The Future of Everything

March 3, 2021

QEF09 – Threshold Effects in Quantum Economics

Some of the strongest empirical evidence for quantum effects in the social sciences are shown by threshold effects. Consider our circuit where we have subjective factors $A$ which are creating a context which influences the decision $B$. If we assume a uniform prior for the various probability terms then as we’ve seen we can assume that interference will add or subtract 25 percent according to quantum decision theory. The difference between a favorable context and an unfavorable one therefore leads to an expected factor of three difference in propensity. Applying our energy formula, we find the change in energy associated with this gap is $\Delta E = \frac{\hbar \omega}{2} \log 3 \approx \frac{\hbar \omega}{2}$ which is the base energy of a quantum harmonic oscillator. This energy could correspond for example to the energy needed to convert a non-buyer into a potential buyer in a transaction. So this energy acts as a kind of threshold that needs to be overcome in order for a transaction to take place.

Many cognitive phenomena show a threshold effect. An example is preference reversal, where a switch from one context to another creates a large change in the propensity. Quantum decision theory normalises the objective terms to create a utility function which describes the objective factors. For example a decision between two possible options with associated costs $x_1$ and $x_2$ has the objective utility function $f\left(x_1\right) = \frac{x_2}{x_1+x_2}$ and $f\left(x_2\right) = \frac{x_1}{x_1+x_2}$. The preference reversal criterion then holds if $\frac{x_2}{x_1} > 3$ (or we can use $e$ as before for mathematical convenience).

A related phenomenon is the endowment effect, where people assign a higher value to an object that they own and are selling, than to one that they do not own and are buying. This can be viewed as another example of preference reversal, since the context has changed from selling to buying. The effect has been illustrated in a number of experiments, the best-known being one in which subjects were given a mug and then offered the chance to sell or exchange it. The experimenters found that people demanded more than twice as much in exchange for the mug (a median selling price of $7.12), as they were willing to spend to purchase the mug themselves (median buying price of$2.87). The price ratio is $\frac{7.12}{2.87} \approx 2.5$ which is again close to e.

Another example is the ultimatum game. Here two subjects are offered an award of say ten dollars, but are given an ultimatum: one must decide how to split the money, and the other has to decide whether to accept the offer. If the offer is rejected, all the money is returned, so they both lose. Standard theory, based on rational utility maximizing behavior, would imply that any offer would be accepted, no matter how low, because it is better than nothing – however the game has been performed in many countries around the world, and the results consistently show that people reject an offer that is overly cheap, with about half of all responders rejecting offers below three dollars. Following the same procedure as above for this threshold gives a utility ratio of 2.33. Again, this could be viewed as a variant of preference reversal, since the context has changed from price setter to price taker.

Such experiments are usually carried out under controlled conditions, however a natural experiment for preference reversal was provided by the observed rate of strategic default during the US housing crisis. According to objective utility maximization, default makes sense if the costs associated with staying in a home exceed the costs associated with selling it – but according to a report from the Federal Reserve, the “median borrower walks away from his home when he is 62 percent underwater” which surprised many observers. Assuming a small downpayment, the cost ratio of finding a replacement at the new lower price, to the cost of staying in the home, is therefore about 2.63, which again is close to e. This threshold effect was important for lenders, because it would have cost an estimated \$745 billion to restore all underwater borrowers.

We can also apply this threshold idea to the money objects which we discussed earlier. For a tally stick with a face value of $x_0$ the energy gap in changing from a default probability of 1 in the absence of coercion (so a 100 percent chance that the person is not going to pay the debt) to a smaller probability of default $p$ due to coercion is given by the formula $\Delta E \approx \frac{\hbar a x_0}{2} \log \frac{1}{p} = \frac{\hbar \omega}{2}$ where $\omega = a x_0 \log \frac{1}{p}$ is a frequency parameter. In physics, the frequency of a photon is associated with color and in American idiom the color of someone’s money means proof that someone is going to pay you, so the quantum interpretation gives another angle on that.

