Post/Author/DateTime	Post
BillTheManiac 06-11-07, 03:20 PM	Pun-pun has Aleph Null actions per round. He can spend an action to increase his stats permanently. Therefore, Aleph Null stats. Therefore, Aleph 1 carrying capacity. If we can find some way to create an item that ways Aleph 1, Pun-Pun can lift it and throw it at himself, dealing Aleph 1 damage and bringing his stats up to Aleph 1 due to masochism. Is there some way to do this?
LordMongoose 06-11-07, 03:38 PM	Wouldn't an infinite plane would contain only Aleph-null mass? I can't figure out a way to find something that weighs more than a plane in D&D. Man, set theory makes my head hurt.
BillTheManiac 06-11-07, 09:08 PM	Wouldn't an infinite plane would contain only Aleph-null mass? I can't figure out a way to find something that weighs more than a plane in D&D. Man, set theory makes my head hurt. Nope, Aleph Null mass. You'd need something on the level of 1 pound per point. It would be a perfect singularity: The density would be Aleph one. You'd need a "create object" power not limited by weight, and a DM who lets you create infinite density materials. Probably impossible. But still, it means that, technically, one of Pun-Pun's stats is Aleph 1.
Djief 06-12-07, 12:42 AM	can't he just punch himself for said amount of damage? I mean he does have enough strengh to do so ;)
BillTheManiac 06-12-07, 04:30 PM	can't he just punch himself for said amount of damage? I mean he does have enough strengh to do so ;) Nope that's Aleph Null damage. AFAIK carrying capacity is the only stat-based exponent in D&D.
psly4mne 06-12-07, 05:15 PM	Stop. Before you try to talk about "different infinities" or anything of that sort, read this post. Then, if you understood that perfectly, remember that that is just the version for dummies and you are probably still underqualified to talk about it. The reality is actually a lot more complicated. To make a long story short, you have no idea what you are talking about. For example, ωω is a countable ordinal, and hence equinumerous with ω. For another example, it does not make sense to talk about ℵ0 ℵ1 as a mass, volume, or density. ℵα is a cardinal. I could go on, but you all seem to be so miserably, hopelessly wrong that it is not worth it.
Think0028 06-12-07, 10:17 PM	Stop. Before you try to talk about "different infinities" or anything of that sort, read this post. Then, if you understood that perfectly, remember that that is just the version for dummies and you are probably still underqualified to talk about it. The reality is actually a lot more complicated. To make a long story short, you have no idea what you are talking about. For example, ωω is a countable ordinal, and hence equinumerous with ω. For another example, it does not make sense to talk about ℵ0 ℵ1 as a mass, volume, or density. ℵα is a cardinal. I could go on, but you all seem to be so miserably, hopelessly wrong that it is not worth it. Heck, I know barely more than this and know that you're wrong. Simply knowing that x*ω = ω is enough to disprove this. Carrying capacity is just an y=ab^x function, roughly. You aren't generating ℵ1 that way.
psly4mne 06-13-07, 12:57 AM	Heck, I know barely more than this and know that you're wrong. Simply knowing that x*ω = ω is enough to disprove this. Carrying capacity is just an y=ab^x function, roughly. You aren't generating ℵ1 that way. However, 2^ℵ0 ≥ ℵ1. The actual value of 2^ℵ0 is independent of ZFC. The Continuum Hypothesis states that 2^ℵ0 = ℵ1. The Proper Forcing axiom implies that 2^ℵ0 = ℵ2. Also, it is not true that 2*ω=ω, although 2*ℵ0 = ℵ0. There is a big difference between cardinal and ordinal numbers. ω is an ordinal, while ℵα denotes a cardinal. Arithmetic is defined very differently on cardinals and ordinals. And it doesn't stop there; there are other number systems too - the extended reals and the surreals, to name two important ones. I did not come the this forum to teach people math, but when I see people pretending to know what they are talking about, I have to say something. If you actually want to learn anything, read a book. Complete Champion doesn't count. Until then, stop spouting this nonsense.
