Wise advice.My thought is, don't sit on it. — Baden
So how it is possible this horn can have limited volume but endless surface area? — Jeremiah
So you are suggesting if it was filled with paint, you could use a finite amount of paint to paint an endless surface. — Jeremiah
It seems to me, that you'd run out of paint, and even if so that still does not resolve the paradox. As abstractly what you have is a cone with a converging volume and a diverging surface area. — Jeremiah
In what way is this in need of 'resolution'? You haven't stated a problem with this scenario.This one is a bit trickier and as far as I know it has not been resolved. — Jeremiah
Clearly the paint would not run out, as it hasn't in your example. It covers the entire surface, and doesn't even need to be spread out to do so, since it has finite thickness (all the way to the center line) at any point being painted.So you are suggesting if it was filled with paint, you could use a finite amount of paint to paint an endless surface.
It seems to me, that you'd run out of paint, and even if you could stretch the paint infinitely thinner, that still does not resolve the paradox. As abstractly what you have is a cone with a converging volume and a diverging surface area. — Jeremiah
In what way is this in need of 'resolution'? You haven't stated a problem with this scenario. Is there some law somewhere being broken, like infinite surfaces must enclose infinite space? There is obviously no such law, as demonstrated by this example. — noAxioms
It is only paradoxical if the same thing both converges and diverges. — noAxioms
Clearly the paint would not run out, as it hasn't in your example. It covers the entire surface, and doesn't even need to be spread out to do so, since it has finite thickness (all the way to the center line) at any point being painted. — noAxioms
Like I said. You are confusing abstract and physical properties that happen to have the same name. — tom
A paradox is usually of the form of "If A is true, then A can be shown to be false". Your original 25 25 50 60 thingy would have been paradoxical had the 60 entry read 0%. What you seem to be reaching for here is not a paradox, but rather a violation of the law of non-contradiction, that a thing cannot be both X and not-X at the same time in the same way. I don't see the violation due to the 'in the same way' part.The horn both converges and diverges, so it fits your personal take on what is needed for a paradox. — Jeremiah
that paints an infinite surface. 'goes on forever' is not what I said, and seems a sort of undefined wording.So you are suggesting a finite amount of paint that goes on forever.
No, the volume is finite. You said that. There is finite (convergent as you put it) volume of ice cream, which could be paint.So in your suggestion the volume of the paint both converges and diverges?
This assertion is exactly that: just an assertion, and a false one at that. There is no mathematical basis for this. The paradox apparently comes from your assumption of this nonexistent law.Any container or solid object that has an endless surface area, but a finite volume is paradoxical, abstractly or otherwise.
Volume is the amount of space it takes up, so if it has endless surface area it should have endless volume. — Jeremiah
Well this is not my paradox, I didn't invent it. It is a well known paradox, and widely recognized as such. Also the mathematical proof is posted in the OP. — Jeremiah
Fair enough. The relevant definition of paradox that pops up says this:So you don't think is a paradox, OK fine, I don't really care. — Jeremiah
The funny cone seems to fall under definition 'a' since it seems opposed to common sense to many people. So yes, it makes sense to 'resolve' such paradoxes by showing that the seeming contradiction is something that is actually the case. The mathematics (a computation of the area and volume) is linked in the OP, but not sure what part of that is a 'proof' of something.a : a statement that is seemingly contradictory or opposed to common sense and yet is perhaps true
b : a self-contradictory statement that at first seems true
c : an argument that apparently derives self-contradictory conclusions by valid deduction from acceptable premises — Webster
I never contested the mathematics, which simply shows that the object indeed has infinite area but finite volume. I can think of more trivial objects that are finite in one way but infinite in another, and your cone did not strike me as a connundrum. But I retract my assertion that it is not a paradox. The definition above speaks.Saying there is no mathematical basis for this just tells me you can't read the math, as it is posted right there for you to review.
Indeed, it is only a mathematical object. A real one could not be implemented, growing too thin to insert ice cream particles after a while.You can say, well it is not in the real world — Jeremiah
That is a feeling. The 18th century British invaders of Australia had a similar feeling when they first saw a platypus. When they found that the object in question was undeniably there in front of them, their 'should not exist' transformed to 'well, I am very surprised'.Such objects should not exist — Jeremiah
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