In general these threshold effects occur when a minimum energy is needed in order to effect change or to close a deal. They are similar to the photoelectric effect in physics which occurs because a quantum of energy is required in order to dislodge an electron from an atom, with money objects playing the role of photons.

Orrell D (2021) The Color of Money: Threshold Effects in Quantum Economics. Quantum Reports 3(2), 325-332.

Orrell D (2021) Quantum Financial Entanglement: The Case of Strategic Default. (Under review.)

Previous: QEF08 – Quantizing Propensity

Next: QEF10 – A Quantum Option Pricing Model

Playlist: Quantum Economics and Finance

March 2, 2021

QEF10 – A Quantum Option Pricing Model

We’ve talked about a quantum walk model of asset price changes and a quantum model of supply and demand so let’s put them together into a quantum model of financial option pricing.

Traditional option-pricing models such as Black-Scholes assume that market prices obey a stochastic differential equation with a drift $\mu$ and volatility $\sigma$. Solving the discrete version of this equation yields the classical binomial model, which was first developed by Cox, Ross and Rubinstein in 1979, and exists in different versions.

In the usual model, the steps up and down in log price are given by $u = \left( r - \frac{\sigma^2}{2} \right) \Delta_t+\sigma \sqrt{\Delta_t}$ and $d = \left( r - \frac{\sigma^2}{2} \right) \Delta_t-\sigma \sqrt{\Delta_t}$

This can be interpreted as a random walk with $u = \sigma \sqrt{\Delta_t}$ and $d=-\sigma \sqrt{\Delta_t}$, in combination with a drift term $r \Delta_t$ due to the risk-free interest rate, and an adjustment term $-\frac{\sigma^2}{2} \Delta_t$. We can follow a similar procedure for the quantum walk, to get a price probability distribution, as in the screenshot below from the online app. Instead of having a normal distribution for our stock prices we’re going to end up with a quantum walk with the distinct peaks on either side. In the quantum walk the distribution depends on the initial condition so if you start with a balanced initial condition then you end up with a balanced distribution. We can also skew it a little bit which has been done here to introduce a small degree of bias in order to reflect optimism on the part of the buyer. So this buyer is looking at this asset price into the future and they’re thinking there are two main possibilities. One is it’s going to grow at a certain linear rate like several percent a year into the future, but that’s also balanced with the idea that it can also go down by by a similar amount. On the other hand there’s a more objective view, which is closer to how asset prices actually do tend to behave over time, which assumes they will follow a roughly normal distribution (red line in the figure).

Now, consider a European-style call option with strike price $K$. After $n$ time steps, the expected value of the payoff is $\left[ exp(S_n) - K \right]^+$ (the exponential is required because the stock price $S_n$ is logarithmic). The option price $V_n$ is the expected payoff discounted to time zero, or $V_n = \left< \frac{1}{(1+r)^n} \left[ exp(S_n) - K \right]^+ \right>$.

Since the quantum walk model reflects subjective factors, while the classical model (i.e. the model with decoherence) is a better match for objective reality, we will use the quantum model to represent the buyer (assumed to be more affected by subjective factors) , and the classical model to represent the seller (assumed to be more objective). The reason for this is that sellers are generally going to have a more objective view based on market data, which you can think of as a kind of decoherence effect which will collapse the model down to the classical model. But people buying options are usually doing so because they have some position that it’s going to go up or down by a certain amount.

We therefore have these two different pictures of how asset prices are going to evolve in the future. For either of them we can calculate what would be the fair option price, and we find that the most noticeable difference is for normalized strike prices which are close to one. For these prices the quantum model is saying the price should be higher and therefore the consensus price is going to appear to be a better deal.

You would therefore expect more interest in these options. One way to picture this is through implied volatility, but another way is through volume. A good thing about the quantum model is that, because it’s based on propensity, we can use it to estimate the volume of transactions at different prices and expiration dates. The result is a plot which looks like the one in the screenshot from the video below. It is highest as we would expect for strike prices close to one. This result agrees quite well with actual empirical data for option prices.

The quantum model incorporates a subjective model of human cognition which is useful because it can accommodate various quantum effects such as interference. But perhaps most importantly from the modeling point of view, it gives us a sense of the probability of transactions and therefore the volume. Finally from a purely technical standpoint a big advantage of the quantum walk model is that it is native to a quantum device so it can be run very fast on a quantum computer or anything that can perform a quantum walk.

Further reading: Orrell D (2021) A quantum walk model of financial options. Wilmott 2021(112): 62-69.

Previous: QEF09 – Threshold Effects in Quantum Economics

Next: QEF11 – The money bomb

Playlist: Quantum Economics and Finance

March 1, 2021

QEF11 – The money bomb

In quantum economics money plays a role rather like energy – so what happens when we get an awful lot of energy together in the same place?

In 1945 the Trinity Test convincingly demonstrated that quantum forces are not limited to the subatomic domain, but can scale up to affect our lives. Since then we’ve learned to exploit the energy inside the atom in different ways, from peaceful nuclear reactors to more recently quantum computing.

Money is a quantum social technology with quantum properties that also scale up to affect the economy as a whole.

Perhaps the most important concept in physics is that of energy. The Trinity Test released some 92 terajoules of energy which is about the same as 20 tank cars full of oil. There is also energy in finance. As an example an empty house close to where I live recently sold for 2.24 million Canadian dollars. One way to equate that with energy is to do a thermodynamic analysis of the world economy and figure out how much energy is needed to maintain a dollar bill. Another way is to simply figure out how much oil it would buy, and actually either method gives roughly similar results which is about 40 tank cars of oil or two Trinity Tests. That’s a lot of energy, so where does this energy come from?

Most money is created not by central banks but by private banks lending money for things like mortgages on houses. As the deputy governor of the Bank of Norway explained in a 2017 speech, when you borrow from a bank the bank just credits your bank account, the bank does not transfer the money from someone else or from a vault, it’s simply created by the bank itself out of nothing. We have already seen this process for a Medieval tally stick, so now instead of a sovereign backed by the divine right of kings, we have your local bank making a loan to someone who wants to buy a house. Instead of a tally stick the output is going to be new money which as we have seen is associated with energy through the equation $\Delta E \approx \frac{\hbar a x_0}{2} \log \frac{1}{p}$. Here the $\frac{1}{p}$ term represents the degree of coercion, so this is ultimately where the energy is coming from.

Now in physics Bohr’s principle of correspondence states that at large enough scales quantum mechanics should converge to classical, but things like nuclear devices don’t wash out. Nuclear reactors are based on self-sustaining nuclear chain reactions, and we get the same kind of self-sustaining exponential growth in the economy. Banks make loans on real estate, this adds to the money supply, it’s used to buy more real estate, and so on, so you find that the growth in house prices in Canada at least matches quite closely the growth in the money supply. And the system needs to grow continuously in order to pay the interest on the debt. It’s ironic that Aristotle thought that money was sterile and should not “breed” as he put it by handing out interest but we ended up with what amounts to a financial breeder reactor. And the product of all this is asset price inflation and inequality.

On top of all this debt is a system of derivatives which has an estimated notional value of some one quadrillion dollars. This quadrillion dollars is really a kind of a magical number because it’s larger than the actual economy. So how do macroeconomists model this financial sector which is so huge? Well really they don’t – one reason the banking crisis of 2007/8 wasn’t predicted was because banks weren’t in the models.

Since then there have been efforts to incorporate financial “frictions” into these models, but when you think about it this is odd because finance is really the the opposite of friction, and a crisis is what happens when friction breaks down completely, which is why plots of price changes during the crisis resemble plots of tremors during earthquakes.

These concerns about the financial system are not exactly new. One person to raise them was Frederick Soddy who was awarded the Nobel Prize in chemistry in 1921 but switched to economics because of his fear that a financial crash would lead to nuclear conflict. Soddy described money as virtual wealth that gives the illusion of being unbound by earthly constraints, and believed that we had to align human law and convention with the needs of thermodynamics.

