The Future of Everything

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.

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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.

 

December 4, 2018

Quantum economics – new paper

Filed under: Economics, Uncategorized — Tags: — David @ 4:54 pm

Abstract: A decade after the financial crisis, there is a growing consensus that the neoclassical approach to economics has failed, and that new approaches are needed. This paper argues that economics has been trying to solve the wrong problem. Economics sees itself as the science of scarcity, but instead it should be the science of money. Just as physicists’ ideas about quantum matter were formed by studying the exchange of particles at the subatomic level, so economics should begin by analysing the properties of money-based transactions, which like quantum entities have a fundamentally dualistic nature. By building on ideas from quantum money, quantum finance and quantum social science, this paper shows that the economy is an archetypal example of a quantum social system, complete with its own versions of measurement uncertainty, entanglement, and so on. This leads to a proposal for a quantum economics, which is to neoclassical economics what quantum physics is to classical physics.

Read the full Quantum Economics paper in Economic Thought, Vol 7, No 2, 2018

 

November 24, 2018

Great forecasting excuses from the crisis

Filed under: Economics, Forecasting, World Finance column — David @ 2:08 pm

It has been 10 years since, on a visit to the London School of Economics (LSE), Queen Elizabeth II asked her hosts: “Why did no one see it coming?” She was referring to the financial storm of 2007/8.

As someone who works in applied mathematics, I know how hard it is to make accurate predictions – I even wrote a book, The Future of Everything, which discussed the topic in the context of weather, health and economic forecasting. But when predictions go badly wrong, the experience often offers information that can be used to update and improve forecasting models. To analyse how that process is (still) unfolding in economics, I present excuses given by economists over the last decade, translated for clarity into their meteorological equivalent.

See full article at World Finance

Weird

Filed under: Books, Physics, Reviews — David @ 2:03 pm

I wrote a review of Sabine Hossenfelder’s Lost in Math: How Beauty Leads Physics Astray after it came out a few months ago. As I mentioned, I enjoyed the book, which is based on revealing and entertaining interviews with eminent physicists. It also backed up the thesis of my 2012 book Truth or Beauty, which advanced the same idea that “scientists’ search for unity and symmetry may be leading them astray” as the Sunday Times put it. It was good to see a physics insider making the same case that the field has been shaped by a classical scientific aesthetic. My main (if rather trivial) gripe was that it cited my book only as arguing that “climate scientists favor elegant models to the detriment of accuracy.”

Without any context or backup, this sounds a little strange (as at least one reader noted). My point was that the development of climate models had been shaped, like other aspects of science, by the scientific aesthetic. And it seemed odd to focus on that when most of the book was about physics.

Anyway I later came across Hossenfelder’s capsule review of Truth or Beauty in a post where she summarises related books. Again, rather than say what the book’s argument is really about, as other reviewers did, Hossenfelder takes a small element – this time the role of gender in science – without giving any context, making it sound … weird. (Or weirder than it is.) In fact the segment (the original includes citations) follows a section where I am summarising the views of a number of authors and theorists including Evelyn Fox Keller, Margaret Wertheim, and so on.

Physics is an area that has long been dominated by men. And the idea that gender plays a role in aesthetics is hardly controversial, at least in philosophy. So it seems worth touching on if the aim is to understand the scientific aesthetic (though as mentioned in the book gender seems to be a bit of a taboo topic in physics).

Rather than simplistically saying that beauty is bad, Truth or Beauty makes the case for an alternative aesthetic, based on complexity rather than order and symmetry. And while Hossenfelder may find it “hard to take [its] argument seriously”, it seems ironic that, of all the books on her list, it is the only one where the central argument is exactly that, throughout history, beauty has been leading scientists astray.

July 5, 2018

Quantum Economics: The New Science of Money – out now in UK!

Filed under: Books, Economics — Tags: — David @ 12:48 pm

A decade after the financial crisis, there is a growing consensus that economics has failed and needs to go back to the drawing board. Quantum Economics argues that it has been trying to solve the wrong problem all along.

Economics sees itself as the science of scarcity. Instead, it should be the science of money (which plays a surprisingly small role in mainstream theory). And money is a substance that turns out to have a quantum nature of its own.

Just as physicists learn about matter by studying the exchange of particles at the subatomic level, so economics should begin by analysing the nature of money-based transactions. This book therefore starts with the meaning of the phrase ‘how much’ – or, to use the Latin word, quantum.

From quantum physics to the dualistic properties of money, via the emerging areas of quantum finance and quantum cognition, Quantum Economics reveals that quantum economics is to neoclassical economics what quantum physics is to classical physics – a genuine turning point in our understanding.

