Any character can use this trick to ascend to ultimate power, thus I will not specify anything about this character. (race, class, etc...)
Method of ascension:
This character uses one free action to perfor a simple thought experiment. He imagines two people in the Dungeons and Dragons universe, one of which has a Quiver of Anariel and the quick draw feat.
Quiver of Anariel:Quivers of Anariel appear to be typical arrow containers capable of holding a score of arrows. However, the quivers automatically replenish themselves with standard or magical arrows, such that they are always full.
n=1 Person 1 pulls two arrows out of the quiver as a free action 3 seconds into his turn. We will call theese "arrow 1" and "arrow 2" and hands them to person 2.
Person 2 takes theese two arrows, and gives arrow 1 to person 1.
n=2 Person 1 pulls out two more arrows 4.5 seconds into his turn. We will call theese "arrow 3" and "arrow 4" and hands them to person 2.
Person 2 takes theese two arrows, and gives arrow 2 to person 1.
This process continues at each time interval of 6-6/(2^n) seconds untill his turn is over (once 6 seconds pass). For clarity, person 1 gives person 2 arrows 2n-1 and 2n, person 2 then gives person 1 arrow n.
Hocus Ponens now realizes that since person 1 gave person 2 two arrows at each time interval, n, and person 2 gave one arrow to person 1, person 2 must have n/2 arrows. If n is infinite, then so is n/2, thus person 2 clearly has infinite arrows.
Furthermore, Hocus Ponens also realizes that for any arrow n, person 2 cannot have it, because he gave it to person 1 at time interval n (time 6-6/(2^n)). Thus, clearly person two has zero arrows.
Hocus Ponens then decides what he wants to do or to have done, we will call this action A.
He assumes he cannot make A happen.
If he cannot make A happen, then person 2 has infinite arrows. (this works through conditional introduction)
However, person 2 clearly has no arrows. (just restating something that was already established)
Therefore Hocus Ponens can make A happen. (using modus tollens) (the principle of explosion or contradiction elimination could have been used instead, however I liked modus tollens more)
This process can be done as a free action for any A, therefore Hocus Ponens ascends to ultimate power one free action into the game, clearly beating out Pun-Pun who requires multiple standard actions. Q.E.D.
This process can be done as a free action for any A, therefore Hocus Ponens ascends to ultimate power one free action into the game, clearly beating out Pun-Pun who requires multiple standard actions.
HUH?
And besides, this was a much better problem with balls and vaces.
Not Pun-Pun.
Hocus Ponens then decides what he wants to do or to have done, we will call this action A.
He assumes he cannot make A happen.
If he cannot make A happen, then person 2 has infinite arrows. (this works through conditional introduction)
However, person 2 clearly has no arrows. (just restating something that was already established)
Therefore Hocus Ponens can make A happen. (using modus tollens) (the principle of explosion or contradiction elimination could have been used instead, however I liked modus tollens more)
Move towards the following:
He assumes he can continue living.
If he continues living, then person 2 has infinite arrows.
However, person 2 clearly has no arrows.
Therefore, Hocus Ponens cannot continue living.
Edit: Ignore this edit: I didn't realize something that you had already accounted for.
Dennis was a menace.
Not Pun-Pun.
:D :D :D :D :D :D :D :D :D
This ... is just dumb. All you end up with is a lot of arrows, not ultimate power.
I think he's trying to set up an exercise in logical thinking here. If you noticed, he's simply imagining the person with the arrows.
Also, Hilbert, I think some people here might need explanation of some of the concepts involved.
Kudos for figuring out how to import that paradox into D&D. Of course, your DM is likely to belong to the "this thought experiment is poorly formulated, because it posits that A's turn ends and yet A's turn cannot end" school of thought :P
Logic, when not associated with ninjas, isn't a great argument to bring up here. But hey, you made my day more interesting, heheheh. Thank you.
Hocus Ponens then decides what he wants to do or to have done, we will call this action A.
He assumes he cannot make A happen.
If he cannot make A happen, then person 2 has infinite arrows. (this works through conditional introduction)
You haven't proved this. More below.
However, person 2 clearly has no arrows. (just restating something that was already established)
First off, there are multiple ways of resolving this problem, and that's only one solution. Second, assuming this is true, the previous conditional (if NOT A, then INFINITE ARROWS) is false. Suppose that A is "having/obtaining a Strength score of -10". This is clearly impossible, as ability scores in D&D cannot go below 0 by design. Thus Hocus Ponens cannot make A happen. But then we have a true statement leading to a false one; thus the conditional is false. And one counterexample to that conditional is all that's required to disprove it.