His solution to all these problems was basically to stop paying tax in order to make “a clean sweep of all the webs woven to entangle humanity by the magicians who have discovered how to get something out of nothing and moreover to make it bear perennial interest.” I’m not sure that strategy would really work today but the split between the virtual and the real which he highlighted was very evident in the spring of 2020 when we had two headlines at the same time: US stocks have their best month since 1987; US now has 22 million unemployed.

This real-virtual split in money is perhaps most evident in our attitude towards the environment. Mainstream economics treats the planet as an inert object, and environmental damage as a market failure (even though markets are optimizing the numbers by growing as fast as they can). One of the main contributions of the quantum approach is to draw our attention to this dual real-virtual nature of money and help us to align our economy and our use of energy with the thermodynamic realities of the planet.

Orrell D (2018) Quantum Economics: The New Science of Money. London: Icon Books.

Soddy F (2003). The Role of Money: What It Should Be, Contrasted with What It Has Become. London: Routledge.

Previous: QEF10 – A Quantum Option Pricing Model

Playlist: Quantum Economics and Finance

June 16, 2020

Quantum gateway

Filed under: Economics, Quantum — David @ 2:08 pm

Prior to my July 1 online talk at the CQF Institute on quantum economics and finance, I spoke with Daniel Tudball from Wilmott Magazine about how quantum computing can serve as a gateway into the subject – the interview is here.

May 16, 2020

Quantum Economics and Finance – new book out now

Filed under: Books, Economics, Quantum — David @ 9:35 pm

Quantum Economics and Finance: An Applied Mathematics Introduction

The word “quantum” is from the Latin for “how much” and the new book Quantum Economics and Finance shows how it applies to the world of economic transactions. Written in clear and accessible language, the book covers the essential mathematics behind topics including quantum cognition, option pricing, and quantum game theory, and delves into the nuts and bolts of quantum mechanics, the principles of quantum economic modelling, and the basics of quantum computer logic. On the way the reader will learn how quantum interference can be used to model cognitive dissonance, how a quantum walk goes further than a random walk, and how financial entanglement explains the rate of mortgage default. It is aimed at anyone who wants to understand the quantum ideas working their way into economics and finance, without getting drowned in wave equations.

As interest in quantum computing grows, many companies from established banks to startups are looking at ways to perform financial simulations using quantum algorithms. But what if we should be using quantum models anyway – because the monetary system has quantum properties of its own, and because they work?

May 10, 2020

The quantum coin trick

Filed under: Economics, Quantum, Talks — Tags: — David @ 3:17 pm

Upcoming free talk at the CQF Institute on July 1:

Quantum Economics and Finance: The Quantum Coin Trick

Quantum economics and finance uses quantum mathematics to model phenomena including cognition, financial transactions, and the dynamics of money and credit. This talk takes a particular route into the subject, through a discussion of the quantum coin. Unlike a classical coin toss, which can be either heads or tails, a quantum coin can be – like Schrödinger’s cat – in a superposition of states. This gives it intriguing properties which can be used to simulate everything from the prisoner’s dilemma, to the credit relationship, to the pricing of options. The talk is based on material from the book Quantum Economics and Finance: An Applied Mathematics Introduction.

May 26, 2019

Quantum entanglement, and the strange case of the missing defaulters

Filed under: Economics, Quantum — David @ 6:11 pm

According to the field of quantum cognition, a decision to act is best expressed as a quantum process, where entangled ideas and feelings combine and interfere in the mind to produce a complex, context-dependent response. While the quantum approach has proved successful at modelling many aspects of human behaviour, it is less clear how relevant this is to the economy. This paper argues that the financial system is characterised by three kinds of entanglement: at the individual level between concepts, at the social level with other people, and at the financial level through the use of credit. These entanglements combine in such a way that cognitive processes at the individual level scale up to affect the economy as a whole, in a manner which is best modelled using quantum techniques. The approach is illustrated by making a retroactive “postdiction” about the prevalence of strategic mortgage default during the financial crisis, and a prediction for future such crises.

