elementary

Most people are probably aware that the ancient Greeks identified four ‘elements’—earth, fire, water and air—although these are not elements in the modern sense. The ancients will have been aware of the existence of gold, silver, iron, copper, tin and lead, but there is no evidence that they recognized them as fundamental. Of course, the Greek conception of elements is purely metaphysical, but it is preserved in English phrases such as ‘braving the elements’, which translates roughly as stepping outside in bad weather.

However, the Greeks had a problem. How many elements should there be? Plato had discovered that there are precisely five regular solids—tetrahedron, cube, octahedron, dodecahedron, icosahedron—and the prevailing wisdom was that by analogy, there must also be five elements. This is a false analogy, but it is the origin of the word quintessence (literally, ‘fifth essence’).

It is less well known that the ancient Chinese recognized a similar system of elements, one that is still in use today, especially in astrology and fung shui. They also identified five elements, although, unlike the Greeks, this was not by analogy with the five Platonic solids. The theoretical basis for Chinese astrology and fung shui is the lo shu square, two examples of which I present here:

The lo shu square is what Western mathematicians describe as a ‘magic square’, the fundamental property of which is that every row, column and diagonal adds up to the same total. This ‘magic square’ has other properties, the most obvious of which is that 5 must always go in the centre cell, and the four even numbers must occupy the four corners. In fact, once the starting condition has been defined, constructing a lo shu square becomes a forced process. And there are only two possible solutions, one of which is a mirror image of the other (see above).

The necessary presence of 5 in the centre cell seems to be why the Chinese decided that there must be five elements, each of which corresponds to one of the four corner cells or the central cell of the square.

So what did the Chinese decide were the five elements? Three—earth, fire and water—are the same as in the Greek classification, but the other two seem to me to be not even remotely elemental. Wood is a hybrid of earth and water, while metal is a hybrid of earth and fire. In this classification of elements, there is no way to explain the force exerted on the sails of a ship or a windmill, which is particularly mystifying given that the Chinese were the first to develop fore-and-aft sails, so they must have been aware of the force. Why did they fail to recognize air as a separate element?

Sound is another phenomenon that requires air for its explanation. It is a pressure wave that propagates through air, or another gaseous medium, and it is directional. It can also be transmitted through solids and liquids, but it does not exist in a vacuum. The earthquake-detection machine built by the Chinese more than 2,000 years ago could only have been designed by someone who understood that the shock waves from an earthquake are also directional, so why did they not make the connection? To be fair, there is no evidence that the ancient Greeks understood sound either, but at least they did have the means to explain it. Nothing in Chinese cosmology explains sound.

And there is another way to look at the Greek interpretation. You could argue that earth, water and air correspond to the three phases of matter: solid, liquid, gas. And there is a fourth phase! Plasma. The temperature at the heart of the Sun is so high that atoms no longer exist. Plasma is simply a fizzing soup of protons, electrons and other subatomic particles. That sounds like fire to me. And one hell of an insight for more than 2,000 years ago.

Meanwhile, perceiving some kind of esoteric magic in a lo shu square seems to me to be like believing in the healing power of crystals, the shapes of which are also the result of a forced process, one that depends solely on the relative size of their constituent atoms.

photographic abstraction #26

Although I keep thinking that I won’t find enough suitable images to continue my series of abstract photographs, I’m still coming up with new ideas and new motifs. Of course, a lot of the images I produce—and reject—are too amorphous to allow me to suggest a meaning through a title, although I think that you will find the present collection both varied and interesting.

What is going on in the first picture? To me, it is a perfect illustration of chaos.

chaos theory

I believe that most people are familiar with Descartes’ famous dictum, cogito ergo sum (‘I think therefore I am’)—indeed, I’ve had it quoted at me on several occasions by someone trying to make a philosophical point, invariably without their realizing that this statement assumes that ‘mind’ and ‘body’ are somehow separate, which is probably an error. The most cogent rebuttal of Cartesian dualism was made by British philosopher Gilbert Ryle, who called it ‘the ghost in the machine’:

ghost in the machine

You don’t need me to point out that the next image isn’t hair, but it is something that’s been brushed. I can’t remember what though.

hair today, gone tomorrow

The impact was on the left, but the target was in the middle. In other words, the attacker missed:

missed

The title I’ve given to the next image refers to the term’s cartographic usage rather than to remission of pain:

relief

It isn’t often that an image is so striking that I simply have to get off my bike and take a photograph, but this is what happened with my final image, which I’ve named after one of the few musical acts of the twenty-first century that I consider worth listening to.

white stripes

recent posts in this series
Photographic Abstraction #21
Photographic Abstraction #22
Photographic Abstraction #23
Photographic Abstraction #24
Photographic Abstraction #25

bittersweet

There may not be a consensus as to how many categories of taste a human being can differentiate—I understand that a new category was defined by scientists recently—but everyone will know what I’m talking about when I mention bitter, sweet and sour. Or will they? A surprising number of people appear to believe that sweet and sour are opposites. That one will cancel the effects of the other. Such people are clearly unaware that the Chinese demonstrated, centuries ago, that sweet and sour can coexist in the same dish, although you won’t know what I’m talking about if your only experience of gu lo yuk (sweet and sour pork) has been in the UK.

The real opposite to sweet is bitter, not only in taste but also in language—one is more often associated with positive outcomes, while the other has only negative connotations. We talk of the sweet spot on a tennis racquet or cricket bat, the spot that provides the maximum impact for the minimum of effort, but we fight to the bitter end—endings are never sweet. The ingestion of something sweet is most likely to elicit a smile, while the reaction to ingesting a bitter compound will probably be an involuntary grimace.

