dynamic equilibrium. It is in equilibrium because all of the forces on it are balanced, and the acceleration is zero. However, the equilibrium is dynamic because the car is in motion.

The daily rotation of the earth on its axis and the annual revolution of the earth around the sun are both examples of dynamic equilibrium. Because each motion is constant, the system in equilibrium, because it is in motion the equilibrium is dynamic.

The water cycle is a more complex example of dynamic equilibrium. The quantity of water in the earth system remains constant as evaporation and precipitation continue to occur.

Dynamic equilibrium is a prevalent concept in various natural processes, where opposing forces or reactions reach a balance that maintains stability over time.

Assignment

Study these Examples of dynamic equilibrium.

Complexity and Chaos Theory

According to Karl Popper, all problems are either clocks or clouds. A clock is something you can take apart, analyze the parts, and understand how it works. A cloud is a dynamic system, you can't take it apart. The way to understand a cloud is to study it in a holistic way. Complexity theory and chaos theory describe and analyze systems that are more similar to clouds than clocks. Clouds emerge in a way that is more complex than a clock. This section studies a few examples of systems that are more like clouds than clocks and concludes that determinism and predictability are very different things. Even if a chaotic system is unpredictable, it is still deterministic.

The three-body problem

Approximate trajectories of three identical bodies located at the vertices of a scalene triangle and having zero initial velocities.

The three body problem is simply stated, yet there is no general closed form solution to the problem.

Consider describing the motions of three objects, for example the sun, earth, and moon. The three-body problem is the problem of taking the initial positions and velocities (or momenta) of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's law of universal gravitation.

Remarkably there is no general closed-form solution to the three-body problem, meaning there is no general solution that can be expressed in terms of a finite number of standard mathematical operations. Moreover, the motion of three bodies is generally non-repeating, except in special cases.

This example illustrates that determinism and predictability are very different things. Even though the motions of the three bodies are unpredictable, their motions are still deterministic. The emerging motion is the result of their initial positions and momentum. The same complex motion will emerge every time whenever a system of three bodies begin with the same three initial positions and momenta.  The motions of the three bodies follow a specific path, even though we cannot predict in advance what that path will be.

Lorenz Systems

A sample solution in the Lorenz attractor when ρ = 28, σ = 10, and β = 8/3

In the 1960’s MIT meteorologist Edward Lorenz was using computer simulations to model weather patterns. Serendipitously he noticed the results of the model were remarkably sensitive to very small changes in the initial conditions. As an example, the Lorenz attractor is a set of chaotic solutions of the Lorenz system. In popular media the "butterfly effect" stems from the real-world implications of the Lorenz attractor, namely that several different initial chaotic conditions evolve in phase space in a way that never repeats, so all chaos is unpredictable.

His work demonstrated that chaotic systems can be completely deterministic yet still be inherently unpredictable over long periods of time. Furthermore, the results are unpredictable not only in practice but in principle.

Prime Numbers

A prime number is a natural number greater than 1 that is not a product of two smaller natural numbers.

The first 25 prime numbers (all the prime numbers less than 100) are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97

There are infinitely many prime numbers, as first proved by the ancient Greek mathematician Euclid.

The largest known prime number (as of October 2023) is 2^82,589,933 − 1, a number which has 24,862,048 digits when written in base 10.

Although the next prime number is determined, it is unknown and cannot be predicted.

Cellular automata

Cellular automata also demonstrate deterministic systems that are unpredictable.

Conway’s game of life is a popular example of cellular automata.

An elementary cellular automaton is a one-dimensional cellular automaton where there are two possible states (labeled 0 and 1) and the rule to determine the state of a cell in the next generation depends only on the current state of the cell and its two immediate neighbors. More generalized cellular automata having more dimensions are also defined.

Rule 22 is particularly interesting. The rule has a three-cell neighborhood, where a cell takes state “1” if there is exactly one neighbor, including the cell itself, in state 1.

Here are the possible results of one iteration applying rule 22:

A pattern emerging from Wolfram Rule 22

In cellular automata simple rules can generate remarkably complex patterns. For example, rule 22 is considered chaotic because:

1. Future configuration of the automaton is completely determined from its initial state because of the deterministic rule and synchronous updating.
2. Development of the automaton is sensitive to initial conditions (tiny perturbation might lead to dramatic events).
3. The resulting global transition graph has dense periodic orbits (attractors).
4. Configurations evolved can be characterized as random.

Although the results of iteration N can only be determined by running the rule N times, the result is always the same and depends only on the initial state. The system is deterministic yet unpredictable.

Summarizing Complex Systems

Various systems attain a level of complexity that makes them more like clouds than clocks. A reductionist approach to analyzing these systems often neglects their defining characteristics. However, although these complex, dynamic, nonlinear, and chaotic systems are unpredictable, they are deterministic.