May 1, 2019

A quantum model of supply and demand

Filed under: Economics, Quantum — David @ 10:25 pm

Here is the abstract for a new paper to be published in Physica A: Statistical Mechanics and its Applications. A draft is available at SSRN.

One of the most iconic and influential graphics in economics is the figure showing supply and demand as two lines sloping in opposite directions, with the point at which they intersect representing the equilibrium price which perfectly balances supply and demand. The figure, which dates back to the nineteenth century, can be seen as a graphical representation of Adam Smith’s invisible hand, which is said to guide prices to their optimal level, and features in nearly every introductory textbook. However this figure suffers from a number of basic drawbacks. One is that it doesn’t express a dynamical view of market forces, so it isn’t clear how prices converge on an equilibrium. Another is that it views supply and demand as deterministic, when in fact they are intrinsically uncertain in nature. This paper addresses these issues by using a quantum framework to model supply and demand as, not a cross, but a probabilistic wave, with an associated entropic force. The approach is used to derive from first principles a technique for modeling asset price changes using a quantum harmonic oscillator, that has been previously used and empirically tested in quantum finance. The method is demonstrated for a simple system, and applications in other areas of economics are discussed.

March 29, 2019

Talk for Quantizing IR panel at ISA 2019

Filed under: Economics, Physics, Quantum, Talks — Tags: — David @ 6:49 pm

This is an edited version of my contribution to the panel discussion “Quantizing IR I: Physicists, Meet Social Theorists!” at the International Studies Association conference in Toronto on March 29. The session was chaired by James Der Derian (University of Sydney) and the other participants were Alexander Wendt (Ohio State University), Shohini Ghose (Wilfrid Laurier University/Perimeter Institute), Kathryn Schaffer (School of the Art Institute of Chicago), Michael Schnabel (University of Chicago), and Genco Guralp (San Diego State University).

One nice thing about quantum is that it looks different to people who come at it from different backgrounds and take different paths. My background is in applied math, and my own interest in applying quantum methods to social questions came about several years ago when I was researching a book on the history of money. And I think money serves as a particularly simple and illustrative example of a quantum social phenomenon, so I will give a quick description of that before getting on to more general points.

The word “quantum” is Latin for “how much” and the money system is a way of answering that question – or “quanto costa” in Italian which makes the quantum connection more clear – which when you think about it is not an obvious thing to do since value is a quality not a quantity. Because of this fundamental incompatibility at its core, and because it is related to the transfer of information rather than of classical objects, the money system turns out to have its own quantum properties including indeterminacy, duality, entanglement, and so on.

The most trivial of these is that money moves discontinuously, in sudden quantum leaps. Schrödinger once said “If we have to go on with these damned quantum jumps, then I’m sorry that I ever got involved” but with money the same thing happens every time you tap your card at a store. There isn’t a little needle that shows the money draining out, it just jumps.

Money is fundamentally dualistic, presenting both as a physical object, like a coin, or a virtual object, like a credit transaction, while still retaining the properties of each. A bitcoin for example is a virtual currency but it exists on a real hard drive.

The money system is indeterminate: the price of something like a home is fundamentally uncertain and is only settled at the time of purchase. Transactions therefore act as a measurement process on value.

Money is entangling: here entanglement means indeterminate but coupled at the same time, an example being the state of a loan between two parties. We can model each participant as being in a quantum superposition of cognitive states. If the borrower defaults that acts as a measurement which collapses the state of the loan, even if the other party only finds out later. Of course this is a simpler version of entanglement than the kind seen in physics (there is only one axis, namely default or no default), but an advantage is that you don’t need sophisticated statistical experiments to tease it out.

So money does not behave classically which is one reason it has traditionally played a small or even non-existent role in economic models, which as many commentators have noted is one reason the financial crisis wasn’t predicted. Conventional models didn’t include a banking sector, let alone the financial entanglements represented by a quadrillion dollars worth of derivatives. The fact that money was left out of the picture seems a remarkable omission given its obvious importance not just to economics, but to everything from marital relations to international relations, but fits with the classical view that money is just an inert medium of exchange.