But are these natural reactions, or are they the result of acculturation? The notion that sweet is good and bitter is bad goes back at least as far as the Old Testament, as the following quotations demonstrate:

Pleasant words are as an honeycomb, sweet to the soul, and health to the bones.

Proverbs 16:24 (Authorized Version)

The full soul loatheth an honeycomb, but to the hungry soul every bitter thing is sweet.

Proverbs 27:7 (Authorized Version)

Ironically, it is bitter compounds that are more likely to be beneficial to the human body, even though when we talk about a setback being a bitter pill to swallow, we are making a negative comment. In fact, the idea that medicine is intrinsically bitter is now so ingrained in popular culture that Mary Poppins could sing about a spoonful of sugar helping the medicine to go down, and Max, aide de camp to the chief blue meanie in the movie Yellow Submarine, could say this to his boss:

Here Your Blueness, have some nasty medicine!

And His Blueness giggled as he slurped it down (blue meanies were contrarians who hated everything that humans found pleasurable, including music).

Yet two of the world’s most popular beverages, coffee and beer, are intrinsically bitter, and the key ingredient in tonic water is quinine, another bitter compound. On the other hand, it is now widely recognized that the consumption of large amounts of sucrose is injurious to health, with serious illnesses such as diabetes a likely result.

I see the bitter/sweet dichotomy as a kind of morality tale in which sweet is the easy option and bitter the hard road, after which ‘but few enquire’:

Don’t you see yon narrow, narrow road,
So thick beset with thorns and briars?
That is the road to righteousness,
Though after it but few enquire.

Don’t you see yon broad, broad road,
That lies across the lily leaven?
That is the road to wickedness,
Though some call it the road to heaven.

Thomas the Rhymer, traditional English folk song.

And what about the well-known oxymoron ‘bittersweet’, which is to my mind essentially meaningless? I suspect that people who use this word are reflecting some level of personal disappointment: they expected a positive outcome to a situation, but it turned out not to be as positive as they had hoped, or expected.

hubris

Hubris is an ancient Greek word that deserves a more frequent airing. It refers to an overblown (and usually misplaced) self-confidence, but in its original meaning those who were guilty of hubris had usually infringed some taboo or other, and they would be punished by the gods for their presumption. Prometheus, who stole fire from the gods, is a typical example.

I’ve just come across some old exam papers from my time at Manchester University, and I was instantly reminded of the most gratifying example of hubris and its consequences in my personal experience. My main subject was geology, but at the beginning of my second year, I was faced with a decision. Which subsidiary subject should I choose to take? All the usual options were on the list—chemistry, physics, botany, zoology, metallurgy—but at the bottom of the page I spotted something unexpected. I could choose to attend a course in logic.

It turned out to be a lot harder than I had anticipated, but this wasn’t due to any intrinsic difficulty. Most of the others in the class were first-year students of mathematics, and much of the course focused on propositional calculus, which is logic reduced to a form of algebra.

You can imagine what happened. The lecturer started by introducing three axioms, from which everything else could be deduced. And the mathematicians in the front row of the lecture theatre were telling him what the next line should be before I’d finished writing down the previous statement. I resented this at the time, because I was writing down stuff that I simply didn’t understand, and I struggled. Fortunately, it did make sense when I was able to read the material at my own pace, and the payback would come in a three-hour examination at the end of the course.

I couldn’t suppress a little chuckle when I picked up the exam paper, which carried the following instructions:

Answer at least ONE question from each section [there were three sections] and ONE other question. At least TWO starred questions should be attempted by mathematicians.

The unstarred questions were easy then, although they make no sense to me now, almost half a century later. Here is an example:

 13. Explain the meaning of the constant terms occurring in Aristotle’s syllogistic.

And here is a question on the same subject for the mathematicians:

*14. Lukasiewicz has suggested the following axioms for Aristotle’s syllogistic:

   ΠaAaa
   ΠaIaa
   ΠaΠbΠcCKAbcAabAac
   ΠaΠbΠcCKAbcIbaIac

   ‘A’ and ‘I’ being primitive terms. Show that the axioms are independent of each other.

The second question seemed difficult then, but it would be impossible for me to answer now. And it is possible that the mathematicians at whom the question was aimed in the first place would have found it easy then. Still, I think that I was entitled to a little schadenfreude. It’s what should happen to people who are too cocky.

the philosophy department

When I started working as a freelance editor for Longman and Routledge in the early 1990s, I put my name down to edit science books. This made sense, given that I have a science degree and a good understanding of science in general. However, I also put my name forward to edit philosophy titles, which made a lot less sense, my only previous encounter with the subject being a one-year course in formal logic that I attended as an undergraduate. My only ‘qualification’ for the role was that I was interested in the subject.

Some of the books I edited turned out to be very rewarding, while others were absolute horror stories. In the first category, I include Epistemology: A Contemporary Introduction to the Theory of Knowledge by Robert Audi, which I edited in 1998 and which I found to be the most intellectually challenging book I ever worked on, mainly because it discusses, from first principles, how we know what we think we know, what justifies us in believing what we believe, and what standards of evidence we should use to reach our conclusions. It was admirably well written, but you can’t edit something that you don’t understand, if you can’t follow the argument, so I had to be careful to ensure that any changes I made did not affect the intended meaning.

I wasn’t aware of it at the time, but Professor Audi had apparently had a bad experience with the editing of his previous book and had asked to see the edited typescript before it went for typesetting. I must have understood the book, because the author asked for my name to be added to the acknowledgements at the front of the book.

