tucked away in the 'news & curiosities' column of this month's prospect magazine (in itself not what you'd call the frothiest of entertainment rags) is a nugget, a little gem of a fact that makes you feel that maybe it is all worthwhile after all: perhaps there is a point, some sort of order or at least an underlying principle in this most chaotic, random world of ours, that is also astonishingly beautiful:
"The average ratio between the actual length of a meandering river and its length as the crow flies is pi." credited as he source of this reassuring insight is fermat's enigma by simon singh, a book i haven't read, and i surmise that simon singh probably has his own fount of knowledge, credited or otherwise, from whence it stems. in any case i have no reason to doubt it.
now i am not a scientist. my maths teachers despaired over me. one of them, one memorable day, after i'd slouched from my seat to the blackboard (we had blackboards in our school) glanced underwhelmed at the the 'problem' on it (i could never quite see what the 'problem' was with any of his questions, they seemed to me so hypothetical as to be irrelevant), shrugged my shoulders and painted, with the chalk he'd handed me most probably not to this specific purpose, a question mark in the place where his expectant face foresaw some sort of 'solution', uttered these words which have stayed with me ever since: 'es ist schade wenn intelligenz brach liegt.' which roughly translates as 'it's a pity when intelligence lies barren', the implication being that i, as its ostensible owner, should till that soil, plant in it seeds and nurture them. even back then i couldn't agree with him more, it's just that the seeds he offered were ill suited to my climate and have remained so to this day.
but π is an altogether different proposition. π to me is philosophy. i have a feeling some scientists (especially mathematicians) would argue that all science (especially all maths) is philosophy. and i would neither have the cause nor the resources to argue with them. but π in itself to me is a symbol of perfection, more potent, more elegant and far more interesting than the circle, part of whose nature it describes:
π is perfect because it remains forever incomplete. which in turn makes it absolute; it is absolutely infinite, at least as far as we know, as far as reason allows us to understand. and there's no end in sight and no pattern - it is pure: no repetitions, no symmetries, not even an approximate way to predict how the sequence will continue, not one hint of certainty, other than that it is.
this is a wonderful, wonderful thing: it tells us more about the nature of our existence than we find in volumes of philosophical treatises.
we can easily grasp the underlying principle and basic character of it, we can apply sophisticated technology and thinking of the highest order to understand its workings in detail, and we can never come to a finite conclusion about it nor can we ever foretell what's in store. we don't even know what the next digit is after the last one we've just calculated, let alone the next few thousand. it's impossible and will remain impossible and that's the way things are. and yet: it's anything but random. it's just that we don't have the capacity to think or to express ourselves in a way that would allow us to know more than that which we can see. and we can see it just fine: the first million digits are right here, for example. but when it comes to the 'big questions' why? for how long, really? according to what rule? we barely have the vocabulary, let alone the answers. yet. who knows, maybe we'll develop that too. over time.
the level of insight we have incidentally is impressive: apparently the value of π has been calculated, so far, to an exactness of more than 1 trillion decimal places. set this against the quaint observation that a value of π 'truncated' to just 39 decimal places (not even a scratch off the trillion or so we have available) will allow us to compute the circumference of any circle so vast that would just about fit into our observable universe with a level of accuracy that corresponds to the size of a hydrogen atom. so you could say we know more than enough. and rational thinking would say yes. human nature though says no. which is why we keep searching.
and the fact that this is all mirrored, played out in natural rivers across the planet, that it's not just mental gymnastics and the pastime of geometers and theorists but that water the way it flows over the surface of the earth follows that precise principle all of its own accord: that is a thing of absolute beauty.
and it has made my day.
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