It was only later, through the work of people like Alexander Wendt, that I connected this with the broader areas of quantum cognition and quantum social science, which of course add many completely new dimensions. One way to think of money is as a kind of prosthetic that extends the dualistic properties of quantum mind, as we mentally collapse value down to price.

I agree with the idea that quantum processes are likely to play a role in human cognition. In itself though I don’t think that this will show or prove that society is quantum or that we are best seen as wave functions, because living systems can’t be reduced to their components. Quantum processes are believed to play a role in avian navigation, but this doesn’t really change the way we think about birds. At a trivial level, we are quantum because the universe is quantum, but what counts is the emergent behaviour. The question from my perspective is whether social systems can be usefully modelled as quantum.

The quantum methodology allows scientists to model things like indeterminacy, interference between incompatible concepts, and entanglement, all of which characterise human relations. Bohr’s theory of complementarity for example was inspired by psychology, and our ability to hold two incompatible ideas in the mind at the same time. This position is a little different from the physicalist argument, because it says that something like money is quantum not because it inherits these properties from subatomic particles, but because it is a quantum system in its own right, and I would argue this holds for other social institutions as well.

In this sense I’m not sure that economics needs a model of consciousness, but the problem is that it already seems to have one, which is that people are lifeless automata. This approach is epitomised by the old and, as economist Julie Nelson points out, rather gendered concept of rational economic man, who makes decisions to optimise his own utility based on preferences that are fixed and known. It would be a great improvement to shift to the connected, fluid, and indeterminate idea of quantum economic person.

It might still sound here that quantum is being used as just a metaphor. But the idea of a metaphor is to explain something complex in terms of something that is concrete and immediate, as in “all the world’s a stage”. A wave function is many things but it is not concrete or immediate. For one thing it involves imaginary numbers, and we have no idea what wave function collapse means, with many different interpretations, which is pretty humbling as Kathryn Schaffer noted.

Instead it makes more sense to go the other way, take human experience at face value, and use it as a metaphor to understand the physical world. One reason we don’t do that obviously is because quantum was applied to physics first.

We also need to distinguish between the system and the model of the system. Quantum models are not reality, even if they appear to give exact results in calculations. Instead they are tools adapted from mathematical techniques.

The original quantum idea came from someone, Max Planck, trying to fit a mathematical model to some strange looking data, for black-body radiation. One of the main tools in quantum mechanics is Hilbert space which is a generalisation of normal Euclidean space. This was developed in the early twentieth century and later used by physicists to formalize quantum mechanics. In general, quantizing a system is a fairly clunky mathematical procedure which converts classical equations into quantum ones.
These mathematical methods were adopted in physics not because anyone liked them but because they worked. Social scientists are permitted to do the same thing (models can be applied to different systems and at different scales).

For example if someone decides to quantize some aspect of the economy, the hope is that the resulting model captures the essence of the underlying system, addresses shortcomings in traditional models, is parsimonious in terms of parameters, and can make useful predictions. Such decisions are the prerogative of the modeller and should be made based on sound principles of mathematical modelling.

Of course there has been a lot of pushback from both physicists and economists to this use of the quantum approach, which is all to the good, but I can address a couple of points that often come up. One common objection is that quantum processes don’t scale up (Bohr’s correspondence principle), so what happens at the micro level doesn’t affect us at the macro level because it all washes out. But quantum processes do scale up, especially through the use of technology. In physics we have the atom bomb (which doesn’t wash out), or a laser pointer for that matter, in society we have the financial system which can be viewed again as a kind of quantum social technology that can be used for good or ill.

Another objection is that quantum social science is the ultimate example of “physics envy” – and there is some danger of that. But as someone pointed at another one of these events, that horse already left the barn. An example is the efficient market hypothesis, which is a central theory of economics and finance. The idea that market prices follow a random walk, and the emphasis on probability, was directly inspired by quantum theory, and was developed in part by the many nuclear physicists who switched to finance after the war. However this was a sanitised version of quantum that picked up on stochasticity but omitted its other features; and the theory was widely misused to justify the financial instruments which played a key role in the crisis.

