Questions to consider when evaluating AI

 I am a slow adopter of new technologies. I have recently been playing around with AI at a very basic level on some research problems. Colleagues are also telling me about their experiences. I want to write something about its potential, both good and bad, for research and teaching. I want to hear from more people, particularly in condensed matter theory. However, before that, I think it is worth stepping back and asking some bigger questions than "Can AI help me publish more papers?" or "How do we stop students cheating on assessment?", as important as they are. I know the mathematics community is going through some angst and has issued a declaration about AI, and it is good to see that level of reflection.

Neil Postman (1931-2003) was a media theorist and cultural critic at New York University who spent a lifetime wrestling with questions about the broader implications of new technologies. In a talk given in 1998, he considered five things we need to know about technological change. Postman's enduring influence and relevance are marked by the fact that these five things featured in a column in The Washington Post, "Is the Internet Evil?" by Christine Emba, published in 2018.

Below, I summarise the five ideas from Postman's talk and provide questions (in italics) we should ask about any technology, particularly Artificial Intelligence (AI).

1. All technological change is a trade-off. 

"the greater the wonders of a technology, the greater will be its negative consequences" 

Don't just ask the question "What will a new technology do?" Also ask, "What will a new technology undo?"

"a sophisticated perspective on technological change includes one’s being skeptical of Utopian and Messianic visions drawn by those who have no sense of history or of the precarious balances on which culture depends."

Through adoption of the technology, what will we lose, individually and as a society?

2. The advantages and disadvantages of a new technology are never distributed evenly among the population.

Who will benefit? Who will be harmed? 

Winners will try to persuade losers that they will benefit as well.

Benefits and harms can relate to employment, finances, social status, health, and political power.

3.  Embedded in every technology are powerful ideas. 

"These ideas are often hidden from our view because they are of a somewhat abstract nature. But this should not be taken to mean that they do not have practical consequences."

"The telegraphic person values speed, not introspection. The television person values immediacy, not history... the computer person values information, not knowledge, certainly not wisdom." 

"The medium is the message."

What ideas are embedded in the technology?

How does it make us use our minds and bodies?

How does it affect our personal relationships and social cohesion?

4. Technological change is not additive; it is ecological. It changes everything.

"The consequences of technological change are always vast, often unpredictable and largely irreversible."

The entrepreneurs who started the television industry "did not mean to turn political discourse into a form of entertainment."

The consequences can be social, economic, political, environmental, religious, and health-related.

What are the unintended consequences of the technology?

5. When a technology becomes mythic, it is always dangerous because it is then accepted as it is, and is therefore not easily susceptible to modification or control.

"...our enthusiasm for technology can turn into a form of idolatry and our belief in its beneficence can be a false absolute. The best way to view technology is as a strange intruder, to remember that technology is not part of God’s plan but a product of human creativity and hubris, and that its capacity for good or evil rests entirely on human awareness of what it does for us and to us."

How does the technology lead to idolatry? Do some people worship it, its creators, or its owners?

Finally,

Do we use the technology or does the technology use us? 

In different words, will we shape our lives to fit the requirements of the technology, rather than have our values shape our use of the technology?

A multi-disciplinary perspective on mental illness

How is mental illness defined? What causes mental illness? How can a person be healed? Answering these questions will be influenced by our answer to the question of what a person is. Returning to the stratification of reality resulting from emergence, we see that there are social, psychological, neurological, physiological, and genetic dimensions to a person. To illustrate the complexity, I now take a brief tour of different university departments to get their unique perspective on mental health. Each represents a different tradition.

Biomedicine

The biomedical model for mental illness is based on the idea that brains are machines involving physical and chemical processes. Mental illness occurs when these processes do not function normally. Over the past few decades, brain imaging techniques have shown differences between the brains of healthy patients and those with mental illnesses such as depression, schizophrenia, and bipolar disorder. The best course of treatment is deemed to be drugs that target the parts of the brain or processes that are dysfunctional. Sometimes, physical interventions such as electrical shock therapies or surgeries are advocated. This biomedical model was embraced and promoted by most psychiatrists until relatively recently.  

Antidepressant drugs have been widely prescribed, and now there are many studies examining their effectiveness, side effects, and biochemical mechanisms. I mention three scientific problems. First, there is a large placebo effect. This is found in studies where two groups of patients are told they are receiving an antidepressant drug. One group receive the actual drug, and the second group receives a placebo, a pill that, unknown to them, does not contain the drug. The proportion of patients reporting a significant improvement in mental health was about 25% for taking the actual drug compared to 10% for those taking the placebo. In other words, it seems that believing one will get better can lead to significant improvements in mental health. 

Second, there is a large variation between patients concerning how effective the drugs are. Patients’ perceptions of change in their mental health range from getting slight worse to no change to large improvements. Third, the biochemical mechanism of the drugs has become controversial. When the class of drugs known as Selective Serotonin Reuptake Inhibitors (SSRIs) were introduced, psychiatrists were confident that they knew how they work. Depressed patients lacked serotonin. SSRIs blocked the reuptake of serotonin into neurons, increasing the levels of this neurotransmitter in the synaptic cleft. However, a recent meta-analysis concluded as follows. 

“The main areas of serotonin research provide no consistent evidence of there being an association between serotonin and depression, and no support for the hypothesis that depression is caused by lowered serotonin activity or concentrations. Some evidence was consistent with the possibility that long-term antidepressant use reduces serotonin concentration.”

In her book, Mind Fixers: Psychiatry's Troubled Search for the Biology of Mental Illness, Anne Harrington, a historian of science at Harvard, commented.  

“Today one is hard-pressed to find anyone knowledgeable who believes that the so-called biological revolution of the 1980’s made good on most or even any of its therapeutic and scientific promises. It is now increasingly clear to the general public that it overreached, overpromised, overdiagnosed, overmedicated and compromised its principles.”

Psychiatry is a tradition, for better or worse. Its proponents persist in their faith that the biomedical model has the best answers to mental illness, even though the evidence for this belief is ambiguous. Science can involve faith. 

The stakes are high. If a patient takes medication, they may get better, worse, or experience no change. If they don’t take medication, they risk missing out on healing.

Psychology 

Psychologists present a multitude of theories of and treatment plans for mental illnesses. The focus is not on biology but on mental processes. Some focus on the subconscious and others on thoughts we are aware of and can articulate. Some focus on current life experience and thinking patterns, whilst others delve into the past, including unresolved childhood conflict or trauma. Sigmund Freud, the founder of psychoanalysis, claimed that depression was due to aggression toward the self.  A century later, there is no empirical evidence to support his claim. Other psychologists claim depression is predominantly a loss of hope. Opinion is divided about the best method of psychotherapy, where a patient has regular sessions with a trained professional to address unhelpful thoughts, emotions, and behaviours. Names for different methods include Cognitive Behavioural Therapy (CBT), Dialectical Behaviour Therapy (DBT), Psychodynamic Therapy, Humanistic Therapy, and Acceptance and Commitment Therapy (ACT).  Central to CBT is the claim that "Irrational thinking is at the root of much emotional distress that people experience."

This diversity of perspectives and treatments highlights the level of scientific uncertainty about both causes and treatment.

I now mention three developments that are receiving increasing attention in psychology research and have a transcendent dimension.

Mindfulness practices. These involve training patients to focus their “attention on the present moment—thoughts, feelings, sensations, and environment—with an attitude of openness, curiosity, and non-judgment. It involves observing experiences directly, rather than overthinking or reacting impulsively. Key elements include breathing techniques, meditation, and bringing awareness to daily activities.”  (Google AI overview).

