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?

What is the integer quantum Hall effect?

And why is it so amazing?

Surprises [about physics in two dimensions] occurred in the 1980s when it became possible to study Landau levels [the quantised energy levels of electrons in a magnetic field] in Flatland. This happens when the electrons are completely constrained to move in only two dimensions. The surface within which the electrons move needs to be extremely flat and free from defects and impurities. Advances in semiconductor technology in the 1970s led to two realisations of this Flatland. Both were developed for technological reasons: the desire to have transistors in which the electrons and holes can move extremely fast. One class of device is silicon MOSFETs (Metal Oxide Semiconductor Field Effect Transistors). The second class is heterostructures, where layers of ultrapure semiconductors such as gallium arsenide are grown on top of each other, one layer of atoms at a time. In both classes of device, a fixed density of electrons (or holes) can be injected at the surface. These charge carriers can move freely in Flatland, acting like a fluid. Things get interesting when the number of charge carriers is small enough and the magnetic field is large enough that the number of charge carriers is comparable to the number of quanta of magnetic flux that pass through the system. Then, the quantum state of most of the charge carriers is one of the lowest Landau energy levels. 

To achieve this regime for the cleanest possible systems requires magnetic fields more than a hundred thousand times stronger than that of the Earth. Furthermore, the magnetic field must be spatially uniform in the region where the semiconductor system is located, stable over the time of the measurements, and the interior of the electromagnet producing the field must be large enough to contain a refrigerator that can cool the charge carriers in the system down to a few degrees above absolute zero. By 1980, all these conditions became possible. Klaus von Klitzing was able to perform measurements of the Hall resistance versus magnetic field in a special high magnetic field laboratory in Grenoble, France. The results were surprising and are shown schematically in Figure 35 below. There are four noteworthy features. 

 

Figure 35. The quantum Hall effect. The Hall resistance is shown as a function of the strength of the magnetic field and has a step-like structure. The integer n is related to the quantized energy that the charge carriers have.

First, there are distinct steps in the curve. At small magnetic fields the Hall resistance versus field is a straight line, as expected for the classical Hall effect. However, at larger fields there are plateaus in the curve.

Second, each of the plateaus is extremely flat. Von Klitzing found that the magnitude of the Hall voltage on each plateau did not vary to one part in ten million. As he varied the magnetic field, he noticed that the first seven digits on the voltmeter he was using did not change. He wondered if the voltmeter was broken and had become jammed. But it was working.

Third, the magnitude of the Hall resistance for all the plateaus has a simple relationship to fundamental physical constants. The quantum of resistance is defined as equal to h/2e^2 . When you calculate this quantity, the answer (25,812.827 ohms) is in the units of electrical resistance. The value of the Hall resistance is precisely equal to this value divided by an integer (n=1,2,3 …) which is related to the highest quantized energy (Landau level) that an electron can have at that magnetic field. That is why it is known as the integer quantum Hall effect.

Fourth, the observed value of the Hall resistance for each of the plateaus is independent of many details, including the temperature, the amount of disorder in the material, the chemical composition of system (silicon versus gallium arsenide), or whether the charge carriers are electrons or holes. [This independence is characteristic of the universality associated with emergent phenomena]. 

These four features are similar to those for the steps associated with the macroscopic quantum effects (magnetic flux in superconducting cylinders, circulation in a superfluid, Josephson effects) discussed in the previous chapter. Again, it is astonishing that a macroscopic measurement – of electrical resistance - of a macroscopic system can determine fundamental constants that are normally associated with properties of atomic systems. Just as the Josephson effect led to a new standard measure for voltage, the quantum Hall effect led to a new standard measure for electrical resistance.

Anyone familiar with building electronic circuits will have used resistors of varying values in ohms (Ω), e.g., 10 Ω or 25 kΩ. When these resistors are made, they are calibrated against some standard. For making integrated circuits with billions of transistors this standard needs to be extremely accurate. In 1990 the international standard for the ohm was changed to be that defined by the quantum Hall effect. Previously, the ohm was defined by the electrical resistance of a column of liquid mercury with constant cross-sectional area, 106.3 cm long, a mass of 14.4521 grams and a temperature 0 °C. Like the Josephson voltage standard, the quantum Hall resistance standard has the advantage of precision, portability, reliability, reproducibility, and independence of platform. 

An extract from Topology Matters, Chapter 8, Condensed Matter Physics: A Very Short Introduction.

