Simple City  

Over on G+, Alexander Kruel pointed me towards an article by Alex Knapp entitled “Why your brain isn’t a computer”.

The point of this post is not to argue whether it is or it isn’t, but to draw attention to a salient point, which I think Alex waves away rather too quickly (and which in any case is important and interesting).

One might reason that there are plenty of different types of ‘computation’ around these days: ordinary computer programs, embedded systems, neural nets, self-modifying code, and so on. So, with all this variety, why should we expect that a human brain, being a neurochemical network, should fall into the same computational category as a laptop? Might it not simply be that the two have different capabilities? As Alex argues “Electric circuits simply function differently then electrochemical ones”.

The problem with this argument is that it overlooks the great robustness of the notion of computability, specifically the Church-Turing thesis.

A bit of history: in the 1930s, Alan Turing was investigating the capabilities of Turing machines, funny little devices which creep along a ticker-tape, and respond to the symbols they find there. Meanwhile over in the US, Alonzo Church was exploring the semantics of a formal system he had developed, called lambda calculus.

On first sight, the two topics appear to have little in common. But when the two men encountered each others’ work, they quickly realised something unexpected and profoundly important: that anything which can be expressed in lambda calculus can also be computed by a Turing machine, and vice versa. Shortly afterwards, a third approach known as recursion was thrown into the mix. Again, it turned out that anything recursive is Turing-computable, and vice versa.

This leads to the assertion we know as the Church-Turing thesis: that a process which is computable by any means whatsoever, must also be computable by a Turing machine.

It is important to stress that the Church-Turing thesis has good experimental support. Every computational system we know of obeys it: cellular automata, neural networks, Post-tag systems, logic circuits, genetic algorithms, string rewriting systems, even quantum computers*. Anything that any of them can do can (in principle) be done by conventional computational means.

So when Alex comments that “the brain itself isn’t structured like a Turing machine”, the obvious response is, “well, no, and neither are lambda calculus, cellular automata, and the rest”. (Come to think of it my phone doesn’t much look like a Turing machine either.)

The ‘dualism’ which distinguishes software from hardware (which Alex argues fails for the human brain), is not something built in from the outset. Rather it emerges from the deep, non-obvious fact that computational systems beyond a certain complexity can all emulate each other.

Needless to say, there have been no shortage of people claiming to have developed systems of different kinds which go ‘Beyond the Turing Limit’. (See Martin Davis’ paper on The Myth of Hypercomputation.) And who knows, maybe our brain embodies such a process. (I have my doubts, but if we’re going to find such a system anywhere, the brain is certainly an obvious place to look.)

The bottom line here is that if you don’t want to accept that

  0)   The human mind is computable

then I’d say you have three positions open to you:

  1)   It requires an extra metaphysical ingredient;
  2)   It’s a hypercomputer which violates the Church-Turing thesis;
  3)  It relies in an essential way on a non-computable process, meaning some inherent element of randomness.

Personally I’d order these 0312, in order of likeliness. (At the same time, I’d say talk of reverse-engineering the human brain is like a toddler planning a manned expedition to Mars. How about we concentrate on crossing the room without falling over first?)

 

*Quantum computers may be able to compute certain things quicker than conventional ones, but they won’t be able to compute essentially different things.

There is a meme circulating in the blogosphere where you have to turn to page 123 of a book you’ve recently read, and post the 5th, 6th, and 7th sentences. Here goes:

“Absolute pitch is not necessarily of much importance even to musicians – Mozart had it, but Wagner and Schumann lacked it. But for anyone who has it, the loss of absolute pitch may be felt as a severe privation. This sense of loss was clearly brought out by one of my patients. Frank V., a composer who suffered brain damage from the rupture of an aneurysm of the anterior communicating artery.”

The book is Musicophilia by Oliver Sacks.

In it, Dr Sacks writes about many strange and fascinating musical and mental topics. Absolute pitch is one, another is synaesthesia: a mingling of the senses in which musical intervals may have taste, or words and letters have colour. Sacks (a practising neurologist, famous as the author of The Man Who Mistook His Wife for a Hat) describes a host of neurological conditions varying from the commonplace (the annoyingly catchy tune which won’t go away) to the extraordinary: people whose uncontrollable musical hallucinations extend to full symphonies; a man with extremely severe and utterly crippling amnesia (of the sort portrayed in the film Memento) who can nevertheless conduct a choir and sight-read music perfectly; a man with a lifelong uninterest in music, who develops an all-consuming passion for composing after being struck by lightning.

Perhaps the most remarkable chapter is that about Williams Syndrome: a rare genetic condition, resulting in a brain 20% smaller than average, and an IQ typically below 60 (comparable to that of a Down’s syndrome sufferer). People with this condition are usually unable to manage simple single-digit arithmetic. But along with these weaknesses come surprising strengths: they are often communicatively gifted, with extensive vocabularies. Very often they are singularly drawn to music. An example is Gloria Lenhoff, a celebrated singer with Williams syndrome who can perform operatic arias in over 25 languages.

Musicophilia doesn’t offer easy answers to the central questions of music and the mind. Music does seem to be hardwired into our brains at a deep level: musical ability can survive remarkably intact, even in brains ravaged by severe Alzheimer’s. Also suggestive is that each component of music (tempo, pitch, melody, harmony, timbre, rhythm) comes with its own form of amusia, where someone is unable to comprehend (for example) rhythm, but their understanding of melody and harmony is almost unimpaired. Similarly, the link between musical intelligence (the ability to understand music analytically) and its emotional impact is very weak: there are people with excellent ears, but whom music leaves cold; vice versa we all know people who can’t hold a single note, but who adore it.

One message to take away from this book, if you thought that “music therapy” was some sort of pseudo-medical hippy claptrap, is that you are profoundly wrong. It works: for example many Tourette’s sufferers find that drum-circles are a powerful way to overcome their symptoms. But beyond that, often it is the only thing which works: music can provide the sole way to communicate with otherwise unreachable minds.