Forgiveness. The American Psychological Association offers a continuing education article that cites studies showing that practising forgiveness can improve mental health.  

Awe and wonder. Dacher Keltner has made extensive studies of the experience of awe and recounted them in a popular book.  In a recent article with Maria Monroy, they:  “review recent advances in the scientific study of awe, an emotion often considered ineffable and beyond measurement. Awe engages five processes—shifts in neurophysiology, a diminished focus on the self, increased prosocial relationality, greater social integration, and a heightened sense of meaning—that benefit well-being. We then apply this model to illuminate how experiences of awe that arise in nature, spirituality, music, collective movement, and psychedelics strengthen the mind and body.”

Integrated medicine

The past few decades have seen the rise of integrated medicine, which promotes the view that many diseases, both physical and mental, are best treated by a holistic approach that combines treatments from different specialists. For mental health, it proposes that treatments might include not just drug and talking therapies but also address lifestyle issues. This means considering the role of sleep, exercise, diet, stress reduction, connection to nature, and screen time. With regard to diet, this builds on recent research showing deep connections between what goes on in the gut and the brain. Perhaps this is not surprising because our brains are not disembodied. They are part of our bodies and are connected to our whole nervous system.

Sociology 

Sociologists have investigated how mental illness can arise from social isolation. Emile Durkheim (1858-1917) was one of the founders of sociology. His book, Suicide: A Study in Sociology was published in 1897 and pioneered the scientific study of social phenomena. He proposed that suicide comes in four types, being distinguished by the level of imbalance of two social forces: social integration and moral regulation. Based on a detailed analysis of statistical data, Durkheim concluded that suicide was more likely in men than women, for single people than those who are married, for people without children than people with children, among Protestants than Catholics and Jews, among soldiers than civilians, and in times of peace than in times of war.

Since Durkheim, many more sociological studies suggest that social isolation and a lack of meaningful relationships can be a major contributing factor to depression. Some of this research has been reviewed in a popular book, Lost Connections: Uncovering the Real Causes of Depression and the Unexpected Solutions by Johann Hari.  He was motivated by his own experience of being prescribed and taking antidepressants for many years without consideration of how his social isolation might be a contributing factor.

This short survey of the perspective on mental illness from a range of scientific disciplines illustrates the complexity of the issue, the multifaceted nature of reality, and scientific uncertainty.

Naturally, this survey of different scientific perspectives raises questions about my own experience. Why did the antidepressant drugs seem to work sometimes and not others? Did I experience a placebo effect? Why was mindfulness helpful to me two decades ago but not more recently? What was the role of stress, childhood experiences, social isolation, personal pride, or introversion in creating my mental illness? I simply don’t know the answers to these questions and don’t think I ever will. What does matter is that, somehow at different times, I did experience degrees of healing that allowed me to function, albeit sometimes at diminished levels. Regardless of which traditions you choose to guide your journey and whatever choices you make, trust (faith) is involved.

Why is the state of universities such an emotional issue for me?

It all about values!

Universities have changed dramatically over the course of my lifetime. Australian universities are receiving increasing media attention due to failures in management and governance. But there is a lot more to the story, particularly at the grassroots level, of the everyday experience of students and faculty. It is all about the four M's: management, marketing, metrics, and money. Learning, understanding, and discovering things for their own sake is alien and marginalised. I have stopped writing posts about this. So why come back to it?

I am often struck how emotional this issue is for me and how hard it is to sometimes talk about it, particularly with those with a different view from me. Writing blog posts (e.g. this one) about it has been a somewhat constructive outlet, rather than exploding in anger at an overpaid and unqualified "manager" or one of their many multiplying minions.

A few weeks ago, I listened to three public lectures by the Australian historian Peter Harrison. [He is my former UQ colleague. We are now both Emeritus. I benefited from excellent seminars he ran at UQ, some of which I blogged about].

The lectures helped me understand what has happened to universities and also why it is a sensitive subject for me. Briefly, it is all about values and virtues.

The lectures are nicely summarised by Peter in the short article, 

How our universities became disenchanted: Secularisation, bureaucracy and the erosion of value

Reading the article rather than this blog post is recommended. I won't try and summarise it, but rather highlight a few points and then make some peripheral commentary.

I agree with Peter's descriptions of the problems we see on the surface (bureaucracy, metrics, and management features significantly). His lectures are a much deeper analysis of underlying cultural changes and shifting worldviews that have occurred over centuries, leading universities to evolve into their current mangled form.

A few things to clarify to avoid potential misunderstanding of Peter's arguments.

Secularisation is defined broadly. It does not just refer to the decline in the public influence of Christianity in the Western world. It is also about Greek philosophy, particularly Aristotle, and the associated emphasis on virtues and transcendence. Peter states:

"The intrinsic motivations of teachers, researchers and scholars can be understood in terms of virtues or duties. According to virtue ethics, the “good” of an activity is related to the way it leads to a cultivation and expression of particular virtues. These, in turn, are related to a particular conception of natural human ends or goals. (Aristotle’s understanding of human nature, which informs virtue ethics, proposes that human beings are naturally oriented towards knowledge, and that they are fulfilled as persons to the extent that they pursue those goals and develop the requisite intellectual virtues.)"

The virtue ethics of Aristotle [and Alisdair MacIntyre] conflicts with competing ethical visions, including duty-oriented (deontological) ethics, consequentialist ethics, and particularly utilitarianism. This led to a shift away from intrinsic goods to what things are "good for", i.e., what practical outcomes they produce. For example, is scientific research "good" and have "value" because it cultivates curiousity, awe, and wonder, or because it will lead to technology that will stimulate economic growth?

Peter draws significantly on Max Weber's ideas about secularisation, institutions, and authority. Weber argued that a natural consequence of secularisation was disenchantment (the loss of magic in the world). This is not simply "people believe in science rather than magic". Disenchantment is a loss of a sense of awe, wonder, and mystery.

Now, a few peripheral responses to the lectures.

Is secularisation the dominant force that has created these problems for universities? In question time, Peter was asked whether capitalism was more important. i.e., universities are treated as businesses and students as customers? He agreed that capitalism is a factor but also pointed out how Weber emphasised that capitalism was connected to the secularising effects of the Protestant Reformation.

 I think that two other factors to consider are egalitarianism and opportunism. These flow from universities being "victims" of their own success. Similar issues may also be relevant to private schools, hospitals, and charities. They have often been founded by people of "charisma" [in the sense used by Weber] motivated by virtue ethics. Founders were not concerned with power, status, or money. What they were doing had intrinsic value to them and was "virtuous". In the early stages, these institutions attracted people with similar ideals. The associated energy, creativity, and common vision led to "success." Students learnt things, patients got healed, and poverty was alleviated. But, this success attracted attention and  the institution then had power, money, status, and influence.

The opportunists then move in. They are attracted to the potential to share in the power, money, status, and influence. The institution then takes on a life of its own, and the ideals and virtue ethics of the founders are squeezed out. In some sense, opportunism might be argued to be a consequence of secularisation. 

[Aside: two old posts considered a similar evolution, motivated by a classic article about the development of businesses.]