Another book that I found interesting was Rules, Magic, and Instrumental Reason by Israeli philosopher Berel Dov Lerner. The passage that has stuck in my memory from this book describes how we use rules that govern common activities such as hammering a nail into a piece of wood, even though those rules are not formally codified. I recall this passage because I spotted that the rules that the author had proposed for hammering a nail wouldn’t work. Not only did Professor Lerner ask for my name to be added to the acknowledgements, he also wanted it noted that I’d ‘saved him from his own stupidity’ by spotting his mistake.

And now for something completely dreadful. The worst book I ever edited was entitled From Hegel to Derrida and was what is known in the trade as a contributed volume. This means that each chapter is by a different author, with an ‘editor’ whose name will appear on the cover of the book and to whom any queries need to be addressed. And I had a lot of queries. Example: why is the title of this chapter enclosed in parentheses? Answer: I’m not sure I understand the parentheses around the title either. But then this guy is known for strange titles. I’d hate to disappoint his fans….

Some of the writing was appalling, especially in the chapter by Jean-Luc Nancy (“I really went cross-eyed with this essay”—the editor). When editing, I had a general rule that if I needed to read a sentence more than once in order to apprehend its meaning, then that sentence should be rewritten. Imagine my horror upon encountering a sentence that ran to fourteen typewritten lines and included eight dashes and three lengthy strings of text within parentheses. I wish I’d kept a copy as an example of how not to write English.

The editor concluded his reply to my queries with the following paragraph:

Thanks for all the work you’ve done on this. I’m sure it was not pleasant. I can imagine that, to a sensibly minded speaker of English, this book would be like trying to copyedit Finnegan’s Wake. Just how do you tell when it’s wrong? As my wife says—why can’t they just write English? Ah! But then we wouldn’t impress each other.

I still have the fax, which I’ve quoted verbatim.

breaking the law

You don’t know what it’s like, you don’t have a clue
If you did you’d find yourself doing the same thing too.
Breaking the law, breaking the law….

Judas Priest, Breaking the Law.

Most, if not all, of the world’s many jurisdictions have laws that impose severe legal sanctions on those of its citizens who commit murder, perpetrate violence or indulge in theft (which includes, but is not limited to, armed robbery, burglary, street mugging, fraud and embezzlement), although whether in these countries the relevant laws apply to everyone is a crucial point in determining the attitudes of ordinary citizens to such laws, and nobody should be in any doubt that such laws are necessary.

In the case of murder, it might seem that there is little room for ambivalence in popular attitudes, but in Decline of the English Murder, having defined the key characteristics of what would be the ‘ideal’ murder from the point of view of a typical reader of the News of the World, George Orwell concludes by writing

With this kind of background, a crime can have dramatic and even tragic qualities which make it memorable and excite pity for both victim and murderer. (italics added)

This quote should not be taken as an endorsement of murder; Orwell was merely pointing out that the domestic poisoning dramas of the late nineteenth and early twentieth centuries were motivated by strong emotions, and that being unmasked as a murderer was somehow less scandalous, less personally embarrassing, than being revealed as an adulterer. He contrasted this with the impersonal nature of many contemporary murders, a trend that has led, in the twenty-first century, to murders being committed for the most absurdly trivial of motives.

However, it is with popular attitudes to the various forms of theft that genuine ambivalence can be detected. At one extreme, the type of thief who preys on old ladies in their own homes is highly likely to face retribution in prison at the hands of other inmates, who themselves have been found guilty of what most law-abiding citizens would regard as serious crimes. In a recent trial in Scotland, the presiding judge actually referred approvingly to the likelihood that the defendant would experience such a fate when sentencing a man who had been found guilty of systematically robbing or defrauding elderly people, which may have been taking schadenfreude a little too far but is probably what most people would want to happen in such circumstances.

At the other extreme are confidence tricksters such as Victor Lustig, the man who ‘sold’ the Eiffel Tower, who are often admired for their daring, coupled with the feeling that the person being defrauded is often a victim of their own greed. It is clear that in these two extremes there is a moral dichotomy, in which the status of the victim rather than the nature of the crime determines the reaction; snatching an old lady’s handbag is seen, by most observers, as more reprehensible, morally, than defrauding an insurance company or robbing a bank.

In a recent survey by a major insurance firm in the UK, less than half of the 2,000 policy holders questioned said that they considered an exaggerated claim to be dishonest, even though such claims are typically for goods that had purportedly been stolen or damaged but that did not actually exist in the first place.

In fact, how one actually defines theft is problematic, and one is often compelled to fall back on legal definitions, which do little to clear up any moral ambiguities. On the bookshelves of my house in the UK, you will find two bookends. They are pieces of Honister slate, the same material that is used to make the thousand and one knick-knacks and ornaments that cram the many gift and souvenir shops in Keswick, a major tourist destination in the English Lake District. However, my bookends were not purchased in such an emporium; they were scavenged from the mine spoil heaps of the Honister Slate Company at the top of Honister Pass, which have long been an eyesore. Technically, this is theft, even though the rocks had been discarded. At the time of the ‘theft’, the mine itself had been closed for many years, but it has recently reopened as a ‘visitor attraction’, and there have been prosecutions of people who have removed material from these spoil heaps.

Another personal reason for equivocation came when I was working in the BBC Publications warehouse in Bermondsey, south London, in 1979. I was asked to clear out a large room full of what was regarded as out-of-date material. I could have completed the job in a day, but this would have gone against the working practices in the warehouse, so I took a week. This gave me the opportunity to see what I was being asked to throw out rather than simply discarding it unseen. It also meant that if anything was worth rescuing I could do so. In fact, very little was worth rescuing, but I did come across two cheaply printed books published in the 1930s for the benefit of BBC announcers and newsreaders. They were guides to the correct pronunciation of every place name in England, Scotland and Wales and are now also to be found on my bookshelves.