While there is no shortage of model abuse in economics, physics envy is not the main problem. Instead it is institutional pressures that encourage the use of models that look good based on the aesthetic criteria of mechanistic science but have so many parameters and moving parts that they can give any answer you want. This is what economist Paul Romer called in a paper “the trouble with economics”. And in fact you see exactly the same issue in physics – Romer’s paper was named after Lee Smolin’s book The Trouble With Physics.

All this raises a couple of questions. One is that if something like the money system can be described as quantum, then does that tell us something useful about how we should interpret physics, for example the role of information (no idea). Perhaps more relevant from a sociological perspective at least is, why has it taken a century for these ideas and methods to feed into the social sciences.

Of course there is the worry that quantum ideas can be dangerous nonsense when applied outside physics. As physicist Sean Carroll wrote in 2016, “No theory in the history of science has been more misused and abused by cranks and charlatans”. However I would argue that the theory misused to the greatest effect in social science is the idea that we are like classical machines: inert automata, slave to the mechanisms of cause and effect. This has done far more damage than anything like “quantum healing”. Why is there so much controversy about social scientists possibly abusing quantum models, when they have been abusing mechanistic models for years?

One reason is that quantum ideas represented a challenge to our traditional scientific world view, and in some ways we still haven’t got used to them. Einstein for example said quantum reality reminded him of “the system of delusions of an exceedingly intelligent paranoiac, concocted of incoherent elements of thoughts”. Yet these concepts such as duality, indeterminacy, and entanglement seem quite reasonable when applied to our own thought patterns. And I think Einstein’s comments would apply quite well to the social world of finance.

As the Torontonian Marshall McLuhan wrote in 1992: “I do not think that philosophers in general have yet come to terms with this declaration from quantum physics: the days of the Universe as Mechanism are over”. So it is exciting that 25 years later that is starting to change.

January 1, 2019

Quantum social science – reality or metaphor?

Filed under: Economics, Quantum — David @ 8:46 pm

Quantum social science exploits ideas and methods from quantum physics in order to model and understand social behaviour. For example, quantum cognition models human decisions as the collapse of a kind of mental wave function to a particular state, in a process akin to the wave function collapse in physics. But is this social wave function an actual physical thing, or just a metaphor?

Most researchers in quantum cognition adopt the stance that quantum techniques just offer a more flexible toolbox for analysing things like interference between incompatible concepts, or social entanglement between people, while distancing themselves from the idea that the brain is actually based on quantum processes. This is obviously prudent from a strategic perspective, since – while quantum biology has revealed a role for quantum effects in things like avian migration or photosynthesis – they have yet to be detected in the brain. And any assertion that humans are actually quantum entities tend to be met with extreme skepticism (even though comparing them with mechanistic entities, as is customary in the social sciences, gets a pass). It also reflects the “shut up and calculate” approach that is common in physics. In this view, quantum physics is therefore just a metaphor for human behaviour.

A few social scientists however do point out that, just because we haven’t yet detected quantum effects in the brain, doesn’t mean they aren’t there; that it seems reasonable that, if bird brains exploit quantum effects to get around, our own brains might make use of them too; and that areas such as quantum cognition provide circumstantial evidence for the radical notion that we are what Alexander Wendt calls “walking wave functions.” In other words, quantum social science is based not on a metaphor, but on physical reality.

Now, one might think that this question can only be settled by physical proof. Either experiments will eventually show that our brains are quantum, or they won’t. However, as with all things quantum, I think the real answer is more complex.

To start with, if quantum physics is being used as a metaphor, it isn’t a very good one.The usual purpose of a metaphor is to explain something that is difficult or abstract in terms of something that is more simple and concrete. When Shakespeare had an actor read “All the world’s a stage” in As You Like It, he was comparing the vastly complex world to a wooden platform on which the actor was actually standing. In quantum physics, we might think of a wave function as real because it can be expressed using mathematical equations, at least for the most simplified of situations. But no one has actually seen or felt an electron’s wave function (for one thing, it involves imaginary numbers). And one of the major drawbacks of the Copenhagen interpretation is that there is no explanation for how a wave function collapses during a measurement.

