1
CHAPTER ONE
CAN WE LEARN TO THINK BETTER?
We can all think. But can we learn to think more effectively? The West’s largest industry, it is called ‘Education’, is largely based on the proposition that we can. In the modern world individuals spend a third of their lives ungainfully employed, absorbing subjects as abstruse as French Literature, Pure Mathematics, Philosophy, Media Studies, Psychology, Anglo-Saxon and Astrophysics. What are they hoping to gain? Surely not direct professional training. A deep learning of say Shakespeare’s sonnets, or stellar structure, will not enable a student to pay back her loan, let alone provide for the rest of her life.
And yet. It is well documented that a British student, for example, can look forward to a lifetime’s earnings greater by well over half a million US dollars than his or her contemporaries with equivalent educational attainments who elect not to go to university. There is a profound mystery here. It amounts to this: every time I give a fifty-minute lecture on theoretical astrophysics, each student in the audience can expect, on average, to increase his or her lifetime’s earnings by one thousand dollars. After thirty years as a university professor I still find this an astonishing, and ultimately mystifying thought.
Neither penniless students, nor impoverished parents, nor even parsimonious governments appear to doubt the dramatic benefits of a so called ‘Higher Education’. And yet no one, least of all the university dons themselves , can offer a coherent account of where in its essence that benefit lies. It cannot lie in the subject matter they teach – which varies enormously from department to department. Nor can it lie in the teaching method, which is utterly idiosyncratic as between one teacher and the next. Indeed most university dons are untrained in teaching techniques – and are proud to remain so.
When asked what precisely they are up to so effectively in their lecture halls and studies most professors will bluster about “teaching my students to think……” or “improving their analytical abilities…..” or “demonstrating the virtues of intellectual rigour…….” or………….. In other words they don’t know – and nor do I. In so far as I have been able to come up with an explanation which covers the undoubtedly successful but extremely varied efforts of my colleagues it would be “We try to teach students how to make better judgments on the basis of imperfect data”.
Yes I agree it is too vague to be useful and too tenuous to deserve either criticism or support. And when aired in the Senior Common Room it attracts as much attention, and of the same kind as a cough or a fart.
Yet something very interesting must be going in the educational process which transcends both the subject matter, and the individuals who profess it. I am going to assume, though I cannot by any means prove it, that part of that something is “learning to think more clearly, and hence to make better judgments in general”. If we are prepared to admit so much, then a tantalising prospect opens up. It may be possible to learn how to think more effectively simply by thinking about thinking without necessarily having to go through five years of English Literature or Theoretical Physics – or whatever.
What I aim to do here is to explain how my own particular colleagues, that is to say my fellow scientists, appear to think. I do so hesitantly because, as you will see, scientists have tended to disagree about the matter rather violently amongst themselves, though a consensus may be congealing at last. I do not suggest that scientists have a unique claim to thinking more clearly than others. What we do have, and it is crucial, is unquestionable scientific progress. As a result we scientists are all eventually discovered in our mistakes. And if we don’t own up to them ourselves our colleagues and rivals will be only too delighted to point them out in public. Anyway a new telescope or a better biochemical technique can turn yesterday’s brilliant theory into tomorrow’s wastepaper. In science, as in no other subject, there is no place for bad thinking to hide – or usually not for long. Scientific history illustrates every folly in thinking one can imagine; fallacious logic, selective choice of evidence, idolatry, arrogance, ignorance, prejudice, fashion, cowardice, lack of imagination, dishonesty – both outright or morally implicit, laziness, gullibility, stupidity, snobbery – even racism. Scientists have been and remain guilty of them all. But sooner or later they have been, or will be, discovered in their folly. History, literary criticism, philosophy, economics, politics, even large parts of medicine and psychology, cannot be said to progress in the same plodding way as science. Opinions, schools and fashions may therefore flourish for as long as scholars are attached to them whereas in science the progressive accumulation of evidence can make a fool out of the very best or most distinguished of us – as we shall see. In our awareness of past fallibility, and in anticipation of future humiliation, we scientists have learned some hard lessons about good and bad thinking , and it is those lessons I will try to distil here.
You might object that scientific thinking is different; that learning about it will not improve the everyday variety. On this point readers must shortly judge for themselves, but I myself have yet to see any such difference in kind. Scientists may think more intensely than the average, and may be more self conscious about the way they do so, but they have mortal brains like the rest of us. Einstein said: “Science is no more than a refinement of everyday thinking”.
