You are suggesting a kind of Einstein-Bose condensate, where a collective of particles becomes one.
Not at all.
I’m just saying that you have an infinite sequence of spheres with the property X. You’re saying that because the sequence is infinite I can’t point to the last sphere and therefore can’t say anything about it. I’m saying that because all spheres in this sequence have the property X, it doesn’t matter that the sequence is infinite.
I’m just saying that you have an infinite sequence of spheres with the property X. You’re saying that because the sequence is infinite I can’t point to the last sphere and therefore can’t say anything about it. I’m saying that because all spheres in this sequence have the property X, it doesn’t matter that the sequence is infinite.
This isn’t true in general. Each natural number is finite, but the limit of the natural numbers is infinite. Just because each of the intermediate shapes has property doesn’t mean the limiting shape has property X. Notably, in this case each of the intermediate shapes has a non-zero amount of empty space, but the limiting shape has no empty space.
Oh, dear. So all the spheres are shadowed, meaning the ray cannot reach any of them, so it just passes through the cube without even noticing it was there. Fee-fi-fo-fum, I smell Zeno!
I didn’t specifically mean the paradoxes, I meant Zeno as the first guy who said “Let’s throw some infinities into a physical-world scenario and see how many amphoras of wine do we need until it starts to make sense...”
Oh, I see. I strongly suspect, that the abstract world of pure mathematics doesn’t handle infinities any better than the real world does. It’s a fundamentally broken. I mean the infinity is a fundamentally broken concept.
Well, I don’t even believe in mathematics outside the physical world. It’s just a game of particles in Zeno’s head. Or Cantor’s or any other human’s head. Okay, heads, papers, blackboards, computers etc. Mathematics lives inside of physics only.
This sounds familiar. Since every point between your nose and your computer monitor has the property X, that there exists another point between it and your computer monitor, no matter how many points you move your nose through, there’s always more points it must go through before reaching the computer monitor. This is why, no matter how you try, you can never touch your nose to a computer monitor.
It’s not a Zeno’s paradox. You CAN touch the screen, if there is no obstacle between.
But here it’s a different story. Every sphere is shadowed, has an obstacle between itself and the incoming ray.
The finite amount of obstacles where there is then the outer obstacle—and everything is fine. Ray bounces back of this outer/unshadowed reflective sphere.
Pretty much like the Yablo’s list. If there is the last member of the list, everything is just fine.
If there is the last member of the list, everything is just fine.
There is no last point between your nose and your monitor.
Let me pose a different problem, to demonstrate what I think is wrong with your argument.
You start with a reflective square slab that is half as thick as it is wide. You place another slab, which is half as thick as the first on top, then another half as thick as that. You continue doing this until your stack of slabs is as tall as it is wide. If you direct an ideal ray at this slab, along the symmetry axis of the stack, what does the ray do?
This situation is, once constructed, identical to the first ray described in your problem (the one that hits the face of the cube), but your argument would imply that the ray won’t reflect back, because whichever slab it would reflect from has another slab shadowing it.
You are suggesting a kind of Einstein-Bose condensate, where a collective of particles becomes one.
An interesting idea, but … I doubt it’s correct way of thinking about this.
Not at all.
I’m just saying that you have an infinite sequence of spheres with the property X. You’re saying that because the sequence is infinite I can’t point to the last sphere and therefore can’t say anything about it. I’m saying that because all spheres in this sequence have the property X, it doesn’t matter that the sequence is infinite.
This isn’t true in general. Each natural number is finite, but the limit of the natural numbers is infinite. Just because each of the intermediate shapes has property doesn’t mean the limiting shape has property X. Notably, in this case each of the intermediate shapes has a non-zero amount of empty space, but the limiting shape has no empty space.
That no ray can come to them from that direction, since it’s eclipsed by the smaller ball toward the corner?
If this is the property X, then all those spheres have it, yes!
Oh, dear. So all the spheres are shadowed, meaning the ray cannot reach any of them, so it just passes through the cube without even noticing it was there. Fee-fi-fo-fum, I smell Zeno!
So it’s looks like.
This does not follow at all.
You should rather smell Yablo.
I didn’t specifically mean the paradoxes, I meant Zeno as the first guy who said “Let’s throw some infinities into a physical-world scenario and see how many amphoras of wine do we need until it starts to make sense...”
Oh, I see. I strongly suspect, that the abstract world of pure mathematics doesn’t handle infinities any better than the real world does. It’s a fundamentally broken. I mean the infinity is a fundamentally broken concept.
Well, I don’t even believe in mathematics outside the physical world. It’s just a game of particles in Zeno’s head. Or Cantor’s or any other human’s head. Okay, heads, papers, blackboards, computers etc. Mathematics lives inside of physics only.
I don’t know about that. It’s a model. “All models are wrong, but some are useful”—George Box
On the other hand: “God created the integers and the rest is the work of man” :-/
This sounds familiar. Since every point between your nose and your computer monitor has the property X, that there exists another point between it and your computer monitor, no matter how many points you move your nose through, there’s always more points it must go through before reaching the computer monitor. This is why, no matter how you try, you can never touch your nose to a computer monitor.
It’s not a Zeno’s paradox. You CAN touch the screen, if there is no obstacle between.
But here it’s a different story. Every sphere is shadowed, has an obstacle between itself and the incoming ray.
The finite amount of obstacles where there is then the outer obstacle—and everything is fine. Ray bounces back of this outer/unshadowed reflective sphere.
Pretty much like the Yablo’s list. If there is the last member of the list, everything is just fine.
There is no last point between your nose and your monitor.
Let me pose a different problem, to demonstrate what I think is wrong with your argument.
You start with a reflective square slab that is half as thick as it is wide. You place another slab, which is half as thick as the first on top, then another half as thick as that. You continue doing this until your stack of slabs is as tall as it is wide. If you direct an ideal ray at this slab, along the symmetry axis of the stack, what does the ray do?
This situation is, once constructed, identical to the first ray described in your problem (the one that hits the face of the cube), but your argument would imply that the ray won’t reflect back, because whichever slab it would reflect from has another slab shadowing it.
Look! Need not to be the last point. Zeno is resolved by infinite sums, which can give us finite numbers.
Yablo isn’t resolved and this is related to Yablo, not to Zeno paradox.