Tleilaxu_Ghola 06-13-07, 06:26 AM	Out of morbid curiosity, did you learn this stuff in a graduate level real analysis class or did you just acquire it via self-inquiry? I'm not in any way questioning your credibility, I'm just wondering what you think would be the best way of learning this stuff. I was half considering taking a graduate level Real Analysis course this next spring (after my graduate school applications are in :P ). IF I had to guess, this material would be in that class, but I'm not certain off the top of my head.
Djief 06-13-07, 11:52 AM	If you actually want to learn anything, read a book. Complete Champion doesn't count. :rofl: And after a crash course on Aleph (a whole big 10 minutes) I have to agree with psly4mne on that one. Damn you guys make me study math again, haven't done that in 6 years.
psly4mne 06-13-07, 02:30 PM	Out of morbid curiosity, did you learn this stuff in a graduate level real analysis class or did you just acquire it via self-inquiry? I'm not in any way questioning your credibility, I'm just wondering what you think would be the best way of learning this stuff. I was half considering taking a graduate level Real Analysis course this next spring (after my graduate school applications are in :P ). IF I had to guess, this material would be in that class, but I'm not certain off the top of my head. I took one undergraduate logic course, but I really learned everything I know about set theory through independent study. We have a directed reading program wherein undergraduates are paired up with graduate students for independent study, and I have been studying set theory through the program. I also took an honors undergraduate real analysis class, though most of what we have been talking about here is set theory. I would recommend Azriel Levy's Basic Set Theory as a good, readable text to start with. Good luck with your grad school apps! What are you going for?
Tleilaxu_Ghola 06-13-07, 03:09 PM	I took one undergraduate logic course, but I really learned everything I know about set theory through independent study. We have a directed reading program wherein undergraduates are paired up with graduate students for independent study, and I have been studying set theory through the program. I also took an honors undergraduate real analysis class, though most of what we have been talking about here is set theory. I would recommend Azriel Levy's Basic Set Theory as a good, readable text to start with. Good luck with your grad school apps! What are you going for? Interesting program. I've got a senior project to do for my math major, and I dunno what I'm going to do. Set theory might be a fun thing to explore for that project. So thanks for the tip on the book! Currently looking at experimental physics for grad school. While I'd like to study nuclear or condensed matter, I may end up in bio-physics, as I have good deal of experience there. I've warmed up to biology, though, after I discovered a small niche within the field wherein they attempt to describe biological processes in a strictly stochastic manner. The math involved in this area is more than enough to keep my math-major side happy, as its filled with partial differential equations, optimization problems, and of course statistics. I doesn't really matter WHAT I study, so long as its got a really solid mathematical background and has some not-so-distant application. I find that these requirements USUALLY point to experimental physics.
Think0028 06-13-07, 11:48 PM	However, 2^ℵ0 ≥ ℵ1. The actual value of 2^ℵ0 is independent of ZFC. The Continuum Hypothesis states that 2^ℵ0 = ℵ1. The Proper Forcing axiom implies that 2^ℵ0 = ℵ2. Also, it is not true that 2*ω=ω, although 2*ℵ0 = ℵ0. There is a big difference between cardinal and ordinal numbers. ω is an ordinal, while ℵα denotes a cardinal. Arithmetic is defined very differently on cardinals and ordinals. And it doesn't stop there; there are other number systems too - the extended reals and the surreals, to name two important ones. ****, I need to pay more attention in math class. My bad.
BillTheManiac 06-14-07, 09:17 PM	I have taken an undergraduate real analysis class at Yale. It didn't cover this stuff. 1. Arithmetic can be seen as an extension of set theory. For example, 2+2=4 is equivalent to [{1, 2} U {a1, a2} is isomorphic to {1, 2, 3, 4}]. In this conception cardinal and ordinal numbers are the same, and 2^N0=N1. 2. I don't know what the proper forcing axiom is but it makes a lot more sense to me that 2^N0=N1 makes a lot more sense. How do you make those symbols? 3. Mass, phyically, is technically the cardinality of the set of protons and neutrons in an object. Weight is mass times strength of gravity, a real number on most D&D planes. 4. In TO, when the D&D rules are unclear, we make assumptions. The D&D rules obviously do not say whether calculations follow Axiom of Choice, Continuum Hypotheses, etc. I am making the assumptions that whatever system it uses sets Pun-pun's carrying capacity at Aleph 1 (or, if you want, Aleph 1 protons/neutrons). I am them asking what kind of abilities can create an object with no weight limit, which could technically create (I assume), an object with Aleph 1 weight.
