I'm surprised they think spacetime granularity might be that large. I haven't tried to make any models myself--just a kind of back of the envelope generic thing that had too many problems. The Mach's principle they mention is a very interesting thought experiment--what effect does the large scale of the universe have on us? I hope they can make some progress on these questions; so far no breakthroughs.
They cite Aristotle as the origin point for his opponent's view, but Hogan’s instinct here is actually quite as old. He's arguing the atomist position, which comes up when you try to get a handle on the problems of how motion is possible in a continuum. This is Zeno stuff: if space is really infinitely divisible, then how can you traverse any distance given that you must first traverse an infinite series of divisions of that distance? It is impossible to get through an infinite sequence, so...
The atomist's position falls out of that naturally enough: well, what if there's not a continuum, but a structure made up of smallest-possible units? Then we just do them one at a time, and it's not an infinite number.
Aristotle's answer to Zeno wasn't that different, actually: he ends up arguing that there are no actual infinities, just potential ones. So, yes, theoretically (or even just conceptually) one could make all those divisions -- but they aren't actually made, so you don't have to traverse an infinite series.
The same thing came up years later when the Neoplatonists were trying to get a handle on the nature of time. It seems that time is also infinitely divisible, and it's most obvious unit -- now -- seems to be infinitely small. So one of the Neoplatonists -- Proclus, I think -- came up with the idea of 'time atoms' just as the earlier ancient Greek physicists had come up with the idea of atoms for space. It's a natural enough thing to think of, but that doesn't mean it's true.
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I'm surprised they think spacetime granularity might be that large. I haven't tried to make any models myself--just a kind of back of the envelope generic thing that had too many problems. The Mach's principle they mention is a very interesting thought experiment--what effect does the large scale of the universe have on us? I hope they can make some progress on these questions; so far no breakthroughs.
They cite Aristotle as the origin point for his opponent's view, but Hogan’s instinct here is actually quite as old. He's arguing the atomist position, which comes up when you try to get a handle on the problems of how motion is possible in a continuum. This is Zeno stuff: if space is really infinitely divisible, then how can you traverse any distance given that you must first traverse an infinite series of divisions of that distance? It is impossible to get through an infinite sequence, so...
The atomist's position falls out of that naturally enough: well, what if there's not a continuum, but a structure made up of smallest-possible units? Then we just do them one at a time, and it's not an infinite number.
Aristotle's answer to Zeno wasn't that different, actually: he ends up arguing that there are no actual infinities, just potential ones. So, yes, theoretically (or even just conceptually) one could make all those divisions -- but they aren't actually made, so you don't have to traverse an infinite series.
The same thing came up years later when the Neoplatonists were trying to get a handle on the nature of time. It seems that time is also infinitely divisible, and it's most obvious unit -- now -- seems to be infinitely small. So one of the Neoplatonists -- Proclus, I think -- came up with the idea of 'time atoms' just as the earlier ancient Greek physicists had come up with the idea of atoms for space. It's a natural enough thing to think of, but that doesn't mean it's true.
I thought the Left has often repeated "that the science was settled".
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