These two examples raise a difficult point: to what extent does the owner of an item retain any ownership rights over that item if they have discarded it? Such a scenario might even have occasioned Karl Marx’s famous dictum that ‘property is theft’. Sadly for budding Marxists, this is not the case: Marx reasoned that if theft implies depriving someone of an item, and ownership of that item means that a second party is thereby deprived of ownership, then the owner is a thief. Given that most of Marx’s theories are on a similar level of absurdity, it is difficult to understand how his ideas ever gained any credence in the first place. They are definitely of no help in the present discussion. However, in fairness to Marx, it is difficult to formulate a comprehensive definition of theft without a corresponding definition of property.

There is certainly a discrepancy between legal and moral definitions of theft, and there is probably a correlation between the size of that discrepancy and position on the social scale. A resident of a leafy suburb is likely to have a notion of theft that is very close to the legal definition, while most residents of inner city public housing estates are likely to be more ambivalent. This is my explanation for the widespread looting that took place in several English cities in August 2011, where hundreds of participants were stupid enough to think that they could get away with stealing items from ransacked shops, having grown up in subcultures where petty dishonesty is routine, where the phrase ‘fallen off the back of a lorry’ is a part of everyday life. Although they would have been well aware that what they were doing was proscribed by law, there would have been no moral restraint on their actions.

So far, I have been discussing laws that have a moral basis, but I was motivated to write this piece by an observation close to home. In order to reach my house from the nearest railway station, I need to catch a minibus. Although these vehicles carry far fewer passengers than Hong Kong’s railway system, they perform a vital function in linking small population centres to the public transport network.

Nowadays, most minibuses have seat belts, and a sign is prominently displayed inside the cabin in both English and Chinese. It exhorts passengers to fasten their seat belts and warns of the consequences of failing to do so:

Passengers who fail to comply are liable to a maximum fine of $5,000 [US$645; £388] and 3 months imprisonment.

You may choose to submit a fraudulent insurance claim, buy cigarettes on which you know excise duty has not been paid, cheat during a game of poker, or sell worthless pieces of paper on the grounds that they represent a sound investment, but this is a moral rather than a practical decision, even if the morality behind such a decision is questionable.

However, given that minibus drivers, as a group, are among the worst in Hong Kong—they routinely drive too close to the vehicle in front (I’ve seen one collision involving this practice), they change lanes without warning, and they even jump red lights—why anyone would ignore this notice is baffling, yet on most occasions I’m the only person in the minibus to avail myself of this obvious safety measure. And it isn’t because I don’t want to be sent to jail that I comply; it just seems like a sensible precaution, and why anyone would consciously risk imprisonment for such a trivial matter is beyond my comprehension.

I, robot

From the Arnold Schwarzenegger character in the Terminator series to Lieutenant-Commander Data in Star Trek: The Next Generation, from R2D2 and C3PO in the Star Wars series to Marvin the paranoid android in The Hitch-hikers Guide to the Galaxy, we have become accustomed to thinking of robots as machines with personalities. We take them for granted and rarely pause to ponder how difficult it might be to construct such a machine. If we did stop to think, we might begin to realize how perfectly suited for its purpose is the human brain.

In fact, the gap between imagination and reality is exceptionally wide. Although it would be a foolhardy prophet who predicted that this gap will never be closed, the human race is not on the threshold of replicating itself in machinery. To imagine otherwise is to underestimate the complexity of the mental processes that humans employ as a matter of routine. The truly awesome aspect of this complexity is not the intellectual output of a William Shakespeare, a Ludwig van Beethoven or an Albert Einstein but the routine calculations performed by the mind of a five-year-old child. They are no less marvellous because they happen below the horizon of consciousness.

Take vision. The cinematic convention for the view through a robot’s eyes is either that of a distorted fish-eye lens or the cross-hairs of a gunsight. We, as viewers, understand the convention because we have brains that have evolved in order to interpret what our eyes see, but such a view would be useless to a robot. The first requirement of any visual system is that it be able to determine where an object ends and the background begins. However, the world is not like a child’s colouring book, with comforting black lines to delineate the boundaries, and the light falling on a human retina does not produce a ready-made picture. It merely generates a series of electrical impulses, which to be of any use must then be interpreted by the brain.

The best analogy for what a robot would ‘see’ is a rectilinear grid of numbers in which each number represents the brightness of a small portion of the visual field, with larger values indicating brighter cells within the grid. We may reasonably expect the robotic brain to be able to interpret any significant difference in the values of adjacent cells as indicative of a boundary, but this is where the process of interpretation becomes vastly more complicated. A large number next to a small number could be the result of a light object against a dark background, a dark object against a light background, a dark and a light object touching each other, the edge of a shadow, two different shades of the same colour on the same surface, and many other combinations, all of which the human brain can distinguish so easily that we fail to appreciate how difficult an achievement this is.

And the difficulties are just beginning. Once the objects and background in the visual field have been delineated and distinguished, a robotic brain then needs to identify these objects, which means that it needs to identify fundamental properties such as colour and composition. At first glance, the problem appears to be a trivial one. Compare a lump of coal and a snowball, one black, the other white. If larger numbers represent brighter regions of the visual field, then large numbers must, intuitively, indicate the presence of a light material such as snow (and small numbers the presence of a dark material such as coal). Not always. More light bounces off a lump of coal outdoors than off a snowball in a typical indoor setting, because the brightness of a given object is merely a measure of the amount of light it reflects. Nevertheless, the human visual system can see a bright outdoor object as black and a dark indoor object as white. Unlike a robotic system, it is not easily fooled by trompe l’oeil confabulations, perceiving the world as it is rather than the world as it is represented on the surface of the retina.

The next problem is the estimation of depth and relative size. In the absence of clues, even the human system can fail here, unless there is a basis for comparison. A postage stamp in your hand and a building on the horizon that is the same shape will produce the same effect on the retina, and it is only by experience that we learn which is which. In my own experience, when working in the barren, featureless landscape of the Sahara Desert, I found it almost impossible to decide whether a distant object was a stick driven into the sand a quarter of a mile away or an oil rig ten miles away.

Finally, having solved the problems of shape, brightness, colour and size, our artificial vision module will also need to assign identifying tags (names) to the objects it detects and be aware of their purpose. This is difficult enough for simple geometric shapes and letters of the alphabet, but it is an almost intractable problem to construct any kind of artificial template for the recognition of human faces. Yet, unless a person has sustained damage to one or more parts of their brain that deal with vision, they will still be able to recognize people whom they haven’t seen for twenty years or more, despite the subtle changes that will have taken place in the intervening period. The template would also have to take into account what a face looks like under a huge range of different lighting conditions, a compensation that a human viewer performs effortlessly.

In other words, a seeing robot simply cannot be built with just the fish-eye viewfinder of movie convention, and it should not come as a surprise to learn that the human visual system is not built this way either. And there is one more factor to consider: an early evolutionary adaptation of our sensory input systems ensures that we pay attention only to signals that are changing. This adaptation is most obvious in relation to our senses of hearing and smell—how often have you totally forgotten an annoying racket emanating from a nearby construction site, or a nauseating smell that made you feel sick when you first encountered it—but even our vision shuts down if absolutely nothing is happening in the visual field, to give our video-processing circuitry a break. There is more to seeing than meets the eye.

Once we have mastered the problems associated with artificial vision, the next challenge is locomotion. The optimum engineering solution to the difficulties that arise in moving an object around is to set that object on wheels, especially if it is heavy. For this reason, it is tempting to think that a robot would be much better off with wheels than with legs, except that wheels are of limited use on rough or uneven terrain.

However, a mere two legs is not the intuitive choice. As one leg moves, the other has to maintain the body’s balance, which involves constant monitoring and feedback in order to make instant fine adjustments. All of this requires processing power. While four legs may be a better technical solution—creatures with four legs can move far more quickly, and far less effort is required to maintain balance—there is an unexpected advantage in bipedalism that offsets these assets.

The human hand, even more than the hand of other primates, is a machine exquisitely adapted to its purpose. And the evolution of that hand, over the last million years, has driven the evolution of the brain, to the extent that a significant amount of grey matter is now dedicated to the operation of the hand. While the human brain has not increased much in size during this period, there has been a considerable increase in the size of the cerebral cortex, especially the frontal lobes, which are associated with such so-called ‘executive functions’ as self-control, planning, reasoning and abstract thought. However, like every part of human behaviour that we take for granted, building a robot with these functions presents challenging engineering problems.

We often hear on the news about the latest in robotic hands, and what they are capable of doing, but if you think about the range of grips that the hand has available, you will quickly realize just how versatile is the human hand, and how much further researchers in the field have to go to design a robotic version of equivalent versatility. There is the grip between thumb, index finger and middle finger used to hold a pen, the grip between thumb and index finger for turning a key in a lock, the grip between two fingers to hold a cigarette or a spliff, the grip that employs all five fingertips to pick up a flat disc like a beermat, and the way we grip a glass of beer or a hammer.

In this last case, the grip is the same, but the amount of pressure applied by the fingers differs considerably, illustrating another characteristic of the human hand: the ability to vary the amount of pressure applied depending on the object to be picked up. And then there is the dazzling dexterity required to manipulate a pair of chopsticks effectively, a skill at which, incidentally, most Chinese demonstrate only moderate competence. The point to bear in mind here is not that the human hand is a masterpiece of engineering, which it is, but that achieving this level of dexterity requires a colossal amount of processing power.

Imagine that we have finally succeeded in designing suitable visual, locomotor and manipulation systems, but there is another problem lurking on the horizon. An intelligent system cannot treat every object that it encounters as a unique entity unlike anything else it has ever seen. It has to have some means of deciding whether a new object belongs in a previously seen category or whether it should be assigned to a new category, and in making that distinction it has to have some way of distinguishing between essential and incidental properties. At the risk of repetition, this is another skill that humans are good at, but designing a comparable artificial system is a massive engineering challenge.

One of the most interesting commentaries on robotics is Isaac Asimov’s novel I, Robot, in particular the book’s three laws of robotics:

• A robot may not injure a human being or, through inaction, allow a human being to come to harm.
• A robot must obey orders given it by human beings except where such orders conflict with the first law.
• A robot must protect its own existence as long as such protection does not conflict with the first or second law.

Asimov showed remarkable insight by including the third law, because self-preservation is not an automatic property of an intelligent system. However, with the first and second laws, the author fell into the trap of echoing the ancient fear, illustrated, inter alia, by the rampaging golem of Jewish legend, Faust’s bargain with the devil, the sorcerer’s apprentice, Frankenstein’s monster, and the computer in 2001: A Space Odyssey, that artificial intelligent systems would one day become so smart and so powerful that they would turn on their creators.

Unfortunately, Asimov was unable to step outside his own thought processes and recognize them as artifacts of his mind rather than universal and scientifically verifiable laws. The human capacity for evil is never far from our thoughts, and it is disarmingly simple to imagine evil to be an inescapable aspect of our existence, just as it is almost instinctive to think that a self-aware system must possess an ego, as envisaged by the title of the novel (and ego, or intention, is a necessary component of evil).