psly4mne 06-15-07, 11:45 AM	I have taken an undergraduate real analysis class at Yale. It didn't cover this stuff.In my analysis class, we discussed how to extend R with ∞ as a metric space, but nothing more. Again, this is set theory, and if you don't know set theory, you will probably embarrass yourself. 1. Arithmetic can be seen as an extension of set theory. For example, 2+2=4 is equivalent to [{1, 2} U {a1, a2} is isomorphic to {1, 2, 3, 4}]. In this conception cardinal and ordinal numbers are the same, and 2^N0=N1.Arithmetic cannot be seen as an extension to set theory. Arithmetic is part of set theory. Cardinal numbers and ordinal number are not the same at all. For example, ℵ0+1=ℵ0, but ω+1≠ω. And 2^ℵ0 is most certainly not necessarily ℵ1. This is the continuum hypothesis, and there is no reason to assume it. In fact, some great mathematicians today believe that it is more natural to assume the proper forcing axiom, which contradicts the continuum hypothesis. 2. I don't know what the proper forcing axiom is but it makes a lot more sense to me that 2^N0=N1 makes a lot more sense.Well, I'm sorry, but mathematicians apparently forgot to take into account what makes sense to BillTheManiac. The value of 2^ℵ0 is independent of ZFC. It could just as well be ℵℵ3. What makes sense and what is true are completely unrelated (see Banach-Tarski). How do you make those symbols?I have a TextEdit open and I am copying characters. 3. Mass, phyically, is technically the cardinality of the set of protons and neutrons in an object.Actually, mass technically is not the cardinality of the set of protons and neutrons in an object. It is technically the total rest energy of the object divided by c2. Technically, this is not at all the same as the number of protons and neutrons. Weight is mass times strength of gravity, a real number on most D&D planes.If you define strength of gravity as weight divided by mass, then I guess you are correct. The rest of us like to think that weight is GmM/r2. 4. In TO, when the D&D rules are unclear, we make assumptions.No. We make reasonable assumptions (and we occasionally decide that a question has no answer, as in the case of Monty-spammer vs Terminator-spammer). The D&D rules obviously do not say whether calculations follow Axiom of Choice, Continuum Hypotheses, etc.The standard set of axioms for set theory is ZFC (some prefer ZF). Thus, if our choice of axioms matters here, we choose ZFC. I am making the assumptions that whatever system it uses sets Pun-pun's carrying capacity at Aleph 1 (or, if you want, Aleph 1 protons/neutrons).That's quite a convenient assumption. You are also making the assumption that it makes sense to talk about ℵ1 weight (carrying capacity is based on weight, not mass). In fact, both these assumptions are wrong, since weight is not a cardinal number. I am them asking what kind of abilities can create an object with no weight limit, which could technically create (I assume), an object with Aleph 1 weight.Wow. You are good at assuming things. Assuming reasonable things, not so much. Apparently, they're letting just about anyone into Yale these days. :nonono:
BillTheManiac 06-15-07, 05:51 PM	Let's take this one step at a time. In my analysis class, we discussed how to extend R with ∞ as a metric space, but nothing more. Again, this is set theory, and if you don't know set theory, you will probably embarrass yourself. In mine we learned measure theory and Fourier series and some other stuff. Arithmetic cannot be seen as an extension to set theory. Arithmetic is part of set theory. That's what I meant. Cardinal numbers and ordinal number are not the same at all. For example, ℵ0+1=ℵ0, but ω+1≠ω. Alright, I was wrong. That doesn't change the fact that ordinal numbers do not apply to the Synchronity loop, because it allows you to add 1 no matter what, and with ordinal numbers there is always another +1, so the statistics are not well defined. And 2^ℵ0 is most certainly not necessarily ℵ1. This is the continuum hypothesis, and there is no reason to assume it. In fact, some great mathematicians today believe that it is more natural to assume the proper forcing axiom, which contradicts the continuum hypothesis. Do all great mathematicians believe it? Because if some do and some don't, both assumptions are equally valid. Well, I'm sorry, but mathematicians apparently forgot to take into account what makes sense to BillTheManiac. The