All entries for April 2005

April 24, 2005

Imagine this scene (published in the Warwick Boar)

Writing about web page

Imagine this chilling scene. You’re nine years old. You’re scared. You have just woken up in war-torn capital Monrovia in Liberia. You’ve lost your brothers and sisters during the brutal civil wars, and your parents died from AIDS way before you had the chance to show them your toddling skills. You soon discover that you don’t have a home, a family, a school to go to. All you have is yourself, and literally, nothing else. All you know is that other children around the block are stuck in the same horrific situation. Your options are limited. If you’re a boy, you can become a soldier to gain respect from your comrades. If you’re a girl, you may become subject to prostitution, sex trafficking or even sex slave. Shocked, you assume this is all a nightmare, one of those that feels so real that you even try to pinch your skin to wake up. But you don’t wake up. You can’t. It is real. How would you feel? What would you do?

The truth is that this scene is far from a dream, illusion, hallucination, head-trip. It is in fact almost a reconstruction of the lives of millions of genuine, real, innocent children in the world today. ‘Almost’ because reality can never be truly characterised into words. And as reality is always far from illusion, not only are they far from us in a physical sense, but so are their lives ridiculously different from ours. I do not pause to consider in detail the realities of the horrific lives of those unfortunate children. I leave this open to interpretation. But before you even consider imagining the horrors those kids have been though, the brutal sexual experiences they have been forced to participate in, or the disheartening conditions that they live in, I beg you to contemplate the following facts.
First things first: the key problems. One in three of the world’s children live without adequate shelter, one in five has no access to safe water, and one in seven has no access to health services. Furthermore, 121 million primary school aged children are out of school, the majority of them girls. Oh! Also, 1.6 million children have been killed in armed conflicts since 1990, while another 20 million have been forced from their homes by conflict or human rights violations. If that wasn’t more than enough, around 2 million children are recruited each and every year (the number is increasing) to work within the sex industry. In total, more than 1 billion children are living in families with a daily income of approximately £1.50. Hold on. That’s not even how much you spend on a pint, is it not?
If you believe in your future, you must believe in the future of children. No matter how much of a cliché this sounds, its nonetheless an accurate statement. You were a child once, right?
There has been much talk on terrorism, human rights, global warming and American politics in the past few years. There exists extensive literature on these topics, as well as other interesting subjects such as Newton’s gravity theory, Shakespeare’s plays, Chomsky’s commentaries etc. and I will not undermine their importance to the world today. But what purpose will it serve if more than 200 million children in the world today cannot read it, let alone understand it, because they don’t have a school to go to? Ultimately, you may ask yourself, why should we co-operate to eradicate not only child poverty, but also help the other 2.6 billion people living below the poverty line? Well that question shall also be left open. However, think about the scene in Monrovia, Liberia, where you had no help, no hope and no future. You were begging for help. Well, right now, they are crying for hope. And its people like you and me that can make a difference. We were born in what they regard as abundant luxury. The pint that you drink could buy them the food for a day, if not a week. I’m not asking you to jump on the next flight to Liberia or any other country and rescue those children nor am I asking you to donate your ‘binge’ money to charities. Far from that. I only beg you to genuinely contemplate that ‘scene’ in Monrovia and share your thoughts, ideas or even projects with others in the community, because it is through great ideas, and great people, that truly good and amazing things are achieved.

Up to their eyes in it

Between 1503 and 1660, 185 thousand kilos of gold and 16 million kilos of silver were shipped from Latin America to Europe. Were the indigenous people of Latin America to charge compound interest on this 'loan', levied at a modest rate of 10 percent, Europe would owe a stack of gold and silver which would exceed the weight of the planet. Yet curiously, many of the 'first-world' nations speak of 'third world debts' as if they didn't owe a single penny.

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On Legal Mathematics(published in the Mathematics Journal, University of Warwick)

Christopher Columbus Langdell, Dean of the Harvard Law School and originator of the “Case Method” of teaching law, famously advocated that Law was a science, whose principles and doctrines could be ‘discovered’ in cases, much as biologists discover the principles of their science in their laboratories. To Langdell ‘science’ conjured up the ideas of order, system, simplicity, taxonomy and original sources. The science of law involved the search for a system of general, logically consistent principles, built up from the study of particular instances. Once the general principles have been found, it is then the task of scholars to work out, in an analytically rigorous manner, the subordinate principles entailed by them. When these subordinate principles have all been stated in propositional form and the relations of entailment among them clarified, they will, Langdell believed, together constitute a well-ordered system of rules that offers the best possible descriptions of that particular branch of law – the best answer to the question of what the law in that area is.

