Musical illusions

Here's the English version of my column on music cognition for the current issue of the Italian science magazine Sapere.

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“In studying [optical] illusions”, writes Kathryn Schulz in her book Being Wrong, “scientists aren’t learning how our visual system fails. They are learning how it works.” What Schulz means is that normal visual processing is typically a matter of integrating confusing information into a plausible story that lets us navigate the world. Colour constancy is a good example: the brain “corrects” for variations in brightness so that objects don’t appear to change hue as the lighting conditions alter. The famous “checkerboard shadow” illusion devised by vision scientist Edward Adelson fools this automatic recalibration of perception.


Adelson’s checkerboard illusion. The squares A and B are the same shade of grey.

In this regard as in many others, auditory perception mirrors the visual. The brain often rearranges what we hear to create something that “makes more sense” – with the same potential for creating illusions. Psychologist of music Diana Deutsch has delved deeply into the subject of musical illusions, some of which are presented on a CD released by Philomel in 1995. Several of these have to be heard through stereo headphones: they deliver different pitches to the left and right ears, which the brain reassigns to create coherence. For example, in the “scale illusion” the notes of two simultaneous scales – one ascending, one descending – are sent alternately to each ear. But what one hears is a much simpler pattern: an ascending scale in one ear, descending in the other. Here the brain is choosing to perceive the more likely pattern, even though it’s wrong.

Another example reveals the limitations of pitch perception. A familiar tune (Yankee Doodle) is played with each note assigned a random octave. It sounds incomprehensible. The test shows that, in deciphering melody, we attend not so much to absolute pitch class (a C or D, say) as to relative pitch: how big pitch jumps are between successive notes. Arnold Schoenberg’s twelve-tone serialism ignored this, which is why the persistence of his “tone rows” is often inaudible.

Perhaps the strangest thing about optical illusions is that we enjoy them, even if – indeed, because – we find them perplexing. Instead of being upset by the brain’s inability to “get it right”, we are apt to laugh – not a common response to wrongness, although it’s actually how a lot of comedy works. You might, then, expect to find musical illusions put to pleasurable use in music, especially by jokers like Mozart. But they are rather rare, maybe because we simply won’t notice them unless we see the score. Something like the scale illusion is used, however, in the second movement of Rachmaninov’s Second Suite for Two Pianos, where two sets of seesawing notes on each piano are heard as two sets of single repeated notes. It seems likely that Rachmaninov (not noted for jocularity) wasn’t just having fun – it’s merely easier to play these rapid quavers using pitch jumps rather than on the same note.

Why brief answers are sometimes not enough

I reviewed Stephen Hawking's last book Brief Answers to the Big Questions for New Scientist, but it needed shortening and, in the print version, didn't come out as I'd intended. Here's the original.

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Most people as famous as Stephen Hawking have their character interrogated with forensic intimacy. But Hawking’s personality was in its way as insulated as the Queen’s, impermeably fortified by the role allotted to him. There’s a hint in Brief Answers that he knew this: “I fit the stereotype of a disabled genius”, he writes. Unworldly intelligence, a wry sense of humour, and tremendous resilience against adversity: that seemed to suffice for the celebrity in the wheelchair with the computerized voice (itself another part of the armour, of course).

It made me uneasy though. The public Hawking was that stereotype, and while it was delightful to see how he demolished the does-he-take-sugar laziness that links physical with mental disability, he did so only by taking matters to the other extreme ("such a mind in such a body!"). It perhaps suited Hawking that the media were content with the cliché – he didn’t give much impression of caring for the touchy-feely. (Eddie Redmayne, who played Hawking in the 2014 biopic The Theory of Everything, reminds us in his foreword that the physicist would have preferred the film to have “more physics and fewer feelings”.) But his story suggests we still have some way to go in integrating people with disabilities into able-bodied society.

I approached this book, a collection of Hawking’s later essays on “big questions”, with some trepidation. You know you won’t go wrong with the cosmology, relativity and quantum mechanics, but in other areas, even within science, it’s touch and go. The scientific essays supply a series of now-familiar Greatest Hits: his work with Roger Penrose on gravitational singularities and their relation to the Big Bang; his realization that black holes will emit energy (Hawking radiation) from their event horizons; his speculations about the origin of the universe in a chance quantum fluctuation; the debate – still unresolved – about whether black holes destroy information. Hawking, as Kip Thorne reminds us in his introduction, helped to integrate several of the central concepts of physics: general relativity, quantum mechanics, thermodynamics and information theory. It’s a phenomenal body of work.