One indicator of the "success" of universities is how their graduates join the elite and hold significant influence in society. [Aside: ignoring the problem of distinguishing correlation and causality. Do universities actually train students well or just select those who will succeed anyway?]  Before (around) 1960, (mostly) only the children of the elite got to attend university. Demands arose that more people should have access to this privilege. This led to "massification" and an explosion in the number of students, courses, and institutions. This continues today, globally. Associated with this was more bureaucracy. Furthermore, the "iron triangle" of cost, access, and quality presents a challenge for this egalitarianism. If access increases, so does cost and quality decreases, unless you spend even more. It is wonderful that universities have become more diverse and accessible. On the other hand, I fear that for every underprivileged student admitted whose mind is expanded and life enriched, many more rich, lazy, and entitled students suck the life out of the system.

Metrics are pseudo-rational

Peter rightly discussed how the proliferation of the use of metrics to measure value is problematic, and reflects the "rationalisation" associated with bureaucracy (described by Weber). Even if one embraces the idea that "rational" and "objective" assessment is desirable, my observation is that in practice, metrics are invariably used in an irrational way. For example, managers look at the impact factor of journals, but are blissfully oblivious to the fact that the citation distribution for any journal is so broad and with a long tail that the mean number is meaningless. The underlying problem is that too many of the people doing assessments suffer from some mixture of busyness, intellectual laziness, and arrogance. Too many managers are power hungry and want to make the decisions themselves, and don't trust faculty who actually may understand the intellectual merits and weaknesses of the work being assessed.

The problems are just as great for the sciences as the humanities

On the surface, the humanities are doing worse than the sciences. For example, if you look at declining student numbers, threats of job cuts, political criticism, and status within the university. This is because science is associated with technology which is associated with jobs and economic growth. However, if you look at pure science that is driven by curiousity, awe, and wonder, then one should be concerned. There is an aversion to attacking difficult and risky problems, particularly those that require long-term investment or have been around for a while. The emphasis is on low-lying fruit and the latest fashion. Almost all physics and chemistry research is framed in terms of potential applications, not fundamental understanding. Sometimes I feel some of my colleagues are doing engineering not physics. In a similar vein, biochemists frame research in terms of biomedical applications, not the beauty and wonders of how biological systems work. 

Are universities destined for bureaucratic self-destruction?

Provocatively, Peter considered the potential implications of the arguments of historian and anthropologist Joseph Tainter concerning the collapse of complex societies. On the technical side, this reminded me of a famous result in ecology by Robert May, that as the complexity of a system (the number of components and interactions) increases, it can become unstable.

I don't think universities as institutions will collapse. They are too integrated into the fabric of modern capitalism. What may collapse is the production of well-educated (in the Renaissance sense) graduates and research that is beautiful, original, and awe-inspiring. This leads naturally into the following question.

Is the age of great discoveries over?

Peter briefly raised this issue. On the one hand, we are victims of our own success. It is amazing how much we now know and understand. Hence, it is harder to discover truly new and amazing things. On the other hand, because of emergence we should expect surprises.

There is hope on the margins

Peter did not just lament the current situation but made some concrete suggestions for addressing the problems, even though we are trapped in Weber's "iron cage" of bureaucracy.

• Re-balancing the structures of authority
• Finding a place for values discourse in the universities
• Develop ways of resolving differences with a sense of the rationality of Alisdair MacIntyre in mind

On the first, I note the encouraging work of the ANU Governance Project.

Peter also encouraged people to work on the margins. I also think that this is where the most significant scholarship and stimulus for reform will happen. A nice example is the story that Malcolm Gladwell tells in a podcast episode, The Obscure Virus Club.

One hundred years of Ising

In 1925, Ising published his paper on the solution of the model in one dimension. An English translation is here.https://www.hs-augsburg.de/~harsch/anglica/Chronology/20thC/Ising/isi_fm00.html

Coincidentally, next week I am giving a lecture on the Ising model to an undergraduate class in statistical mechanics. To flesh out the significance and relevance of the model, here are some of the interesting articles I have been looking at:

The Ising model celebrates a century of interdisciplinary contributions, Michael W. Macy, Boleslaw K. Szymanski and Janusz A. Hołyst

This mostly discusses the relevance of the model to understanding basic problems in sociology, including its relation to the classic Schelling model for social segregation.

The Ising model: highlights and perspectives, Christof Külske

This mostly discusses how the model is central to some work in mathematical physics and probability theory.

The Fate of Ernst Ising and the Fate of his Model, Thomas Ising, Reinhard Folk, Ralph Kennac, Bertrand Berche, Yurij Holovatche.

This includes some nice memories of Ising from his son, Thomas.

Aside: I wanted a plot of the specific heat for the one-dimensional model. According to Google AI "In a 1D Ising model with no external magnetic field, the specific heat is zero at all temperatures."

Quantifying the obscurity of academic writing

 Occasionally The Economist publishes nice graphs capturing social and economic trends. Here is one.

It is part of a nice article

Academic writing is getting harder to read—the humanities most of all

The downward trend in the humanities and social sciences is dramatic and perhaps not surprising.

I was surprised that in the natural sciences the trend wasn't worse. The Flesch reading ease score goes from about 26 around 1960 to about 18 today. 

However, this metric misses a lot. It only measures the number of words per sentence and the number of syllables per word. Thus, it is not sensitive to the amount of technical jargon or to overall clarity.

Emergence talk at University of the Philippines

Today I am giving a seminar on emergence at the University of Philippines Los Banos, in the Institute of Mathematical Sciences and Physics.

Here are my slides.

10 key ideas about emergence

Consider a system comprised of many interacting components. 

1. Many different definitions of emergence have been given. I take the defining characteristic of an emergent property of the system is novelty, i.e, the individual components of the system do not have this property.

2. Many other characteristics have been associated with emergence, such as universality, unpredictability, irreducibility, diversity, self-organisation, discontinuities, and singularities. However, it has not been established whether these characteristics are necessary or sufficient for novelty.

3. Emergent properties are ubiquitous across scientific disciplines from physics to biology to sociology to computer science. Emergence is central to many of the biggest scientific challenges today and some of the greatest societal problems.

4. Reality is stratified. A key concept is that of strata or hierarchies. At each level or stratum,  there is a distinct ontology (properties, phenomena, processes, entities, and effective interactions) and epistemology (theories, concepts, models, and methods). This stratification of reality leads to semi-autonomous scientific disciplines and sub-disciplines.

5. A common challenge is understanding the relationship between emergent properties observed at the macroscopic scale (whether in societies or in solids) and what is known about the microscopic scale: the components (whether individual humans or atoms) and their interactions. Often a key (but profound) insight is identifying an emergent mesoscopic scale (i.e., a scale intermediate between the macro- and micro- scales) at which new entities emerge and interact with one another weakly.

6. A key theoretical method is the development and study of effective theories and toy models. Effective theories can describe phenomena at the mesoscopic scale and be used to bridge the microscopic and macroscopic scales. Toy models involve just a few degrees of freedom, interactions, and parameters. Toy models are amenable to analytical and computational analysis and may reveal the minimal requirements for an emergent property to occur. The Ising model is a toy model that elucidates critical phenomena and key characteristics of emergence.

7. Condensed matter physics elucidates many of the key features and challenges of emergence. Unlike brains and economies, condensed states of matter are simple enough to be amenable to detailed and definitive analysis but complex enough to exhibit rich and diverse emergent phenomena.

8. The ideas above about emergence matter for scientific strategy in terms of choosing methodologies, setting priorities, and allocating resources.

9. An emergent perspective that does not privilege the parts or the whole can address contentious issues and fashions in the humanities and social sciences, particularly around structuralism.