CoverFinal

 

 

July 4, 2018

Lost in Math

Filed under: Books, Physics, Reviews — David @ 3:14 pm

In which I read a book written on the same theme as something I wrote six years ago, and write a response in the style of the book.

I’m sitting at my computer when I come across a mention on a blog of a new book called Lost in Math, by the physicist Sabine Hossenfelder. The subtitle – How Beauty Leads Physics Astray – peaks my curiosity. In 2012 I wrote a book called Truth or Beauty which was about how science has been “led astray by the search for a particular type of beauty” as I put it. I think there might be a connection.

I see the book has received some excellent reviews, including one from the UK science writer Brian Clegg, who writes that the author “is saying that people in her profession need to step back from the coalface and take stock of what they are really doing and whether this particular approach really makes sense.” Some within the narrow high-energy physics community have been markedly less enthusiastic, but then they’re biased, aren’t they.

*

I order the book from my public library and it comes available within a few days. I pick it up at my local branch. It seems they are closing for renovations for 26 months (?), so they have free biscuits, and someone is playing classical guitar. I flip through the pages while I eat a chocolate chip biscuit.

The basic argument (scientists being led astray by beauty) seems to be the same as in my book, but the format and style is completely different. While I started at the beginning with the ancient Greeks and worked forward to the Large Hadron Collider, taking on subjects such as quantum mechanics and string theory on the way, Hossenfelder jumps around (literally – she always seems to be in transit), mixing interviews with commentary and snippets of historical content. It looks like a good read, sprinkled with pithy comments and interesting quotes.

I see there are also lots of breaks in the text, which always helps with readability. I scan my library card at the machine next to the guitar player, and leave with the book.

*

I walk back through the ravine, wondering about the book, and the lofty topic of aesthetics. I stop at a bench to read the opening sections. Science has always been shaped by aesthetics, in particular the principles of unity, symmetry, and stability. These were first articulated by the ancients, but they appear in modern form in theories such as supersymmetry, which asserts that every particle has a (so-far undetected) symmetrical twin; or the quest for a unified theory of everything. The most popular of these by far is string theory, in which subatomic particles are actually strings in a higher-dimensional space.

One aesthetic criterion favoured by physicists is the notion of naturalness, which means that dimensionless numbers in models (such as the ratios of particle masses) should be reasonably close to 1. No one can offer a good explanation of why this approach makes sense. It seems to be taking the concept of unity a little too literally.

When the Large Hadron Collider in Geneva opened for business in 2009, experimental results quickly confirmed the existence of the particle known as the Higgs boson, which had first been predicted in the 1960s. But most physicists working in the field were looking for more, expecting to see signs of supersymmetric particles, or something else pointing to new physics that would match their conception of beauty. For the last decade they have scoured the data in vain. As a result they have become “confused” as Hossenfelder puts it. Perhaps the universe doesn’t care about their sense of aesthetics?

“It’s either me who’s the idiot,” writes Hossenfelder, “or a thousand people with their prizes and rewards.”

*

I’m on my sofa reading the book more carefully. The style is very much in the here and now, mixing high science with the details of everyday life in an attractive way. A disadvantage is that the actual science part isn’t explained very clearly for those who think an SU(3) is a new kind of sports utility vehicle, rather than a mathematical object used in particle physics. The author also makes no effort to frame her book in the context of previous works, since “really I am more interested in the future than the past.”

I don’t for example come across any reference to my book, which I must admit seems odd given that it too was all about how science is “obsessed with beauty” as the Globe and Mail put it, but wonder if my response is related to what the physicist Nima Arkami-Hamed, interviewed in Chapter 4, calls the “narcissism of our times.” He calls out all those physicists who are worried because their pet theories didn’t work out: “It’s ludicrously narcissistic. Who the fuck cares about you and your little life? Other than you yourself, of course … Who cares about your feelings?”

I make myself another strong coffee and continue reading.

*

I am surrounded by packing boxes in an office. Framed works of art are stacked against the wall. This isn’t because I am an itinerant temporarily employed physicist, it’s just the way I roll.

Even before the LHC was complete, some physicists were starting to question the cult-like reverence that had developed around fields such as string theory. Peter Woit’s Not Even Wrong: The Failure of String Theory & the Continuing Challenge to Unify the Laws of Physics, and Lee Smolin’s The Trouble with Physics: The Rise of String Theory, the Fall of a Science, and What Comes Next, both appeared in 2006.

