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Friday, October 26, 2012

Quantum lemonade

Seth Lloyd's popular book* on quantum computation, life and the universe impressed me when I first read it a few years ago. I had the sense that Lloyd was saying something very important for our understanding of reality, of what ultimately underlies the whole shebang.

I still think the basic thesis of the book - that the cosmos is a quantum computer - is fascinating and maybe even true. Certainly, the parallels between thermodynamics and information theory suggest that information (bits, or qubits, and their operations) is absolutely fundamental to an understanding of the world and - speaking very loosely - the basic stuff out of which we and the cosmos are made.

But this recent article by Seth Lloyd disappointed me in a couple of ways.

Lloyd's book is beautifully written, a model of popular science writing. The science is clearly and simply presented, and there is some good - if at times only tangentially relevant - autobiographical background material. (The story of the death of Heinz Pagels is unforgettable. 'Heartbreaking', one reviewer called it.)

By contrast the article is in large part a rehash of things Lloyd has said many times before (for example, about the recalcitrance of atoms and sub-atomic particles, their reluctance to do what we want them to do and the need for infinite guile and patience on the part of quantum engineers). And unfortunately the metaphors are strained and distracting, in my opinion, and just a touch condescending. I think Lloyd is trying too hard not to sound like a boffin.

But the most significant thing about this recent piece is that in it Lloyd doesn't attempt (as he might well have done) to talk up the prospects for serious quantum computers. On the contrary, the whole program to develop and build useful quantum computers, about which he was so sanguine in his book, is presented as being somewhat problematic.

He writes: "The quantum sensitivity [Nobel Prize-winner Serge] Haroche identified certainly makes quantum computers hard to build, but it's also that very sensitivity that makes funky quantum phenomena such as Schrödinger's cat states the basis for hypersensitive detectors and measurement devices... What's bad for quantum computation is good for precision measurement - if life deals you quantum lemons, make quantum lemonade."

In other words, if we can't have miraculously powerful computers of an entirely new kind, we can at least have very accurate clocks. Mmm.

Guess I was a bit naïve to believe the hype.

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Come to think of it, years ago I was quite excited about artificial intelligence. And they can't even do a convincing natural language interface yet.

Frankly, though, I don't much care about whether these technologies eventuate or not. What interests me more is the light that research into computing - digital and quantum - has thrown on some perennial questions.

The old answers to fundamental questions are just no good any more. And if some of the old answers do get a new lease on life, it will only be, I suspect, because they happened to prefigure an explanation informed by information theory, quantum mechanics and/or other recent theoretical work in physics or related sciences.

There is hype about technology and hype about basic science. But the fact is, though progress seems slow in both spheres, progress is indeed occurring.

Which is more than can be said of perhaps any other area of human life or endeavour.



* Programming the Universe: A Quantum Computer Scientist Takes on the Cosmos (Knopf, 2006).

Friday, October 12, 2012

One, two, many

The question of the relevance of natural language to counting and calculating capacities has been raised in recent years in connection with two similar research projects.

In a well-known study published in 2004, the counting abilities of the Piraha people of the Amazon were examined. Their language lacks number words (other than for one and two). The researchers suggested that language (rather than other societal or environmental factors) was the crucial factor in explaining the poor counting abilities of members of this tribe.

Though not everyone was convinced by the researchers' claims, more recent research on several adults in Nicaragua who were born deaf and never learned Spanish or a formal sign language provided some slightly more convincing evidence of the importance of language for counting ability.

Elizabeth Spaepen (of the University of Chicago) and her colleagues conducted experiments involving, for example, the experimenter knocking her fist against the subject's fist a number of times and asking the subject to respond with the same number of knocks. (Iteration, note, rather than objects.)

'So if I were to knock four times on their fist,' commented Dr Spaepen, 'they might knock my fist five times.' *

The earlier research on the Piraha involved similar tests and similar results, but there was nothing to say that language was the crucial factor. A stronger case for language being the key factor can be made on the basis of the more recent research, as the Nicaraguans, unlike the Piraha, were living in a culture rich in counting systems.

Daniel Casasanto (of the Max Planck Institute for Psycholinguistics) points out that the human brain is good at approximating, e.g. distinguishing between ten and twenty objects, but needs a counting system to distinguish between ten and eleven, say.

'What language does,' he explains, 'is give you a means of linking up our small, exact number abilities with our large, approximate number abilities.'

As I see it, language provides for individuals, societies and cultures a kind of bridge to sophisticated forms of counting and calculation. Number words (in conjunction with other aids like fingers) facilitate simple forms of counting and these form a basis for more advanced techniques incorporating symbols and calculating devices.

Though number words are an intrinsic part of language, counting systems by and large are not. And - significantly - the more sophisticated the counting and calculating systems are, the less dependent they are on natural language.

So I don't see any necessary or intrinsic link between natural language and counting systems.

Historically, it may well be that only societies with number words went on to develop sophisticated counting systems and mathematics generally. And it may well be that, for most human children, learning number words is a prerequisite for learning to count and do basic arithmetic.

But this does not mean that arithmetic is in any fundamental way dependent on natural language.

Even in terms of human psychology, the link between language and calculating ability is pretty tenuous.

Think of autistic savants, for example. Are there not many instances of individuals who lack the ability to use and process language and yet whose brains display advanced calculating abilities?



* Wittgenstein would have had a field day with this!