On this date in 474 AD, Zeno became emperor of Byzantium. Zeno was a great warrior, but he was not the really interesting Zeno.
The interesting Zeno was born almost a thousand years before and flourished in the city of Velia in southern Italy , first as a student and then colleague of Parmenides. He is thought to have invented the argument reductio ad absurdum, a key rhetorical device.
He is also the author of Zeno’s Paradoxes, kind of philosophical koans that have puzzled and challenged great brains for centuries. (They are of particular interest to mathematicians and physicists.) Reportedly he created 40 of them, but only nine are known and of those, the most famous are these three: Achilles and the Tortoise, the Dichotomy Paradox and the Arrow Paradox. Here’s a summary of the Arrow Paradox:
In the arrow paradox (also known as the fletcher’s paradox), Zeno states that for motion to occur, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one instant of time, for the arrow to be moving it must either move to where it is, or it must move to where it is not. However, it cannot move to where it is not, because this is a single instant, and it cannot move to where it is because it is already there. In other words, in any instant of time there is no motion occurring, because an instant is a snapshot. Therefore, if it cannot move in a single instant it cannot move in any instant, making any motion impossible.
All of these arguments are in support of Parmenides’ assertion that motion – and thus change – was illusory. Parmenides thought that the knowledge of the cosmos could only be understood intellectually, that sensory experience was more than misleading – it was an illusion. Very eastern, actually.
Bertrand Russell said of Zeno,
“In this capricious world nothing is more capricious than posthumous fame. One of the most notable victims of posterity’s lack of judgement is the Eleatic Zeno. Having invented four arguments all immeasurably subtle and profound, the grossness of subsequent philosophers pronounced him to be a mere ingenious juggler, and his arguments to be one and all sophisms. After two thousand years of continual refutation, these sophisms were reinstated, and made the foundation of a mathematical renaissance…”
In the photo of Velia – known to Parmenides and Zeno as Elea – the remains of temple columns can be seen in the foreground. It is almost possible to imagine the temple and columns and the men who walked in and around them arguing about time and space and reality and being and knowing, more than two thousand years ago. Maybe Parmenides was right and there is no such thing as change.
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Many happy returns to the inimitable Carole King: