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. ...
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12
votes
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 ...
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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 ...
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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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3
votes
Philosophical question about space, time, space-time and the arrow of time
We don't know whether spacetime is continuous or discrete. You might suspect it is discrete, on the grounds that almost everything else seems to be. As you know, there are various efforts underway to ...
- 24.8k
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
votes
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
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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 ...
- 18.5k
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 ...
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1
vote
Final Steps and Zeno's Paradox
I think the simple answer is that the SEP article is wrong.
The argument seems to be:
The infinite sequence 100m, 150m, 175m, ... has no final term
The infinite sequence 100m, 150m, 175m, ... ...
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Final Steps and Zeno's Paradox
Your first question is:-
if the journey is from point A to point B, and the completion of the journey entails reaching point B by traveling point by point, how can one complete "every step" ...
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1
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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 ...
- 24.8k
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