value of 2^ℵ0 is independent of ZFC. It could just as well be ℵℵ3. What makes sense and what is true are completely unrelated (see Banach-Tarski). Banach-Tarski is based on the Axiom of Choice. That's an assumption. We can chose the assumptions that makes sense to me, or the assumptions that make sense to Psly4mne. This is my thread so my assumptions are used, as long as they are as valid as yours. On the Pun-Pun thread anyone who wants to argue about whether using Divine Minion to qualify for Master of Many Forms works is turned away (or at least the parts I read). Actually, mass technically is not the cardinality of the set of protons and neutrons in an object. It is technically the total rest energy of the object divided by c2. Technically, this is not at all the same as the number of protons and neutrons.It is when objects are at rest. If you define strength of gravity as weight divided by mass, then I guess you are correct. The rest of us like to think that weight is GmM/r2=gm where g is Gm/rpsup2[/sup]. Seriously. Just because I don't say things exactly the way you like doesn't mean I'm wrong. No. We make reasonable assumptions (and we occasionally decide that a question has no answer, as in the case of Monty-spammer vs Terminator-spammer). Is the continuum hypothesis not reasonable? The standard set of axioms for set theory is ZFC (some prefer ZF). Thus, if our choice of axioms matters here, we choose ZFC.Um, but YOU JUST EXPLICITLY STATED the answer is independent of ZFC. That's quite a convenient assumption. You are also making the assumption that it makes sense to talk about ℵ1 weight (carrying capacity is based on weight, not mass). In fact, both these assumptions are wrong, since weight is not a cardinal number. Weight is a multiple of mass. Mass is a multiple based on speed of rest mass, which is approximately 1 per proton or neutron. Wow. You are good at assuming things. Assuming reasonable things, not so much. Is one thing I assumed unreasonable? I don't know this stuff that much, so I just wonder: If 2^omega=omega then why is omega+1>omega? If omega+1>omega then what is omega-1? Other thing: Stop me when I'm wrong. Aleph1 is the cardinality of R is isomorphic to [0,1), which is the set of all .a1a2a3... where ai=0 or 1, which is {0,1}Aleph0, whose cardinality should be 2Aleph0
Tleilaxu_Ghola 06-15-07, 06:53 PM	Much as I'd like to help (either side), I have no idea what the hell is going on. *Sits back, cracks a Dew* This should be entertaining.
psly4mne 06-15-07, 07:53 PM	Alright, I was wrong. That doesn't change the fact that ordinal numbers do not apply to the Synchronity loop, because it allows you to add 1 no matter what, and with ordinal numbers there is always another +1, so the statistics are not well defined.Stop. With natural numbers you can aways add 1 likewise with cardinal numbers, or surreal numbers. You obviously don't know what you are talking about. Do all great mathematicians believe it? Because if some do and some don't, both assumptions are equally valid.I was not suggesting that we assume PFA. I was merely pointing out that it would be stupid to assume CH. CH is not at all accepted or used as an axiom. Banach-Tarski is based on the Axiom of Choice. That's an assumption. We can chose the assumptions that makes sense to me, or the assumptions that make sense to Psly4mne. This is my thread so my assumptions are used, as long as they are as valid as yours. On the Pun-Pun thread anyone who wants to argue about whether using Divine Minion to qualify for Master of Many Forms works is turned away (or at least the parts I read).Hmmm. I'll start a thread in which I assume that Pun-Pun contracted a terminal disease that resisted all magic, and he subsequently died. Then I'll claim Pun-Pun was killed. Nope, doesn't work. You have to make justifiable assumptions. If you want to assume AC, or don't, that's fine with me. You are "assuming" things that are either not accepted, or blatantly wrong. That doesn't fly here. It is when objects are at rest.This is simply not true. Physicists don't all agree on what to call mass, but nobody says that it is the number of protons+neutrons in an object. There are electrons. There is a measurable relativistic effect from potential energy. Give it up. Is the continuum hypothesis not reasonable?No, it is not an accepted axiom. Um, but YOU JUST EXPLICITLY STATED the answer is independent of ZFC.Um, I'm not