Still, when Truth or Beauty came out in 2012, its emphasis on aesthetics seemed rather provocative and controversial – especially given that the American Association for the Advancement of Science was about to hold its huge annual meeting on the theme of “The Beauty and Benefits of Science.” A common reaction at the time was that I was unqualified to comment, since my experience in physics was limited to working on the design of particle accelerators such as the Superconducting Super Collider. “Is it presumptuous for a nonphysicist,” asked the Chronicle of Higher Education rhetorically, “to criticize the work of the mighty minds that have defended string theory, including Brian Greene, author of The Elegant Universe, and Leonard Susskind, of Stanford University, and the Nobel Prize-winning Steven Weinberg, of the University of Texas at Austin?” Well, no insider was going to have a go at mocking the scientific aesthetic! Until now, that is. Things have changed, which is certainly refreshing.

I enjoy the book’s interviews, especially the one with Weinberg – once a champion of the SSC – who makes some insightful remarks. “I think the Newtonian revolution may have occurred because Newton did not find force acting at a distance ugly, whereas Descartes did … It was a change in aesthetic.”

The interview style seems to consist of sitting down with famous physicists and letting them prattle on unobstructed about truth and beauty, often to amusing effect. These physicists do like their symmetry. According to Dan Hooper for example, “All over the world, thousands of scientists have been imagining a beautiful supersymmetric universe.”

One of the best quotes is from an actual textbook on string theory, which announces: “The almost irresistible beauty of string theory has seduced many theoretical physicists in recent years. Even hardened men have been swept away by what they can already see and by the promise of even more.” Hmm.

*

I am on a bus to downtown when I read in the final chapter that “the mathematician David Orrell has argued that climate scientists favor elegant models to the detriment of accuracy.”

Huh? This description strikes me as misleading – even asymmetric? A third of a chapter was about meteorological models, the rest of the book as reviewers wrote was about how “scientists’ search for unity and symmetry may be leading them astray” or “leads too many researchers astray” or “has led them astray,” with an emphasis on physics. [Update: As an example of how this misleads readers, see this blog review which gets the wrong impression.]

I suppose the reason is that I did my D.Phil. on the predictability of nonlinear systems, with applications to weather forecasting – so from an insider perspective, what could I know about the aesthetics of high-energy physics? It would make as much sense as asking an art writer to comment.

*

Hossenfelder’s interviewees are nearly all famous physicists who are firmly in the mainstream. An exception of sorts is the Hawaii-based physicist/surfer Antony Garret Lisi, who tells her: “If you want to find a theory of everything, your aesthetic sense is pretty much all you have to work with.” While his lifestyle certainly sounds fun and adventurous, his sense of aesthetics seems deeply conventional. (In my book I compared a diagram of the E8 group, which is the basis of his theory, to a seventeenth century Theory of Everything by Robert Fludd.)

The interviewees are also all male, apart from one woman, included near the end, who according to Hossenfelder is famous on the internet because she was once retweeted by JK Rowling.

It still seems a little surprising that these people all regurgitate the same tired (and I argued gender-influenced, as in “hardened men”) aesthetic when questioned. On the other hand there is no effort to speak with complexity scientists, for example, or physicists who might have a different (more complex?) view of beauty. The one person who gives a different opinion is the author’s mother, who apparently likes to say that “symmetry is the art of the dumb.”

It is certainly the art of the old-fashioned. As Hossenfelder writes in the final chapter, “I spent nine chapters making a case that theoretical physicists are stuck on beauty ideals from the past.” Or as the art writer Benjamin Eastham wrote in a review of Truth or Beauty for V&A Magazine, “This conception of beauty, wedded to principles pre-dating Socrates, might to anyone even loosely familiar with a century’s progress in art, poetry and music seem at best archaic and at worst reactionary.”

Equations may only be understandable by a minority of trained experts – but aesthetic principles are rather more democratic. And they are open to change, as Newton knew.

In a review, physicist Peter Woit worries that the emphasis on “symmetry, unification and naturalness” risks over-simplifying the issues and doesn’t see “putting them together as ‘beauty’ to be helpful.” I would argue that Hossenfelder is on the right track – sometimes the problems really are simple.

*

I am finished with the book and try to return it to the library, but forgot that the library branch is closed for LHC-style multi-year renovations. The nearest alternative is a few miles away. It’s a nice day, so I decide to walk.

Asking why beauty has shaped physics, Hossenfelder mentions cognitive biases. One of these biases is not being able to see something if it doesn’t come from within your own community. Or as she put it “We disregard ideas that are out of the mainstream because these come from people ‘not like us’ … And we insist that our behavior is good scientific conduct, because we cannot possibly be influenced by social and psychological effects, no matter how well established.” It’s like when you review (or write) a book: it’s hard to be objective, but you should do your best to know your biases and declare your connections.

