Author Topic: Creating An Up-To-Date List of Pun-Pun's Best Abilities and (Nigh-)Infinities  (Read 123797 times)

Offline Amechra

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Re: Creating An Up-To-Date List of Pun-Pun's Best Abilities and (Nigh-)Infinities
« Reply #180 on: December 07, 2012, 03:14:27 AM »
Allow me to repeat my earlier post:

By the way, due to Psycarnum Infusion Infinite Essentia through Soul Boon, Pun-Pun has infinite reach.

He also has an infinite% miss chance.
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Offline awaken_D_M_golem

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Re: Creating An Up-To-Date List of Pun-Pun's Best Abilities and (Nigh-)Infinities
« Reply #181 on: December 07, 2012, 04:17:35 PM »
So Pun-pun can create an intelligent magic item that has his abilities using Nybor's Psychic Imprint. However, I can't seem to find anyway to link intelligent item abilities scores with price so this may not help much. If anyone can find anything, please tell me.

On an unrelated note, I have managed to achieve an infinite number of non-gimped bodies, based off an extension of the Body Outside Body trick (see the spoiler below the listing in the OP for more details).

hmm ... Pun targets his Super-BOB and gets an item with: 
"(gaining the personality, Intelligence, Wisdom, Charisma, alignment, general memories, and languages known of the target creature) "
Your codpiece is a mimic.

Offline Halinn

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Re: Creating An Up-To-Date List of Pun-Pun's Best Abilities and (Nigh-)Infinities
« Reply #182 on: December 07, 2012, 07:58:00 PM »
Will experience gained by a BOB clone go to main Pun-Pun? If so, just have each of the infinite clones give a magic item (xp cost above zero) to one of your followers. Infinite xp spread out over infinite encounters.

Offline Quillwraith

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Re: Creating An Up-To-Date List of Pun-Pun's Best Abilities and (Nigh-)Infinities
« Reply #183 on: December 07, 2012, 08:43:09 PM »
Aleph(1) = 2^aleph(0) ?


[badly explained ideas]
get a two wide, aleph(0) long line of BOB clones with Jovoc auras. Stand at one end of the line, have the pair of clones at the other end hit each other.
In a finite line, the pair at the begging of it would each damage the next pair, so those take double the original damage. The 3rd pair take twice that, and so on. At the end of an infinitely long line of these, the damage will have been doubled aleph(0) times, for  result of Aleph(1).
Technically, an infinite line can't have 2 ends, so each pair has to hit each other, rather than only the first.
Use the omnicificer trick to turn the Aleph(1) damage into other stats.
[/badly explained ideas]

I/we better clarify this later. Just thinking aloud.

Offline Halinn

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Re: Creating An Up-To-Date List of Pun-Pun's Best Abilities and (Nigh-)Infinities
« Reply #184 on: December 07, 2012, 09:54:45 PM »
Sidethought from Quillwraith's idea: assuming that Pun-Pun didn't use one of his many ways to not die from damage, would Aleph(1) damage kill her through her Aleph(0) hit points?

Also, for the infinite spell resistance listed on first post, a simpler method is the spell.

Would it be worth listing her +infinity weapon and armor?

Offline Bauglir

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Re: Creating An Up-To-Date List of Pun-Pun's Best Abilities and (Nigh-)Infinities
« Reply #185 on: December 08, 2012, 01:06:22 AM »
The latter two do require RoS. I still maintain that strict RAW prevents that from helping, but that varies from everyone else's mileage.

Offline Quillwraith

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Re: Creating An Up-To-Date List of Pun-Pun's Best Abilities and (Nigh-)Infinities
« Reply #186 on: December 08, 2012, 10:24:03 AM »
Sidethought from Quillwraith's idea: assuming that Pun-Pun didn't use one of his many ways to not die from damage, would Aleph(1) damage kill her through her Aleph(0) hit points?
It should. Aleph(1) > Aleph(0).