sure what you're getting at here. Any consistent axiomatization will be incomplete. There will have to be questions to which we will have to answer "this is undetermined". Weight is a multiple of mass. Mass is a multiple based on speed of rest mass, which is approximately 1 per proton or neutron.As an approximation, that is reasonable. However, one cannot define weight as a cardinal number, since it is not actually quantized. Is one thing I assumed unreasonable?You assumed: Ability scores, weights, masses, and everything else are to be represented as cardinal numbers. Pun-pun's stats are ℵ0, with no justification given. A strength of ℵ0 grants a carrying capacity of ℵ1. Lots of leaps of (bad) logic in your second post I don't know this stuff that much, so I just wonder: If 2^omega=omega then why is omega+1>omega? If omega+1>omega then what is omega-1?2ω≠ω. Oops. For a limit ordinal α, 2α := sup {2β | β<α}. Therefore 2ω=sup{2α | α<ω} = ω. However, it is still the case that ω+1 > ω. Ordinal arithmetic is funky that way. ω-1 does not exist. One cannot subtract ordinals. Other thing: Stop me when I'm wrong. Aleph1 is the cardinality of RStop. You obviously did not read the post I linked to above. Read it. Then stop spewing nonsense. Actually, I would prefer that you stop spewing nonsense before you read the post. But I'm not picky.
Tleilaxu_Ghola 06-15-07, 08:44 PM	As an approximation, that is reasonable. However, one cannot define weight as a cardinal number, since it is not actually quantized. By the Einstein approach that all mass can be written in terms of energy and that all energy is fundamentally quantized, one certainly has some right to claim that weight is quantized. (Read further to see why I remain ambivalent on the issue). Any particle of arbitrary mass, regardless of how it obtained that mass, can be described as a wave of wavelength hc/pc, where pc is approximately (2*KE*rest-mass energy)0.5, by the De Broglie equation. The presence of h in that equation indicates that a particle's wavelength is fundamentally quantized. Since the wavelength is inversely proportional to momentum we can definitely conclude that momentum is quantized. Now, here's the ambiguity: the uncertainty principle states essentially that knowing a particle's energy and momentum simultaneously is impossible. Since both momentum and energy can be written in terms of mass and velocity, it basically means that either mass or velocity is quantized or perhaps both are. I cannot, with my knowledge, tell you whether or not mass is definitely quantized or not, but I can see how one could assume it. Delving a little further into a realm that I have little knowledge of... (so I may be wrong), I believe mass is communicated via the higgs boson. This is an elementary particle, thus mass must necessarily be communicated in quantized packets, much like energy. The symmetry of this conclusion is certainly pleasing and fits with the De Broglie model I showed above. The higgs boson is not fully confirmed, however, but there is strong evidence for its existence (at least in theory, and somewhat in practice). Bottom line: If I had place a bet, I'd bet that mass is quantized. So, I'm not sure how that fits in with this argument, but there's my opinion on the matter. Carry on.
BillTheManiac 06-15-07, 09:32 PM	Look. Your only purpose is to catch me in logic traps. Would it have been different if Aleph 2 was in the thread title? No. Or 2^(Aleph 0)? No. You just feel like you have to catch every unimportant error I make. OK. Instead just make a thread "Psly4mne is better at advanced set theory then BillTheManiac". As TG just stated, matter is quantized. It doesn't matter if I don't use the correct terms, because I know in ordinary matter the effect of electrons is very, very small. Matter is quantized, therefore it uses set theory. Therefore cardinal numbers. Therefore 2^Aleph 0 greater then or equal to Aleph 1 greater then Aleph 0. Therefore there is a point to this project. If I made a post saying i^2=1, you shouldn't come and complain that i could stand for the index in a series, in which case that statement is false. The assumptions I make are implicit. Is it stupid to make an assumption when you literaly cannot solve the problem without making it or a different assumption? Anyways, back to this thread. Does the epic seed "Create" allow creation of a purely theoretical and physically impossible material?
