12
votes
Is there a distance so small it can't be further divided?
Is there a distance so small it can’t be further divided?
The modern solution to this problem is the use of infinitesimals, as used by Leibniz and Newton in their development of the calculus. ...
- 6,110
12
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Is there a distance so small it can't be further divided?
The time it takes for the arrow to reach one half of the distance, is one half of the time.
So the total length traveled by the arrow is one half the distance, plus one half of one half, plus one half ...
- 573
4
votes
Is there a distance so small it can't be further divided?
I do not wish to leave this post in original format as comments have made clear that my assumption was not totally accurate, see below.
In physics the shortest possibly lenght is called the Planck ...
- 251
4
votes
Is there a distance so small it can't be further divided?
There does not have to be some distance so small that it can't be divided in half, to solve the paradox.
The infinitesimals referred to by Mark Andrews become the differentials in calculus as first ...
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2
votes
Is there a distance so small it can't be further divided?
"Is there a distance so small it can't be further divided?" I searched through the existing answers and discovered that neither "atomism" nor "Democritus" are mentioned. ...
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2
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Is there a distance so small it can't be further divided?
I think there are two questions here: Zeno's Paradox, and the smallest indivisible unit of length.
Smallest Unit of Length
If you want an answer from physics, rather than philosophy, you're talking ...
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2
votes
Is there a distance so small it can't be further divided?
As far as natural numbers go, when they are represented as distances, they all admit of being broken in half. Zero is the sort-of-exception, except that 0/2 is determinately evaluable (unlike division ...
- 12.2k
2
votes
Is there a distance so small it can't be further divided?
ε
Epsilon is the smallest value that can be added to a number such that n+ε>n. In practice I have mostly seen it used in computer modeling to solve the case that when you have material that is 1 ...
- 121
2
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Why is Diogenes the Cynic's solution to Zeno's Dichotomy Paradox insufficient?
My two cents.
Diogenes solution was a practical démonstration that refuted Zeno's claim. Diogenes demonstrated in practice that Zeno's theoretical construction is not a correct description of this ...
- 2,143
1
vote
Is special relativity immune to the paradox of Achilles?
Yes, there are n things wrong with your argument, where I estimate n to have an upper bound of around 10. Here are some of them...
None of the versions of Zeno's paradox about Achilles that I have ...
- 12.8k
1
vote
Experiencing and sensing time dilation when a person dies and the logic of
It seems that our experience of the passage of time in the absence of any visual cues is linked to the rate at which certain periodic processes take place in the brain. Crudely, if you wanted to make ...
- 12.8k
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