10. Emergence is also at the heart of issues in philosophy including the nature of consciousness, truth, reality, and the sciences.

Emergence and the Ising model

The Ising model is emblematic of “toy models” that have been proposed and studied to understand and describe emergent phenomena. Although originally proposed to describe ferromagnetic phase transitions, variants of it have found application in other areas of physics, and in biology, economics, sociology, neuroscience, complexity theory, …  

Quanta magazine had a nice article marking the model's centenary.

In the general model there is a set of lattice points {i} with a “spin” {sigma_i = +/-1} and a Hamiltonian

where h is the strength of an external magnetic field and J_ij is the strength of the interaction between the spins on sites i and j. The simplest models are where the lattice is regular, and the interaction is uniform and only non-zero for nearest-neighbour sites.

The Ising model illustrates many key features of emergent phenomena. Given the relative simplicity of the model, exhaustive studies since its proposal in 1920, have given definitive answers to questions often debated about more complex systems. Below I enumerate some of these insights: novelty, quantitative change leads to qualitative change, spontaneous order, singularities, short-range interactions can produce long-range order, universality, three horizons/scales of interest, self-similarity, inseparable horizons, and simple models can describe complex behaviour.

Most of these properties can be illustrated with the case of the Ising model on a square lattice with only nearest-neighbour interactions (J_ij = J). Above the critical temperature (Tc = 2.25J), and in the absence of an external magnetic field the system has no net magnetisation. Below Tc, at net magnetisation occurs. For J > 0 (J < 0) this state is ferromagnetic (antiferromagnetic).

Novelty

The state of the system below Tc is qualitatively different than that at very high temperatures or the state of a set of non-interacting spins. Thus, the non-zero magnetisation is an emergent property, as defined in this post. This state is also associated with spontaneous symmetry breaking and more than one possible equilibrium state, i.e., the magnetisation can be positive or negative.

Quantitative change leads to qualitative change

The qualitative change associated with formation of the magnetic state can occur with a small quantitative change in the value of the ratio T/J, i.e., either by decreasing T or increasing J. Formation of the magnetic state is also associated with the quantitative change of increasing the number of spins from a large finite number to infinity. 

Singularities

For a finite number of spins all the thermodynamic properties of the system are an analytic function of the temperature and magnitude of an external field. However, in the thermodynamic limit, these properties become singular at T=Tc and h=0. This is the critical point in the phase diagram of h versus T. Some of the quantities, such as the specific heat capacity and the magnetic susceptibility, become infinite at the critical point. These singularities are characterised by critical exponents, most of which have non-integer values. Consequently, the free energy of the system is not an analytic function of T and h.

Spontaneous order

The magnetic state occurs spontaneously. The system self-organises. There is no external field causing the magnetic state to form. There is long-range order, i.e., the value of spins that are infinitely apart from one another are correlated. 

Short-range interactions can produce long-range order.

Although there is no direct long-range interaction between spins, long-range order can occur. Prior to Onsager’s exact solution of the two-dimensional model, many scientists were not convinced that this was possible.

Universality

The values of the critical exponents are independent of many details of the model, such as the value of J, the lattice constant and spatial anisotropy, and the presence of small interactions beyond nearest neighbour. Many details do not matter. This is why the model can give a quantitative description of experimental data near the critical temperature, even though the model Hamiltonian is a crude descriptions of the interactions in a real material. It can describe not only magnetic transitions but also transitions in liquid-gas, binary alloys, and binary liquid mixtures.

Three horizons/scales of interest

There are three important length scales associated with the model. Two are simple: the lattice constant, and the size of the whole lattice. These are the microscopic and macroscopic scale. The third scale is emergent and temperature dependent: the correlation length, i.e., the distance over which spins are correlated with one another. This can also be visualised as the size of magnetisation domains seen in Monte Carlo simulations. 

The left, centre, and right panels above show a snapshot of a likely configuration of the system at a temperature less than, equal to, and greater than the critical temperature, Tc, respectively.

Understanding the connection between the microscopic and macroscopic properties of the system requires studying the system at the intermediate scale of the correlation length. This scale also defines emergent entities [magnetic domains] that interact with one another weakly and via an effective interaction.

Self-similarity

At the critical temperature, the correlation length is infinite. Consequently, rescaling the size of the system, as in a renormalisation group transformation, the state of the systems does not change. The system is said to be scale-free or self-similar like a fractal pattern. This is an example of self-organised criticality.

Inseparable horizons

I now consider how things change when the topology or dimensionality of the lattice changes or when interactions beyond nearest neighbours are added. This can change the relationships between the parts and the whole. Some details of the parts matter. Changing from a two-dimensional rectangular lattice to a linear chain the ordered state disappears. Changing to a triangular lattice with antiferromagnetic nearest-neighbour interactions removes the ordering at finite temperature and there are an infinite number of ground states at zero temperature. Thus, some microscopic details do matter.

The main point of this example is that to understand a large complex system we have to keep both the parts and the whole in mind. It is not either/or but both/and. Furthermore, there may be an intermediate scale, at which new entities emerge.

Aside: I suspect heated debates about structuralism versus functionalism in social sciences, and the humanities are trying to defend intellectual positions (and fashions) that overlook the inseparable interplay of the microscopic and macroscopic that the Ising model captures.

Simple models can describe complex behaviour

Now consider an Ising model with competing interactions, i.e. the neighbouring spins of a particular spin compete with one another and with an external magnetic field to determine the sign of the spin. This can be illustrated with the an Ising model on a hexagonal close packed (hcp) lattice with nearest neighbour antiferromagnetic interactions and an external magnetic field. The lattice is frustrated and can be viewed as layers of hexagonal (triangular) lattices where each layer is displaced relative to one another.

This model has been studied by materials scientists as it can describe the many possible phases of binary alloys, AxB1-x, where A and B are different chemical elements (for example, silver and gold) and the Ising spins on site i has value +1 or -1, corresponding to the presence of atom A or B on that site. The magnetic field corresponds to the difference in the chemical potentials of A and B, and is related to their relative concentration.

The authors studied the Ising model on the hexagonal close-packed (hcp) lattice in a magnetic field. The authors are all from materials science departments and are motivated by the fact that the problem of binary alloys AxB1_x can be mapped onto an Ising model. A study of this model found rich phase diagrams including 32 stable ground states with stoichiometries, including A, AB, A2B, A3B, A5B, and A4B3. Even for a single stoichiometry, there can be multiple possible distinct orderings (and crystal structures). Of these structures, six are stabilized by purely nearest-neighbour interactions, eight by addition of next-nearest neighbour interactions. The remaining 18 structures require multiplet interactions for their stability. 

A second example is the Anisotropic Next-Nearest Neighbour Ising (ANNNI) model, which supports a plethora of ordered states, including a phase diagram with a fractal structure, known as the Devil’s staircase.

These two Ising models illustrate how relatively simple models, containing competing interactions (described by just a few parameters) can describe rich behaviour, particularly a diversity of ground states.

An emergentist perspective on public policy issues that divide

How is the whole related to the parts?

Which type of economy will produce the best outcomes: laissez-faire or regulated?

Can a government end an economic recession by "stimulus" spending?  

What is the relative importance of individual agency and social structures in causing social problems such as poverty and racism?

These questions are all related to the first one. Let's look at it from an emergentist perspective, with reference to physics. 