The emergence of hadronic matter from interacting quarks and gluons

 A characteristic of emergent phenomena is how novel and complex properties can emerge from apparently simple laws. Quantum ChromoDynamics (QCD) describes the interaction of quarks and gluons. The classical Lagrangian is remarkably simple.

It has an SU(3) local gauge symmetry and the A_v^mu are the associated gauge fields (gluons).

The quarks are fermions with fractional electrical charge. The only parameters in the theory are the coupling constant g_s, which describes the self-interaction of the gluons, and the bare masses of the quarks, m_f. The gluons are massless. In the limit where the bare mass of quarks vanishes, the Lagrangian has chiral symmetry, which transforms quarks with left-handed symmetry into right-handed.

Frank Wilczek states that QCD "is conceptually simple. Its realisation in nature, however, is usually very complex. But not always."

Hadronic matter (nucleons and mesons) has properties that are qualitatively different from its components (interacting quarks and gluons). In other words, it is emergent. In hadronic matter, there are no particles with fractional electrical charge or massless bosons. Chiral symmetry is broken. Consequently, hadrons do not come in pairs with opposite parity and equal energy. Quarks are confined and this is associated with a string tension. The order parameter associated with confinement is the Polyakov (or Wilson) loop. The connection between chiral symmetry breaking and confinement is subtle. For a long time they were thought to be intimately connected but now that is not the case.

Although the underlying Lagrangian is simple, the spectrum of hadrons and their interactions is complex. There is a "zoo" of particles. This all comes from a single coupling constant!

On the one hand, this complexity is surprising. On the other hand, it is similar to how there is a simple coupling constant (the electronic charge) in the Hamiltonian that describes most of chemistry and condensed matter physics. Most of the particles are unstable and can be viewed as quasiparticles as they have a finite lifetime, even in the absence of electroweak interactions. 

The emergent state of hadronic matter only exists at "low" temperatures and densities. It "melts" at the high temperatures associated with the Big Bang, relativistic heavy ion colliders, or the high densities associated with neutron stars. But that and the associated phase diagram of QCD is another story...

Update. I revised this post due to some helpful clarifications from Chris Allton, who was visiting UQ this week.

Topology matters in condensed matter physics

Topology is the field of mathematics describing the properties of geometric objects that do not change when they are smoothly deformed. These properties only change in steps by cutting or gluing. Concepts in topology can be illustrated with everyday objects such as balls, doughnuts, coffee cups, and pretzels. For example, a doughnut can be gradually and smoothly deformed into the shape of a coffee mug (Figure 33). No ripping or cutting is required. In contrast, it is impossible to turn a ball into a doughnut without cutting a hole. The number of holes in an object is referred as a topological invariant. For a ball, doughnut, and the simplest pretzel these numbers are zero, one, and two, respectively. Topology is about qualitative differences not quantitative details such as distances, angles, and sizes.

Figure 33. A doughnut can be smoothly deformed into a coffee cup. From the perspective of the mathematical field of topology all the objects above are identical.

In chapter 4 it was noted that in ordered states of matter, some properties are determined by topological defects, such as vortices in superconductors. These are topological objects in the following sense. In a superconductor, there is an electrical current circulating around a vortex and a magnetic field that passes through the centre of the vortex. The magnetic flux is equal to one unit or quantum of the magnetic flux. If the spatial distribution of the electrical current around the vortex is smoothly changed the total magnetic flux remains the same. Furthermore, it is not possible to smoothly deform the system in any way to make the vortex disappear. The magnetic flux associated with the vortex is a topological invariant.

Condensed matter physics is about qualitative difference: states of matter are qualitatively different from one another. Until the 1980s these differences were only associated with different types of symmetry, which in turn reflect the underlying ordering in the state. This chapter describes unanticipated discoveries of new states of matter that could not be described in terms of this traditional symmetry picture. But they can be described in terms of topology. These states exhibit macroscopic quantum effects, reminiscent of superconductors and superfluids. Understanding these states of matter involves venturing back into Flatland and also into some abstract mathematical spaces. Remarkably, these abstractions can be related to practical questions about international standards for electronic circuits.

An extract from Topology Matters, Chapter 8, Condensed Matter Physics: A Very Short Introduction 

Measuring the social, ethical, and political values of different AI models

I continue to enjoy reading my hard copy of The Economist every week. Occasionally, I post examples of insightful graphics presented in articles.