On the other hand, although machines built originally by humans are unlikely to turn on their creators, we have no way of knowing whether other civilizations on other planets have developed machines that are programmed to kill. Even now, it is possible that a civilization in a not too distant star system, having picked up I Love Lucy on its radio telescopes, many years after the original broadcasts, has dispatched a fleet of murderous robots, like the Cylons in Battlestar Galactica, to exterminate the perpetrators of this outrage.

explanations

Human beings have always looked for explanations, at least in recorded history. However, we can only speculate whether the earliest humans offered themselves any kind of explanation for a range of observable natural phenomena—a rainbow, thunder and lightning, rain and snow, floods, the wind, tides, day and night, the waxing and waning of the moon, seasons, earthquakes, volcanic eruptions—but by the time of the first city-states, explanations were being offered, and accepted.

Unfortunately, these early explanations always seemed to involve supernatural entities, who were invariably capricious and/or malevolent, to be propitiated by any means available, including the sacrifice of fellow humans. Over the next few millennia, this crude stereotype became more sophisticated in its explanations, and in the range of categories, physical and psychological, for which it offered these explanations. These, in their new and more refined state, became widely believed, even though their acceptance did not depend on an objective analysis of the evidence, because none was offered. None was required. Unquestioning belief in the efficacy of the explanations was the sole stipulation. Later commentators would call this phenomenon religion.

Meanwhile, fed up with the obvious lacunae in the above explanations, groups of humans decided that knowledge is the key to explanation, and the only sure road to knowledge is through the application of reason. The best-known proponent of this viewpoint is probably Aristotle, who believed, inter alia, that the Moon is a perfect translucent sphere, because any other explanation for what he saw in the night sky would violate the dictates of reason. It is interesting to speculate on his reaction, should there be some way to bring it to his attention, to Galileo’s perfect rebuttal of this ludicrous assertion: if the Moon had been a perfect sphere, then the amount of light reflected by the centre of the disc would have been much greater than that reflected around the edges. Of course, Galileo had the advantage of the knowledge, gained by using a telescope, that the surface of the Moon is not smooth; it is covered in mountains and craters. This affords an explanation for what is actually observed, because an irregular surface reflects light equally in all directions, hence there is no discernible difference in brightness between the centre and the periphery of the lunar disc. It is ironic that Aristotle’s approach to explanation came to be known as philosophy, given that the word derives from the Greek philosophia, ‘lover of wisdom’. ‘Lover of guesswork’ would be a more accurate description.

Although these two systems for explaining the world we live in should have been mutually incompatible, and priests and sages should have regarded each other with deep suspicion, by the late Middle Ages in Europe they had come together to formulate a definitive explanation of, well, everything. The sage claimed that the Sun revolves around the Earth on philosophical grounds, while the priest averred that any other explanation contradicted the authority of his book of legends and was therefore false. The ancient Greek conception of the wheel as the ideal of perfect motion became official Roman Catholic doctrine, and the Church found itself committed to the ‘wheel of the heavens’. It was as if Ptolemy’s system had been invented not by a Roman citizen living in Egypt and writing in Greek but by the Almighty himself.

By this time, however, a third method for seeking explanations for natural events had begun to challenge this uneasy alliance, a method based on observation and measurement. This was the start of science, which really did offer an explanation for everything. At least, that is what its practitioners claimed to be able to do.

In the vanguard of this challenge was a Polish priest, Nicolaus Copernicus, who published On the Revolutions of the Celestial Spheres in 1543. This book rejected the then current explanation of the movement of heavenly bodies, postulating that the Earth revolves around the Sun rather than vice versa. Nowadays, we are apt to think of ‘revolution’ as meaning some kind of radical and possibly violent change, but this is a secondary meaning that the word acquired as a direct result of the work of Copernicus.

However, the bigger revolution, in progress while the book was being researched and written, was someone else’s fault. Martin Luther had decided to muddy the religious argument by insisting that you didn’t need a priest to explain things; you could work it out for yourself. There was just one snag. The book of legends was your research material. Meanwhile, the Counter-Reformation, an ultimately futile attempt to reassert the Catholic Church’s authority over its uneducated adherents, was kick-started in response to Luther’s heresy, and it was inevitable that Copernican cosmology would come under scrutiny.

Yet it was to be another ninety years before the heliocentric view faced a major challenge. In 1633, Galileo was hauled before the Holy Office of the Inquisition to explain the views that he had expressed in Dialogue Concerning the Two Chief World Systems, published a year earlier. Galileo thought, naively, that all he had to do was to demonstrate that Copernicus had been correct and everyone would listen.

He had reached this conclusion twenty years earlier, but he had judged that the time was not right for a challenge to the accepted order. Then, in 1623, a new and intellectual pope was elected, Maffeo Barberini. The climate seemed right.

Galileo had long conversations with the new pope, but he was unable to persuade him to withdraw or at least by-pass the Church’s prohibition of the Copernican worldview. Nevertheless, he believed that the pope would permit the new ideas to be assimilated slowly into the Church’s teachings, because this was how the ideas of Aristotle and Ptolemy had become official doctrine in the first place. He was wrong.

Perhaps Galileo should have noted the early behaviour of this extravagant pope. Barberini had bronze taken from the roof of the Pantheon, a Roman-era building that had survived the Visigoths and the Vandals, to construct the Baldacchino, the preposterous canopy that towers over the papal throne in St Peter’s, an act of vandalism recorded by an anonymous wag in one sentence: quod non fecerunt barbari, fecit Barberini (‘what the barbarians didn’t do, Barberini did’).

The trial of Galileo was a clash of principles: Galileo believed that the ultimate test of any theory can only be found in nature, while Barberini considered this to be an infringement of God’s right to rule the universe by miracle. The eventual verdict, that Galileo was ‘vehemently suspect of heresy’ and was thus required to recant, had one important consequence: the centre of gravity in the development of science moved to northern Europe, and no notable scientists worked in Italy for the next two hundred years.