Sometimes there’s a plainness to his prose that can be touching even while it sounds like an anodyne self-help manual: “Be brave, be curious, be determined, overcome the odds. It can be done.” Who would argue with Hawking’s right to that sentiment? His plea for the importance of inspirational teaching, his concerns about climate change and environmental degradation, his contempt for Trump and the regressive aspects of Brexit, and (albeit not here) his championing of the NHS, sometimes made you glad to have Hawking on your side. People listened.

A common danger with collections of this kind is repetition, which the editors have been curiously unconcerned to avoid. But the recurring and familiar passages are in themselves quite telling, for they show Hawking curating his image: the boy who was always taking things apart but not always managing to put them back together again, the man who told us to “look up at the stars and no down at your feet.”

There’s no doubt that Hawking cared passionately about the future of humankind and the potential of science to improve it. His advocacy resembles the old-fashioned boosterism into which H. G. Wells often strayed in later life, tempered like Wells by an awareness of the destructive potential of technologies in malicious or plain foolish hands. But what are Hawking’s resources for developing that agenda? One of the most striking features of this book is the lack of extra-curricular references – to art, music, philosophy, literature, say. This would not matter so much (though it’s a bit odd) if it were not that the scope of some of pieces exposes these gaps painfully.

Beginning an essay called “Is there a God” by saying that “people will always cling to religion, because it gives comfort, and they do not trust or understand science” tells you pretty much what to expect from it, and you’d not be wrong. God, as no theologian said ever, is all about explaining the origin of the universe. And most people, Hawking tells us, define God as “a human-like being, with whom one can have a personal relationship.” I suspect “most people’s” views of what a molecule or light is would bear similarly scant resemblance to what well-informed folks say on the matter, but I doubt Hawking would give those views precedence.

As for history, try this: “People might well have argued that it was a waste of money to send Columbus on a wild goose chase. Yet the discovery of the New World made a profound difference to the Old. Just think, we wouldn’t have had the Big Mac or KFC.” The lame joke might have been just about tolerable if one didn’t sense it is there because Hawking could think of nothing to put in its place. This remark, as you might guess, is part of a defense of human space exploration, during which Hawking demonstrates no more inclination to probe the real reasons for the space race in the 1960s than he does to examine what Columbus was all about. He feels that the human race has no future if we don’t colonize space, although it isn’t clear why his generally dim view of our self-destructive idiocies becomes so rosy once we are on other worlds. Maybe the answer lies with the fact that here, as elsewhere, his main point of reference is Star Trek. But I suspect he knew he was preaching to the converted, so that mere assertion (“We have no other option”) was all he needed in lieu of argument.

There’s a glib insouciance to some of the other scientific speculations too. “If there is intelligent life elsewhere”, he writes, “it must be a very long way away otherwise it would have visited earth by now. And I think we would’ve known if we had been visited; it would be like the film Independence Day.” Assertion again replaces explanation in Hawking’s assumption apropos artificial intelligence that the human brain is just like a computer, as if this were not hotly disputed among neuroscientists. Here too, his vision seems mainly informed by the science fiction within easiest reach: his fears for the dangers of AI conjure up the Terminator series’ Skynet and tropes of supercomputers declaring themselves God and fusing the plug. Science fiction has plenty to tell us about our fears of the present, but probably rather less about the realities of the future.

It is best, too, not to rely on Hawking’s history of science, which for example parrots the myth of Max Planck postulating the quantum to avoid the ‘ultraviolet catastrophe’ of blackbody radiation. (Planck did not mention it.) Don’t expect more than the usual clichés: here comes Feynman, playing the bongos in a strip joint (what a guy!), there goes Einstein riding on a light wave.

This is all, in a sense, so very unfair. Hawking was a great scientist who had a remarkable life, but in another universe without motor neurone disease (well, he did like the Many Worlds interpretation of quantum mechanics) we’d have no reason to confer such authority on his thoughts about all and sundry, or to notice or care that he entered the peculiar time-warp that is Stringfellows “gentlemen’s club”. We would not deny him the right to his ordinariness, and we would see his occasional brash arrogance and egotism for no more or less than it is.

There’s every reason to believe that Hawking enjoyed his fame, and that’s a cheering thought. The Hawking phenomenon is our problem, not his. He likes to remind us that he was born on the same date that Galileo died, but it’s Brecht’s Galileo that comes to mind here: to paraphrase, unhappy is the land that needs a guru.