You haven't proved this. More below.
The way conditional proofs work is by first assuming some A, then showing that some B holds. From this you, it is proven that A implies B. Since I assume not A, then restate that person 2 has infinite arrows, I can form the conditional not A implies that person 2 has infinite arrows.
First off, there are multiple ways of resolving this problem, and that's only one solution.
Yes, there are multiple ways of solving this problem. That is why, in a universe in which this problem is allowed to exist, there is an inherent contradiction. From the principle of explosion, a contradiction can imply anything which is why Hocus Ponens can do or have done anything he wants, including "rule violations" (though he wouldn't be breaking the rules because he would be using the principle of explosion to show that what he is doing is legal.)
Second, assuming this is true, the previous conditional (if NOT A, then INFINITE ARROWS) is false. Suppose that A is "having/obtaining a Strength score of -10". This is clearly impossible, as ability scores in D&D cannot go below 0 by design. Thus Hocus Ponens cannot make A happen. But then we have a true statement leading to a false one; thus the conditional is false. And one counterexample to that conditional is all that's required to disprove it.
If NOT A, then INFINITE ARROWS hs to be true because it follows from the simple rules of first order logic. However, ZERO ARROWS is also true. This leads to the use of modus ponens ((~A-->B & ~B) ==> ~~A) and the use of double negation elimination (~~A ==> A) to prove that Hocus Ponens can do A, no matter what it may be, even having a strength score of -10.
This hapening would make the universe colapse and stand still at the same time, starting a loophole from wich the players can't get out.
Really, you kinda missed the point there.
Based on that, therefore, infinite is not logical. Since infinite is not logical, you cannot use logic against it.
Since computers (and me) only understand logic, pun-pun, due to being sub-infinite, exists. However, this arguement does not.
***
On another point, Pun-Pun can pretend he has arrows too. Pun-Pun wins.
I would ask my computer what would happen, but any infinite loops tends to crash its poor little logical mind.
Where's Multivac when you need it? :P Cookie for the reference, and with what group looks represented in this thread, I better start bakin'!
But seriously, never bring logic into DnD. Logic is not 3.5 compatible, never got an errata, and doesn't look like it's been incorporated into the 4.x world as of yet.
And then I read the Wikipedia post.
You, sir, lose two points for taking a perfectly simple logical exercise and brutally maiming it beyond all recognition.
You lose two more points because someone would have to have ranks in an appropriate Knowledge skill in order to know what a Quiver of Anariel is.
Also, I believe you might even lose two more points, because AFAIK taking an object someone hands to you is a move action.
P.S. This is an inherently flawed exercise because it attempts to define infinity in algebraic terms when, in fact, infinity is simply a theoretical possibility, not a number.
Where's Multivac when you need it? :P Cookie for the reference, and with what group looks represented in this thread, I better start bakin'!
The Last Question (actually multiple Asimov stories).
The Last Question (actually multiple Asimov stories).
:D ah GOD I love everything he wrote. That, y'know, I've read. Oooooh, interesting build has just popped into meh mind.....Weight Of The World is so godlike it isn't funny.
The way conditional proofs work is by first assuming some A, then showing that some B holds. From this you, it is proven that A implies B. Since I assume not A, then restate that person 2 has infinite arrows, I can form the conditional not A implies that person 2 has infinite arrows.
First off, this quote doesn't make sense in a few key places. Second, you still haven't proved that NOT A => infinite arrows holds so much as asserted it. I understand what a conditional proof is in that you prove A => B by assuming A and then proving B. Or pulling a proof by contrapositive by assuming NOT B and then proving NOT A. But you've done neither; you simply asserted the conditional and then immediately employing it. So Pun-Pun can be topped if your conditional is true...which it isn't.
Yes, there are multiple ways of solving this problem. That is why, in a universe in which this problem is allowed to exist, there is an inherent contradiction. From the principle of explosion, a contradiction can imply anything which is why Hocus Ponens can do or have done anything he wants, including "rule violations" (though he wouldn't be breaking the rules because he would be using the principle of explosion to show that what he is doing is legal.)
But that assumes that contradictions are valid for proof in the first place. Which they aren't; otherwise you throw out the law of non-contradiction and thus proof by contradiction (aka reductio ad absurdum), considered to be a valid proof technique. Proof by contradiction is considered to work precisely because contradictions are invalid.
If NOT A, then INFINITE ARROWS hs to be true because it follows from the simple rules of first order logic. However, ZERO ARROWS is also true. This leads to the use of modus ponens ((~A-->B & ~B) ==> ~~A) and the use of double negation elimination (~~A ==> A) to prove that Hocus Ponens can do A, no matter what it may be, even having a strength score of -10.