Offline Scottzar

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Re: Creating An Up-To-Date List of Pun-Pun's Best Abilities and (Nigh-)Infinities
« Reply #187 on: December 08, 2012, 07:04:07 PM »
get a two wide, aleph(0) long line of BOB clones with Jovoc auras. Stand at one end of the line, have the pair of clones at the other end hit each other.
In a finite line, the pair at the begging of it would each damage the next pair, so those take double the original damage. The 3rd pair take twice that, and so on. At the end of an infinitely long line of these, the damage will have been doubled aleph(0) times, for  result of Aleph(1).
Technically, an infinite line can't have 2 ends, so each pair has to hit each other, rather than only the first.
Use the omnicificer trick to turn the Aleph(1) damage into other stats.

Assuming this works, this gives us any aleph we want because Aleph (2) = 2^Aleph (1), etc. etc.
We actually couldn't restrict it to Aleph (1) because at each point in the line, it is sent backwards, which includes the 'end' where it is Aleph (1) already. Due to this, and the fact that the Jovoc aura's trigger instantly, this should give us Aleph (NI).
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Offline Halinn

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Re: Creating An Up-To-Date List of Pun-Pun's Best Abilities and (Nigh-)Infinities
« Reply #188 on: December 08, 2012, 08:43:31 PM »
We actually couldn't restrict it to Aleph (1) because at each point in the line, it is sent backwards, which includes the 'end' where it is Aleph (1) already. Due to this, and the fact that the Jovoc aura's trigger instantly, this should give us Aleph (NI).
I'm not knowledgeable enough about mathematics to know if we'd actually stack up like that, but assuming it's true, wouldn't we get Aleph(Aleph(0))?

Offline Bauglir

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Re: Creating An Up-To-Date List of Pun-Pun's Best Abilities and (Nigh-)Infinities
« Reply #189 on: December 09, 2012, 01:11:03 AM »
get a two wide, aleph(0) long line of BOB clones with Jovoc auras. Stand at one end of the line, have the pair of clones at the other end hit each other.
In a finite line, the pair at the begging of it would each damage the next pair, so those take double the original damage. The 3rd pair take twice that, and so on. At the end of an infinitely long line of these, the damage will have been doubled aleph(0) times, for  result of Aleph(1).
Technically, an infinite line can't have 2 ends, so each pair has to hit each other, rather than only the first.
Use the omnicificer trick to turn the Aleph(1) damage into other stats.

Assuming this works, this gives us any aleph we want because Aleph (2) = 2^Aleph (1), etc. etc.
Hmm... Existing planes only contain, at best, infinite volume. This could pose problems for arranging our clones if we wanted to chain upward through separate iterations this way, since we have to create our own planes and to do that with Genesis requires getting the casting time down far enough that you can cast a number of them per turn equal to 1 power of Aleph less than what you're trying to get your damage output to be equal to. Fortunately that works out to be exactly the power of Aleph you're starting with, but you need a way to convert that directly into actions. If, and this is a big if, the Celerity Engine works, you still only get up to Aleph(0) with it, and there's no way I know of to hook them back into themselves since traps don't use actions (to my knowledge), and I'm not sure there's a way to make a Von Neumann Trap.

We actually couldn't restrict it to Aleph (1) because at each point in the line, it is sent backwards, which includes the 'end' where it is Aleph (1) already. Due to this, and the fact that the Jovoc aura's trigger instantly, this should give us Aleph (NI).
However, if this is true, then what I just said only applies to jumping from one... power of powers(?) of aleph to the next. There's a term for this, I just cannot for the life of me remember it. Still, somebody smarter than me will be along shortly, I'm sure.