Consider the Ising model in two or more dimensions. The presence of nearest neighbour interactions between spins leads to emergent properties: long-range ordering of the spins, spontaneous symmetry breaking below the critical temperature, and singularities in the temperature dependence of thermodynamic properties such as the specific heat and magnetic susceptibility. Individual uncoupled spins have neither property. Even a finite number of spins do not. (Although, a large number of spins do exhibit suggestive properties such as an enhancement of the magnetic susceptibility near the critical temperature). Thus, the whole system has properties that are qualitatively different from the parts. 

On the other hand, the properties of the parts, such as how strongly the spins couple to an external field and interact with their neighbours, influence the properties of the whole. Some details of the parts matter. Other details don't matter. Adding some interaction with spins beyond nearest neighbours does not change any of the qualitative properties, provided those longer-range interactions are not too large. On the other hand, changing from a two-dimensional rectangular lattice to a linear chain removes the ordered state. Changing to a triangular lattice with an antiferromagnetic nearest-neighbour interaction removes the ordering and there are multiple ground states. Thus, some microscopic details do matter.

For illustrative purposes, below I show a sketch of the temperature dependence of the magnetic susceptibility of the Ising model for three cases: non-interacting spins (J=0), two dimensions (d=2), and one dimension (d=1). This shows how interactions can significantly enhance/diminish the susceptibility depending on the parameter regime.

The main point of this example is to show that to understand a large complex system we have to keep both the parts and the whole in mind. In other words, we need both microscopic and macroscopic pictures. There are two horizons, the parts and the whole, the near and the far. There is a dialectic tension between these two horizons. It is not either/or but both/and.

I now illustrate how this type of tension matters in economics and sociology, and the implications for public policy. If you are (understandably) concerned about whether Ising models have anything to do with sociology and economics, see my earlier posts about these issues. The first post introduced discrete-choice models that are essentially Ising models. A second post discussed how these show how equilibrium may never be reached leading to the insight that local initiatives can "nucleate" desired outcomes. A third post, considered how heterogeneity can lead to qualitative changes including hysteresis so that the effectiveness of "nudges" can vary significantly.

A fundamental (and much debated) question in sociology is the relationship between individual agency and social structures. Which determines which? Do individuals make choices that then lead to particular social structures? Or do social structures constrain what choices individuals make. In sociology, this is referred to as the debate between voluntarism and determinism. A middle way, that does not preference agency or structure, is structuration, proposed by Anthony Giddens.

Social theorists who give primacy to social structures will naturally advocate solving social problems with large government schemes and policies that seek to change the structures. On the other side, those who give primacy to individual agency are sceptical of such approaches, and consider progress can only occur through individuals, and small units such as families and communities make better choices. The structure/agency divide naturally maps onto political divisions of left versus right, liberal versus conservative, and the extremes of communist and libertarian. An emergentist perspective is balanced, affirming the importance of both structure and agency.

Key concepts in economics are equilibrium, division of labour, price, and demand. These are the outcomes of many interacting agents (individuals, companies, institutions, and government). Economies tend to self-organise. This is the "invisible hand" of Adam Smith. Thus, emergence is one of the most important concepts in economics. 

A big question is how the equilibrium state and the values of the associated state variables (e.g., prices, demand, division of labour, and wealth distribution) emerge from the interactions of the agents. In other words, what is the relationship between microeconomics and macroeconomics?

What are the implications for public policy? What will lead to the best outcomes (usually assumed to be economic growth and prosperity for "all")? Central planning (or at least some government regulation) is pitted against laissez-faire. For reasons, similar to the Ising and sociology cases, an emergentist perspective is that the whole and the parts are inseparable. This is why there is no consensus on the answers to specific questions such as, can government stimulus spending move an economy out of a recession? Keynes claimed it could but the debate rages on.

An emergentist perspective tempers expectations about the impact of agency, both individuals and government. It is hard to predict how a complex system with emergent properties will respond to perturbations such as changes in government policy. This is the "law" of unintended consequences.

“The curious task of economics is to demonstrate to men how little they really know about what they imagine they can design.”

Friedrich A. Hayek, The Fatal Conceit: The Errors of Socialism

I think this cuts both ways. This is also reason to be skeptical about those (such as Hayek's disciples) who think they can "design" a better society by just letting the market run free.

The challenge of useful data in the social sciences

A major challenge for the social sciences is obtaining data that is reliable, gives significant insight, and could be used to test theories. Each week I read The Economist. Many of their articles feature graphs of social or economic data. To me, some of the graphs are just random noise or show marginal trends that I am not convinced are that significant. But other graphs are quite dramatic or insightful. Previously, I posted a famous one about smoking.

This week I saw the graph below in The New York Times, as part of a long article, Childbirth Is Deadlier for Black Families Even When They’re Rich, Expansive Study Finds, based on this preprint.

The data clearly shows the distressing fact that "The richest Black women have infant mortality rates at about the same level as the poorest white women."

Different dimensions to emergence for specific scientific disciplines

Emergence is a concept relevant to a wide range of scientific disciplines, from physics to sociology. Emergence is also at the heart of some of the biggest questions and challenges in each discipline. How might I justify that claim? How do we move beyond "emergence" just being a trendy buzzword?

Here I suggest some different facets of a specific discipline that with an emergent perspective may help to understand the discipline and to plan scientific strategy. This post will be primarily descriptive and the next prescriptive. Later I will illustrate both aspects with specific disciplines. Although, some of the facets below may be somewhat obvious, others are profound. 

Presence of distinct scales. Scales may involve length, time, or number of components in a system of interest. Different phenomena are observed at different scales.

Stratification and separation of scales. Distinct phenomena as usually seen over some range of scale and a distinct stratum can be associated with that scale. 

The image is from here.

Sub-disciplines (or sub-fields) are associated with each stratum. The discipline can be viewed as stratified. For example, biology has sub-disciplines associated with ecosystems, organisms (animals and plants), organs, cells, genes, and molecules. This is nicely captured in a series of articles in The Economist.

The system can be viewed as interacting components. The system of interest is composed of many parts. Identifying the relevant components and their interactions may be non-trivial or at least was in the past. For example, consider the discovery of atoms in chemistry, quarks in nuclear physics, Cooper pairs in superconductivity, and DNA in genetics.

Emergent properties. Systems of interest have distinct properties that the components of the system do not. These properties may have certain characteristics such as universality, irreducibility, or unpredictability.

Emergent entities. These distinct entities can only be defined at certain scales and emerge from interactions between components that are defined at some smaller scale. In biology, emergent entities include organisms, organs, cells, genes, and proteins. In condensed matter physics emergent entities include quasiparticles and topological defects.

Emergent phenomena. This is closely related to emergent properties and may be redundant. But a property is something that a system has and a phenomenon is something that it does. 

Different experimental probes for different scales. For example, for condensed matter different types of electromagnetic radiation from x-rays to microwaves are used to investigate a material at different length scales. The nature of the instruments used and the type and quality of information gained can be quite different for the different scales.

Simple theoretical models of interacting components.  From the perspective of the smallest scales most systems with emergent properties are complex in that they involve many degrees of freedom and so large amounts of information and parameters are required to define the state of the system. The system may also be complex in the sense that the emergent properties are non-trivial and hard to describe theoretically. But with insight simple models with just a few parameters and state variables can exhibit and describe the emergent properties. Examples of such models in condensed matter physics include Ising, Hubbard, and non-linear sigma models. Examples from sociology include agent-based models such as the Schelling model for racial segregation. Simple models can be viewed as effective theories, valid at a particular scale, and can illustrate universality.

