An extra long offering this week. I thought I would share a piece I wrote last week for group I go to. The brief for the evening was: Choose something in history and write about your own take on it ….
It will probably not be a surprise to hear that I’ve never had much time for conventional history. Stories of great men doing great things … As far as I can see, the greatness often has an exponential relationship with the number of dead bodies accumulated. Not a fact that’s going to impress me.
I am much more interested in the history of ideas and of particular people. So when I read the brief for this evening – ‘Choose something in history’ – my mind immediately went to a topic that covers both those interests. I decided to write something about nothing. I chose to delve into the history of Zero.
Zero is a fascinating concept, not least because it has not always existed. Obviously, the absence of things has always been a possibility but the representation of this as a numerical digit has not. Even the ancient Babylonians, who are commonly credited with the introduction of a place-holder (a symbol representing the absence of a digit in a longer number such as 204 in decimal systems), did not actually use a circle for this, nor indeed, any consistent notation.
Zero does not appear in Europe until 1202 when Fibonacci used it as part of his numerical system, developed from the Hindu-Arabic decimal system which included a circle ‘to keep the rows’. This circle was named sifr, an Arabic word for ‘empty’. Even then, it took a further four hundred years before the first recorded English use of the word.
At various times, the concept of zero has created enormous controversy, even being considered as dangerous. And one can get a glimpse of why, when its numerous mathematical functions are considered. Added to, or subtracted from, any other number, it makes absolutely no difference whatsoever. Similarly, when placed at the start of a longer number, or at the end of a number including a decimal point, it has no impact at all.
However, use zero in multiplication and it has the power to wipe out any other number completely. And if one were foolish enough to consider using it in division, one would quickly conjure up that other numerical anomaly: infinity.
A very dangerous idea, indeed.
The ancient Greeks took the safe approach by having no name for zero, and by never using a place-holder, for – as any logical person knows – how can nothing be something?
The challenge, however, could not be ignored. Any philosopher worth his salt would be found bringing an argument to bear about the uncertain interpretation of, the nature and existence of, zero. The debates summoned the best minds in both philosophy and religion. Enter Zeno of Elea.
Zeno was a Greek philosopher who pre-dated Aristotle and Plato, and just about overlapped Socrates. But Zeno was, perhaps, less interested in ascertaining the truth than it pointing out it wasn’t really there. He was a lover of paradox, and reminds me of those children I used to teach who, after I had delivered a brilliant and carefully prepared explanation of some mathematical or scientific theorem, would ask the single question that immediately exposed its flaws. This appears to have been Zeno’s talent, too.
I’m sure you have within your panoply of knowledge a record of his famous explanations for why the arrow can never reach its target, and how Achilles can never overtake the tortoise. But just in case you have forgotten, I’ll reiterate the second story, as briefly as I can. I was brought up on these anomalies so they are favourites of mine – for what is life without paradox?
However, as a youngster, there was always an added complication for me, since I was also often quoted the story of the hare and the tortoise. Sometimes, it was difficult to remember which tortoise I was dealing with, since they both seemed to be involved in a race which they could not possibly win, but always did. I believe, when I was asked what I wanted to be when I grew up, I privately thought: ‘a tortoise’.
Achilles, it seems, did not share my admiration of tortoises and rather cockily, began his race by giving the tortoise a head start. In fact, he was so confident, that he suggested the tortoise start halfway down the track. Zeno would explain to his audience that by the time Achilles had reached this halfway point, the tortoise would have moved forward by, say, a tenth of the distance Achilles had covered. Then, as Achilles, moved across the ground to reach this tenth further, the tortoise would have moved a further tenth of that distance, thus remaining in front of his pursuer.
Obviously, however far Achilles ran down the track, the tortoise would always be just one tenth of the previous distance ahead of him. Obviously.
By all accounts, Zeno would drive his contemporaries nuts with his stories. And not just his contemporaries. All down the ages, from Diogenes the Cynic to Bertrand Russell, philosophers have proposed solutions to, and refutations of, the tortoise’s success. Men the world over have spent valuable time trying their best to point out logically just where Zeno got it wrong. Though I find Diogenes’ highly intellectual response one of the most amusing. Apparently, he just turned his back and left the room!
I think Lewis Carroll had the best take on it when he transcribed an imaginary conversation between Achilles and the tortoise, which concludes with yet another innocent question on the part of the tortoise, who refuses to accept the logic placed in front of him. Achilles’ logical response? ‘Then Logic would take you by the throat and force you to do it!’
Zeno, you see, understood that logic alone cannot account for the workings of the Universe. He was also a student of metaphysics, so concepts such as zero and infinity held only fascination for him, not fear. In fact, his stories turn out to be pre-cursors of the wonderful paradoxes which are now a recognised part of quantum physics: Schrodinger’s cat, for example, who is both alive and dead at the same time; the discovery that light behaves both as a wave and particles at once; the realisation that the position of an electron in an atom can only be estimated as a probability, never as a certainty, since as soon as an observer observes, the scenario changes. This last phenomenon has now been labelled as the Quantum Zeno Effect. And let’s not forget that most of what’s in the atom is emptiness, anyway!
Which brings us full circle. Circle. Sifr. Zero.
I am with Zeno and Carroll on this. I find myself a subscriber to Conventionalism. The proposition that fundamental principles are often grounded on shared societal agreements rather than on an external reality. Zero, you see, is both something and nothing.