Thus began the so-called ‘Age of Reason’, although it should be pointed out that ‘reason’ in this context differs from the original Greek definition of the term. The new paradigm was inductive logic: make specific observations or measurements, then infer a general explanation for the phenomena that are observed. Not all such explanations were sound: for example, the phlogiston theory of combustion, popular in the late seventeenth century and most of the eighteenth, did explain many of the observed characteristics of combustion, and it was comprehensively disproved only with Lavoisier’s discovery of oxygen in 1778.

New branches of science opened up in the nineteenth century, including geology, thermodynamics and genetics, together with a major theory that greatly upset the religious lobby: the theory of evolution by natural selection. And some apologists for religion remain upset, because it contradicts their own explanations.

The twentieth century saw even more developments in science, including some with serious philosophical implications. Schrödinger’s cat is a good example. This subject of a famous thought experiment ends up simultaneously alive and dead as a result of quantum mechanical effects. However, chaos theory is the concept that carries the greatest philosophical loading in modern science, precisely because its predictions are counterintuitive.

The tired old analogy of a hurricane in the Atlantic being caused by the flapping of a butterfly’s wings in the Amazon rainforest does nothing to explain chaos, so a different category of explanation is required. And neither philosophy nor religion can provide it.

The ‘different category of explanation’ turns out to be art, and the visual arts in particular. However, it should be borne in mind that art provides an insight into the meaning of a given concept rather than what we conventionally think of as an explanation. After all, there are no words, and we are programmed to use words when constructing an explanation. The best insight into the nature of chaos can be found by examining the later paintings of Jackson Pollock, especially the ones that earned him the nickname Jack the Dripper.

Jackson Pollock, No. 1, 1950 (Lavender Mist) [National Gallery of Art, Washington].

When news broke in 2006 that Pollock’s No. 5, 1948 had just been sold for $140 million, Britain’s Sun newspaper produced a painter and decorator who said that he could knock out a painting that was just as good for £19.95. It is unlikely that it would have been mistaken for a genuine Pollock, because neither the Sun nor the hapless painter understood what they were trying to poke fun at. However, it is possible to produce a reasonable imitation of a Pollock painting by employing what physicists call a chaotic pendulum to apply the paint to the canvas.

Pollock used household paints, which are much more fluid than conventional art pigments and can thus be dripped and flicked onto the canvas more readily from the sticks and caked brushes that he habitually used. Critics who despise Pollock invariably justify their dislike by pointing out that all these canvases were painted while he was blind drunk. What they don’t realize is that in getting drunk, Pollock was transforming himself into a human chaotic pendulum, although he probably wasn’t aware of this interpretation of his modus operandi.

Look again at Lavender Mist. It is not a random mess, although it may seem like it to the untutored eye. It is an illustration of chaos, which is not the same thing. If you understand this distinction, you are well on the way to understanding the fundamental truth about explanations: if you want to understand something, you don’t have to be clever; you just need the right explanation.

knowledge or certainty

‘Epistemology’ is not a word that you can infiltrate into everyday conversation, but it is a word that is frequently used by academics who want to sound clever. Unfortunately, such people tend to use the word inappropriately, as a mere synonym for ‘knowledge’, as in the phrases ‘social epistemology’ and ‘feminist epistemology’. However, the word’s true meaning can be summed up in the title of a book that I once edited for Routledge: Epistemology: A Contemporary Introduction to the Theory of Knowledge by Robert Audi, which is concerned with how we know what we think we know, what justifies us in believing what we believe, and what standards of evidence we should use in seeking the truth about human experience of the world.

This is especially relevant in discussions about religion, which tend to degenerate into a shouting match between confirmed skeptics (scientists and atheists mostly) on one side and religious fundamentalists on the other. I believe that atheism is the default rationalist position and that a belief in God is completely irrational. However, I have no quarrel with anyone who has a personal faith in God; it is their choice, and I respect that. It is with the extreme ends of the spectrum that I take issue. There is no doubt that militant atheists, Richard Dawkins being the best-known example, actually sneer at believers, even if they are not aware that they are doing so. Because they have reached their conclusions by a process of rational deduction, they look down on those who have reached their conclusions entirely on faith. Obviously, religious faith is, ipso facto, the acceptance of a set of beliefs without concrete evidence, but that is not a good reason to ridicule those who hold those beliefs unless, as a result of their beliefs, they stray into areas of thought about which they know nothing.

The problem with the fundamentalist viewpoint is that those who hold it know that they have the necessary evidence, a principle source of that ‘evidence’ being the Bible, the Qur’an or other ‘holy’ book. From this point, however, I will confine my commentary to the Bible, which is the only scriptural text with which I am reasonably familiar. A common phrase that you will read on Christian websites is “the Bible is inerrant”. In other words, everything that you read in the Bible is a true account. I think that the Bible contains a great deal of wisdom, the passage from Ecclesiastes that I referenced in Fact or Fiction being a classic example. However, to suggest that there are no errors in the Bible is a logically untenable point of view. Out of the many examples I could have selected, I put forward just two, one from the Old Testament and one from the New Testament:

3 And God said, Let there be light: and there was light.
…
5 And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day.
…
16 And God made two great lights; the greater light to rule the day, and the lesser light to rule the night: he made the stars also.
17 And God set them in the firmament of the heaven to give light upon the earth,
18 And to rule over the day and over the night, and to divide the light from the darkness: and God saw that it was good.
19 And the evening and the morning were the fourth day.

Genesis 1 (Authorized Version).