Tleilaxu_Ghola 06-15-07, 09:37 PM	Anyways, back to this thread. Does the epic seed "Create" allow creation of a purely theoretical and physically impossible material? If it says it does, then yes. If not, you have to ask the DM. He's probably not going to be thaat complicit. Here's the text: Conjuration (Creation) Spellcraft DC: 21 Components: V, S Casting Time: 1 minute Range: 0 ft. Effect: Unattended, nonmagical object of nonliving matter up to 20 cu. ft. Duration: 8 hours Saving Throw: None Spell Resistance: No This seed creates a nonmagical, unattended object of nonliving matter of up to 20 cubic feet in volume. The caster must succeed at an appropriate skill check to make a complex item. The seed can create matter ranging in hardness and rarity from vegetable matter all the way up to mithral and even adamantine. Simple objects have a natural duration of 24 hours. For each additional cubic foot of matter created, increase the Spellcraft DC by +2. Attempting to use any created object as a material component or a resource during epic spell development causes the spell to fail and the object to disappear. The conjure seed can be used in conjunction with the life and fortify seeds for an epic spell that creates an entirely new creature, if made permanent. To give a creature spell-like abilities, apply other epic seeds to the epic spell that replicate the desired ability. To give the creature a supernatural or extraordinary ability rather than a spell-like ability, double the cost of the relevant seed. Remember that two doublings equals a tripling, and so forth. To give a creature Hit Dice, use the fortify seed. Each 5 hit points granted to the creature gives it an additional 1 HD. Once successfully created, the new creature will breed true. Read for yourself. The hardest you're going to get is adamantine, which means that's probably the densest you're going to get.
The_Mad_Linguist 06-16-07, 12:43 AM	But black holes aren't hard at all.
Djief 06-16-07, 12:59 AM	But black holes aren't hard at all. Prove it.
Tleilaxu_Ghola 06-16-07, 02:43 PM	Prove it. Seconded.
The_Mad_Linguist 06-16-07, 06:29 PM	The trait of hardness is meaningless when applied to a black hole. You can't scratch it, or scratch anything with it. A hammer dropped on it won't rebound. It doesn't resist anything trying to poke it. Massive time dilation causes major problems with most measurements as well.
psly4mne 06-16-07, 06:57 PM	The caster must succeed at an appropriate skill check to make a complex item.Knowledge (Nature) DC what now?
The_Mad_Linguist 06-16-07, 07:47 PM	Knowledge (Nature) DC what now? Black holes aren't complex. Just big. You could even argue they're the simplest thing to make. "Hmm... where do I need to put all my mass. I could try to do an even distribution across a volume defined by the equations... aw screw it, I'll just stick it all right there."
psly4mne 06-16-07, 07:55 PM	Black holes aren't complex. Just big. You could even argue they're the simplest thing to make. "Hmm... where do I need to put all my mass. I could try to do an even distribution across a volume defined by the equations... aw screw it, I'll just stick it all right there." The structure is not complex, but the concept may be considered complex. To me, that seems to introduce DM fiat. I see your point, of course, but it's not really clear-cut IMO.
Tleilaxu_Ghola 06-16-07, 08:05 PM	The trait of hardness is meaningless when applied to a black hole. You can't scratch it, or scratch anything with it. Baseless assertions. There are black holes which are larger than others; that is they exert more force on objects than other black holes. This would indicate that they are more than mere singularities of "infinite" mass. In fact, black holes carry three intrinsic properties: mass, angular momentum, and charge. As far as "scratching" is concerned... a black hole, having electric charge and mass, is capable of interacting with massive and charged lattices, such as crystals. It is unlikely that anything could scratch (or remove) anything from the lattice structure that composes a black hole, but I do believe a black hole could remove matter from the lattice structure of another object quite easily. A hammer dropped on it won't rebound. It doesn't resist anything trying to poke it. Massive time dilation causes major problems with most measurements as well. I fail to see how this helps your case. If you are attempting to say that a black hole has hardness "undefined or unknown" then, you cannot create it with the creation seed. The creation seed allows objects to be created with a well defined range of hardness. Undefined hardness is not included in that list. Hardness 0 is included; most creatures do not have a hardness score, that is to say they have hardness 0.