Organising principles and concepts at each scale. The principles and concepts are only meaningful and relevant at a particular scale. An example from condensed matter physics and elementary particle physics is spontaneous symmetry breaking.

In another post, I will discuss how an emergentist perspective plays out in scientific strategy.

The value of "simple" models for complex systems

Significant understanding of emergent phenomena in quantum materials has come from the study of model Hamiltonians such as those associated with the names Hubbard, Anderson, Kondo, Heisenberg, Kitaev, Haldane, BCS,...

I had not appreciated until recently that an early key to the Modern Synthesis of evolutionary biology (that brought together Darwinian natural selection with Mendelian genetics) was the development of simple mathematical models. The discussion below is taken from

Towards a unified science of cultural evolution 

Alex Mesoudi, Andrew Whiten and Kevin N. Laland 

Significant advances were made in the study of biological [micro]evolution before its molecular basis was understood, in no small part through the use of simplified mathematical models, pioneered by Fisher (1930), Wright (1931), and J.B.S. Haldane (1932)... 

Mathematical models such as [those for cultural evolution and gene-culture coevolution] are often treated with suspicion and even hostility by some social scientists, who consider them to be oversimplifications of reality... The alternatives..., however, are usually either analysis at a single (purely genetic or purely cultural) level or vague verbal accounts of “complex interactions,” neither of which we believe to be productive. Gene-culture analyses have repeatedly revealed circumstances under which the interactions between genetic and cultural processes lead populations to different equilibria than those predicted by single level models or anticipated in verbal accounts... as illustrated by the aforementioned examples of dairy farming and handedness.  

Interestingly, fifty years ago the same reservations about simplifying assumptions were voiced about the use of population genetic models in biology by the prominent evolutionary biologist Ernst Mayr (1963). He argued that using such models was akin to treating genetics as pulling coloured beans from a bag (coining the phrase “beanbag genetics”), ignoring complex physiological and developmental processes that lead to interactions between genes. 

 

In his classic article “A Defense ofBeanbag Genetics,” J. B. S. Haldane (1964) countered that the simplification of reality embodied in these models is the very reason for their usefulness. Such simplification can significantly aid our understanding of processes that are too complex to be considered through verbal arguments alone, because mathematical models force their authors to specify explicitly and exactly all of their assumptions, to focus on major factors, and to generate logically sound conclusions. Indeed, such conclusions are often counterintuitive to human minds relying solely on informal verbal reasoning. 

Haldane (1964) provided several examples in which empirical facts follow the predictions of population genetic models in spite of their simplifying assumptions, and noted that models can often highlight the kind of data that need to be collected to evaluate a particular theory. Ultimately, Haldane won the argument, and population genetic modelling is now an established and invaluable tool in evolutionary biology (Crow 2001). We can only echo Haldane’s defence and argue that the same arguments apply to the use of similar mathematical models in the social sciences.

A more recent version of J.B. S. Haldane's argument is Not Just a Theory—The Utility of Mathematical Models in Evolutionary Biology Maria R. Servedio,Yaniv Brandvain, Sumit Dhole, Courtney L. Fitzpatrick, Emma E. Goldberg, Caitlin A. Stern, Jeremy Van Cleve, D. Justin Yeh 

All models are wrong but some are useful. I first learnt this aphorism from Scott Page, in his wonderful course Model Thinking at Coursera.  This short talk discusses how models help us think more clearly. Simple quantitative models, such as agent-based models, in the social sciences, have the value that their assumptions can be clearly stated, and then the consequences of these assumptions can be investigated in a rigorous manner.

There is also a nice discussion of the importance of model building for science in John Holland's beautiful book, Emergence. 

Hysteresis, hype, niches, nudges and social change

The world is a mess. Most people want a better world. Sometimes nothing changes. Sometimes things change incredibly rapidly. Sometimes changes are positive. Other times the change is negative. Often this change is unanticipated, even by experts who have been studying the relevant topic for decades. Wicked problems are things that seem to be incredibly resilient to change. Examples of rapid changes that were (largely) positive and unanticipated were the peaceful collapse of the former Soviet empire, smoking in public becoming taboo, and increased public concern about climate change. Examples of negative changes include the rise of Trumpism, misinformation on social media, and the global financial crisis of 2008.

Many people in government, public policy, NGOs, and social activists want to implement policies and take actions that will produce outcomes that (they believe) are positive. Here I discuss some basic but very important insights from "social physics", such as discussed in my previous two posts.

Suppose the system of interest can be modelled by some type of Ising model where the pseudospin corresponds to two choices (good and bad) for each agent in the system. The policy maker wants to change something such as increase the incentive for agents to make the "good" choice. There are two qualitatively different possible behaviours and they are shown in the Figure below (taken from Bouchaud). 

The vertical axis is the "magnetisation", i.e, the fraction of agents who make the good choice. The horizontal axis is the "external field", i.e, the level of incentive provided for agents to make the good choice. 

Case I. Smooth curve (blue). This occurs when the interaction between agents is weaker than some threshold strength. Suppose that a small but not insignificant minority of agents are already making the good choice and then incentive is increased slightly. If one is near the steep part of the blue curve then this "nudge" can produce a desired outcome for the society.

Case II. Discontinuous curve (red). This occurs when the interaction between agents is greater than some threshold strength. People's choices are influenced more by their friends than by what the government or an NGO is telling them to do. Then one has to provided very large incentives to get a change in agent choice, far beyond the incentive required for a single isolated agent. The system is stuck in a state that is not good for the society as a whole. It is a metastable state, as shown in the figure below.

On the other hand, if the "polarisation field" is sitting near a critical value (5 in the figure, a tipping point), then a "nudge" can lead to a dramatic change for good. 

I think there are important implications for social activists of all stripes. Realistic expectations are key.

1. Don't expect even the best-designed and well-intentioned policy or action to necessarily have the impact you hope for.

2. Be sceptical about hype and ideology. In the public space there are a lot of claims, whether from political parties, pundits, or NGOs, that if we just do X (change this law, donate money, do what my book says, ...) then the good Y will inevitably follow.

The problem with unrealistic expectations is that they lead to disappointment, disillusionment, and burnout. People give up. Then the next fad or "silver bullet" comes along...

Inspired by a rugged landscape perspective, a better and more sustainable approach is that of learning and adaptation. One identifies what one thinks the best "nudge" is, tries something, evaluates the effect, adapts, and tries out some new ideas. One does not claim or expect the first few iterations to produce a significant desired effect. Here, somewhat "random" sampling of the landscape may help. Here a diversity of perspectives and methods can play a positive role. A more concrete version of this argument is in a paper concerned with public health initiatives. Rugged landscapes: complexity and implementation science, by Joseph T. Ornstein, Ross A. Hammond, Margaret Padek, Stephanie Mazzucca & Ross C. Brownson 

Postscript. After posting this I remember reading a recent article in The Economist pointing out how nudges often do not work.

Evidence for behavioural interventions looks increasingly shaky 

The academic literature is plagued by publication bias 

It references three recent Letters in PNAS, including this one, that come to the opposite conclusion to an earlier PNAS paper.

The effectiveness of nudging: A meta-analysis of choice architecture interventions across behavioral domains 

Stephanie Mertens, Mario Herberz, Ulf J. J. Hahnel, and Tobias Brosch

Sociological insights from statistical physics

Condensed matter physics and sociology are both about emergence. Phenomena in sociology that are intellectually fascinating and important for public policy often involve qualitative change, tipping points, and collective effects. One example is how social networks influence individual choices, such as whether or not to get vaccinated. In my previous post, I briefly introduced some Ising-type models that allow the investigation of fundamental questions in sociology. The main idea is to include heterogeneities and interactions in models of decision. 