This ‘mechanical jurisprudence’, often criticised by American realists, resembles at first the methodology used in mathematics in deriving conclusions from basic axioms and logical deductions. When a lawyer writes a brief for a case in which he has to convince the judge that his argument should prevail, he structures it just like a geometric proof. He starts with all the given facts, then states the relevant laws and precedents that relate to the case. Then he makes his argument based on these facts using deductive logic, exactly as if he were doing a mathematical proof.

Mathematicians have the ability to analyse problems and principles just as lawyers have the ability to dissect dictums and rules from cases. Comprehending certain laws, for example taxation law, is as challenging as understanding some of the most complicated mathematical theories you will encounter. Most solicitors involved in civil cases, in which people are suing others, must be able to calculate percentages, interest rates and the like to determine what is or isn't a fair settlement for the parties involved. Likewise, lawyers involved in tax or corporate law have to perform a lot of computations involving money, interest rates, percentages and proportions. Patent lawyers who work on behalf of inventors generally must also have a degree in engineering because they must be able to understand the inventions and the mathematical formulas involved in the physics or chemistry applications of the product.

Although a comparative study of the relationship between the Law and Mathematics wouldn’t result in any offspring, there exists nonetheless methodological devices used in mathematics which corresponds to those used in the application of the Law. From its birth in ancient Greece, and for over two thousand years, mathematics has been viewed a body of collective truth, being the basis of innumerable scientific theories which describe the world around us. To achieve such powerful results, early mathematicians employed deductive reasoning in their examination of new hypotheses. This logical methodology created the assumption that mathematics is a certain science. But more recent realisations in the world of mathematics have revealed that it is not the body of truths once assumed to be, and further, that the very deductive reasoning used to create and develop these truths contain flaws.
In his book Mathematics: The Loss of Certainty, Morris Kline claims that ‘the current predicament of mathematics is that there is not one but ‘many’ mathematics and that for numerous reasons each fails to satisfy the members of different schools. Uncertainty and doubt concerning the future of mathematics have replaced the certainties and complacency of the past. The disagreements about the foundations of the 'most certain' science are both surprising and, to put it mildly, disconcerting. The present state of mathematics is a mockery of the hitherto deep-rooted and widely reputed truth and logical perfection of mathematics.’ However disorganised the world of mathematics may be today, contradictions have always existed in bodies of knowledge – especially in the Law – just after periods of major revision in which inevitable periods of uncertainty follow, new ideas are allowed to reach fruition.

Accordingly, although the promulgation of the law claims to guarantee its certainty and consistency, its application is a different matter. The courts, and indeed judges, play a significant role in applying the law in the real world in real situations, thus making the ambiguity of the Law vulnerable to ultra vires interpretation. ‘Statutes are not laws by virtue of their enactment. They only become law when applied by a decision of the courts’ argued J C Gray, 20th century American realist. Thus instead of being regarded as a body of abstract rules and principles, the law shall be understood from a broader angle. Legislation is therefore no more than a source of law: it is the courts that ‘put life into the dead words of the statutes’.

Likewise, mathematical laws and principles are no more than an instrument to an end: it requires real-world situations in order for its true efficacy to be understood. The efficiency of symbols and numbers in mathematics only becomes evident when assembled in theories and applied to real problems. Although both disciplines endeavour to be certain, they are both subject to the creative interpretation and ambiguity of human minds. In other words, they are both subject to the concept of relativity. Searching for the Truth in mathematics mirrors the search for Justice in the Law; objectives which appears to be unattainable for sceptics. Unfortunately, the ordinary citizen fails to contribute to this quest for Truth and Justice, as both disciplines remain perceptibly ‘inaccessible’ by the populace at large.

Perhaps I place too narrow a definition upon Truth and Justice – for despite the seeming contradictions of mathematics and the disagreements which characterise its past, one evident theme remains. Mathematics has always been and remains to be a remarkably effective method of describing the mechanics of the world around us. Accordingly, the Law has always been and remains to be the fundamental element that holds society together. Both disciplines are of respectable value and utility, even complementary at times, and both are consistently evolving towards the same uncertain future. Even if one is to disregard absolute certainty in mathematics, the Law, or in any body of knowledge, we must not give up the search for Truth and Justice, or allow our limitations to overcome us.

April 2005

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