Thursday, October 18, 2007

The Magic of Numbers 1



Ideas and Numbers and Other Philosophical Digressions:

How do ideas for writing (or indeed ideas for anything for that matter) come? Do you get your ideas before you begin or do you get them while you are writing or is it a mix of both? For me I am stimulated by my reading and then the ideas therefrom are both consciously and unconsciously assimilated. Many other things, of course, mould these ideas further as well as giving me different ideas entirely. These “other things” as I’ve rather generally called them comprise everything that goes to make up human experience – our everyday encounters with what we term, in short, LIFE.

Recently, the mystery of numbers and measurement has been intriguing me. From time to time I like dwelling on the odd puzzle to see if I can work out the answer. At school it so happened that mathematics and the sciences were emphasized to the detriment of languages and the liberal arts. I was quite good at maths and the sciences, though never an A student. I belonged to the B group and managed to get my results at Honours level. However, I had to work hard for the results I got, not being a natural scientist or mathematician, though I did really enjoy these subjects and learned so much from my fine teachers and the colleagues in my class at school. I also did manage to get a pass B.A. in mathematics many years ago – not a mean feat in itself, though no great mathematical achievement either.

Why this rather long prolegomenon? Well, I have gone on to further studies in languages, literature, philosophy and theology since the old days. I also find myself reading a lot in these subjects as well as teaching both Irish and some Italian. However, numbers lurk there all the time in the background. I love reading general science and general mathematics insofar as these have a bearing either on lived life, philosophy – what is the nature of the universe and other big questions, or on practical applications to living. Pure mathematics and Theoretical Physics are decidedly beyond my ken. Yet, say the books of Stephen Hawking, Richard P. Feynman and Eric Mlodinow intrigue me in the extreme as they seek to find one overarching general theory or one overarching law that might sum up the main laws of physics. Here physics, both theoretical and astronomical, overlap with philosophy and theology, which also seek to find one basic principle behind whatever reality is, in their own unique ways. I suppose theoretical physics and mysticism could be linked when both are seen as attempting to encapsulate the universe in a unity of “understanding” or “being,” whether that mysticism be of a religious or spiritual or even agnostic/psychological shade.

Often when we are asked a question which does not have a very clear or defined answer, we might retort with that wonderful old chestnut: “How long is a piece of string?” Well, obviously the answer to that question is quite rightly something like: “as long as you, the questioner, want it to be.” From there we are back to another old adage that “we see things not as they are in themselves, but as we are,” a wise and brilliantly perspicacious statement that has been variously attributed to the Talmud and Carl Gustave Jung and many more besides.

The measurement of things was and is a primary activity for the human being both in commerce and engineering and more besides and it is from this physical activity obviously that all the theoretical and pure mathematics developed which then, in turn, fed back into further and more accurate measurement of things, time and space. A colleague on my staff did his Masters in Computer Applications and wrote his thesis on encryption which involved as far as I recall a lot of “number crunching” and contemplating bundles of numbers and attempting to find primes. Prime numbers in themselves are indeed infinitely interesting in all the meanings of the epithet applied. One wonderful mathematical site, which I shall mention in greater depth in a later post, by the wonderful Irish mathematician, John B. Cosgrave http://services.spd.dcu.ie/johnbcos/ is always mind-bogglingly interesting and captivating. Cosgrave discovered the Millennium Prime, that is, a prime number with exactly 2000 digits which he had specially printed for the occasion.

However, one Greek mathematician stands out for his wonderful algorithm for finding primes and indeed the method is eponymous. It’s called The Sieve of Eratosthenes. This Eratosthenes was the director of the famous Library of Alexandria in Egypt and lived from 276 -194 B.C., that is, over 2000 years ago. He was a Greek, a mathematician, a poet, an athlete, a geographer and also an astronomer. Like a lot of ancient scholars he was a polymath. He is noted for devising a system of latitude and longitude, and for being the first known to have calculated the circumference of the Earth. The Sieve of Eratosthenes is simple to use. Just follow the following algorithmic steps:

 Write a list of numbers from 2 to the largest number you want to test for primality. This is our first list. Call it List A for handiness.
 Write the number 2, the first prime number, in another list for primes found. Call this List B.
 Strike off 2 and all multiples of 2 from List A.
 The first remaining number in the list is a prime number. Write this number into List B.
 Strike off this number and all multiples of this number from List A. The crossing-off of multiples can be started at the square of the number, as lower multiples have already been crossed out in previous steps.
 Repeat steps 4 and 5 until no more numbers are left in List A.