What follows is drawn from Sections 2 and 3 of the following paper from the Journal of Statistical Physics. 

Crises and Collective Socio-Economic Phenomena: Simple Models and Challenges by Jean-Philippe Bouchaud

Bouchaud first considers a homogeneous population which reaches an equilibrium state. This is then described by an Ising model with an interaction (between agents) J, in an external field, F that describes the incentive for the agents to make one of the choices. The state of the model (in the mean-field approximation) is then found by solving the Curie-Weiss equation. In the sociological context, this was first derived by Weidlich and in the economic context re-derived by Brock and Durlauf.  (Aside: The latter paper is in one of the "top-five" economic journals, was published five years after submission, and has been cited more than 2000 times.)

As first noted by Weidlich, a spontaneous “polarization” of the population occurs in the low noise regime β>β c , i.e. [the average equilibrium value of S_z] ϕ ∗≠1/2 even in the absence of any individually preferred choice (i.e. F=0). When F≠0, one of the two equilibria is exponentially more probable than the other, and in principle the population should be locked into the most likely one: ϕ ∗>1/2 whenever F>0 and ϕ ∗<1/2 whenever F<0.

Unfortunately, the equilibrium analysis is not sufficient to draw such an optimistic conclusion. A more detailed analysis of the dynamics is needed, which reveals that the time needed to reach equilibrium is exponentially large in the number of agents, and as noted by Keynes, "in the long run, we are all dead." This situation is well-known to physicists, but is perhaps not so well appreciated in other circles—for example, it is not discussed by Brock and Durlauf.

Bouchaud then discusses the meta-stability associated with the two possible polarisations, as occurs in a first-order phase transition. From a non-equilibrium dynamical analysis, based on a Langevin equation, 

one finds that the time τ needed for the system, starting around ϕ=0, to reach ϕ ∗≈1 is given by: 𝜏 ∝ exp[𝐴𝑁(1−𝐹/𝐽)], where A is a numerical factor. This means that whenever 0<F<J, the system should really be in the socially good minimum ϕ ∗≈1, but the time to reach it is exponentially large in the population size.  The important point about this formula is the presence of the factor N(1−F/J) in the exponential.

In other words, it has no chance of ever getting there on its own for large populations. Only when F reaches J, i.e. when the adoption cost C becomes zero will the population be convinced to shift to the socially optimal equilibrium...

This is very different from the standard model of innovation diffusion, based on a simple differential equation proposed by Bass in 1969 [cited more than 10,000 times].

In physics, the existence of mutually inaccessible minima with different potentials is a pathology of mean-field models that disappears when the interaction is short-ranged. In this case, the transition proceeds through “nucleation”, i.e. droplets of the good minimum appear in space and then grow by flipping spins at the boundaries. 

This suggests an interesting policy solution when social pressure resists the adoption of a beneficial practice or product: subsidize the cost locally, or make the change compulsory there, so that adoption takes place in localized spots from which it will invade the whole population. The very same social pressure that was preventing the change will make it happen as soon as it is initiated somewhere.

This analysis provides concepts to understand wicked problems. Societies get "trapped" in situations that are not for the common good and outside interventions, such as providing incentives for individuals to make better choices, have little impact.

In the next post, I hope to discuss the role of heterogeneity (i.e. the role of a random field in the Ising model). A seminal paper published in the American Journal of Sociology in 1978 is Threshold models of collective behavior  by Mark Granovetter. It has been cited more than 6000 times. The central idea is how changes in heterogeneity can induce a transition between two different collective states.

Aside: The famous Keynes quote was in his 1923 publication, The Tract on Monetary Reform. The fuller quote is “But this long run is a misleading guide to current affairs. In the long run we are all dead. Economists set themselves too easy, too useless a task, if in tempestuous seasons they can only tell us, that when the storm is long past, the ocean is flat again.”

Models for collective social phenomena

World news is full of dramatic and unexpected events in politics and economics, from stock market crashes to the rapid rise of extreme political parties. Trust in an institution can evaporate overnight.

The world is plagued by "wicked problems" (corruption, belief in conspiracy theories, poverty, ...) that resist a solution even when considerable resources (money, personnel, expertise, government policy, incentives, social activism) are devoted to addressing the problem. 

Here I introduce some ideas and models that are helpful for efforts to understand these emergent phenomena. Besides rapid change and discontinuities, other relevant properties include herding, trending, tipping points, and resilient equilibria. Some cultural traits or habits are incredibly persistent, even when they are damaging to a community. 

I now consider some key elements for minimal models of these phenomena: discrete choices, utility, incentives, noise, social interactions, and heterogeneity.

Discrete choices

The system consists of N agents {i} who make individual choices. Examples of binary choices are whether or not to buy a particular product, vote for a political candidate, believe a conspiracy theory, accept bribes, get vaccinated, or join a riot. For binary choices, the state of each agent is modelled by an "Ising spin", S_i = +1 or -1. 

Utility

This is the function each agent wants to maximise; what they think they will gain or lose by their decision. This could be happiness, health, ease of life, money, or pleasure.  The utility U_i will depend on the incentives provided to make a particular choice, the personal inclination of the agent, and possibly the state of other agents.

Personal inclination

Let f_i be a number representing the tendency for agent i to choose S_1=+1. 

Incentives

All individuals make their decision based on the incentives offered. Knowledge of incentives is informed by public information.  This incentive F(t) may change with time. For example, the price of a product may decrease due to an advance in technology or a government may run an advertising program for a public health initiative.

Noise

No agent has access to perfect information in order to make their decision. This uncertainty can be modelled by a parameter beta, which increases with decreasing noise. According to the log-it rule the probability that of a particular decision is

1/beta is the analogue of temperature in statistical mechanics and this probability function is the Fermi-Dirac probability distribution! 

Social interactions

No human is an island. Social pressure and imitation play a role in making choices. Even the most "independent-minded" individual makes decisions that are influenced somewhat by the decisions of others they interact with. These "neighbours" may be friends, newspaper columnists, relatives, advertisers, or participants in an internet forum. The utility for an individual may depend on the choices of others. The interaction parameter J_ij is the strength of the influence of agent j on agent i.

Heterogeneity

Everyone is different. People have different sensitivities to different incentives. This diversity reflects different personalities, values, and life circumstances. This heterogeneity can be modelled by assigning a probability distribution rho(f_i).

Putting all the ideas above together the utility function for agent i is the following.

This means that the minimal model to investigate is a Random Field Ising model. It exhibits rich phenomena, many of which are similar to the social phenomena that were mentioned at the beginning of the post. Later posts will explore this.

The discussion above is drawn from a nice paper published in the Journal of Statistical Physics in 2013.

Crises and Collective Socio-Economic Phenomena: Simple Models and Challenges by Jean-Philippe Bouchaud.

Emergence matters (in a nutshell)

Emergence is one of the most important concepts in the sciences: from physics to biology to sociology. Most of the big questions in science involve emergence. Yet there is no consensus about what emergence is, how to define it, or why it matters. This is my attempt to clarify some of the important issues and questions. For reasons of brevity, I give no references and only a few examples. They can come later. Here I am trying to take a path that is intermediate between the precision of philosophers and the looseness of condensed matter physicists' discussion of emergence. My goals are clarity and brevity.