Downward causation

If I am sitting at my desk and decide I would like a bowl of ice cream, I get up from my desk, walk to the kitchen, open the freezer, take out a box of ice cream and indulge.

When the wheel turns, so must each spoke.

This is an example of downward causation. Thoughts emerging from my (higher level) brain eventually cause motor neurons to fire in ways that contract muscles and propel me toward the box of ice-cream.

Here are several more examples.

When a wheel is rolling the (high-level) wheel-ness causes the constituent wheel parts to do forward rolls.

Changing climate conditions can cause various species to migrate toward new regions or become extinct.

In another example the state of the economy can influence the purchasing behavior of individuals. People  are more likely to purchase goods when the economy is growing than during a recession. Note there is a feedback loop here. Individual purchases also effect the overall state of the economy.

Various social norms can cause an individual to go along to get along—conform to the group norm to have acceptance and security.

While these examples demonstrate that an emergent phenomenon, such as the mind, climate, economy, or group behavior, can influence the actions of an individual neuron, organism, or individual behavior, it is a mistake to believe that the higher-level system causes the building blocks themselves to acquire new skills. Neurons act as neurons even when getting a box of ice cream. Base elements do not behave in novel ways when they operate as part of the higher-order system.

Self-referential Loops

Self-referential loops, explored in the book "I Am a Strange Loop" by Douglas Hofstadter, are fascinating phenomena that occur in nature and cognition.  These loops involve systems that reference themselves in a cyclic manner, giving rise to intricate patterns and emergent properties.

Prominent examples are the emergence of consciousness and self-awareness. Because our mental model of the world includes a model of ourselves, we become aware of ourselves, and subjective experiences arise in our conciseness.

The liar paradox, “this statement is false” demonstrates the enigma of self-references.

Assignment:

Study these examples of Self-referential loops.

Complex Adaptive Systems

A complex adaptive system is a system that is complex in that it is a dynamic network of interactions, but the behavior of the ensemble may not be predictable according to the behavior of the components. It is adaptive in that the individual and collective behavior mutate and self-organize corresponding to the change-initiating micro-event or collection of events.

Typical examples of complex adaptive systems include: climate; cities; firms; markets; governments; industries; ecosystems; social networks; power grids; animal swarms; traffic flows; social insect (e.g. ant) colonies; the brain and the immune system; and the cell and the developing embryo. Human social group-based endeavors, such as political parties, communities, geopolitical organizations, war, and terrorist networks are also considered as complex adaptive systems.

Problems create knowledge

In the grand narrative of human advancement, the intricate relationship between problems and knowledge creation has been a driving force that propels us toward greater understanding and progress. The foundation of this concept, which finds resonance in the philosophical insights of Karl Popper, underscores how challenges stimulate our intellectual growth, guide our explorations, and shape the contours of our collective wisdom.

Encountering problems and thereby creating knowledge is an important mechanism that often causes emergence.

Assignment

Read the essay Problems Create Knowledge.

Evolution and Emergence:

Evolution, one of the most remarkable processes in nature, is deeply intertwined with emergence. Through the mechanism of natural selection, complex and adaptive behaviors, traits, and structures emerge over time. The evolution of the eye, for instance, involves the gradual emergence of light-sensitive cells, followed by the refinement of these structures over millions of years to create sophisticated visual organs.

The evolutionary emergence of complex ecosystems showcases how the interaction between species leads to intricate relationships, with each species influencing and being influenced by others. This interplay gives rise to emergent properties such as ecological stability, biodiversity, and intricate food webs.

Development—the growth and maturing of an organism or system over time—is distinct from evolution—the change in heritable characteristics of organisms across generations.

In short, evolution is powered by free energy, and constrained by reality.

Assignment

The book The Emergence of Everything, by Harold J. Morowitz, describes the emergence of everything in the universe in a series of 28 steps beginning with “the first emergence” (the origins of the big bang) and ending with “the spirit”. Interested students may wish to read that book and identify the four claims for each claimed emergence.

Powered by free energy

Free energy—energy available to perform work—provides the power that enables emergence. This free energy is often in the form of a naturally occurring gradient.

A gradient is the difference between two interacting systems that creates instability, whether it be a difference in temperature, pressure, chemical concentration, electrical charge, or some other characteristic. A hillside is a common example of a gravitational gradient.

When such a difference exists, there will be spontaneous flow from one system to the other until that difference, or the gradient, is eliminated, and a stable equilibrium is achieved. This happens spontaneously to dissipate the free energy contained in the gradient. As an example, materials tend to move downhill in response to the gravitational gradient.

Identifying the source of free energy helps to answer why this emerged.

Assignment

Complete the Wikiversity course on Gradients in Nature.

