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A View From the Top
Thinking of causation as a "two-way street"—along which the passage of information can be inverted—could have implications for the origin of life.
Classic Article: Black Holes, Paradox Regained
In 2004, Stephen Hawking famously conceded that black holes do not devour all information when they swallow matter—seemingly resolving the "black hole information paradox" that had perplexed physicists for decades. But some argue that the paradox remains open, and we must abandon our simple picture of spacetime to unravel it.
BOB COECKE University of Oxford Credit: Valerio Scarani
It’s not just what you say that matters, but how you say it: If you’re making an app for a phone, for instance, it’s best to use Java script; fairy tales weave together words that draw you into their magical world; and music combines pitch, tone and rhythm for expression. So what language is best for understanding quantum mechanics—the strange theory that describes how things behave in the atomic realm?
For most physicists, the answer is: mathematics. But Bob Coecke’s idea is more radical. Perhaps fittingly for the one-time artist, turned physicist, Coecke has developed a new graphical language to represent the mathematics of quantum processes. Onto this canvas he has been painting a picture of possible quantum theories, including some that extend beyond the version that we know and love and which may also encompass gravity. If the quest for quantum gravity wasn’t enough, Coecke is also applying this visual framework to probabilistic reasoning, linguistics, AI and cooking—underpinning a theory of everything indeed!
Coecke has taken an unconventional path en route to becoming the Professor of Quantum Foundations, Logics and Structures at the computer science department of Oxford University, UK. Visiting him at his office—where I narrowly missed sitting on his pet plastic snake—I quickly realize that Coecke is not your stereotypical physicist. Easy-going and verging on modest, he recounts to me the chaotic series of life choices that conspired to lead him here. Having grown up in a tiny Belgian village, home of the famous beer Duvel (a favorite of Coecke’s), he dreamt of being an artist. When that did not pan out, he set out to study engineering, which he hated. That was followed by a switch to architecture—but Coecke found the summer work experience "just horrible—building ugly houses for people with bad taste"—before settling on physics and math.
Coecke has no fear about casting off years of accepted dogma.
- Prakash Panangaden
Even then, Coecke’s reasons for embarking on a doctorate at the Free University of Brussels were unorthodox: "I was attracted by the idea of doing a PhD because then I could spend a lot of time doing music, it was as simple as that," says Coecke. Why quantum foundations? Because a guy at university was doing it and "so I ended up doing my PhD with him." In the 1990s, work on quantum foundations received very little funding, and Coecke struggled to get a postdoc, remaining unemployed for about a year. During that time he wrote a novel that was published in Flemish. He tried to get serious about music and worked with some professional composers, and in schools, and later had a job interview at the Art Institute of Chicago, but they didn’t take him on. "A week later I got a postdoc at the computer science department at Oxford University and I said to myself, forget about the art, you’re a failure, do some science!"
The way Coecke tells it, I could be fooled into thinking that his haphazard history makes him ill-suited to life as a physicist. But his laid-back nature belies the tremendous success of his diagrammatic framework of quantum theory, and in quantum foundations in general—possibly because of the varied roads he has taken. As Prakash Panangaden, a computer scientist at McGill University, in Montreal, Quebec, explains, "he has no fear about casting off years of accepted dogma and pursuing his ideas."
Tossing Out Syntactic Garbage
Coecke is currently pursuing his ideas with the help of an FQXi grant of over $111,000. His new graphical language is based on category theory, a branch of mathematics that allows you to describe collections of objects and how they change—or map—from one set to another. For example, if you had a set of positive integers (1, 2, 3, 4) and a set of negative integers (-1, -2, -3, -4) then you could draw an arrow to represent how the sets are linked (in this case the arrow represents the function "multiply by -1"). (See "The Art of Math" for more on category theory.)