Of course, artists would probably ignore such advice.

I certainly agree with the book and hope it will make a difference. I recommend people read it. But a major problem with the physics profession is its extreme insularity. Physicists may travel a lot, and study the universe, but they live in a very small world. So if physicists want to revitalise their sense of aesthetics, they need to look outside their own narrow community – hell, even go to an art show. After all, as Tracey Emin once said, “art is for everybody” – not just a small elite – and the same goes for aesthetics in science.

*

Perhaps this will happen, now that someone inside the silo has said it – an aesthetic whistle-blower, if you like. As Clegg notes, it’s a brave book. But I still think the impetus for real aesthetic change will come from somewhere else.

I leave the book in the returns slot outside the library, and hope that its next collision is with a physicist.

Update: In which I discover that during the course of her research Hossenfelder wrote a capsule summary of my book and concluded that it was possibly “a joke”. Lesson learned: sometimes things are weird

April 24, 2018

Storm warnings

Filed under: Economics, Forecasting — Tags: — David @ 2:17 pm

“The test of science is its ability to predict”
— Richard Feynman

As if governed by some deterministic law, the current debates between economists and critics follow a predictable path. Critics begin by mentioning the failure of economists to predict or warn of the crisis. Howard Reed for example recently wrote in Prospect that ‘When the great crash hit a decade ago, the public realised that the economics profession was clueless.’

Thus provoked, economists then reply by pointing out that macroeconomic forecasting is only a small part of what economists do, that their models are based on mathematics and logical consistency, and that it is critics who don’t know what they are talking about – as in the riposte by Diane Coyle, which describes Reed’s piece as ‘lamentable’, a ‘caricature’ and an ‘ill-informed diatribe’ that furthermore ignores existing guidelines on what criticism is ‘good’ and ‘bad’ (the former includes ‘The criticism is by an economist’ which doesn’t seem in the multidisciplinary spirit, and would rule out this piece since I am an applied mathematician).

In a similar debate last year in Times Higher Education, Steve Keen wrote that the global financial crisis caught ‘leading economists and policy bodies completely by surprise. A decade later, economics is a divided and lost discipline.’ Christopher Auld responded that ‘Criticism of economics that relegates the field to … failed “weather” forecasting is not just misguided, it is anti-intellectual and dangerous.’

Over in the Guardian, Larry Elliott wrote that ‘Neoclassical economics has become an unquestioned belief system and treats those challenging the creed as dangerous’. A group of economists from the Institute for Fiscal Studies (IFS) appeared to confirm the latter when they called the article ‘dangerous’ and ‘ill-informed expert bashing … Like most economists, we do not try to forecast the date of the next financial crisis, or any other such event. We are not astrologers, nor priests to the market gods. We analyse data.’

The usual excuse offered for failing to predict the crisis, as Robert Lucas put it in 2009, is that ‘simulations were not presented as assurance that no crisis would occur, but as a forecast of what could be expected conditional on a crisis not occurring.’ That is like a weather forecaster saying their forecast was explicitly based on no storms. (The claim here reflects the efficient market-related idea that changes are caused by random external shocks.) Another is that no one else predicted it either – though a number of heterodox economists and others would beg to disagree.

But for both sides, the debate soon veers from discussing the crisis, to the topic of politics, with critics saying that economic models have been exploited by the right, while mainstream economists claim that in fact they are terribly progressive.

I would argue though that the debate isn’t really about politics, and less so about what most economists do with their time (the oft-advertised fact that economists apply their models to many things other than macroeconomic forecasting isn’t necessarily reassuring to a critic). Instead it is one of scientific legitimacy, and it as old as the word ‘forecast’.

Forecast

The argument between orthodox economists and their critics resembles one that occurred in weather forecasting in the mid-nineteenth century, with the establishment of the UK Meteorology Office in 1854 by Admiral Robert FitzRoy.

As captain of the Beagle, FitzRoy had taken Charles Darwin on the trip around the world that sparked Darwin’s theory of evolution. Seeing the potential that weather forecasting had to save lives by warning mariners of storms, he set up a network of 40 weather stations around the UK, with weather reports published in London newspapers.

However FitzRoy’s efforts were not well received, either by the public or the scientific establishment. At the time, weather prediction was something practised by astrologers, and the popular press enjoyed themselves comparing the Met. Office’s inaccurate predictions with those from sources such as ‘Zadkiel’s Almanac’. The mainstream scientists saw this prediction contest as a threat to their reputation, just as economists do today.