Offline Scottzar

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Re: Creating An Up-To-Date List of Pun-Pun's Best Abilities and (Nigh-)Infinities
« Reply #190 on: December 10, 2012, 01:34:13 AM »
We actually couldn't restrict it to Aleph (1) because at each point in the line, it is sent backwards, which includes the 'end' where it is Aleph (1) already. Due to this, and the fact that the Jovoc aura's trigger instantly, this should give us Aleph (NI).
I'm not knowledgeable enough about mathematics to know if we'd actually stack up like that, but assuming it's true, wouldn't we get Aleph(Aleph(0))?
I don't know enough about this maths to be sure, but doesn't the fact that each process is triggered mean that it can't reach truly infinite? If you have a magic computer repeat an action with no delay, but only 1 at a time, it can only have triggered a defined (but unknowable) number of times. E.G. the number move actions for meta-magic-less Greater Celerity via Alter Reality looping would be NI.



Let's look a the Omnicifier's original damage trick, than go from there. I think circular looping may be the key to this.
A thought occurs: incorporeal creatures can share each others space. Even if they can't, we can use living wall's amalgam to do it, probably.

Thus, Aleph (0) clones in one space. If each performs the clone spawning routine, we have Aleph (0) ^ 2 clones.
This repeats to Aleph (0) ^3 clones.
Via repetition, we thus have Aleph (0) ^ (Number of repetitions we can have) clones. Via input of damage and use of aura's, we can convert this to stats.

Aleph (0) ML temporal acceleration gives us Aleph (0) rounds to do this in, which means we can thus have (Current Aleph) ^ (Current Aleph) clones, and thus, via AOE damage, stats.
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Offline Bauglir

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Re: Creating An Up-To-Date List of Pun-Pun's Best Abilities and (Nigh-)Infinities
« Reply #191 on: December 10, 2012, 02:06:07 AM »
Hm, temporal acceleration is probably a much more efficient mechanism than Greater Celerity. Unfortunately, while I'm pretty sure we have to agree that infinite looping produces a true infinity (this is how the Omniscificer does it - through infinite looping of a finite amount of damage), progress at that rate doesn't jack us up to the next degree of Aleph, since (I think) we're only ever taking Aleph(whatever) to an arbitrarily high power, rather than an arbitrarily large base to the Aleph(whatever) power. Unless we can automate it, I think. Which I just now realized is a problem with hitting level infinity - we're going to need to automate entire adventures so they execute infinitely many times.

Offline Scottzar

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Re: Creating An Up-To-Date List of Pun-Pun's Best Abilities and (Nigh-)Infinities
« Reply #192 on: December 10, 2012, 05:35:31 AM »
Hm, temporal acceleration is probably a much more efficient mechanism than Greater Celerity. Unfortunately, while I'm pretty sure we have to agree that infinite looping produces a true infinity (this is how the Omniscificer does it - through infinite looping of a finite amount of damage), progress at that rate doesn't jack us up to the next degree of Aleph, since (I think) we're only ever taking Aleph(whatever) to an arbitrarily high power, rather than an arbitrarily large base to the Aleph(whatever) power. Unless we can automate it, I think. Which I just now realized is a problem with hitting level infinity - we're going to need to automate entire adventures so they execute infinitely many times.

I think you misunderstand. To reach Aleph (1), you need 2^ Aleph (0)
I am providing a clone output equal to (Initial Clone input) * (Number of clones produced per process) ^ (Number of duplications).
Since we can input at least 2 clones, if not Aleph (0), and we can always duplicate at least once in a round, due to arbitrary action numbers, and we have Aleph (0) rounds due to temporal acceleration, the process is:
Let X be > or = 2, and Y = Pun-Pun's current Aleph of caster level (e.g. Aleph (0)), Z = psuedo-round number,
Have X clones. Each of these clones uses temporal acceleration, and once every turn performs the process to produce Y un-gimped clones. Each Un-Gimped clone uses temporal acceleration and once every turn performs the process to produce Y un-gimped clones.

Thus, if we use > to represent a pseudo-round passing:
X clones > X * Y clones > X * Y^2 clones >>>>>> X * Y ^ Z clones, and since we have Y rounds, therefore Z = Y, thus:
X * (Y^Y), where Y equals our current aleph.

