I honestly never expected such a response when I opened this thread.
What I will say is this: There are some very clever and intelligent people on this board and I thank all of you for your responses.
And with that I’ll bow out.
::phew::
What happens when an irresistable force meets and immoveable object?
Simple.
The irresistable force continues on its way without being modified in any way.
The immoveable object is not moved in any way.
Actually, I’d say I’ve got four scenarios: the two with just the balls, and the two with the balls and me trying to stop them. However, that was not the point of my little exercise, merely to show that under your definition, there is no difference between the two ball-only situations, while I argue there must be, since the balls themselves don’t change because of my addition to the scenario, yet the outcome is different.
It’s irrelevant that the balls themselves don’t change–immovability is a property that depends on the existence or not of things that can move the object. That is, it’s a property of the scenario as a whole, not the object on its own. So when you change the situation, there’s no reason to expect that property to remain the same.
See, I’d say that unstoppability* has to be a property of an object, otherwise we run into ambiguities, as is illustrated by my example; think of it this way, we have the two balls, A and B, moving through space like nobody’s business, unstoppable according to your definition, making for a symmetric situation. Then, we symmetrically apply a force to both balls, and notice something curious: ball A is accelerated, ball B is not. Obviously, this means there is a difference between the two objects, independently of the scenario, i.e. the situation is asymmetric now, and hence cannot have been symmetric in the first place, since everything we’ve done to it was perfectly symmetric by definition. Thus, the unstoppability of ball A isn’t equivalent to the unstoppability of ball B, and, since only one of them has shown to preserve the property of being unstoppable, I think you can make a very good case that it was the only one being unstoppable in the first place.
*Are we, by the way, agreed that unstoppability/immovability in this particular context is merely a matter of the choice of reference frame?
I’d use a definition of unstoppability like this: any object that could not ever be stopped by any possible object is unstoppable. The definition that you seem to be using is: any object that has not been stopped before now is unstoppable. I prefer my definition because it is universal, while what I’m understanding of yours is that it is temporally dependent.
If you use my definition, can you see why changing the situation will affect the conclusion? I can’t decide if an object is unstoppable without knowing all the possible objects (or lack of) that could stop it.
To lay out the logic in simple form:
Definition of unstoppable: an object that could not ever be stopped by any possible object is unstoppable.
Definition of immovable: an object that could not ever be moved by any possible object is immovable.
Premise 1: There exists a ping pong paddle.
Premise 2: There exists a bowling pin that cannot be moved by the paddle.
Premise 3: These exists a bowling bowl continually orbiting the pin that cannot be stopped by the paddle.
Conclusion 1: The pin is immovable because neither the paddle or the ball can move it.
Conclusion 2: The ball is unstoppable because neither or the pin can stop it.
Conclusion 3: An unstoppable object and immovable object coexist.
There, we have a logically consistent example of an UF and IO coexisting. Yes, it is a simple universe (with only three objects), but that’s enough to show that it’s not logically impossible to have both an UF and IO.
~ ~ ~ ~ ~
I’m completely ignoring real-world relativity. It doesn’t matter for the discussion of whether it’s logically impossible for an UF and IO to coexist. We only need to consider logically consistent scenarios.
I disagree - the “able” in the words “immovable” and “unstoppable” demonstrate that it’s not a question of what is happening; it’s a question of what could happen in any theoretically possible scenario. If an object is able to be stopped, if I happened to take any object or objects that exist and stick it in the way, then it is not unstopable.
You are essentially adding qualifiers to the definition and then trying to fold them into the definition - you’re saying that an object is unstoppable [added qualifier]if all the things that can stop it happen to stay out of the way[/added qualifier]. This is like saying that any food that isn’t in the end eaten is, and always was, inedible. Nonsense - this simply isn’t what the word means. Just as a car that is never driven is not undriveable, a rock that is never carved is not uncarveable, and an object that is never moved is not, by virtue of the lack of interaction, unmoveable.
Yes, but what would happen if an irresistable force acts upon an immovable object. (Admittedly, this is not precisely the quesiton asked in the OP, but I think is in the same spirit.)
Here, by “immovable object” I mean “An object of infinite mass, initially at rest (in some inertial frame).” By an irresistable force, I suppose I mean “a force that will produce a nonzero acceleration in an object of any mass.” I guess it follows that the force is infinite.
The tongue in cheek answer I gave upthread aside, my first inclination is to agree with those who say that this is a logical contradiction. That is, that these two things cannot both be said to exist.
But if we interpret “infinite” to mean “in the limit where some quantity goes to infinity” (which is essentially what it always means), then there are many possible answers.
Suppose that the mass of our object is m, and that the force is defined in terms of m, say as F = m a[sub]0[/sub] for some acceleration a[sub]0[/sub]
In the limit as m goes to infinity, the object can reasonably be said to be immovable (since its mass is infinite), and the force can reasonably be said to be irresistable (since its magnitude is infinite). And yet, the force produces a finite acceleration in the object, namely a[sub]0[/sub].