FitzRoy tried to blunt the comparison with astrology by avoiding use of loaded words such as ‘prediction’, and instead invented a new word of his own: forecast. ‘Prophecies or predictions they are not; the term forecast is strictly applicable to such an opinion as is the result of a scientific combination and calculation.’ In 1863, he published The Weather Book, which tried to make the weather comprehensible to people of average education. However the attempt to popularise the subject only further annoyed elitist scientific institutions like the Royal Society.

Two years later, FitzRoy took his own life at the age of 59. He may have been affected by his association with Darwin’s theory of evolution, which, as a creationist, he considered blasphemous. However it appears that the primary cause of his depression was being caught between the so-called astro-meteorologists on the one side and the scientific establishment on the other.

After his death, a committee chaired by Darwin’s cousin, Sir Francis Galton, released a report which claimed that his forecasts were ‘wanting in all elements necessary to inspire confidence’ and storm warnings were suspended. However FitzRoy was not without supporters; fishermen, maritime insurers, and the Navy had actually found the warnings useful, and they were reinstated in 1867. And today of course we rarely head out on a trip without checking the forecast.

Deniers

Now, one might think that astrology and creationism would have little to do with a debate over the scientific legitimacy of modern economic forecasting, but it seems that not much has changed. Indeed, in recent years – when most people have found economic forecasts ‘wanting in all elements necessary to inspire confidence’ – economists have been as anxious to draw distinctions between what they see as science and non-science as FitzRoy once was.

Diane Coyle for example writes that Reed’s piece conforms to a list of ‘bad’ criticisms helpfully compiled by Auld, which begins: ‘Every mainstream science which touches on political or religious ideology attracts more than its fair share of deniers: the anti-vaccine crowd v mainstream medicine, GMO fearmongers v geneticists, creationists v biologists, global warming deniers v climatologists. Economics is no different.’ Economist Pieter Gautier similarly explained the existence of heterodox approaches by saying that ‘You also see this happening in the other sciences; in biology you have intelligent design, in climate science you have the climate skeptics.’ Pontus Rendahl told the Financial Times in 2016 that calling for more pluralism in economics is ‘the same argument as the creationists in the US who say that natural selection is just a theory,’ while Michael Ben-Gad said that student groups want to be ‘liberated from neoclassical economics’ dogmatic insistence on internal logic, mathematical rigour and quantification … Still, we do not teach astrology or creationism in our universities, though some students might enjoy them more than physics.’ According to Simon Wren-Lewis, the problem with pluralism is ‘obvious once you make the comparison to medicine. Don’t like the idea of vaccination? Pick an expert from the anti-vaccination medical school.’ Or as the IFS economists put it, ‘We are not astrologers’.

Just as Robert FitzRoy had to defend the Met. Office against astrologers (though not creationists, since he was one), so economists are in a battle for what counts as science – which as Feynman noted has always been associated with the ability to predict. The difference is that, while FitzRoy was distancing himself from actual astrologers, mainstream economists tar a broad range of critics as ‘ill-informed’ and ‘dangerous’ deniers, regardless of their background or experience, in what looks like a kind of Hegelian ‘othering’.

Reality check

However, the issue is not ‘political or religious ideology’, it’s science. Predictions are obviously an important part of the scientific method, and when predictions do go badly wrong, it should serve as a reality check. While providing storm warnings is far from being the only job of economists (and expectations are much lower than in something like meteorology), it is surely one of the most important, which is why central banks for example devote considerable resources to it. And reflexively stamping critics and heterodox economists as anti-scientific deniers doesn’t seem very scientific – especially when some of them actually seem to be better at the prediction stuff.

Of course, as I point out in my forthcoming book Quantum Economics, economics should not be compared directly with weather forecasting. For one thing, the fact that economists’ predictions and models affect the economy (the financial crisis of 2008 for example was in part caused by faulty economic risk models) means that their responsibility is more like that of engineers or doctors. Instead of predicting exactly when the system will crash (no one has ever asked for a precise ‘date’), they should warn of risks, incorporate design features to help avoid failure, know how to address problems when they occur, and be alert for conflicts of interest and ethical violations. The profession’s failings in these areas, rather than any particular forecast, are the real reason so many are calling for a genuinely new paradigm in economics, as opposed to a rehashed version of the old one.

In the meantime, perhaps economists should just follow FitzRoy’s lead and invent a new word for their predictions. Econo-prognostications?

This piece first appeared at openDemocracy on April 24, 2018.

