Crawling to infinity
Is that Calculus I see peeking through the curtain?
Today we look at one of Zeno’s Paradoxes. This is the one about Achilles and the tortoise, and why the former, πόδας ὠκύς though he was, could never catch the tortoise. Of course, the problem is idealised, but I like it to my record of games of Freecell. At the moment, I win about 75% of them, but, of course, even if I never lose another game of Freecell in my life, the number will only approach 100%, but never actually reach it. In other words, the goal of 100% always remains in front of me just as the tortoise, at least as a mathematical construct, remains ahead of Achilles.
Zeno, according to the book, considered the problem of continuity vs. discretion in matters of time and space. If time is continuous, there can be no present; if it’s a series of infinitely small, discrete moments, then it can only ever be present and unchanging. Space could be similarly described. At least with regard to time, I’ve long wondered whether we experience being rather than time. If, for example, I never changed and the world around me never changed (at least not at a level perceptible to humans), then I probably wouldn’t understand the idea of time because it is through change that we know time passes. However, that would mean a completely inert existence.
Similarly, how I, as a changing creature, would perceive time would probably depend on my lifespan. A gnat might live a full and happy life in a time span that’d seem all too brief to me. To the gnat, my lifespan would seem marvellously long.
Human perception is always behind the curve because by the time I register Now, it’s always Then. Everything I can see is in the past, but my brain is too slow for this to affect my perception of the world. It’s only at extraterrestrial distances that looking into the past makes any serious difference because a star which is 60,000 light years away is not the star which is actually contemporary with me. It might’ve exploded ten minutes ago, but we’re not going to know that for another 60,000 years.
The same might be true of space for similar reasons. By the time I know I’m Here, I’m actually There, not necessarily because time/being has passed because, although I don’t notice it, I’m always moving. The Earth rotates on its axis; it orbits the sun; the sun orbits the galaxy and the galaxy is flying around in space.
Anyway, I think we’re insulated from the problem because of our perceptions and our Newtonian niche in the universe. If we were quantum-level creatures, things might be very different. I suspect that Zeno’s space-time paradoxes, interesting little brain-teasers though they are, are like Achilles and the tortoise – born out by the maths, but not by reality.
Zeno, according to the book, considered the problem of continuity vs. discretion in matters of time and space. If time is continuous, there can be no present; if it’s a series of infinitely small, discrete moments, then it can only ever be present and unchanging. Space could be similarly described. At least with regard to time, I’ve long wondered whether we experience being rather than time. If, for example, I never changed and the world around me never changed (at least not at a level perceptible to humans), then I probably wouldn’t understand the idea of time because it is through change that we know time passes. However, that would mean a completely inert existence.
Similarly, how I, as a changing creature, would perceive time would probably depend on my lifespan. A gnat might live a full and happy life in a time span that’d seem all too brief to me. To the gnat, my lifespan would seem marvellously long.
Human perception is always behind the curve because by the time I register Now, it’s always Then. Everything I can see is in the past, but my brain is too slow for this to affect my perception of the world. It’s only at extraterrestrial distances that looking into the past makes any serious difference because a star which is 60,000 light years away is not the star which is actually contemporary with me. It might’ve exploded ten minutes ago, but we’re not going to know that for another 60,000 years.
The same might be true of space for similar reasons. By the time I know I’m Here, I’m actually There, not necessarily because time/being has passed because, although I don’t notice it, I’m always moving. The Earth rotates on its axis; it orbits the sun; the sun orbits the galaxy and the galaxy is flying around in space.
Anyway, I think we’re insulated from the problem because of our perceptions and our Newtonian niche in the universe. If we were quantum-level creatures, things might be very different. I suspect that Zeno’s space-time paradoxes, interesting little brain-teasers though they are, are like Achilles and the tortoise – born out by the maths, but not by reality.
Tomorrow, the infinite containers paradox (a name which I just invented).
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