Constrained by reality

Any system, including emergent systems, must become stable to persist. This requires emergent systems adapt to their environment. We often learn in everyday life by trial and error. In biological evolution this is called the survival of the fittest. In the context of adaptation, it is called variation and selection. In scientific research this is called conjecture and refutation or simply hypothesis testing. In Artificial Intelligence it is called generate and test.

In each case the viable possibilities are constrained by reality. Reality serves as the ultimate reference standard against which all ideas, theories, and perspectives are measured and validated. It is the foundation that guides our exploration of the universe, shapes our perceptions, and directs our pursuits of what is real and what us true.

Although everything in existence has emerged, it is not true that anything whatsoever can emerge.

Assignment

• Study the essay Reality is the Ultimate Reference Standard.
• Study the essay Aligning worldviews.

Weak and Strong Emergence

The term ‘emergence’ often causes confusion in science and philosophy, as it is used to express at least two quite different concepts. We can label these concepts strong emergence and weak emergence. Both of these concepts are important, but it is vital to keep them separate.

Weak Emergence:

Weak emergence occurs when the emergent properties of a system can be understood and explained by analyzing its constituent parts and their interactions. The behavior of a system at a higher level emerges from the interactions of its components, and while surprising, it is not fundamentally irreducible. The synchronization of fireflies and the flocking behavior of birds are examples of weak emergence.

Assignment:

1. Study these Examples of Weak Emergence.
2. Choose one or more examples to study for this assignment.
3. Identify and describe each of the four claims that pertain to the example phenomena chosen.

Strong Emergence:

Strong emergence is a hypothesized kind of emergence that creates the existence of something ontologically new in nature. Most researchers who have studied these claims reject the existence of strong emergence.

Strong emergence suggests that emergent properties cannot be fully explained by the interactions of constituent parts. In other words, the whole is more than the sum of its parts, and new properties arise that cannot be predicted from a reductionist perspective. Consciousness, subjective experience, and the emergence of novel biological functions are often cited as examples of strong emergence. “In strong emergence, the behavior of a system with many parts is not reducible to the aggregate behavior of all those parts, even in principle.”

For example, when considering behavior of a particular atom that is part of a human body, an advocate of strong emergence might claim:

“That atom is part of you, a person, and you can’t predict the behavior of that atom without understanding something about the bigger person-system. Knowing about the atom and its surroundings is not enough.”

Sean Carroll remarks “If it’s how the world actually does work, then our purported microscopic theory of the atom is simply wrong. ”

There is no direct evidence of this happening. Strong emergence claims to explain consciousness, or establish the existence of free-will, souls, or an afterlife. Claims of strong emergence are generally dismissed as magical explanations for mysteries that are not yet understood.  

Assignment:

1. Study these Examples of Strong Emergence.
2. Choose one or more of the examples to study.
3. Decide if you believe 1) the phenomena described is an illusion, or 2) the emergent phenomena will eventually be explained in terms of presently known and understood constituent parts, or 3) the emergent phenomena is the result of yet to be discovered constituent parts, or newly discovered behavior of the constituent parts.

What there is

Our studies throughout this course allow us to provide a more nuanced description of what there is, what is real in our universe. Below is a table, adapted from The Big Picture, chapter 13. The fundamental building blocks of the universe are listed in the left-most column. These are discovered and described using techniques of scientific reduction, drilling down and continuously decomposing objects into the constituent parts.  We then see higher levels that emerge from the fundamental building blocks where useful analysis can also take place. Chemists study atoms, molecules, compounds, chemical bonds, chemical reactions, and energy transfers. Biologist study proteins, cells, tissues, organs, and organisms. Continuing toward the right, we include the subjective realm. There are certainly real concepts of morality, aesthetics, and aspirations, however the mechanisms and arrangements of the constituent parts are not yet well understood. All of that is real, some is fundamental, and some is emergent. The right-most column lists previously hypothesized substances that are now known to be illusions. Phlogiston was a good theory while it lasted, but as our understanding evolved, it is now known to be a superseded theory based on an illusion.

The existence of free will, the soul, afterlife, and an almighty god are still debated. Perhaps these will also be generally accepted as illusions or proved conclusively to exist. The investigations, and dialogue continue.

Fundamental	Emergent / Apparent
Underlying Physical Reality, The Standard Model of Particle Physics, Relativity	Psychology, Biology, Chemistry,   Physics	Morality, Aesthetics, Asperations	Phlogiston, Aether, Caloric, Élan vital, Unicorns
Real			Illusions
←←← Factual / Objective →→→		Constructed / Subjective	Obsolete, Superseded, Fantasy, Myth
←←←← Reduction →→→→		←←←Emergent →→→	Dreaming, Storytelling, Understanding evolves

Assignment

1. Read the essay What there is.
2. Read the essay The role and limitations of scientific reduction.
3. Carefully examine the table above. Add or move entries in the table to align with your best understanding of what there is.