Aleph (0) ^ Aleph (0) = Aleph (1), I believe. And we can repeat this with our new Aleph. And with that new aleph, etc. etc.

Unrelated, but amazing:
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Offline Bauglir

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Re: Creating An Up-To-Date List of Pun-Pun's Best Abilities and (Nigh-)Infinities
« Reply #193 on: December 10, 2012, 12:08:36 PM »
Yeah, but the problem is that we actually have to construct and execute an infinite sequence of decisions when we say that we're doing something some number of times every round for Aleph(0) rounds. I might be completely misunderstanding it, but I think it's the same reason why you can't go from NI of something to Aleph(0) just by saying so. Remove the decision-making, though, and it's no longer arbitrary whether the cycle continues at a given iteration, and you can therefore actually take limits.

Can we figure out a way to automate the production of clones in a way that still fundamentally ties it to a current statistic? If I read it correctly, traps are fixed at Aleph(0) unless you can automate trap production.

Offline Scottzar

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Re: Creating An Up-To-Date List of Pun-Pun's Best Abilities and (Nigh-)Infinities
« Reply #194 on: December 10, 2012, 03:58:23 PM »
Yeah, but the problem is that we actually have to construct and execute an infinite sequence of decisions when we say that we're doing something some number of times every round for Aleph(0) rounds. I might be completely misunderstanding it, but I think it's the same reason why you can't go from NI of something to Aleph(0) just by saying so. Remove the decision-making, though, and it's no longer arbitrary whether the cycle continues at a given iteration, and you can therefore actually take limits.

Can we figure out a way to automate the production of clones in a way that still fundamentally ties it to a current statistic? If I read it correctly, traps are fixed at Aleph(0) unless you can automate trap production.

AFAIK, the reason why linear decision making can never reach an Aleph is that repeating a process a non-infinite times per iteration for a non-infinite amount of time can at most give uncountable, arbitrarily large values (given the delay = 0), as opposed to infinites. Actions are limited in that you must perform them one after the other.

The reason you can't go from NI to Aleph (0) on, say, the Imp of Cania is that:
If the imp of Cania went to a timeless plane, did it's trick for ever, and came back, it would only have performed the trick an uncountable number of times. You can't reach Aleph (0) by waiting through time, as you have always spent a countable number of turns there.

However, my Pun-Pun gets around this by having a known amount of time, namely Aleph (0). Assuming we perform each spawning loop at least once per round, which we can, we will thus have an iteration number equal to or greater than the number of rounds.
(Input) ^ 2 ^ (Iteration Number)


About your other points:
Tying clone production to a statistic kills the process. By tying clone production to each clone (because remember, when we split it doesn't keep magic items), 2 is to the power of the round variable.
By tying it to a statistic, it would stay at (Input) + (Clones per use) * (Rounds). This is not nearly high enough.

Your traps are not Aleph (0). They are only NI; you are dividing by zero, which doesn't reach true infinities.
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Offline Halinn

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Re: Creating An Up-To-Date List of Pun-Pun's Best Abilities and (Nigh-)Infinities
« Reply #195 on: December 10, 2012, 06:44:58 PM »
Thus, Aleph (0) clones in one space. If each performs the clone spawning routine, we have Aleph (0) ^ 2 clones.
This repeats to Aleph (0) ^3 clones.
Via repetition, we thus have Aleph (0) ^ (Number of repetitions we can have) clones. Via input of damage and use of aura's, we can convert this to stats.

Aleph (0) ML temporal acceleration gives us Aleph (0) rounds to do this in, which means we can thus have (Current Aleph) ^ (Current Aleph) clones, and thus, via AOE damage, stats.
Aleph(0)^n = Aleph(0). We need 2^Aleph(0) to reach Aleph(1).

Also, temporal acceleration can only give us NI rounds, since we have to choose an amount of times we augment it.