It hardly needs to be said that science is a wildly successful activity. Max Perutz, who disentangled the structure of blood haemoglobin put it thus: “………….”. You can measure that success on two levels: on the practical level of wars won, diseases vanquished, machines invented and so on. But I prefer to measure its impact on the philosophical level. Where science has penetrated it has largely displaced the old superstitions; first witchcraft, then fundamentalist religion, now even astrology. Knowledge and rational explanation have pushed fear of the unknown, fear of the evil eye or of the sudden plague, fears which haunted all of our ancestors, to the very periphery of modern vision. I believe it is for this gift of ease, for this liberation from fear that we have to thank science the most. Where science has so far largely failed, as for instance in finding a cure for many cancers, or in understanding violent climate change, or in predicting earthquakes, or identifying the cures and causes of psychiatric depression, then the fear, the haunting and the necromancy remain.
This is not an account of Science itself, but of ‘The Scientific Approach’, of which science is the product. Here we try to identify the thinking ‘processes’ of science, rather than its very many and very different applications and outcomes. What mental and cultural processes, if any, do naturalists studying gorillas in the cloud forest share with astronomers observing galaxies through a telescope? If we can identify their common thinking process, and share it among ourselves, we may, like Prometheus, have stolen a second but more potent fire from the Gods.
To illustrate what one means by ‘The Scientific Approach’ let us begin by looking to see how it has worked to fateful effect in a context quite outside the normal field of scientific enquiry – in total war.
Both the World Wars turned on their respective battles of the Atlantic, the battles which above all others would decide the outcome. As Churchill said in his history of the Second World War: “……………………”. In both wars the British blockaded Germany on the surface of the Atlantic while the Germans attacked the Allied supply lines using unrestricted submarine warfare which led to the sinking, each month, of hundreds of vessels and millions of tons of shipping. In both wars the loser faced gradual starvation and certain defeat.
The key to victory over the U-boat turned out to be the convoy system – herding the cargo vessels together in huge formations, and shepherding them “across the pond” with armed escort vessels. The advantages of such a convoy system are by no means obvious. Tragically the British Admiralty failed to see them until it was almost too late in the First World War (1917), the US Navy in the Second. Herding cargo vessels together was after all offering a whole fleet of largely defenceless ships – necessarily moving at the speed of the slowest, to the marauding wolf-packs. And no seaman who had survived such a convoy attack and watched torpedoed ships and their crews going down all around him in blazing oil, was likely to think of a convoy as the safer alternative. Only dispassionate scientific analysis was able to overcome such natural fear. The fates of ships travelling both in and out of convoys could be compared. The mathematical chances of a submarine or wolf-pack first finding a convoy, then penetrating its escort cordon and sinking so many ships, could also be estimated. Convoys were the way to win, and did win, despite the instincts of the experienced sea-dogs involved. In Nature birds flock and fish shoal for the very same reason. The lucky eagle who does find the flock can only eat one of its members at a time.
The Second Battle of the Atlantic revolved around code-breaking. The Germans broke the British Convoy Code, enabling them to station their wolf-packs in wait. Then the British broke into the U-boat code to find, to their horror, the secret of the previous wolf-pack success. Convoys were then slipped past the waiting submarines by last minute re-routing. The Americans broke the Nippon naval code, and so sank the Japanese carrier fleet at Midway. The British broke into Germany’s highest level cipher used by Hitler to command his armies on the Eastern Front. From this source they learned precise plans for a mighty armoured assault by the German panzer armies at Kursk in 1943. Forewarned, the Russians built a giant tank-trap fifty kilometres across into which the German Army charged towards slaughter and eventual defeat.
As it is often portrayed the code-breakers war was a personal tournament between individual minds, with hero’s such as Alan Turing. The true story is at once more interesting and less heroic.
Imagine that you are an allied scientist charged with breaking into the notorious Enigma machine widely used by the Nazis. Studying the specimen before you, smuggled out by the Poles, you realise that its combination of rotors and plugboard connections can be set in no less than ******************* different ways, and is changed every day. This number, which is about one with sixteen noughts behind it, is so large that we will name it Godzilla.
At first sight the situation looks hopeless. To break even a simple message you would have to try out Godzilla different combinations before hitting upon the right one. Even an army of code-breakers (100,000 say) taking no more than 100 seconds each to try out one particular combination would need a million years to complete the task. This is why the Germans felt so secure. Despite the damning evidence that all his milch-cows (supply submarines) were vanishing at sea, Admiral Doenitz the U-boat supremo, reassured by the size of Godzilla, persisted with the use of Enigma in the Atlantic. Thank God.