"It’s a much more natural way to write things," says Coecke. "It cuts out a lot of syntactic garbage in the usual models of maths. Going to the more complicated stuff is still sort of rationally manageable." That means you can go on to describe the relations between different, and complicated, quantum processes in a clear and simple way—an especially useful trick when you want to represent some of the strange features of quantum theory, such as entanglement, nonlocality and teleportation.
In Coecke’s scheme, quantum mechanical processes are signified as boxes. If processes interact, they are connected by wires. The diagrams provide a clear, visual way to see at a glance how things change in a system, as time progresses across the diagram, depicted by the changing connectivity of the boxes. Difficult quantum calculations can be reduced to simple changes to the picture, retaining quantitative information. "We saw that quantum teleportation is nothing more than sort of yanking a line" for instance, says Coecke.
QUANTUM TELEPORTATION Pictures are worth a thousand math symbols in Coecke’s framework.
By describing processes in diagrams, the laws that govern their ordering—their causal structure—are implicit. "The computing is in the re-ordering of the diagram, it’s really intuitive," says Coecke. "Things that are fairly hard to express become completely trivial using diagrams."
To understand the advantage of the scheme, Coecke refers to a common example encountered by computer programmers. "If someone gave you a computer program written in zeroes and ones, there’s no way you could see what it does," he notes. But if, instead, someone gave you a pictorial flow chart representing the algorithm you are hoping to recreate, you would immediately understand what the program does. "For us, these diagrams are a high-level language to reason about physics," says Coecke.
This novel application of category theory has impressed mathematicians and physicists alike. "Bob Coecke’s work has done a lot to get the quantum foundations community interacting with category theorists," says FQXi member John Baez, a mathematician at the Centre for Quantum Technologies, in Singapore. "We’re learning a lot of new things about both subjects thanks to this interaction."
The diagrammatic approach does more than just simplify how physicists manipulate the math of quantum theory. It can also be applied to other theories too, including alternatives to quantum physics that nature does not employ. It may seem strange that physicists would want to investigate nature’s rejects. But over the past decade, quantum theorists have been trying to understand the strangeness of quantum theory by looking at alternatives theories that share some, but not all, of its spooky features and could conceivably fit in with the other laws of physics that we have. Yet nature passed over those in favor of the version of quantum theory that we observe. The question perplexing physicists is, why? They hope that by understanding the answer they may uncover why quantum theory has the features that it does. (See "Why Did Nature Choose Quantum Theory?")
Rob Spekkens, of the Perimeter Institute (PI) in Ontario, Canada, is one such theorist who has developed a workable alternative to quantum theory. "People have been trying to focus on a mathematical framework to describe alternatives to quantum theory because once you have a landscape of theories—many possibilities for the way the world could be—then you’ve got a richer context in which to talk about what’s special about quantum theory," Spekkens says.
Upon meeting him, Coecke immediately made an impression on Spekkens—and not just because his diagrammatic framework was pretty much the only one capable of describing Spekkens’ alternative accurately. Spekkens recalls how, on Coecke’s first extended visit to PI, he wasn’t satisfied with the heat of the chilli sauce provided in the bistro, so he went to the shops to buy himself a bottle and thereafter brought it with him to every meal. "We keep it for him now and he reclaims it every time he’s here for a visit," says Spekkens.
Another long-term advantage of exploring the quantum landscape is to search for quantum theories that could stretch into a theory of quantum gravity, the Holy Grail for many foundational physicists hoping to incorporate Einstein’s general relativity, according to which gravity manifests because of the way that heavy objects warp spacetime. Current mathematical formalisms of quantum theory are incompatible with gravity, so it’s likely that we need a new mathematical framework to contain the two. Coecke’s canvas could be just what’s needed because it can describe the geometry of spacetime simply through the topology of the diagram, which mathematically tracks how surfaces are stretched and deformed. "This is very much ongoing," adds Coecke, emphasizing that any progress towards a quantum theory of gravity will be slow. But a good place to start is by investigating those quantum theories in the landscape that could describe gravity.