Here are some graphics that struck me recently. They are taken from a fascinating article. AI models’ values are very different from most people’s

The first figure shows a comparison of the answers given to the World Values Survey by different Large Language Models and people from different regions (cultures) of the world. The vertical axis goes from traditional values at the bottom to secular values at the top. The horizontal axis goes from survival (or communal) values on the left to self-expression on the right.

Note how the different cultures do not overlap. Furthermore, the LLMs are distant from almost everyone. Just a few are close to the English speaking world. 

The second graph compares answers to the VOTER survey of political questions. The horizontal and vertical axes correspond to Social and Economic issues respectively. Positive and negative values correspond to conservative and liberal respectively. Answers from LLMs are compared to a sample of Trump and Biden voters from the 2020 USA Presidential election. Note the clear political polarisation. Furthermore, the AI models are all liberal.

I offer no comments on whether any of this is good or bad. I do suggest two implications. First, extensive use of AI will tend to shift peoples values in a particular direction, just like media (music, TV, movies, art) does. Second, given the conflict of values with most people these biases will offend or concern many communities and increase the backlash against AI companies and its widespread adoption. Consequently, some will modify the training of their models so they align more with the values of vocal communities. Whether or not that is seen as a good thing, will depend on whether you think some of those values should be affirmed.

What do you think?

Macroscopic quantum effects in superconductors and superfluids

Quantisation of magnetic flux in a superconductor

Magnets and electrical currents produce magnetic fields, regions of space where other magnets and electrical wires experience a mechanical force. For a circle of wire in the presence of a magnetic field the magnetic flux is defined as the strength of the magnetic field passing through the circle multiplied by the area of the circle. A law of electromagnetism states that if the field varies with time, then a voltage is produced in the wire with a magnitude that is proportional to the rate at which the magnetic flux through the circle changes. This is the physics behind all electrical motors and electrical generators. In the everyday world magnetic flux can have any value and can be varied continuously by changing the strength of magnetic field. In the quantum world that is not the case. Magnetic flux is quantised.

In 1961, two experimental groups independently reported the first observation of a macroscopic quantum effect, the quantisation of the magnetic flux passing through a superconducting cylinder (Figure 30). One team was Bascom Deaver and William Fairbank and the other Robert Doll and Martin Nabauer. A tall thin cylinder made of tin was placed in a magnetic field and cooled down to a low enough temperature that it entered the superconducting state. The magnetic flux passing through the cylinder was then measured as the magnetic field was varied. The resulting graph has four noteworthy features. First, there are clear steps, showing that the magnetic flux has discrete values. In contrast, in the normal metallic state the graph was a straight line. Secondly, the magnitude of the steps was the same, to within about one per cent, suggesting quantisation of a single unit of magnetic flux. Thirdly, the value of this quantum of magnetic flux was equal to the value of h/2e. Thus, it was completely determined by the two fundamental constants, h and e, Planck’s constant and the charge on an electron, respectively. And fourthly, graphs with the same three features noted above were later observed in other superconducting materials and cylinders. This showed that flux quantisation is independent of details such as the chemical composition and dimensions of the cylinder. This flux quantisation is a macroscopic quantum effect. It is macroscopic because the system is macroscopic, and the magnetic flux is a macroscopic property. It is quantum as and the magnitude of the quantisation is determined by Planck’s constant.

                                                                       (b)

Figure 30. Quantisation of magnetic flux in a superconducting cylinder. (a) A tall thin cylinder of tin was placed in a magnetic field. (b) The graph shows the value of the magnetic flux passing through the cylinder as the magnetic field was varied. Note the step like structure, showing quantisation of the flux.

The quantum of magnetic flux is denoted Φ0 (= h/2e) and has the value 2.067833848...×10−15   tesla (metre)2. This number also determines the scale of quantum interference effects between two superconductors, as we will see shortly. The flux quantum is also relevant to vortices that form when some superconductors are placed in a magnetic field (Figure 20). A persistent electrical current flows around the vortex and the magnetic field penetrates the core of the vortex. It can also be shown, both theoretically and experimentally, that the magnetic flux associated with each vortex is exactly equal to one quantum of flux. Something similar happens in superfluids.

