The problems with the zero – and its mysterious twin the infinite – seemed to have been solved in the nineteenth century, only for them to re-emerge in quantum mechanics and relativity, when scientists began to push mathematics about the atom and the universe – the infinitely small and the infinitely large – to its limits.
Quantum mechanics, in particular, seemed to indicate a breakdown in the logic that has been central to our drive to understand the universe in which we live. As Richard Feynman noted: ‘The problem is, when we calculate all the way down to zero distance, the equation blows up in our face and gives us meaningless answers – things like infinity. This caused a lot of trouble when the theory of quantum electrodynamics first came out. People were getting infinity for every problem they tried to calculate.’
Meanwhile, there are other problems that crop up when the infinite universe is chased back to its beginning with a zero, at the Big Bang. These logical barriers that maths seems to come up with at the extremes seem to some to indicate that if we can solve the logical problems connected with zero, then maybe it will unlock some profound truth about our existence.
[1] This was a myriad or 10,000. Archimedes, in trying to reckon how many sand grains there are in the world, found an ingenious way around this, by using multiples of myriads. His intention was to show that however many grains of sand there are in the world, it is a real number, not a limitless infinity.
[2] It led Zeno in the fifth century to create the most famous of his paradoxes. In it Zeno proves that even running at his fastest, Achilles can never catch up with a tortoise. He does this by showing how far each runs in increments. Achilles runs at a foot per second and the tortoise at half that speed. The tortoise is given a foot’s head start. In the first second, Achilles runs a foot, but the tortoise has moved ahead half a foot, too, so is still ahead. In the next half second, Achilles has run that half foot, but the tortoise has moved a quarter of a foot further on. In the next quarter of a second, Achilles runs a quarter of a foot, but the tortoise has moved on a further eighth of a foot. You can go on like this for smaller and smaller distances. Yet Achilles will, of course, never catch up. Of course, everyone knows Achilles would catch up quickly, but it was hard for the Greeks to find a flaw in Zeno’s logic. The reason they couldn’t is that they didn’t have zero, and so no concept of a limit. Once we know the journey has a limit, and that the limit is zero, we don’t have to go on dividing the fractions infinitesimally. So the paradox disappears.
[3] Brahmagupta was born in Rajasthan in 598. He is known as an astronomer but there was at that time no real distinction between mathematics and astronomy, since the main purpose of maths was to better calculate the motions of the stars. Besides his pioneering of the number zero, Brahmagupta is famous for his work on quadratic equations and his method for finding square roots.
#14 Democracy
No words seem to endorse the thrilling power of the democratic ideal more resonantly than the closing sentence of US President Abraham Lincoln’s brief speech in honour of the dead in the legendary American Civil War Battle of Gettysburg in 1863. ‘We here highly resolve that these dead shall not have died in vain – that this nation, under God, shall have a new birth of freedom – and that government: of the people, by the people, for the people, shall not perish from the earth.’
Lincoln’s ringing words seem so heroic and so simple that it is hard to see how anyone could deny the righteousness of democracy. Indeed, since Lincoln’s day, democracy has become such a mantra for fair and enlightened government that, in the Western world at least, nations are thought of poorly if they do not live up to certain standards of democracy. And undemocratic behaviour by a politician or organisation tends to automatically be seen as wrong.[1]
The idea of democracy seems to have originated in the Ancient Greek city of Athens, reaching its height in the fifth century BC in the time of Pericles. But in Ancient Greece, democracy meant something different from what we think of as democracy today. Democracy today usually means representative democracy, in which government is delegated to a small number of people elected by the rest. The original Ancient Greek idea was direct democracy – that is, the passing of laws not by elected representatives but through a direct vote by the people.