February 14, 2018

Of minds and money

Filed under: Economics — Tags: — David @ 3:04 pm

Post written for the Rebuilding Macroeconomics blog of the UK’s Economic and Social Research Council (ESRC), 23 February 2018

In 2017, when the ESRC announced that it was setting up a network of experts from different disciplines to “revolutionise” the field of economics, I thought it sounded like a very good idea. But in the spirit of that disruptive mandate, what if the revolution has already happened – and economics just needs to recognise it? I am talking about the quantum revolution which overturned physics at the start of the last century.

Of course, the thought that economics has anything to do with quantum physics will sound to many economists (or physicists) like a particularly severe case of physics envy. But my point is not that economics can be reduced to quantum physics (in my book Economyths I argue against such reductionist approaches). Nor is to assert that we can use quantum physics as a fuzzy metaphor to understand the economy. Instead, it is to say that the economy is a complex quantum system in its own right and should be treated as such. This recognition has the potential to disrupt all the pillars of mainstream economics, including its models of human behaviour, markets, and the macroeconomy.

To see why (and starting with the obvious), recall that quantum physics grew out of the empirical discovery by scientists that energy is transmitted, not continuously, but in discrete chunks they called quanta, from the Latin for “how much”. This violated the basic principle that Natura non facit saltum (nature makes no sudden leaps), as the epitaph of Alfred Marshall’s Principles of Economics read at the time (and until the final 1920 edition). But of course the same is true of money. When you pay for an item with a card, the money doesn’t drain out in a continuous flow, it goes as a discrete transmission.

Quantum objects can magically appear out of the void, and disappear back into it. In the economy, we have the creation of money by private banks issuing loans, and its destruction when loans are repaid. Again, these are discrete processes that take place “instantaneously and discontinuously” as a 2015 Bank of England working paper observed, so don’t fit easily with the continuous nature of conventional models – one reason they are typically excluded.

Another discovery of quantum theory is that matter has two complementary aspects, a “real” particle aspect and a “virtual” wave aspect. Money too combines the virtual properties of a number, with the real properties of an owned object – a bitcoin seems pretty virtual, unless you lose the computer it’s on – and it is this dualistic nature which gives money its confounding properties.

In quantum mechanics, a particle doesn’t have a well-defined location or momentum. In the economy, prices of something like a stock, or a house, are similarly indeterminate, and there is no unique intrinsic value (or eigenvalue in the quantum jargon). This is why some traders, along with researchers in the field of quantum finance, model the markets as a quantum system, with its own version of an uncertainty principle.

One of the more mysterious features of quantum reality is that subatomic particles can become entangled so that a measurement on one instantaneously affects the state of the other. Suppose I take a mortgage out with a bank. If I choose to default, then from that moment on the state of the loan has changed. Of course it will take time for the bank to learn what happened and settle the matter, but it takes time to measure particles too, during which other effects may come into play. It is a financial version of the social entanglement studied in quantum social science (see for example the 2015 book Quantum Mind and Social Science by political scientist Alexander Wendt).

Finally, another key property of quantum systems is interference: as in the double-slit experiment, where shining a light beam through two slits produces an interference pattern on the other side, even if only one photon passes at a time. Of course, money objects don’t interfere with each other, which is good because otherwise they might cancel out in your pocket. But the purpose of money is to put a number on the idea of value, and dissonance between these two things – objective number and subjective value – does produce interference patterns in our minds, of the sort modelled by researchers working in the area of quantum cognition.

In fact, instead of following classical logic when making decisions, it turns out that we are better described as following a version of quantum logic. As physicists Vyacheslav Yukalov and Didier Sornette note, “It is the appearance of interference terms that makes the structure of quantum expressions richer than the related classical ones and that allows one to explain those psychological phenomena that, otherwise, are inexplicable in classical decision making.”

As an example of a quantum economics phenomenon, suppose that you come under financial stress and are deciding whether to pay the latest installment on your mortgage, or default. Your mental state – and that of the loan – can then be treated, following the methods of quantum cognition, as being in an indeterminate superposition of two states. The emergent consequences in the entangled economy can be modelled at a societal level using complexity methods, including quantum agent-based models, though as always the system eludes reduction or exact computation.

Until now, money has played no more role in the quantum social sciences than in neoclassical economics, where it has traditionally been treated as an inert medium of exchange. But as seen above, quantum ideas are perfectly suited to things like the creation of money, entanglement through loans and other contracts, and credit default – all of which were at the heart of the 2007/8 crisis, but nowhere in the macroeconomic models.