Macroscopic quantum effects in superfluids

When a cylinder containing a fluid is rotated about an axis passing down the centre of the cylinder the fluid will also rotate. The faster the cylinder is rotated the faster the fluid rotates. A physical quantity known as the circulation is proportional to the speed of rotation and the diameter of the cylinder. With a variable speed motor, the rotation speed can be continuously varied and in normal fluids the circulation has continuous values. But not in a superfluid, as shown in a beautiful experiment done by W.F. Vinen in 1961 using liquid 4He. He observed that when the liquid was cooled below the superfluid transition temperature that the circulation could only take on discrete values. Furthermore, these discrete values are multiples of h/M where h is Planck’s constant and M is the mass of one atom of helium. This value was predicted by Lars Onsager in 1949 who identified h/M with the circulation of a single vortex in the superfluid. This is another macroscopic quantum effect.

The quantisation of magnetic flux in superconductors and of circulation in superfluids showed that both superconductors and superfluids can be classified as quantum states of matter. The close similarity of these quantum phenomena, even though superconductivity occurs in solids and superfluidity in liquids. This indicates a deep underlying unity, demonstrated through the study of condensed matter physics. 

This is an extract from Chapter 7, Quantum Matter, in Condensed Matter Physics: A Very Short Introduction.

Rudolph Marcus (1923-2026): theoretical chemical physicist

Rudolph Marcus died last week. He was 102. There is a nice obituary in The New York Times. He was best known for his theory of electron transfer, for which he was the sole recipient of the Nobel Prize in Chemistry in 1992.

Although the theory was proposed for electron transfer in a polar solvent it applies to a wide range of other systems, where two quantum states are coupled to one another and to an environment. One example is for Forster transfer of excitons between molecules, which is central to photosynthesis.

I will give a physics perspective, based on a talk I gave in Slovenia back in 2013. Slides are here.

Basically, Marcus proposed an effective Hamiltonian for two diabatic states and calculated a transition rate in a limit that is relevant to most chemical contexts.

The Hamiltonian can be viewed as the spin-boson model, in which a two-level system is coupled to a bath of harmonic oscillators. 

[The dense book by Weiss on Quantum Dissipative Systems makes the connection explicit in detail. A more accessible treatment may be chapter 16 in the book Chemical Dynamics in Condensed Phases by Nitzan.]

The Hamiltonian is 

This defines a spectral density, which is important for quantum decoherence, but not so much here, except it defines a timescale that determines the classical limit, which Marcus assumed.

This can be used to define a quantity central to Marcus' theory, the reorganisation energy.

The transition rate between the two quantum states is given by

I consider this to be one of the most important equations in chemical physics, particularly for the understanding and design of functional materials.

Aside. Much of this is equivalent to Holstein's 1959 treatment of incoherent polaron transport (see Mahan, Many-body physics).

A key experiment by John R. Miller, Lidia T. Calcaterra and Gerhard L. Closs in 1984 showed how good the theory was and how its predictions were counter-intuitive. The authors considered a family of molecules that allowed them to tune epsilon, the energy difference between the two electronic states. [On the graph below epsilon = - Delta G].

The vertical scale is the reaction rate on a logarithmic scale. It varies by four orders of magnitude.

What is surprising? As stated at the Nobel prize award ceremony:

"The quadratic equation predicts that electron transfer reactions will occur more slowly the larger the driving force of the reaction is. This phenomenon received its own name, “the inverted region.” To a chemist, the phenomenon is just as unexpected as when a skier finds himself gliding more slowly down a slope the steeper it is."

The theory implies an important design principle for functional materials: if optimising functionality means maximising the reaction rate, then tune the energy difference epsilon to equal the reorganisation energy E_R.

The theory illustrates two important aspects of emergence: effective theories and universality. Many different systems can be described by the same theory. The environment may involve many degrees of freedom and its coupling to the system is characterised by many parameters (the M_alpha above). However, only one parameter matters, the reorganisation energy.

For Australians, there is some ambivalence about the way Marcus' name is often solely associated with electron transfer theory. We often refer to it as Marcus-Hush or Hush-Marcus theory because Noel Hush did similar work around the same time. Some of the history is recounted here by Ian Rae and Jeff Reimers. There are also subtle debates about whether the electron transfer is adiabatic or non-adiabatic.

My only personal interaction with Marcus was in 2011 when I visited the chemistry department at Caltech. Marcus kindly took me to lunch at the faculty club, along with his research group. Then he was 84 years old. He kept publishing papers until he died.