Of course, in the Ancient Athens of Pericles, direct democracy was practical because only a tiny minority of Athenian citizens were actually considered eligible to join the Assembly of the People. Such a system might just work in small city states, but was totally impractical in large nation states. After the defeat of Athens by the Spartans, moreover, the Greek idea of democracy fell into disrepute, especially when attempts to restore democracy led to the persecution of the great philosopher Socrates. The treatment of Socrates turned his student Plato into a vehement critic of democracy. Democracy, for Plato, was the tyranny of the masses, in which minorities were abused by the mob majority, and Plato’s student Aristotle echoed his views.[2]
For 2,000 years, democracy was largely abandoned as an intellectual idea. Enlightened thinkers championed instead the moral obligations of monarchs and oligarchs, and how people should be best ruled by the one or by the few. In the Middle Ages and beyond, however, an alternative route to democracy, the democracy of delegation, gradually emerged in the English notion of parliament, moved not by theoretical ideas but pragmatic demands. Parliaments had started in the Nordic world as assemblies of noblemen, but the English parliament in particular was forced to acquire a wider constituency under the pressure of broadening prosperity, as first lords and then prosperous farmers fought to rein in the power of the monarch, especially over taxes.
In the eighteenth century, two great English thinkers, John Locke and Thomas Hobbes, began to explore the intellectual and moral implications of this representative democracy. Locke argued that there must be a ‘social contract’ among those who have ‘consented to make one community or government … wherein the majority have the right to act and conclude the rest’. These two ideas, the consent of the governed and majority rule, have become the central planks of democracy, although Locke did not use the word ‘democracy’ himself.
Locke didn’t specify the form that consent would take, and it took a little while for the philosophers of the Enlightenment, radicals of the eighteenth century such as Thomas Paine, and the profound upheavals of the French and other revolutions to help the idea of representative democracy to clearly emerge. But in 1820, Scottish philosopher James Mill proclaimed ‘the system of representation’ to be ‘the grand discovery of modern times’, while his son John Stuart Mill later declared that representative democracy was the ‘ideal type of a perfect government’. The gradual shift of Western governments towards democracy over the next century, though, was perhaps as much to do with the failure of other systems as with the perceived benefits of representative democracy.
With the victory of the Allies after the First World War, for instance, the time of kings and counts seemed finally to have passed. With the Second World War, the lure of fascism was extinguished. And in the 1990s, communism collapsed and economic failure drove many South American dictators from power. All the time, the spread of market economies drained power from centralised institutions, it seems, and delivered more into the hands of the middle and working classes.
In 1972, just 40 countries could be described as democracies. But a wave of liberalisations, from the Indonesian Revolution of 1998 to the Cedar Revolution in Lebanon in 2005, has dramatically boosted the number of democratic countries to 123. In the 1990s, American philosopher Francis Fukuyama predicted that liberal democracy will eventually take over the world, leading to what he described as the ‘End of History’.
But the road to democracy is not proving quite as one-way and rapid as expected. Russia’s leaders are developing their own brand of oligarchy, which they call ‘sovereign’ democracy. China is not moving as obviously towards democracy as people once thought. The Tulip Revolutions in Kyrgyzstan and the Orange Revolution in the Ukraine hav
e not gone quite as expected and many African countries, such as Zimbabwe, have failed to develop the genuinely democratic institutions once hoped for.
What’s more disturbing for champions of democracy is that democratic experiments often demonstrably fail to improve people’s lives. ‘Millions now believe that they run more risk of being killed or remaining poor under an electoral system than under a dictatorship,’ writes Humphrey Hawksley in Democracy Kills. ‘The average income in authoritarian China, for example, is now twice that of democratic India. In the same way, Haitians who are allowed to elect their government live twenty years less than those in dictatorial Cuba where average life expectancy is seventy-seven years.’
In Iraq and Afghanistan, American foreign policy seems to be predicated on the belief that if they can establish democracy there, these countries will become safe, stable and prosperous. That, they say, is what happened after the Second World War in Germany and Japan. But the historical evidence is not entirely on their side.
