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Notes -
So, what are you reading?
I'm still on McGilchrist's The Master and his Emissary. He posits that classical paradoxes like Achilles and the Tortoise are fundamentally left-hemisphere phenomena, which try to build up something from parts and run headlong into the problems of this way of thinking due to its rejection of interconnectedness and context.
Recently these kinds of thoughts seem recurring, that is, that there might be natural approaches to long-standing problems which make them simple, if only I could learn them. But it also seems like the touchy-feely approach which is often given as an alternative to bottom-up thinking needs much refining.
A Memory Called Empire by Arkady Martine
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I just finished reading Orwell's long essay "Inside the Whale" and I'm once again struck by how relevant his political writing still is. He was describing what we now refer to as "the God-shaped hole" in 1940.
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Achilles and the Tortoise isn’t a paradox due to building up something from parts. It’s a paradox due to doing it sloppily.
By analogy, there are various “proofs” that 0 = 1 that rely on bad math, but nobody would argue that the problem is with math. The problem is with people incorrectly using math.
For Achilles, the problem arises because, just as the distance covered gets cut in half, so does the time it takes to cover it.
If it takes you 1 second to cover 1 meter, 0.5 seconds to cover 0.5 meters, etc., the fact that this series never exceeds 2 says you can’t pass 2 meters in less than 2 seconds.
The "paradox" is that Achilles will never pass the tortoise, and "how far can Achilles get in 2 seconds" says nothing meaningful about this.
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