Ockham’s Razor, ABC Radio National

Robyn Williams: If you’re a regular reader of New Scientist magazine, the chances are you’ll have seen Len Fisher’s friendly face staring from an ad about travel in Europe. It’s a scientific tour, led by Len, and they set out this week.

So it’s a good time to hear from the man himself. Len once worked for CSIRO but now lives in Bristol, in England. His book, mentioned here before, is How to Dunk a Doughnut – the science of everyday life. But this time, he’s keen to talk about our patron, William himself. Len.

Len Fisher: Scientists tend to disparage philosophers. Having a foot in the first camp and a toe in the second, I try not to take sides, but there’s no doubt that there is one philosophical principle that all scientists accept. It is the principle of Ockham’s Razor, which says that, all other things being equal, one should give preference to explanations that require the fewest number of assumptions. It sounds almost self-evident, but I argue that scientists have sometimes got it badly wrong, to the detriment of themselves and their science.

The principle is attributed to William of Ockham, a 12th century Franciscan friar who took his name from the village in Surrey where he was born. The village of Ockham still exists. It is near Junction 10 of the M25 motorway, and William’s picture takes pride of place in the recently installed stained glass window in the village church. This is ironic in a way, because some philosophers have argued from his principle that the God in whom he professed a belief is Himself an unnecessary assumption and should be discarded.

The way that William put his principle was that ‘plurality should not be posited without necessity’. He used this argument to great effect in his frequent theological disputes with the Pope, although he was not its inventor – that honour goes to Aristotle, who lived more than a millennium earlier. It was William of Ockham’s writings, though, that popularized the principle among philosophers.

The use of the principle by scientists gained a huge boost in the mid-19th century, when the Irish mathematician William Hamilton promoted it using a metaphor invented by the French philosopher Etienne de Condillac a hundred years earlier. Condillac had suggested that Ockham’s principle could be used as a razor to cut away unnecessary assumptions and reveal the simplest explanation. The metaphor of ‘Ockham’s Razor’ was a powerful one; so powerful in fact, that some scientists have grasped it with too much avidity. I have no argument with those who use it as a guide to the discovery of simple models, since such models are the most susceptible to rigorous testing against reality. My problem is with those who have used Ockham’s Razor to cut their own throats, by assuming that it is not only a helpful first step, but actually means that simpler explanations are somehow more likely to be true than more complex ones.

I wish that they were right. It would make married life much simpler, for a start, since marital disagreements would be resolved in favour of the husband, whose point of view is invariably more simplistic than that of his more realistic wife. Unfortunately, the equating of simplicity with truth doesn’t often work in real life. It doesn’t often work in science, either.

Take the case of the double-helical structure of DNA, discovered by Jim Watson and Francis Crick in the early 1950s. Watson says in his book The Double Helix that the path to the discovery was characterised by the belief that ‘the truth, once found, would be simple as well as pretty’. The structure that he and Crick came up with was indeed very pretty, and was based on a very simple picture of the way that the parts of the molecule fitted together in space.

There is no doubting the importance of this discovery. According to Watson and Crick’s boss at the time, Sir Lawrence Bragg, it ’caused an explosion in biochemistry which has transformed the science.’ Subsequent events have done nothing to diminish its importance. The biologist Steve Jones has said that Darwin may have knocked man off his pinnacle, but DNA grinds his face into the biological mud. It provides the hopes and fears involved in cloning, and has achieved the ultimate accolade of being the basis of a series of Hollywood movies. Its structure shows us that men and chimpanzees share 99% of their genes, and that men are more closely related to bananas than two apparently indistinguishable bacteria may be related to each other. It has also provided ammunition for those who believe that simplicity equates with truth.

Watson writes that, when he and Crick were lunching together in a Cambridge pub after they had made their discovery, they were ecstatically ‘telling each other that a structure this pretty just had to exist.’ I wonder whether Aristotle and his contemporaries had a similar discussion over a goblet of wine two-and-a-half-thousand years ago, after Aristotle had come up with the insidiously persuasive and simple idea that objects only move if they are pushed or pulled, and that when they move they tend to return to their ‘natural’ places of residence? Or whether the Greek astronomer Heraclides knocked back a few ouzos with his mates while revelling in his insight that all planets must follow circular orbits around the Sun, since circles are a ‘perfect’ shape, and all things in the Heavens must be perfect?

Both Heraclides and Aristotle were wrong, of course, but the appeal of their simple pictures was so strong that these were held as unquestionable truths for nearly 2,000 years, until Galileo came along and demolished both ideas by appealing to actual observations, losing his university job and nearly losing his life in the process.

The problem with using Ockham’s Razor to equate beauty and simplicity with truth is that beauty and simplicity may appeal to the human mind, but there is no guarantee that Nature will be in a mood to comply. When Jim Watson was searching for an idea as to the way that two DNA chains might associate to form a double helix, he first came up with a picture that was even simpler than the one which eventually worked. Each chain is lined with chemical structures called bases, labelled by scientists as A, G, T and C. Watson was struck by the idea that the As on one chain might link preferentially with the As on the other chain, and Ts with Ts and so on. The idea was so simple, and had such strong implications for biological reproduction, that he felt that it must be true, and he writes in The Double Helix that ‘Only for brief moments did the fear shoot through me that an idea this good could be wrong.’ He was so convinced, in fact, that he mentioned his new idea in a letter to the American geneticist Max Delbruck. The letter was still on its way to America when he found that his brilliant idea could not possibly be right, simple though it was. Luckily for him, he discovered the correct model before the letter had reached America – that the As on one chain only form links with Ts on the other chain, and Cs with Gs. Otherwise, as he himself admits, he would have been in the dreadful position of having to admit that he had written of an idea which was only 12 hours old and lived for only 24 hours before it was dead. Watson himself seems not to have noticed the irony of claiming the final model as a success for equating simplicity with truth, without noticing that the failure of his earlier model led to quite the opposite conclusion.