Faced with Enigma the scientific mind, possibly Turing’s in this instance (though I have no evidence) would have asked the question: “If I could guess the precise German wording of a section of a coded message, how long would that section have to be to provide me with all the information I need to work backwards and infer all the rotor and plugboard settings within the machine for this day?”
Consider a 3-letter word. Since there are 26 letters in the alphabet there are 26*26*26=17,576 possible 3-letter words you could compose. By the same token there are 26*26*26*………..(twelve times) different 12-letter stretches of text one could devise. Twenty-six to the power of 12 is a very large number – let’s call it ‘Alfred’. Turing would then have argued as follows: “If Alfred is greater than Godzilla, which it is, and if I can guess some 12-lettered stretch of a Nazi cipher correctly, I will have, at least in principle, more than enough information to work backwards and infer all the settings of the Enigma machine which enciphered it. And once I have the settings for one machine for today I will have most of the settings for all the other machines on the network today”.
This feasibility conclusion was the truly vital breakthrough because guessing sections of messages, or ‘cribs’ as they were called, wasn’t too difficult if you could trace wireless messages back to their source using radio directional finding. For instance identical weather forecasts were broadcast by the German meteorological bureau in both high and low-level codes every day. Snap! Break one code and in principle you’ve broken the lot. The challenge for the British code-breakers was to devise a system of sufficient speed to work back from a crib to the Enigma setting of the day in order to make use of any deciphered information before it was out of date. Enter Tommy Flowers the Post Office engineer from Dollis Hill who built ‘Colossus’ the first ever electronic computer.
The same scientific approach has been used to enquire into the causes of world wars and may have prevented the third, and possible Armageddon. After the First and Frightful World War with its unprecedented millions of casualties Lewis Fry Richardson a Quaker meteorologist, was among those mystified historians who looked into the causes of an apparently senseless conflagration which to many seemed like a motiveless accident. Around 1910 the Germans and their allies on the one side, the British and theirs on the other, embarked on an arms-race. Virtually all the nations and foundries of Europe were stampeded into an ever accelerating charge for martial supremacy. The battleships and cannon pouring out of the factories on one side only redoubled the efforts of their rivals to compete. Richardson wrote down two simple equations, one for each side in the race, embodying the likely responses of either to the arms building efforts of the other. He then solved the coupled equations and discovered a fateful result. Provided that each side could ramp down or demobilise their forces faster than they could build them up, then the arms race might remain stable – if the underlying will for the peace was there. But if the adversaries could mobilise faster than they could disarm then the arms race must spiral out of control: even two sides committed at heart to peace would find themselves sucked helplessly into war. And according to Richardson that is what most likely happened in 1914.
Fortunately by 1960 the top people on both sides of a different and far more dangerous arms race understood what Richardson, using a scientific approach, had been trying to say. The installation of a ‘hot-line’ between Washington and Moscow was designed to tip the balance in Richardson’s equations away from inevitable war.
None of the above three insights into war required a genius to make it. At the same time all of them were very from obvious because they evaded most of the sharpest minds of their day. Applied to the right questions, systematic quantitative thinking of a kind which scientists have learned to use as a matter of course, and which we propose to investigate here, was in each case the vital step.
The world wars are thankfully over but of course, as we always shall, today we face fateful challenges of other kinds: global warming, AIDS, GM foods, overpopulation, traffic congestion, pollution, under-taxation, and so on. These however are public challenges about which we as individuals can do very little. We worry, that is to say we have to think about, issues far closer to home, issues such as: ‘What will I do if I lose my job?’, ‘Our house is far too small, but can we afford a bigger one?’, ‘How can I stop my boss bullying me?’, ‘Should we move elsewhere where the prospects look better?’, ‘How much should we save for our retirement?’, ‘What degree course should I enter for?’, - and so on. They all require the clearest thinking we are capable of, and they all involve making judgments when only some of all the information we would like to have is available. You don’t know how your boss will react if you threaten to take her to court. You cannot be certain what your mortgage repayments will be in ten years time. But you still have to make the call. In other words you will be making decisions based on incomplete data. We humans are pretty good at that because our ancestors who weren’t left very few genetic successors behind.
Solving puzzles appears to be a basic human instinct. I remember walking along a crowded beach in Crete and noticing that almost all the adults who weren’t in the water were doing crosswords, or deep in puzzle books, or reading who-dunnits, or playing cards or board games. They had come all this way South to relax in the sun, but were instead puzzling, or in other words thinking. So thinking about thinking, which we propose to do in this book, and especially thinking about situations where all the facts are not in, may be an enjoyable, as well as a productive way to spend some time.