Coecke describes his quantum graphics in this FQXi video:
Panangaden says Coecke’s graphical framework has had quite significant impact already. Though it’s not the dominant paradigm in quantum foundations, its influence is growing. "The most important thing is how it has focussed attention on quantum processes, and how one combines them to get more complex processes," Panangaden says.
That impact is reflected by the growth of Coecke’s research group and his professional success since he, in his words, got his head down and tried to "do something with my life that actually worked out!" When he started his postdoc position at Oxford University ten years ago he was the only person doing research in quantum logic. Now a professor, his research group has ballooned to 35, and counting. "I’ve got 20 PhD students at the moment, that’s actually a bit too many," he laughs. Coecke’s conceptual stance on quantum theory has also been attracting a lot of interest from the ’big-guns’—for example the US navy—because by creating a framework for putting together quantum processes you are essentially modeling a quantum computer.
Why is Coecke so good at what he does? Panangaden puts it down to his "intellectual boldness that allows him to go where others would hesitate." Indeed, Coecke is most proud of how his diagrammatic approach can be applied to other parts of our daily reality, such as linguistic processes—an arena that few quantum physicists would dare to enter.
Surprisingly, the way words interact to make up a sentence is similar to the way quantum processes interact. Google takes no notice of the order of words on a page, but actually the ordering can completely change a sentence’s meaning. Coecke has used his graphical approach to connect individual words in a sentence so their meaning can be extracted according to both the content of each word and its positioning. This is quite an achievement: most models of human language either focus on individual words or grammatical rules, not both. "Our categorical model blows away the existing language processing models," says Coecke.
Coecke is now working on a linguistics model with Mehrnoosh Sadrzadeh, Ed Grefenstette and Dimitri Kartsaklis in his group, and linguists Stephen Pulman at Oxford and Stephen Clark of Cambridge University. They are testing it with samples from the British National Corpus—a 100 million word collection of written and spoken British English. The team plans to incorporate language processing tasks to calculate the meaning of sentences, for example to include words that are ambiguous—such as ’Mars’ which might refer to the planet, a Roman god, or the chocolate bar, among other things. They also need to untangle compound types—when two words are joined together, such as sandpaper.
"I’m looking forward to seeing what comes out of his research group in the next few years," says Spekkens.
The fact that Coecke’s high-level approach to understanding quantum information has such power when applied to other diverse fields, including linguistics, may point to a higher truth: that there are structures common to all layers of reality. "I used to think that physics was the only real deal, the foundation of everything," says Coecke. "I think that perspective is very naïve now."
While mulling over that philosophical issue, Coecke’s also getting back into music, tempted by the growing experimental music scene in Oxford. He’s even building his own studio. Let’s hope quantum theory maintains its attraction—and the canteen its chilli sauce.
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GEORGINA PARRY wrote on November 3, 2012 Hi Po,
I think this pictorial language is different, not a substitute but something additional. It seems to me this language isn't about spatial or topological relations but about sequences of events and relations within and between those. The information transfer and alteration rather than locations and actions in space.I agree that how objects and data spreads through space is also important and quaternion (and some will argue Octonian )algebra can be useful for thinking about and...
GEORGINA PARRY wrote on November 3, 2012 In my mind that then becomes not just a wonderfully complex illustration on paper but something that would make a brilliant animation. Or better still a sculpture or interactive program that can be looked at from many different angles and scales to see what is going on overall or in parts. To make conventional mathematics into such a physical or digital sculpture might seem bizarre ( though having just said that i would quite like to do for that very reason) but the pictorial representation...
GEORGINA PARRY wrote on November 3, 2012 Hi Bob, I took a look at Quantum Picturalism
I think it is a marvellous way to make the subject accessible without loosing information. It is particularly interesting to me because I am (so to speak )one of those kindergarten kids.I would very much like to play with this kind of thing and have it produce the same answers as the conventional notation. Will take more time to fully understand what you have presented.However...
Something struck me looking at the cooking section....