Summary and Conclusions

Key conclusions studied in this course are summarized here.

• Remarkably, everything in the universe emerged from the basic laws of physics.
• A property of a system is “emergent” if it is not part of a detailed “fundamental” description of the system, but it becomes useful or even inevitable when we look at the system more broadly.
• While reductionism tells us what there is, emergence helps us understand what there can be; what can be constructed.
• Although this is really new, there is really nothing new.
• Several hypothesized substances, such as Phlogiston, and caloric were never found because they never existed, they were only an illusion.
• Claiming the “B emerged from A” makes four subsidiary claims: 1) B is novel, 2) B is composed only of A, 3) the transformation mechanism is identified, and 4) the energy source powering the transformation is identified.
• Emergence is about science, not magic.
• Many mechanisms may explain the emergence. These include phase transitions, the kinetic theory of gasses, self-organization, dynamic equilibrium, complexity and chaos theory, downward causation, self-referential loops, and complex adaptive systems.
• Although complex and chaotic systems are unpredictable, they are deterministic.
• In downward causation, it is a mistake to believe that the higher-level system causes the building blocks themselves to acquire new skills.
• Problems create knowledge.
• Both development and evolution result in change over time. Development—the growth and maturing of an organism or system over time—is distinct from evolution—the change in heritable characteristics of organizations across generations.
• In short, emergence is powered by free energy, and constrained by reality.
• Free energy—energy available to perform work—provides the power that enables emergence. This free energy is often in the form of a naturally occurring gradient.
• In each case the viable possibilities are constrained by reality. Reality serves as the ultimate reference standardagainst which all ideas, theories, and perspectives are measured and validated. It is the foundation that guides our exploration of the universe, shapes our perceptions, and directs our pursuits of what is real and what us true.
• Although everything in existence has emerged, it is not true that anything whatsoever can emerge.

In conclusion, emergence is a captivating lens through which we can perceive the interconnectedness of the universe. From the synchronous fireflies to the intricate web of neural connections in our brains, the world is teeming with examples that highlight the emergence of complexity from simplicity. Whether weak or strong, emergence reveals the elegance with which nature orchestrates a harmonious dance of elements. In the grand narrative of evolution, emergence serves as the catalyst for innovation, adaptation, and the breathtaking diversity that defines life's journey.

While reductionism is successful at understanding much of our world, it has its limits. Chaos, complexity,  self-organization, self-referential loops, and the harnessing of free energy demonstrate that many interesting and real phenomena can only be understood by analyzing systems in addition to identifying their components.

Recommended Reading

Students who are interested in learning more about emergence may wish to read these books:

• Strogatz, Steven H. (March 5, 2003). Sync: The Emerging Science of Spontaneous Order  . Hachette Books. pp. 338. ISBN 978-0786868445. 
• Morowitz, Harold J. (November 7, 2002). The Emergence of Everything: How the World Became Complex  . Oxford University Press. pp. 224. ISBN 978-0195135138. 
• Azarian  , Bobby (June 28, 2022). The Romance of Reality: How the Universe Organizes Itself to Create Life, Consciousness, and Cosmic Complexity  . BenBella Books. pp. 320. ISBN 978-1637740446. 
• Sapolsky, Robert M. (October 17, 2023). Determined: A Science of Life without Free Will  . Penguin Press. pp. 528. ISBN 978-0525560975. 
• Hoel, Erik (July 25, 2023). The World Behind the World: Consciousness, Free Will, and the Limits of Science  . Avid Reader Press. pp. 256. ISBN 978-1982159382. 
• Hofstadter, Douglas R   (February 5, 1999). Gödel, Escher, Bach: An Eternal Golden Braid  . Basic Books. pp. 824. ISBN 978-0465026562. 
• Hofstadter, Douglas R   (July 8, 2008). I Am a Strange Loop  . Basic Books. pp. 432. ISBN 978-0465030798. 
• Carroll, Sean (May 16, 2017). The Big Picture: On the Origins of Life, Meaning, and the Universe Itself  . Dutton. pp. 496. ISBN 978-1101984253. 
• West  , Geoffrey (May 15, 2018). Scale: The Universal Laws of Life, Growth, and Death in Organisms, Cities, and Companies  . Penguin Books. pp. 496. ISBN 978-0143110903. 
• Pearl, Judea (August 25, 2020). Book of Why  . Basic Books. pp. 432. ISBN 978-1541698963. 
• Zemansky  , Mark Waldo (September 1, 1981). Heat and thermodynamics. McGraw-Hill. pp. 560. ISBN 978-0070666474. 

I have not yet read the following books, but they seem interesting and relevant. They are listed here to invite further research.

• Vital Dust: The Origin and Evolution of Life on Earth, by Christian De Duve