Again, that initial conditional is not necessarily true; you're conjuring it out of thin air. You keep saying that it follows from other stuff; what is that other stuff? Besides, you still haven't addressed the contradiction I've given you that it is both possible and impossible for a particular A to occur when taking the above conditional as a premise. Care to address the apparent proof by contradiction that such conditional does not necessarily hold?
You have two cows. One of them has infinite arrows. Apparently this means something.
Actully, it appears you have a 50% chance of having infinite arrows, or none at all. Depending on who you talk to.
Still, Pun-Pun can pretend he has arrows too. This is why Pun-Pun is the ultimate blue mage. He learns to use and do anything and everything by loreing threads & books.
In any case, if we assume that some proposition B is true, then the statement A -> B will be true. Taking an example,
A: You get 50% or more on the exam.
B: You pass the exam.
A -> B: If you get 50% or more on the exam, you pass the exam.
Now... let's say you bribed the teacher, and can guarantee B is true. The statement A -> B is still true. If you get 50% or more on the exam, you will pass the exam. Note that the statement doesn't cover the fact that if you get less than 50%, you fail the exam. That would be covered by A <=> B.
So, if person 2 has infinite arrows, (which was a viable way of looking at the problem), then "p -> person 2 has infinite arrows" is true for all p.
Hocus Ponens ascends to ultimate power one free action into the game, clearly beating out Pun-Pun who requires multiple standard actions. Q.E.D.
Point 1: you can not take actions outside of your turn, even free ones. Exception: immediate actions.
Point 2: the number of free actions you can take per turn has a "reasonable limits" [SRD]. An unlimited amount of actions clearly doesn't fall within it.
No dice.
A: I am not a billionaire
B: Pigs grow wings naturally
A -> B
Since pigs do not grow natural wings, the statement is false, which means that A cannot be true because it would make B true. Therefore I must be a billionaire. However, since A and B are arbitrarily defined and don't have any actual link in the real world I am not a billionaire.
What you need is something more like this statement:
A: An airplane fell on my
B: I am dead
A -> B
Since this statement has grounding in the real world, it does do something useful. If I am alive (B is false) then an airplane could not have fallen on my head. If I am dead (B is true) then an airplane may or may not have fallen on my head.
In more math like terms, the problem is that for something useful to occur A -> B must be a true statement (that is, A must actually imply B).
This process continues at each time interval of 6-6/(2^n) seconds until his turn is over (once 6 seconds pass).
Nice choice of new name, BTW.
Anyway, I'm a little concerned about your setup. If we're looking at an infinite number of "free" actions happening closer and closer together in time as we asymptotically approach t=6 seconds, asking what the state of the system is at t=6 seems meaningless and ill-formed.
Furthermore, I'm worried that the two actors in the scenario would both catch fire as their arms started moving too quickly. In that case, neither would have any arrows, as they would have no arms to hold them.
edit: But yeah, from the information given, you can't actually derive any information about the state of the system at or beyond t=6.
edit2: Also, the problem you restate abuses the concept of infinity. This makes the baby Alvis cry.
edit3: You haven't shown where the rules state you can think out this entire scenario in the span of one free action, so setting aside the logical problems, you haven't even fit it into the D&D rules.
The audience gasps, and is held captivated.
The magician then pulls out some little red balls, and places them inside some plastic cups.
The audience, slightly confused, continues watching with rapt attention.
The magician mumbles something incomprehensible.
The audience assumes this is how the magic works, and continues watching.
The magician now tells us he both does and does not have infinite little red balls.
...
The Magician now bows with a flourish, and walks off the stage.
Problem is Free Actions take negligable time and not zero time. Negligable x infinity is still infinity since negligible is defined to be > 0.
An infinite sequence of positive reals can still sum to a finite value if you choose it properly. But considering that free actions all consume about 1/100th of a second at minimum, it is impossible to get an infinite series of them in a finite amount of time.
Oh, and I pretty much agree with Grei. We don't even need a variant on the ball-and-vase problem; that just hinders the argument more than it already is.
Can you explain what the goal of this exercise is, in three words or less?
Nothing is infinity.
Now give me a cookie, damnit.
Can you explain what the goal of this exercise is, in three words or less?
Another failed challenge
Pisses people off
Faulty logic trickery
Pun-Pun still stands
Suppose we have a magician. We'll call him Hocus Bogus. The magician tells us he's going to saw a woman in half.
The audience gasps, and is held captivated.
The magician then pulls out some little red balls, and places them inside some plastic cups.
The audience, slightly confused, continues watching with rapt attention.