That’s not to say that Ockham’s Razor doesn’t provide a useful starting point, nor to deny that it occasionally takes us straight to the heart of a problem. One famous example is the prediction of the existence of the positron by the mathematical physicist Paul Dirac, whose picture I pass every time I traverse the hallway to my office in the Physics Department at Bristol University. The picture is there because Dirac originally trained in engineering at Bristol, but he earned his Nobel Prize later when he found that his quantum mechanical equation describing the properties of the electron had two solutions. The solutions were so elegant, so simple and so symmetrical that Dirac was convinced that both must correspond to something real, with one corresponding to the negatively charged electron and the other corresponding to a then-unknown positively charged equivalent of the electron which we now know as the positron.

Dirac’s prediction has been hailed as a dramatic success for the use of Ockham’s Razor as a predictor of truth, but for every dramatic success there have been a thousand unmentioned failures, and a belief in Ockham’s Razor as a guaranteed guide to truth has led scientists down many a blind alley. One of my favourite examples concerns the nature of heat. Up until the middle of the 19th century, scientists believed that heat was a real fluid that flowed from hotter to colder places. This simple picture fitted with the known properties of heat, including the fact that cold bodies expand as they warm up, because they had to make space for the incoming fluid, which was called ‘caloric’. The argument for the existence of ‘caloric’ was so persuasive that the French scientist Lavoisier listed it as an element when he published the very first table of the elements. Even when it was shown that heat and physical work could be freely converted from one to the other, and that both were forms of a mysterious entity called ‘energy’ that later came to encompass light, radio waves, X-rays and so on, many people refused to accept the change. ‘Why’, they argued, ‘should we believe in such a complex explanation when a relatively simple one is available?’

My own answer to this frequently asked question is that we should be on the lookout for complex explanations because Nature herself is complex. Simple explanations may appeal to our relatively simple minds, but only as a guide towards truth, not as a picture of the truth itself.

Sometimes, too, the guide points us in the wrong direction as it did with the astronomers who followed on from Heraclides and his idea that planets must follow circular orbits. The Alexandrian astronomer Ptolemy made accurate observations which showed that this could not possibly be the case, but rather than give up the circle idea he added circle upon circle in a series of ‘epicycles’ to describe the planetary motions by a series of massively complex calculations that only a parent could love, and which eventually collapsed under their own weight.

Modern astronomers are faced with a not unrelated problem in the case of stellar evolution. They describe this in terms of a ‘main sequence’ of events that stars go through between their birth and their death. This simple, elegant picture was considerably upset in 1953 by the discovery of ‘blue stragglers’ – stars that lie near the main sequence but which are bluer and brighter than the turn-off that is appropriate for their age. Their very existence disrupted the simple picture that astronomers had evolved with the help of Ockham’s Razor, to the extent that the astronomer Mario Livio has recently argued that these starts demonstrate the failure of Ockham’s Razor itself. Only complexity, he says, can explain them. Their existence cannot be accounted for on any one simple picture, but only if they are formed via many different but equally likely, pathways.

Even when Ockham’s Razor guides us to a usefully simple explanation, Nature is still there waiting to pull the rug out from under us and our pretensions at understanding how she works. The fate of the Watson-Crick model for DNA provides a classic example. The original simple picture devised by Watson and Crick provided a powerful guide to the behaviour of DNA, but the more closely that they and other scientists examined that behaviour, the more they discovered a mass of hidden complexities. Now, some fifty years on, we know that a huge variety of other molecules following complex chemical reactions, are required to control DNA stability and its replication pathways that initially seemed so simple. Much of the DNA that we possess, moreover, seems to perform no useful function at all. To quote Steve Jones once again, ‘No longer is DNA a simple set of instructions. Instead it is a desert of rigidity and waste, mitigated by decay.

The complexities of DNA, though like the complexities of planetary movement and stellar evolution, would never have been found if there had not been a simple model available to tests in the first place. This is where Ockham’s Razor exerts its power, by guiding us toward a base from which we can launch our investigations. Our explorations from that base frequently reveal complexities that can only be understood by using Ockham’s Razor to establish a new base. We must recognise, however, as many modern philosophers have done, that the bases are at least as likely to be built on sand as they are on rock. As the Nobel Prize winning chemist and part-time poet, Roald Hoffman has said, when speaking of the use of Ockham’s Razor in chemical discovery, ‘Ockham’s Razor is an instruction in an operating manual, not a world view.’ It is a sentiment of which I am sure that William of Ockham would have been the first to approve.

Robyn Williams: Doubtless. Len Fisher, once of CSIRO, now in Bristol.

Thanks are due to Robyn Williams and the ABC for permission to reproduce the full script of this talk.

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