However, it is possible to choose other definitions of F in terms of m such that in the limit where F -> infinity and m -> infinity, it is possible to have F/m -> 0 or F/m -> infinity.
In general, the answer is indeterminate, as the acceleration is infinity/infinity (and thus depends on precisely how the numerator and denominator approach infinity in this limit.)
The way I read your definition is: any object that has never been stopped and will never be stopped is unstoppable. In contrast, my definition would be: any object that can never be stopped is unstoppable. It’s precisely the difference between the two balls: the condition of unstoppability for ball B is a stronger one than for ball A, since even if ball A was never stopped and will never be stopped, it can be stopped; ball B can not.
Every force produces a nonzero acceleration in an object of any mass, unless I’m drunk out of my mind. 
No, I’m saying it’s unstoppable if there are no things that could stop it. It doesn’t matter if a thing that could stop it actually does; merely it’s existence is enough to keep an object from being unstoppable.
In my scenario, the bowling ball is unstoppable, because nothing is capable of stopping it. There’s no “happen to stay out of the way”–the capabilities of the objects are described by the premises. The pin is immovable, so can’t get in the way, and the paddle can get in the way, but isn’t able to stop it.
And it’s a similar argument for the bowling pin. The paddle can try to move it, but isn’t capable of doing it. And the ball cannot attempt to move the pin, because it’s constrained to orbit it. So, the pin is immovable.
Then I did not clearly describe my definition. Please assume I’m using the one I state in my quote here.
Could the pin stop the ball if they ever should come into contact?
If this question is unanswerable by virtue of the two never coming into contact, it seems to me that your definition of unstoppable is indistinguishable from ‘any object that has never been stopped and will never be stopped’.
So, the only reason the pin is unmoveable is because the bowling ball happens to be in an orbit that doesn’t hit it. And the only reason the bowling ball is unstoppable is because the pin happens to be in the center of the orbit it happens to be in, and thus happens to be staying out of its way. That’s what you’re saying, right?
If there was anything about the ball and pin that was fundamentally preventing them from having been able to exist in a configuration that allowed an eventual collision (like an ‘unbendable’ rod between them, maintaining a distance), then you might have a point. But there’s not - you’re just saying that because nothing’s going to hit the pin, it’s “immovable” - but if that bowling ball did hit it, by golly, it sure wouldn’t be!
To me, that’s not what the word means. The words you are searching for are “unmoved” and “unstopped”.
It seems like our disagreements come down to what “could” means. “Could” implies a potential to do something. In my scenario, there is no potential for the pin and ball to interact. There is no potential because that’s the way the situation is constructed–that’s fundamentally preventing their interaction. That the pin/ball is immovable/unstoppable is demonstrated with the paddle.
Please, reread the logic laid out in Post 106. Given the definitions and the premises, do you disagree with the conclusions?
You’re right, I meant to say something like:
There exists a particular acceleration A, such that for all masses m, the acceleration of a body of mass m due to the force F is greater than or equal to A.
But like I said I think this really just amounts to saying F is infinite.
Your use of the definitions is bad - the definitions say “could not”, and your conclusions say “can not”. I don’t consider those to be equivalent terms - one implies a complete lack of other conditions, and the other is “because nothing is happening to get in its way”.
(And also the logic is bad - you omit the premise “continually orbiting the pin -> can not ever be stopped by the pin”. That may be understood - but since the shape the pin and the radius and shape of the orbit aren’t established, you haven’t established that it’s not going to whack into the protruding neck of the pin someday. This may be a minor point, but it still renders your argument as written fallacious, beyond the can/could.)
So no, your logic is bad on two counts. Three, if you count the two misapplications of the can/could definition separately.
The conclusions just flat-out don’t follow from your premises; it is merely established that neither the paddle nor the ball will move the pin, but not that they can’t. Take that same pin, and that same bowling ball, and put them on a collision course; you’d either have to argue that they aren’t in fact the same objects, or that something logically consistent will happen when they collide.
Putting it another way: in my scenario involving balls A and B, there clearly is a difference such that one can be accelerated by an outer force while the other can’t. Is that difference present when no force is acting on either? If not, where does it come from? If there is a difference, does the term ‘unstoppable’ really have the same meaning for both balls?
If you throw a bowling ball out into infinitely empty space, it will merely be unstopped, not unstoppable.
But… but… in this case, the question itself (immovable object v. unstoppable object) is even more nonsensical, isn’t it? “Never the twain shall meet”.
- In begbert’s scenario (regardless of other rules) the two supposed objects are able to meet each other. Thus, one of them will be proven wrong (or, in other words, one of the will actually live up to its name, the other one won’t)
- In your scenario the two objects can never meet. And thus the question has no meaning.
Yes, I meant to agree with your reasoning that the definitions of unstoppable or immovable are rendered meaningless by imposing a non-interacting condition; did I misunderstand your post?