Characteristics of emergent phenomena

Consider a system that is composed of many interacting parts. If the properties of the system are compared with the properties of the individual parts, a property of the whole system is an emergent property if it has the following characteristics.

1. Novelty 

An emergent property of the system is a property that is not present in the individual parts of the system.

2. Modification of parts 

An emergent property of the system is associated with a modification of the properties of and the relationships between the parts of the system. 

3. Universality

An emergent property is universal in the sense that it is independent of many of the details of the parts. As a consequence, there are many systems that can have the emergent property.

4. Irreducibility

An emergent property cannot be reduced to properties of the parts.

5. Limited predictability

An emergent property is difficult to predict solely from knowledge of the properties of the parts and how they interact with one another.

Here are a few issues to consider about the five characteristics above. 

First, “emergent property” could possibly be replaced with emergent phenomenon, object, or state.

Second, for each of the five characteristics is it necessary and/or sufficient for the system property to be emergent?

Third, one of the most contested characteristics concerns predictability. “Difficult to predict” is sometimes replaced with “impossible”, “almost impossible”, “extremely difficult”, or “possible in principle, but impossible in practice.” After an emergent property has been observed sometimes it can be understood in terms of the properties of the parts. An example is the BCS theory of superconductivity, which provided a posteriori, rather than a priori, understanding. A keyword in the statement above is “solely”.

Examples of properties of a system that are not emergent are volume, mass, charge, and number of atoms. These are additive properties. The property of the system is simply the sum of the properties of the parts.

Scales and hierarchies

Central to emergence is the idea of different scales. Emergent properties only occur when scales become larger. Scales that are simply defined, and might be called extrinsic, are the number of parts, length scale, and time scale. A more subtle scale, which might be called intrinsic, is a scale associated with the emergent property. This emergent scale is intermediate between that of the parts and that of the whole system.

Emergent scales lead naturally to hierarchies, such as those associated with different scientific disciplines, as shown below. Hierarchies also occur within individual disciplines.

At each level there are distinct phenomena, concepts, theories, and scientific methods.

Another important scale is that of complexity. Generally, as one goes up the hierarchy one says that the level of complexity increases. Giving a precise version of such statements is not simple.

Complexity

Simple rules can lead to complex behaviour. This is nicely illustrated by cellular automata. It is also seen in other systems with emergent properties. For example, the laws describing the properties of electrons and ions in a crystal or a large molecule are quite simple (Schrodinger’s equation plus Coulomb’s law). Yet from these simple rules, complex phenomena emerge: all of chemistry and condensed matter physics!

There is no agreed universal measure for the complexity of a system or with many components. One possibility is the Kolmogorov measure. Using such measures to elucidate emergence, such as how complexity changes with other scales, is an important challenge.

Other issues

There are a host of other issues and topics that enter discussions about emergence. Some of these are of a more philosophical nature. Here I just list them: robustness, quality vs. quantity, objective vs. subjective, universality vs. particularity, ontology vs. epistemology, discontinuities, incommensurability, theory reduction, asymptotic singularities, top-down causation, supervenience, differentiation and integration (not calculus) of system parts, reductionism, foundationalism, fundamentalism, strong versus weak emergence, and criteria for theory acceptance.

Discussion of some of these issues can be quite abstract but to make the discussion above more precise they may need to be considered. 

Emergence is relevant to practical matters such as scientific strategy, priorities, allocation of resources, and our dispositions as scientists. Too often views on these issues are implicit and not reflected upon. 

The practical matter of scientific strategy

When studying a system, the first choice that must be made is what scale or scales to focus on. For example, in materials science, the options range from the atomic scale to the macroscopic. This choice determines the tools and methods, both experimental and theoretical, that can be used to study the system. In different words, the scientist is making a choice of ontology: the object they choose to study. This then determines epistemology: the concepts, theories, and organising principles a scientist may use or hope to discover. Effective theories and toy models enter here. 

When systems have been studied by a range of methods and at a range of scales, a challenge is the synthesis of the results of these studies. Value-laden judgements are made about the priority, importance, and validity of such attempts at synthesis. Often synthesis is relegated to a few sentences in the introductions and conclusions of papers.

For known systems and emergent properties, there is the possibility of creating new methods and probes to investigate them at appropriate scales.

New systems can be created and investigated in the hope of discovering new emergent properties (e.g., new states of matter) or more modestly, that manifest an emergent property that is more amenable to scientific study or technological application.

As emergent properties involve multiple scales they are often of interest to and amenable to study by more than one scientific discipline. This creates opportunities and challenges for interdisciplinary collaboration.

Individual scientists must and do make decisions about the relative priority of the different strategies outlined above. Research groups, departments, institutions, professional societies, and funding agencies must and do also make decisions about such priorities. The decision outcomes are also emergent properties of a system with multiple scales from that of the individual scientist to global politics. I claim that too often these weighty decisions are made implicitly, rather than explicitly following debate and deliberation.

The disposition of the scientist

All scientists are human. In our professional life, we have hopes, aspirations, values, fears, attitudes, expectations, and prejudices. These are shaped by multiple influences from the personal to the cultural to the institutional. We should reflect on the past century of our study of emergent systems from physics to biology to sociology. If we honestly evaluate our successes and failures I think this may lead us to have certain dispositions that are interrelated.

Humility. There is so much we do not understand. Furthermore, we fail abjectly at predicting emergent properties. This is not surprising. Unpredictability is one of the characteristics of emergent properties. There is a hubris associated with grand initiatives such as “the theory of everything”, the Human Genome Project, “materials by design”, and macroeconomic modelling. 

Expect surprises. There are many exciting discoveries waiting. They will be found by curiosity and serendipity.

Wonder. Emergent phenomena are incredibly rich and beautiful to behold, from physics to biology to sociology. Furthermore, the past century has seen amazing levels of understanding. But this is a “big picture” and “coarse-grained” understanding, not the description that the reductionists lust for and claim possible. 

Realistic expectations. Given the considerations above I think we should have modest expectations of the levels of understanding possible, and what research programs, from that of individual scientists to billion-dollar initiatives, can achieve. We need to stop the hype. Modest expectations are particularly appropriate with respect to our ability to control emergent properties.

The holy grail

“The philosophers have only interpreted the world, in various ways. The point, however, is to change it.”

Karl Marx

Understanding complex systems with emergent properties is an ambitious scientific challenge. This enterprise has intrinsic intellectual merits. But a whole other dimension and challenge is to use this understanding to modify, manipulate, and control the properties of systems with emergent properties. This enticing prospect appeals to technologists, activists, and governments. Such promises feature prominently in grant applications, press releases, and reports from funding agencies. Diverse examples of this control goal include chemical modification of known superconductors to produce room-temperature superconductivity, drug design, social activism, the leadership of business corporations, and governments attempting to manage the economy. 

However, we should honestly reflect on decades of “scientifically informed” and “evidence-based” initiatives in materials science, medicine, poverty alleviation, government economic policy, business management, and political activism. Unfortunately, the fruit from these initiatives is disappointing, particularly compared to what has often been promised.

My goal is not to promote despair but rather to prevent it.  With more realistic expectations, based on reality rather than fantasy, we are more likely to make significant progress in finding ways to make some progress (albeit modest but worthwhile) in learning how to manipulate these complex systems.

This post contains many claims that require discussion, refinement or abandonment. I welcome suggestions on how to improve these ideas.