It would therefore make more sense to explain the quantum world using human behaviour as a metaphor, then the other way round (it is easier to relate to the experience of a state of uncertainty collapsing to a particular decision, than it is to an electron’s wave function collapsing to a particular eigenvector). But we don’t do that because quantum physics was discovered first. And this raises another question, which is why – given its similarities with human behaviour – quantum physics is usually described as being somehow alien.

Einstein for example said quantum reality reminded him of “the system of delusions of an exceedingly intelligent paranoiac, concocted of incoherent elements of thoughts.” Physicist Steven Weinberg said in an interview that “quantum mechanics, although not inconsistent, has a number of features we find repulsive … What I don’t like about quantum mechanics is that it’s a formalism for calculating probabilities that human beings get when they make certain interventions in nature that we call experiments. And a theory should not refer to human beings in its postulates.” Yet concepts such as duality, indeterminacy, and entanglement seem quite reasonable when applied to our own thought patterns. And consciousness is of course one thing that all human beings have direct personal experience of, no physics course required.

So it doesn’t seem right to say that quantum physics is a metaphor for human behaviour, given that we know less about the former than the latter. But another problem with the metaphor vs physical reality question is that physical proof of quantum processes in the brain would not directly show that our mental processes are best understood as quantum. In the end, everything in the physical world, including our brains, is based on quantum reality at the level of subatomic particles – so in a trivial way we are quantum creatures. But a common argument directed against quantum social science is Bohr’s principle of correspondence, which states that these effects wash out at large scales. So even if quantum effects were shown to play a role in the brain, this wouldn’t in itself indicate that social behaviour is a quantum phenomenon.

Now, while the correspondence argument makes sense for many phenomena, it ignores the fact that quantum effects do scale up all the time, because we design them to. Quantum technologies include everything from lasers to semiconductors to atom bombs. If we can learn to exploit quantum effects to build devices, why shouldn’t eons of evolution accomplish the same thing? Futhermore, quantum behaviour can also appear at large scales in things like phonons – sound waves in crystals or metal bars which appear as discrete quasi-particles and have their own quantum properties. So demonstrating that the brain is quantum would not prove that social behaviour is quantum. And conversely, proving that the brain is based on mechanistic interactions wouldn’t in itself prove that social interactions are not best modelled as quantum phenomena.

This is seen clearly in quantum economics, where money has its own dualistic properties because it merges the incompatible concepts of number and value, and prices are best seen as an emergent property of the money system. As physicist Robert Laughlin notes, “physical law is a rule of collective behavior, it is a consequence of more primitive rules of behavior underneath (although it need not have been), and it gives one predictive power over a limited range of circumstances. Outside this range, it becomes irrelevant.” Quantum behaviour at the level of the money system is not the same as quantum physics at the subatomic level; so while one can make a convincing argument that the brain is probably based on quantum processes, and evidence that this is the case would certainly change the conversation around quantum effects in the social sciences, it isn’t necessary or even apposite in economics to try and draw a direct connection between the two (proof that neurons are quantum wouldn’t prove that dollars are quantum). Instead, each should be handled on its own terms.

One answer to the question of interpretation, then, is to say that we can usefully model society as if it were a quantum system; while at the same time remembering that any mathematical model is only a sketch of the real thing. This might seem like a kind of intellectual dodge – the social sciences version of “shut up and calculate” – but in fact it is the standard practice in mathematical modeling: we model reality as if it obeyed our quantum rules too, even though we know the theory has limitations, which is why physicists continue to work on new ones. And when Max Planck first proposed the idea of the quantum, he didn’t do it in order to make a profound point about the ontology of the universe, he did it because it worked.

In this view, rather than quantum physics being a metaphor for human behaviour, it is more accurate to say that quantum models are a kind of metaphor for both physics and society. And the fact that these have something in common might be telling us something interesting about the nature of both.