The_Mad_Linguist 06-16-07, 08:16 PM	Baseless assertions. There are black holes which are larger than others; that is they exert more force on objects than other black holes. This would indicate that they are more than mere singularities of "infinite" mass. In fact, black holes carry three intrinsic properties: mass, angular momentum, and charge. As far as "scratching" is concerned... a black hole, having electric charge and mass, is capable of interacting with massive and charged lattices, such as crystals. It is unlikely that anything could scratch (or remove) anything from the lattice structure that composes a black hole, but I do believe a black hole could remove matter from the lattice structure of another object quite easily. Which still isn't scratching it. As it happens, there is an in-game definition of hardness (which ought to trump any real physics), so all we have to do is say that it doesn't resist damage inflicted upon it. Hardness Each object has hardness—a number that represents how well it resists damage. Whenever an object takes damage, subtract its hardness from the damage. Only damage in excess of its hardness is deducted from the object’s hit points (see Table: Common Armor, Weapon, and Shield Hardness and Hit Points; Table: Substance Hardness and Hit Points; and Table: Object Hardness and Hit Points). And I think only objects have to have hardness... at least, the section on hardness seems to indicate that. Animated objects blur the line a little, I admit.
BillTheManiac 06-16-07, 08:26 PM	The structure is not complex, but the concept may be considered complex. To me, that seems to introduce DM fiat. I see your point, of course, but it's not really clear-cut IMO. Pun-Pun thinks: I need an infinite amount of mass. Let me invent a material that has infinite density. I'll do it by squeezing infinite mass together. Also Knowledge (Nature) DC what now? This is Pun-Pun we're talking about here. Hardness/HP: This infinite black hole would either have |R| hardness or |R| HP? Why? Because the gravitational energy is |R| so that much energy is required to split it. |R| energy=|R| damage is the most reasonable assumption, I would say. So the question is: Can you make a small "dent" in a black hole? I would say no. Infinite gravity. Maybe Pun-Pun should actually make it Aleph 1 so with the negation of the continuum hypothesis it is only a light load. |R| carrying capacity and |R| weight is kind of iffy. Aleph 1 and Aleph 2+? Clear-cut.
The_Mad_Linguist 06-16-07, 11:13 PM	Could Pun-Pun change the gravity of his divine realm such that the weight of an object is Aleph 1?
BillTheManiac 06-17-07, 10:11 AM	Can you invent your own traits, like "super-infinite gravity?". If so, then yes. If he is limited to "heavy gravity", then no. I'd look it up in the SRD. Ambiguous, but I would rule he can't.
SoAnIs 07-09-07, 12:38 PM	My post (http://boards1.wizards.com/showthread.php?p=13007855#post13007855) on the use of Arcane Nova outputting Limited Celerity may be of assistance here. While I deliberately kept it to layman's terms as much as I can, and thus introduced inaccuracies, the creation of an infinite mass black hole seems inevitable from the loop. If it didn't destroy the entire universe with it this would be perfect for Pun Pun's use. Unfortunately, I think it would make Pun Pun cease to exist, along with everything else. However, since causality does not exist (properly at least) in D&D Pun Pun may be able to achieve the carrying capacity needed before actually doing the whole Arcane Nova. Also, on the quantization of velocity: There is a Planck length and a Planck time, these are thought to be the minimum possible distance and time. One Planck Length Per Planck Time would be the minimum velocity, thus quantizing velocity. This is, of course, wrong now that I think about it. Planck Length/Time are merely the minimums at which measurement of distance/time are measurable. Distance and time break down at these scales without a working theory of quantum gravity, which we sadly lack. This shows that I shouldn't try quantum mechanics without sleep.