One is bound to ask, if the first thing that God allegedly created was light, how is it that he didn’t create the source of that light until the fourth day.

1 Now when Jesus was born in Bethlehem of Judaea in the days of Herod the king, behold, there came wise men from the east to Jerusalem,
2 Saying, Where is he that is born King of the Jews? for we have seen his star in the east, and are come to worship him.

Matthew 2 (Authorized Version).

It is a reasonable deduction that these wise men will have come from somewhere in the region of Mesopotamia, so if they were following a star in the east, how is it that they didn’t end up in India?

Of course, these are trivial errors that do not invalidate the Bible’s status as a valuable document. You will perceive a problem only if you believe that the Bible is the word of God and is therefore inerrant. On this subject, I came across an interesting article while researching this essay. The author starts by quoting an acceptable albeit imperfect definition of science as “knowledge of natural phenomena that is subjected to some degree of skeptical rigour and explained by rational causes.” He then states:

Natural, in this definition, is opposed to supernatural. Rational is opposed to philosophical, spiritual or theological. Science, according to this definition, only allows for the examination of the natural. It will not allow the possibility of the supernatural.…No matter what evidence these scientists see, they are not allowed to see God.…Evolution, therefore, begins on a godless foundation. You don’t arrive at evolution because the evidence demands God played no part. You arrive at evolution by removing God’s involvement before you even look at the evidence.

Franklin Church of Christ (The Origins of Man: Fact vs. Story).

You have to look very closely to see the flaws in this argument. First, the word ‘evidence’ is not used in anything like the sense that most people understand it. It suggests, misleadingly, the process used in a court of law to determine the guilt or innocence of someone accused of a crime. Evidence in the scientific sense is even more rigorous than its forensic equivalent: scientific evidence is verifiable, or it is not evidence. Claiming that the Bible is the word of God because you believe it to be so because it says so in the Bible is, unfortunately, a self-referencing or circular argument. It is certainly not evidence.

Second, there is the a priori assumption that God exists, which violates the mediæval scholastic principle known as Occam's razor (entia non sunt multiplicanda praeter necessitatem: ‘entities must not be multiplied beyond necessity’), explained by Sir Isaac Newton as “We are to admit no more causes of natural things than such as are both true and sufficient to explain their appearances.” The bulk of the writer’s argument is therefore invalidated by the absence of verifiable evidence for his conjecture. However, this should not be taken to imply that science doesn’t make assumptions; it does. A classic example is Newton’s laws of motion, which do work well enough in everyday situations and were the best approximation to reality for 200 years. However, they are based on the assumption that space is absolute; in other words, Newton regarded space as a Euclidean three-dimensional grid that stretches unchanging into infinity, so it was inevitable that this limitation, pointed out at the time by Liebnitz, would eventually have to be confronted. And although the successor to Newton’s laws, Einstein’s theory of relativity, eliminates Newton’s assumption, it too is an approximation to reality, albeit a closer approximation than its predecessor. The interesting philosophical question that arises here is whether it will ever be possible to explain absolutely everything.

Science has also made plenty of wrong guesses in the past, the phlogiston theory of combustion and the æther theory of light transmission being classic examples. There may be more to come, although the theory of evolution won’t be among them: hard, real, evidence for this theory is being accumulated on an almost daily basis. However, I did suggest one possible candidate in Who’s Fooling Who? In fact, there are key areas of science where a measure of faith is a prerequisite. Theoretical physics is a case in point: modern entrants to the discipline have been schooled in mathematics and taught that experiment and observation are an inferior road to knowledge. This leads to concepts such as string theory, an elegant hypothesis for which there is no observational evidence and which produces no testable predictions. Another example is the Higgs boson, a subatomic particle the existence of which has been calculated mathematically but never confirmed experimentally. However, the difference between this and religious belief is that experiments are now underway (the Large Hadron Collider at CERN in Switzerland) that will either confirm or deny the existence of this hypothetical particle. Science never stands still, while theism is frozen in time and space.

Third, there is the implicit assumption that the theologian is as much an expert in his field (the supernatural) as the scientist in his, someone whose opinions carry as much weight. And because the theologian deals in certainty, he assumes that the scientist does too. However, this is a delusion. The scientist deals with uncertainty; the scientist knows that there is a limit to what we can know, what we can prove beyond reasonable doubt. The scientific basis for this insight is Werner Heisenberg’s principle of uncertainty, which relates to the subatomic world and states that if you know how fast an electron is travelling, you will have no way of knowing where it is. Conversely, if you know where it is, you will have no way of determining its speed of travel. I have to confess that this is a crude formulation of what is in practice a very precise law, one of the bizarre consequences of which is that an electron can be everywhere in its orbit at once. Well, not really. The orbit is merely the sum of the probabilities of all the possible positions that the electron may be in, a tolerance within which all possible information is confined.

I have used the word ‘tolerance’ here in its engineering sense, but it would be equally appropriate to use it in its conventional meaning. It is one of the grim ironies of history that within a few years of Heisenberg’s seminal work, Hitler had risen to power in Germany. The idea that science is an adventure on the borderland between knowledge and uncertainty was suddenly confronted by the arrogance of monstrous certainty, of dogma.

Dogma has its roots in beliefs that are unshakeable, beliefs that the holder will never countenance changing. Which is why I detest it. Dogma is a denial of the human spirit, a closing of the mind against questioning, against adventure, against discovery, against knowledge. Dogma would turn us into a regiment of ghosts, a tortured host of manipulated automata.

However, it is important not to confuse dogma with faith, and I do not do so. I close with a quote from Oliver Cromwell, a man not otherwise noted for his tolerance:

I beseech you, in the bowels of Christ, think it possible you may be mistaken.