Which I just now realized is a problem with hitting level infinity - we're going to need to automate entire adventures so they execute infinitely many times.
Body Outside Body gives us an infinite amount of clones. Have each of those make a magic item with their divine ability and give it one of your followers that hasn't yet gotten an item. Aleph(0) separate encounters each giving some amount of experience through your magister template power.

Offline Scottzar

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Re: Creating An Up-To-Date List of Pun-Pun's Best Abilities and (Nigh-)Infinities
« Reply #196 on: December 11, 2012, 10:26:14 PM »
Thus, Aleph (0) clones in one space. If each performs the clone spawning routine, we have Aleph (0) ^ 2 clones.
This repeats to Aleph (0) ^3 clones.
Via repetition, we thus have Aleph (0) ^ (Number of repetitions we can have) clones. Via input of damage and use of aura's, we can convert this to stats.

Aleph (0) ML temporal acceleration gives us Aleph (0) rounds to do this in, which means we can thus have (Current Aleph) ^ (Current Aleph) clones, and thus, via AOE damage, stats.
Aleph(0)^n = Aleph(0). We need 2^Aleph(0) to reach Aleph(1).

Also, temporal acceleration can only give us NI rounds, since we have to choose an amount of times we augment it.

Augmenting is not something we have to do multiple times per use of a power. Augmenting is: I spend X extra power points, and the power says for every Y extra power points spent something extra is added on. In this case:
(X = Aleph (0))/(y=4)*(1 round) = Aleph (0) Extra Rounds.

Aleph (0) ^ Aleph (0) is, indeed, not = Aleph (0). It is equal to Aleph (1).
However, if that isn't simple enough for you, just use two starting clones. Then you have 2 ^ Aleph (0).
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Offline dman11235

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Re: Creating An Up-To-Date List of Pun-Pun's Best Abilities and (Nigh-)Infinities
« Reply #197 on: December 12, 2012, 01:42:07 PM »
First off, it would be x*y, not x/y, but the math ends up the same, being aleph(0)*(1round/4PP)=aleph(0).

But that's not the issue.  The issue is that in those aleph(0) rounds, each one is taken discreetly, which means you have an NI number of rounds taken, not I rounds taken.  If you could automate it, where the first round has the second happen simultaneously, and so on, then you would have taken aleph(0) rounds in the span of 1 round, rather than continuing indefinitely in the same round.  The issue we're having is that we can't seem to get an infinite loop to happen, and that's what's needed.
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Offline Halinn

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Re: Creating An Up-To-Date List of Pun-Pun's Best Abilities and (Nigh-)Infinities
« Reply #198 on: December 12, 2012, 02:27:13 PM »
Augmenting is not something we have to do multiple times per use of a power. Augmenting is: I spend X extra power points, and the power says for every Y extra power points spent something extra is added on. In this case:
(X = Aleph (0))/(y=4)*(1 round) = Aleph (0) Extra Rounds.
You can't choose to treat infinity as a number in saying that you choose to spend infinite power points on a power. In the same way, you can't claim that you have truly infinite swift actions from infinite turnings etc.

Offline Bauglir

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Re: Creating An Up-To-Date List of Pun-Pun's Best Abilities and (Nigh-)Infinities
« Reply #199 on: December 12, 2012, 03:13:28 PM »
Augmenting is not something we have to do multiple times per use of a power. Augmenting is: I spend X extra power points, and the power says for every Y extra power points spent something extra is added on. In this case:
(X = Aleph (0))/(y=4)*(1 round) = Aleph (0) Extra Rounds.
You can't choose to treat infinity as a number in saying that you choose to spend infinite power points on a power. In the same way, you can't claim that you have truly infinite swift actions from infinite turnings etc.
I think you can do the first because it's a single decision (you don't augment by 1 pp, then another, and so on, you just augment all at once and you can spend whatever you like, subject to the usual caps). The second can't be done because it requires an infinite number of separate decisions, and saying you're going to do it infinitely many times is just shorthand. At least as I understand it.