In both Japan and Germany, it seems that American policies were more punitive than encouraging, and the drive towards democracy in Germany came from the German people, not from their American conquerors. Political scientist James L. Payne suggests that democracy evolves when people are ‘ready’ for it, which means, essentially, that their leaders have given up employing force against each other, and democracy is the ‘default’ mode of settling disputes. That, perhaps, is why it may take a long time to achieve in Iran and Afghanistan.
So if countries arrive at democracy essentially by default, what’s so great about it – and why shouldn’t it be consciously replaced with other systems? John Stuart Mill put three key arguments in its favour. The first is that democracy forces the decision-makers to take notice of most people’s interests and rights. Indian thinker Amartya Sen argues that ‘no substantial famine has ever occurred in any independent country with a democratic form of government and a relatively free press’. The second is that democracy is more likely to lead to the right decisions, because instead of just a few people judging the effectiveness of policies, it is the maximum possible number. Mill’s third argument is that democracy encourages people to think for themselves, and to think rationally and carefully about the consequences of their decisions.
For many people, though, the experience of democracy is not half as empowering as Mill hoped, bringing more a sense of powerlessness than empowerment. When cast against thousands or even millions of others, their single vote seems a futile gesture. Moreover, the political process seems to drive politicians towards similar ways of looking at things, leading Gore Vidal to say, cynically, that: ‘Democracy is supposed to give you the feeling of choice, like Painkiller X and Painkiller Y. But they’re both just aspirin.’ Mahatma Gandhi argued that democracy was not even what really mattered. ‘What difference does it make to the dead, the orphans, and the homeless, whether the mad destruction is wrought under the name of totalitarianism or the holy name of liberty or democracy?’
Yet whatever the flaws in democracy, and they are many, Lincoln’s simple summation of its values still makes more sense of a way to run society than any other. It has proved the most capable of moving forward of any political system; the most capable of giving its citizens freedom and a sense of control over their lives; and the most capable of having the moral authority to create laws. It may not be able to save nations from war. It may not be able to save people who live under it from privation or ill health. It may not even be able to save people from injustice. But if nations and their people do suffer from any of these misfortunes, democracy maximises the chances of those responsible being held accountable.
[1] Interestingly, when America’s founders framed their Declaration of Independence, sometimes thought of as the starting point of modern democracy, not all of them focused on democratic ideals. They intended America to be primarily a republic that championed liberty and rights, not a democracy. ‘A democracy,’ wrote Thomas Jefferson, ‘is nothing more than mob rule, where fifty-one percent of the people may take away the rights of the other forty-nine.’ Another of America’s founding fathers, John Adams, was if anything more damning: ‘Democracy … while it lasts is more bloody than either [aristocracy or monarchy]. Remember, democracy never lasts long. It soon wastes, exhausts, and murders itself. There is never a democracy that did not commit suicide.’ For them, the purpose of elections was as the most reliable way of keeping the government ‘more or less republican’ in nature, not the embodiment of a great ideal.
[2]Plato also argued that democracy tends to undermine the expertise needed to govern society well, encouraging only those who are expert at winning elections. Plato finds a remarkable modern echo in the criticism that the party leaders’ debates on television reduced the 2010 British elections into a political X Factor, turning on presentation and a winning smile, not policies and expertise. The awkward-looking Gordon Brown, in particular, felt disadvantaged by this, trying to negate it by asserting: ‘If it’s all about style and PR, count me out.’
#13 The Wheel
The wheel is the apocryphal starting point of civilisation – the breakthrough invention. Once the wheel was invented, mankind was on a roll and it was progress all the way to the modern age – and maybe, one suspects, towards the automobile which was seen as the pinnacle of human progress at the time when the invention of the wheel began to be heralded.