The magician mumbles something incomprehensible.
The audience assumes this is how the magic works, and continues watching.
The magician now tells us he both does and does not have infinite little red balls.
...
The Magician now bows with a flourish, and walks off the stage.
The Aristocrats! :D
Can you explain what the goal of this exercise is, in three words or less?
Infinity's messed up.
Really messed up.
The Aristocrats! :D
^ win
Can you explain what the goal of this exercise is, in three words or less?
Principle of explosion.
I now realize that one cannot get infinite free actions in a turn, therefore the contradiction I was trying to exploit does not actually exist, however, if there is a way to get infinite actions in a turn, one can use this paradox, simply by knowing about it, and combine it with the principle of explosion to do anything. I'm off to search for a way to preserve my paradox.
However, if there is a way to get infinite actions in a turn, one can use this paradox, simply by knowing about it, and combine it with the principle of explosion to do anything. I'm off to search for a way to preserve my paradox.
Still doesn't work. See post #26. As soon as more than two people are involved, one of them has to take actions out-of-turn. There's strict limits on that.
Hocus Ponens then figures out that the answer to his question is most clearly not 42, so it is certainly not the question he is looking for.
seeing as how it is imposable to truly reach a infinite limit making this no longer viable?
Still doesn't work. See post #26. As soon as more than two people are involved, one of them has to take actions out-of-turn. There's strict limits on that.
Two people are not required for this paradox, as it was originally invented with one person and a vase. One person could simply make a pile of arrows instead of giving them to another person, then remove arrows from that pile.
Two people are not required for this paradox, as it was originally invented with one person and a vase. One person could simply make a pile of arrows instead of giving them to another person, then remove arrows from that pile.
Of course I'm aware of that. I was merely pointing out that your proposal had flaws beyond the one you acknowledged.
I can't remember where I read the first part, but I'm quite certain about the 1 round bit.
Still a darn fine Quiver though. I'd like one, maybe two, or perhaps a rucksack that spawns infinite Quivers of Anariel. Someone get on that. <_<
This character uses one free action to perfor a simple thought experiment.
In his mind.
Therefore Hocus Ponens can make A happen.
In his mind.
Hocus Ponens ascends to ultimate power
In his mind.
I can imagine anything I care to as well. I don't think I have ascended to ultimate power...
Anyway, read the Meditations on First Philosophy for more information (they're not particularly enjoyable though unless you like that sort of thing).
@Vaelan: ...you probably have. :le sigh:
However, I'd like to point out that since time is the same thing as distance, just along a different axis, this is Zeno's paradox dressed up in a different costume. Achilles and the tortoise are persons A and B and the distance they travel is the time it takes to change arrows. That was disproved long ago.
On a more concrete PoV, Planck time is the smallest measurable time interval, so a 'free action' (wich RaW require a very small amount of time) require at least (approx) 1*10^-36s
This doesn't have an effect on pun-pun.
However, I'd like to point out that since time is the same thing as distance, just along a different axis, this is Zeno's paradox dressed up in a different costume. Achilles and the tortoise are persons A and B and the distance they travel is the time it takes to change arrows. That was disproved long ago.
Except in Zeno's Paradox, the time and distance were both halved with each iteration. With the pile of arrows, the time is halved with each iteration, but the same number of arrows is extracted from the quiver.
I'm pretty sure Descartes would say that Hocus Ponens cannot even imagine infinite arrows because Hocus Ponens has only a finite amount of formal reality. In order to create anything, the creator of that thing must have more formal reality than the objective reality of the thing being made. Since the objective reality is the amount of reality contained in the idea of the thing, the objective reality of infinite arrows is infinite and thus exceeds the reality Hocus Ponens has. He has only finite reality because he is not perfect. This is because he has the concept of a thing greater than himself already by virtue of the concept of infinity (and knowing himself not to be that thing; I avoid Descartes' use of God because that can be debated).
Anyway, read the Meditations on First Philosophy for more information (they're not particularly enjoyable though unless you like that sort of thing).
@Vaelan: ...you probably have. :le sigh:
Descartes was a tool, and all his major proposals started with the assumption that they were true in the first place. He actually tries to use that principle (sufficient reason, wasn't it?) to prove itself at one point, which is even more absurd than the OP's assertion that a thought experiment causes you to ascend to ultimate power.
-_- I'm not here to discuss Descartes (I hated reading his Meditations - it was assigned reading for our Humanities Core course this past Fall). I was simply tossing it out there since everyone's pulling out theories that D&D has no rules for anyway.
We were so offtopic anyway... Just thought I'd throw it out there.
