Have you read the letter? Among other bizarre things, it ends with "If you change your mind having to do with this most important summit, please do no...
So you're agreeing with me that movement is possible if it is discrete rather than continuous. The issue is where one argues for continuous movement, ...
It needs to be there regardless. Even if we considered the idea of instantaneous counting then it would still be impossible to count the rational numb...
It's not about time. It's about there not being a first position to move to. Even if you assume you could count at infinite speed (whatever that would...
Yes, if you're counting up the natural numbers then it can't be finished; if you're counting down the natural numbers (or up or down the rational numb...
So you're saying that because we can sum a geometric series then we can coherently talk about this program terminating (although again; what is the va...
There's also no smallest half-way point (by which I mean \frac{1}{2^n}m). You can't move to 0.5m before moving to 0.25m, just as you can't count to 0....
Can you specify the task of movement recursively? “Move to the first half-way point”? It’s a lot like counting the rational numbers between 0 and 1 in...
If you're not a utilitarian but, say, a deontologist, then you will pick the option that is right according to deontology but possibly wrong according...
Which is why it can't ever be finished. So the simple answer to Thomson's lamp and Zeus counting is that it is incoherent for a supertask to occur in ...
Counting up from 1 is a task but counting down to 1 isn't? Why is that? I don't know. It seems a truism that if one has completed a series of consecut...
He's right if utilitarianism is correct. That's not a contradiction. The rest of your points are more concerned with it being difficult to correctly a...
Maybe if you could be less ambiguous with what you mean by power? Are you in a position of authority, like a President? Because the problem with that ...
The same could be asked about the dreaming dens in Inception. I'd rather stay in the Matrix/the dream. I care more about fulfilling experiences than a...
It might be useful to consider a similar scenario. Zeus counts backwards to 1, getting slower as he counts. It took him 1 second to count from 2 to 1,...
He will get to any integer but at no point has he ever gotten to every integer. This is Thomson's lamp paradox, except the question in this case will ...
Loop quantum gravity is a theory of discrete space-time, and causal sets is a theory of discrete space-time. These are viable alternatives to quantum ...
This is ambiguous. By "laws of physics" are you referring to our models or the way things actually behave? If the latter then I would argue that, if Z...
Let's try this another way: P1. Zeno's paradox shows that either motion is not a supertask or supertasks are possible. P2. Thomson's lamp shows that s...
An object moving through an infinite number of half-way points in succession is like counting the rational numbers between 0 and 1. If the latter is i...
This is exactly what I said here. And given that completing a supertask is demonstrably impossible, it must be that motion isn't a supertask. But for ...
So is it possible to count the rational numbers between them? No. And for the same reason it's impossible for any object to pass through all the \frac...
You were talking about it being possible to finish counting (if "infinitely fast") a countably infinite set weren't you? The above was an example to s...
For the programmers, assume a computer that could run "infinitely fast" counts each integer and checks to see if it is even. What is the value of $sta...
Could you, though? Is there a way to prove it without begging the question, as this "solution" does, and taking as a premise that it takes n seconds t...
Not necessarily space but movement. I don't see a problem with continuous space but with movement occurring by "jumping" from one position to the next...
Then to make it simpler, imagine a machine moving from A to B, where B is 1 metre from A. At set intervals the machine records the distance in metres ...
Yes, rationals. That's the right term. Except to keep this analogous to movement the counting has to be in ascending order. We don't jump to the half-...
Here's the typical solution to Zeno's paradox: But now let's apply this reasoning to my example of counting the reals: It will take me some fixed time...
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