Because of the perceived importance of the wheel, many people telling the story of its invention have been tempted to fill in the gaps with pure speculation. The interest is especially in cartwheels. Experts describe in detail how the cartwheel must have been invented. Heavy loads, the scenario goes, were originally dragged on sledges with runners. This, modern experiments show (but no archaeological evidence does), was how the great stones were hauled to Stonehenge. Then some bright spark had the idea of laying down tree trunks as rollers beneath them. It would have been a laborious practice, since you’d have to continually carry the rollers round from the back to the front. Then maybe someone thought of trapping the rollers between two pegs. And then, finally, someone turned the trapped rollers into wheels and axles. The cart was invented.[1]
Yet there is almost no evidence that this is how it happened. The closest thing to it is an ancient pictogram from Uruk, in Iraq, the site of one of the earliest Sumerian civilisations. The pictograms date from about 5,500 years ago and clearly show a sledge. They also clearly show what looks like a sledge on wheels. And neither sledge, with or without wheels, looks much like what we’d call a cart. Interestingly, Sumerian cuneiform script also shows how the symbol for a ‘sledge’ did indeed look like a sledge – and this evolved into the symbol for a ‘cart’ which looked like a sledge on wheels. There is no evidence whatsoever for the rollers. Indeed, there just weren’t the trees to make such rollers in Mesopotamia where the wheel is supposed to have been invented!
Interestingly, the thinking that links the invention of the cart and the rise of civilisation with Mesopotamia isn’t actually quite backed up by archaeological evidence, either. There is actually evidence for carts in eastern Europe, far from ‘civilisation’, just as old as that in Mesopotamia. At Bronocice in Poland, for instance, a ceramic vase dating from 5100–5450 BC was found showing what looks like five four-wheeled carts, while clay models from Hungary up to 5,600 years old show clear pictures of four-wheel carts. Then there are some full-sized wooden wheels from around the same date that have been found in Switzerland and Slovenia. And most impressive of all, there are remains of complete wagons from the Novotitorovka culture in the Caucasus in Georgia, also dating from maybe 5,500 years ago.
The argument is that the technology of the cart was so marvellous that it spread rapidly across Europe and Eurasia, and later on to India and China. There is some evidence for this, interestingly, in the very word ‘wheel’, which is strikingly similar in languages across Eurasia. The Sumerian for wheel was girgir, the Hebrew galgal, the Georgian gorgal and the Proto-Indo-European *kwel-
kwel. Even the Chinese bears some similarity, with the Mandarin being gulu and the Cantonese gukluk. All of this suggests at least a connection.
Yet the idea that the cartwheel was the breakthrough invention that kick-started technology doesn’t seem to stand much scrutiny. Why, for instance, did places like Europe and Georgia remain firmly prehistoric long after the arrival of the cart? And why in Sumeria, the place where the wheel was apparently invented, do carts seem to have been used mainly as hearses? It took 1,000 years before carts were widely used for the transport of goods in Mesopotamia and equally long before they began to be used as moving platforms for javelin throwers in battle.
Perhaps there is a simple explanation for this delay. Carts are virtually useless without proper wide tracks, and even the best cart-tracks frequently become impassable in bad weather. Until suitable roads developed, pack animals were a much better way of carrying goods. Tellingly, while Roman roads ensured people in Europe carried on using carts, the use of carts for transport was almost entirely abandoned over much of the Middle East – including Mesopotamia – after the introduction of camels. Camels were much better for travelling through desert and drier areas. Oxcarts are very slow, and the oxen need lots of water and grass.
There is another aspect of the wheel story that is worth considering. The first wheel invented may not have been a cartwheel at all, but the potter’s wheel. A stone potter’s wheel found at the Mesopotamian city of Ur dates back at least 5,100 years, and there are even older fragments of pottery clearly thrown on a wheel. Some experts suggest that the potter’s wheel was in use up to 10,000 years ago. If so, that would make it twice as old as the cartwheel. The suggestion is that the cartwheel was created, eventually, when someone thought of turning the horizontal potter’s wheel on its side. If so, it took them a very long time. It’s more likely that the cartwheel was introduced only when there was a need for it.[2]
The World's Greatest Idea Page 22