As I argue in a discussion paper and in more detail in a forthcoming book, the quantum approach has implications not just for finance, or macroeconomic modelling, but for all the basic assumptions and conclusions of mainstream economics; and points the way to a new economics which is to its neoclassical version what quantum physics was to its classical version. Economics isn’t physics, but can learn from it; and if the intention is to rebuild macroeconomics, the natural place to start is with the quantum, dualistic nature of both mind and money.

January 12, 2018

Aeon piece on quantum economics – responses

Filed under: Economics, Physics — David @ 12:32 pm

Thanks to readers for taking the time to comment (via Twitter) on my recent Aeon piece Economics is quantum. Since it is hard to reply in strings of 140 characters, this post addresses some of the questions and criticisms that came up (edited for clarity).

After physicist Richard Jones wrote that the piece was “confused & misleading” (not a completely unusual reaction, I must admit) I asked him to clarify which parts of the text he was referring to. 

Jones: “Why do you think the brain is a quantum phenomenon? Direct involvement of consciousness in wave-function collapse is not mainstream view, & I’m very sceptical of any role of coherence in mental phenomenon.”

What I wrote was: “a number of scientists believe that the problem is not so much that people are being irrational; it is just that they are basing their decisions, not on classical logic, but on quantum logic. After all, quantum systems, such as us, are intrinsically uncertain and affected by history and context.” [As an example, see: Wang, Z., Solloway, T., S., M., R., & Busemeyer, J. R. (2014). Context effects produced by question orders reveal quantum nature of human judgments. Proceedings of the National Academy of Sciences, 111(26), 9431-9436.] Note that the fact that a system shows quantum properties does not mean it can be reduced to quantum mechanics. I don’t claim that consciousness is the product of quantum coherence, though it may well be. See for example: Atmanspacher, Harald and Thomas Filk (2014) “Non-Commutative Operations in Consciousness Studies,” Journal of Consciousness Studies.

Why is it helpful to compare the Scholes-Black equation to the Schrodinger equation? It’s a diffusion equation. I understand the math correspondence between the diffusion equation and the Schrodinger equation – it’s very useful in my own field as a formal device – but it involves imaginary time which seems unphysical here. In any case the Scholes-Black equation isn’t actually accurate as a representation of markets, as a diffusion equation doesn’t describe a random walk with step sizes whose variance is undefined (a Levy flight).”

This refers to the section: “It turned out that many of the formulas regularly used by ‘quants’ to value derivatives such as options (the right to buy or sell a security for a set price at a future date) could be restated as quantum effects. The Black-Scholes equation, for example, can be expressed as a version of the Schrödinger wave equation from quantum physics.” I am not claiming that this is particularly useful. My book The Money Formula (written with quant Paul Wilmott) discusses how the Black-Scholes equation and others have been abused in finance. Such equations were influenced in large part by quantum physics and the nuclear program, but only took part of the message (randomness). The quantum finance approach can address some of these shortcomings, by relaxing assumptions such as high liquidity, efficiency, etc.

“But why would you think a Schrodinger equation would help us understand economics better anyway? It’s a deterministic, linear equation of exactly the same class that you criticise economics for relying on.”

Not sure which part of the text this refers to, and I am not making exactly this claim. The main advantage of the quantum approach in areas such as decision making is that it allows us to consider effects such as context and history. Interesting that this was argued back in 1978 by Qadir, before behavioural economics was invented. Qadir, A. (1978). Quantum Economics. Pakistan Economic and Social Review, 16(3/4), 117–126.

“You compare money both to an observable – which has an uncertainty relationship with a conjugate variable (which is?) & also with a particle, so it has wave-particle duality. Isn’t this confusing an object with a property of the object?”

I define money objects to be transferable entities, created by a trusted authority, which have the special property of a defined monetary value, specified by a number and a currency unit (see The Evolution of Money, and this paper). They therefore combine the mental idea of a numerical quantity of money – the virtual wave attribute – with the physical idea of an object that can be possessed or transferred – the real particle attribute. Money objects are unique in that they have a defined value, so there is no chance of e.g. interference effects (a five-dollar bill doesn’t interfere with a ten-dollar bill in your wallet). However money objects are used to price goods through transactions in markets, where such effects can occur. In quantum finance, the conjugate variables for something like a stock are price and momentum. And one of the main findings of quantum cognition is that many behavioural economics effects can be explained in terms of interference. See e.g. Yukalov, V. I., & Sornette, D. (2015). Preference reversal in quantum decision theory. Frontiers in Psychology, 6, 1-7.

“I agree with you that economics needs to put more thought into understanding what kind of things money and value are & agree that money’s trying to do more than a simple scalar variable can manage. But it seems to me that invoking quantum mechanics doesn’t bring much more to the problem than a bunch of rather forced analogies.”