Sunday, October 14, 2007

Vanity of vanities, saith the Preacher, vanity of vanities; all is vanity. (Ecclesiastes 1:2)



The Sound of Our Own Voice

There are certainly those amongst us who like the sound of their own voice. Can a worse fate be conceived than being forced to sit beside the local or even out-of-town intellectual at a party or soirée or serata or some other nicely named occasion for celebration? Probably not. He or she loves the cleverness of their speech, the lightness of their words and the aptness of their choice of phrase as these same words trip from their tongue. I have been dipping into several books of late by such intellectual types. Now I am not going to dismiss these books in any cavalier sense as I am learning much from them and actually quite enjoy the examples and humour used in their debating their chosen issues. I refer to several authors here and their noteworthy though provocative and often insensitive books or rather styles. However, that these books are sincere and well argued is, of course, beyond question. I will review these books in a later post when I have fully read and digested their contents. To review them without such pondering and genuine evaluation of their contents would be more than cavalier – it would be dismissive and intellectually superficial and high handed in the extreme.

The books I refer to are The God Delusion by Richard Dawkins, God is Not Great: The Case Against Religion by Christopher Hitchens and lastly Six Impossible Things Before Breakfast by Lewis Wolpert. These authors are all atheistic, if not downright anti-theistic in their arguments. In short all three authors set out to disprove the believer’s viewpoint as illogical and incredible and this same believer as a very credulous, gullible and superstitious type in the extreme. All three books are well worth reading and mulling over and digesting. I have read roughly one third ways through each and will review them in the pages of this blog later. (I have always had this habit of reading three, four or five books simultaneously much to the annoyance of some of my friends. Are their any readers out there with this same propensity?) All I want to do here is to make some preliminary comments.

All three gentlemen are very well educated and rate as top intellectuals, with two being professors and the other, Mr Hitchens, being counted among the top 100 intellectuals in the world. However, let us go back to that armchair intellectual we all know who loves the sound of his or her voice. I have included both sexes here for the sake of equality, but from my experience these armchair types are mostly men. They simply delight in hearing their own voice and especially in winning the debate or in scoring points of “one-up-man-ship”. They seem to be very sure of their positions. Not for them the philosophical dictum of Socrates who advocated first the declaration of one’s own ignorance before going further on in one’s debate. Not for them either the questioning of their own suppositions and axioms. They start out from certain a priori positions which for them are simple incontrovertible. All good philosophers know that we should at least take a good look at our own presuppositions and declare certain things as axioms, and then even say why these axioms are so self-evidently clear. At least Hitchens has the good taste to criticize Dawkins for his snobbish elitism by abrogating to himself and others of high intelligence (which obviously all atheists, they seem to argue, really are) the term “Brights.” Hitchens, at least concedes that believers can be intelligent, too! Well done, Mr Hitchens! Obviously Dawkins would term the three of them as “Brights.” Presumable the rest of us are the less intellectual and certainly the believers, in Dawkins’ language, would be “Dullards.” Who is wearing the dunce’s hat? All those billions of deluded folk of all the various religions in the world presumably! Such a position is surely intellectually untenable and extremely dismissive of others, if not possibly “racist” in some sense. (“racist” is not the most precise word here – maybe bigoted would be a better term).

Also all three could do with reading Straw Dogs, an altogether more revolutionary book than any one of the three alone or even these three tomes taken together. Its author, Professor John Gray, outlines his reasoning very clearly and cuts away all the mist from the bog as it were. He clearly shows that even modern science, the clear heir of Enlightenment Reasoning is in itself a type of Religion proposing a Heaven of its own, namely Infinite Progress. It's just that in one view (Religion) salvation is Heaven and in the other view (Science/Atheism) salvation is infinitive progress or passing on healthy genes. Indeed, I feel, Gray is nearer to the truth, he cuts away all the obfuscating growth of weeds to reveal quite a bear garden of reality which both Religion and Science really have not seen at all. I will review this book also somewhat later in these pages. Once again, I feel that I need to do a lot of digesting to get my own views clear. I might add here that there are hundreds of blogs which have reviewed all of the above books. These blogs are worth perusing. Obviously all four authors have hit on a nerve somewhere.

At this stage in my life I hate being preached at whether by evangelical or proselytizing Christians/Believers or equally evangelical or proselytizing Atheists/Unbelievers. The Truth (singular) is, or perhaps more correctly Truths (plural) are, considerably more complex. In short, I feel and think that Shakespeare got it right in the words of Hamlet to Horatio: “There are more things in heaven and earth than are dreamt of in your philosophy, Horatio.” For the moment, to sustain the Shakespearean allusion, the rest must be silence, at least for some few days.

A reminder of our mortality - a picture I took in Rouen June 2006.