The Unstoppable Force Paradox

[Vahnavoi]

i came up with the phasing solution too when I was around 13... and immediately realized it isn't an actual solution. It doesn't follow from anything, it just posits an additional axiom to make the problem go away. As stated upthread by Rydiro, this isn't a trick paradox, it's an actual logical contradiction, it doesn't have a logical answer. Quantum tunneling is just another non-sequitur, quantum mechanics do not posit nor deal with unstoppable forces or immovable objects, there is neither physically nor philosophically meaningful connection between this paradox and quantum tunneling.

[Quizatzhaderac]

Does anybody here know how to divide aleph numbers? If we can do that then we can calculate the acceleration.

No, nobody does. You can't really do arithmetic with transfinite numbers. In general, I'd recommend against trying to apply transfinite numbers to anything apart from the most surreal fiction (and definitely not anything real).

You can, however, use hyper real numbers. Application comes down to asking if the force is more or less unstoppable than the object is immovable.

This is basically how Pokemon handles having a bunch of moves the "always" go first or last. The move alters the pokemon's speed by +/- ω for the turn. Larger infinite number wins, finite numbers break a tie.

[georgie_leech]

No, nobody does. You can't really do arithmetic with transfinite numbers. In general, I'd recommend against trying to apply transfinite numbers to anything apart from the most surreal fiction (and definitely not anything real).

You can, however, use hyper real numbers. Application comes down to asking if the force is more or less unstoppable than the object is immovable.

This is basically how Pokemon handles having a bunch of moves the "always" go first or last. The move alters the pokemon's speed by +/- ω for the turn. Larger infinite number wins, finite numbers break a tie.

Eh, that's an extremely dramatic way of describing their Move Priority system which scales all the way from -7 to 5. It's a separate check, not adding ω to anything.

[Quizatzhaderac]

I'll grant is an extremely dramatic way to describe it, but apart from word choice, this exactly what's happening.

Both comparing hyperfinite numbers and determining pokemon move order are each one compound check composed of multiple simple integer checks. Not only is the outcome the same, but the exact steps to resolve them are the same.

[Vahnavoi]

Yup. Pokemon is a fairly complex game. Describing how the game works in a mathematically exact way will look rather "dramatic" to anyone not used to mathematical notation.

[georgie_leech]

I'll grant is an extremely dramatic way to describe it, but apart from word choice, this exactly what's happening.

Both comparing hyperfinite numbers and determining pokemon move order are each one compound check composed of multiple simple integer checks. Not only is the outcome the same, but the exact steps to resolve them are the same.

Yup. Pokemon is a fairly complex game. Describing how the game works in a mathematically exact way will look rather "dramatic" to anyone not used to mathematical notation.

"Moves in this set go first" doesn't mean the pokemon games are using ordinal notation/mathematics to calculate anything. Like, don't get me wrong, I know how deep the rabbit hole can go, but both needing you to compare multiple integers doesn't mean you add ω to anything, anymore than rolling a 20 in D&D means you need to break out countable infinity analysis to figure out what it can hit. You can if you really want, but...

[MrStabby]

Ok then. How about we treat the force as infinite and the object as having infinite intertial mass.

Does anybody here know how to divide aleph numbers? If we can do that then we can calculate the acceleration.

Is this really needed?

I have been out of this game for a while but I thought the basic high school approach of dealing with ratios of limits with Taylor Series and L'Hopital's rule would work here?

[Radar]

Is this really needed?

I have been out of this game for a while but I thought the basic high school approach of dealing with ratios of limits with Taylor Series and L'Hopital's rule would work here?

Those would require for us to have some function that grows to infinity for both the force and the object - this is what defines the outcome of taking the limit. As those functions are not given, a pure inffinity/infitnity is an undefined expression.

As was said before, in order to solve the paradox, we need to embed it in a different problems that adds more assumptions. As those assumptions are pretty arbitrary, the general problem of unstoppable force (however we define force without anything material exerting that force on something) vs immovable object is ill defined and does not have an answer at all.