The piece does not evoke forced analogies,  it is saying that the money system is a quantum system in its own right, with its own versions of duality, indeterminacy, entanglement, and so on. This is not the same as saying that it is identical to quantum physics or reduces to it.

“E.g. quantum entanglement means something really very precise that isn’t at all the same as saying that people are connected, or even that one persons credit is someone else’s debt.”

To quote my textbook (Rae), “the word ‘entanglement’ refers to a quantum state of two or more variables, where the probabilities of the outcome of measurements on one of them depend on the state of the other – even though there is no interaction between them.” The classic example is of two entangled photons A and B, where a result of positive spin measured along a certain axis for A implies that a later measurement of B “can now yield only a negative result.” Suppose now that person A has a loan from person B. From the viewpoint of quantum decision theory (or just a mathematical model), we can view A’s decision to default as a measurement process similar to the measurement of a particle’s spin; and this decision changes the status of the loan instantaneously – it can only yield a negative result – as B will find if they try to get their money back. Obviously it is hard to think how one could perform something like a Bell’s test (designed to tease out relationships between entangled particles) on a loan agreement, since such tests require measurements along different spin axes, but that doesn’t mean entanglement does not occur.

“So I agree with you that there’s lots to be done in economics & it should learn from physics, but I think (as has already begun) the place to look is in stat mech (including complexity & network theory) rather than qm.”

I have been advocating for a complexity approach in several books (Economyths, Truth or Beauty, etc.), but I see the quantum approach as backing up that claim.The point is not that economists should try to build elaborate quantum models of the economy – indeed, the neoclassical emphasis on microfoundations is misplaced. Instead, prices are best seen as emergent properties (see this paper). At the same time, the quantum effects of money can scale up and affect the economy as a whole. An example is the quadrillion dollars worth of derivatives which have been strangely absent from mainstream macroeoconomic models – now that is confused and misleading.

Update: response to more twitter comments.

Economist David Harbord: “This bit of silliness by @d_orrell should be enough to keep @Noahpinion wound up for a day or two …”

Niels Bohr asked of one physics theory, “The question is whether it is crazy enough to be have a chance of being correct.” The economics version is that this theory might be silly – but is it silly enough?

“I recall someone showing up at the LSE when I was a graduate student claiming that the problem with economic theory was the assumption Newtonian time & space, hence we needed an Einsteinian revolution in economics! Might be worth checking up on progress in that research program.”

Over a century ago some people showed up claiming that economics should be based on Newtonian mechanics. We all know how that research program is going.

“Both suggestions focus on phenomena at the wrong scale for modelling economic activity. If you can produce a model in which quantum effects matter & make predictions that ‘Newtonian’ economics cannot (lots of scope there!), then I’ll admit you are on to something.”

I’m not saying economics reduces to quantum physics – I am saying that money has its own quantum properties, which do scale up. But read the book when it comes out and judge for yourself. For my thoughts on prediction, see this recent article for Newsweek Japan.

Thread begun by science communicator Natalie Wolchover from Quanta:

What a load of hogwash.”

Like traditional economics then – with the nice difference that it doesn’t act as the PR wing for an out-of-control financial sector.

Further comments by various people on the same thread:

“I thought these guys were starting to get passed the physics envy.”

I actually trained in math and physics, so perhaps this should be economics envy. In my previous books such as Economyths I have done as much as most people to argue against the idea that economics can be simply transposed from physics. However metaphor is intrinsic to our thought processes, and neoclassical economics has long been replete with metaphors from Victorian mechanics – one of its founders Vilfredo Pareto for example said that “pure economics is a sort of mechanics or akin to mechanics” – so perhaps it is time to expand our mental toolbox. After all, it isn’t just quantum mechanics which has been “misused and abused” (to quote Sean Carroll). Also, while I did study quantum mechanics, and use it in my work (my early career was spent designing superconducting magnets which rely on quantum processes for their function), my intention is not to further mathematicise economics – quite the opposite. The core ideas of the theory proposed are very simple.

“Can hardly wait for the forthcoming quantum astrology piece.” “Or auto repair done by quantum mechanics.” “I would be happy to have dollars tunnel from pockets of rich folks to mine.” “That’s about two steps away from Deepity Chakra.” “I think he means a paradigm shift.” “To quote physicist Wolfgang Pauli, this is not even wrong.”

Not even funny … Physicists have been very careful to put up a lot of filters around quantum ideas, which is understandable, but is also one reason social scientists are stuck in an oddly mechanistic view of the world. So we need more discussion between these areas.

For more comments and responses, see the comments thread in the article.

 

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