DrStalker 07-14-07, 03:46 AM	Assuming ℵ0 is defined as the "smallest" countable infinity with a 1:1 correspondence with the set of positive integers: If Pun-pun uses his ℵ0 actions to cast ℵ0 Ice Assassin spells to create ℵ0 Pun-Puns, and each of those then makes ℵ0 Pun-Puns there will (if I remember my infinity theory correctly) end up being more than ℵ0 pun-puns, all of which are under the complete control of Pun-Pun0 either directly or because they are under complete control of someone under his complete control. Now get ℵ0^ℵ0 Pun-Puns to gather into a huge ball of Pun-Pun that Pun-Pun0 throws. Or just have them all attack for ℵ0^ℵ0 * Pun-Puns damage, whatever insanely high amount that ends up being. ℵ0^ℵ0 is greater than ℵ0, but this is getting to my limits on set theory! [edited to fix some assumptions and be clearer]
psly4mne 07-14-07, 11:20 AM	If Pun-pun uses his ℵ0 actions to cast ℵ0 Ice Assassin spells to create ℵ0 Pun-Puns, and each of those then makes ℵ0 Pun-Puns there will (if I remember my infinity theory correctly) end up being more than ℵ0 pun-puns, all of which are under the complete control of Pun-Pun0 either directly or because they are under complete control of someone under his complete control. You do not remember your "infinity theory" correctly.
DrStalker 07-14-07, 12:14 PM	You do not remember your "infinity theory" correctly. Oh well. Let me know when something comes up that ℵ0^ℵ0 Pun-Puns can't handle.
psly4mne 07-14-07, 02:14 PM	Oh well. Let me know when something comes up that ℵ0^ℵ0 Pun-Puns can't handle.To clarify, the process you described does not produce more than countably many clones.
DrStalker 07-14-07, 09:45 PM	To clarify, the process you described does not produce more than countably many clones. I think I misplaced one. Mind counting them for me? :-)
Callix 07-15-07, 07:23 AM	So we have a countably infinite number of pun-puns, all with arbitrarily large stats? Why are we worried? What exists that N where N is large pun-puns can't handle, whether or not this truly counts as "infinity"? This is "Conquer the entire multiverse, infinite or otherwise" territory. In case you can't tell, I haven't done any set theory yet. But I will soon. Maths majors can only avoid it for so long.
DrStalker 07-15-07, 08:27 AM	It's not about being worried, it's just that nothing expresses the spirit of the Theoretical Optimization board better than trying to beat infinitely powerful by the creation of something more infinitely powerful.
BillTheManiac 07-15-07, 12:12 PM	We're worried if someone ELSE finds a way to get Aleph 1 (or higher, depending on whether the Continuum Hypotheses is true) stats, then bluffs all our Aleph 0 Pun-Puns into taking the Corpse feat. 1/root(1-(v/c)^2) should really only go up to Aleph 0. For v>c wouldn't that mean imaginary stats?
DrStalker 07-15-07, 05:46 PM	RAW do not state what mathematical system to use, so there is nothing to stop use of imaginary numbers. If you had a cursed item with a negative cost and tried to reverse engineer the bonus (k.X˛) you'd end up with an imaginary modifier, for example. I'm not sure how that helps here though!
BillTheManiac 07-15-07, 06:05 PM	There is. In C there can be no ordering, but D&D requires you to compare numbers very frequently. The imaginary number thing comes from an equation assuming v<=c.
psly4mne 07-15-07, 06:33 PM	I've said it before and I'll say it again - relativity and D&D don't mix. The rules of D&D clearly contradict the laws of relativity in multiple places. For example, the rules make it explicit that, even without magical assistance, it is possible to travel faster than the speed of light (enough people in a line, all with readied actions, and pass a bucket of water down the line - it will reach the end in 6 seconds).
DrStalker 07-15-07, 07:49 PM	There is. In C there can be no ordering, but D&D requires you to compare numbers very frequently. The imaginary number thing comes from an equation assuming v<=c. So we define our own comparison function, for even greater potential abuse. :-)
BillTheManiac 07-15-07, 09:15 PM	Not possible. I proved it in a problem set once.