In the book from the Hellbound set, "The Dark of the War", there is a discussion as to whether or not the Tanarri are infinite in number. Then a argument is presented that, while there may be infinite Tanarri, only a finite portion of them fight in the Blood War. Wherupon, the narrator claims that this is nonsense, since any subset of an infinite set must, by definition, be infinite. This doesn't sound right to me! If you take one away from infinity, you'd have the original infinite set and a new set of one, right? And one is obviously NOT infinite, so isn't the above argument barmy?
Infinite Tanarri?
Mon, 2007-10-15 19:32
#1
Infinite Tanarri?
Tue, 2007-10-16 14:39
#3
Infinite Tanarri?
This, of course, begs the question: "Why are there more Chaotic Evil petitioners-turned-Tanar'ri than Lawful Evil (and thus Baatezu)?" It would seem that attrition would be on the Tanar'ri's side, since if the Baatezu are finite, then given an infinite (or near-infinite) timeframe, it is very likely that all the Baatezu can be killed or die or whatever before the supply of Tanar'ri runs dry. It wouldn't matter how "ordered" the Baatezu resistance was, it is sheer numbers and increasing probabilities.
Of course, who says the Baatezu are finite? Do Chaotic Evil beings kill each other more often, therefore creating more fodder for the Tanar'ri? I know I'm making some assumptions, but it just seems an unbalanced war, at best. There are, of course, a multitude of mitigating factors that happen at the war's periphery that alter the scales. I'm sure it isn't all about how chaotic the Tanar'ri are, ending up fighting one another more than their "real" enemies, etc.
Tue, 2007-10-16 16:56
#4
Infinite Tanarri?
I think the point the author was attempting to make was saying that any given percentage of infinity is still infinite. Assuming that only 20% of tanar'ri are involved in the Blood War, for example, would be the same as saying there are an infinite number of tanar'ri fighting in the Blood War. If you take the subset of 'manes', then you could argue that there are an infinite number of manes. Similarly, would that also imply that there are an infinite number of balors? Is their infinity smaller than the manes' infinity?
Actually, no. If we say there are an infinite amount of tanar'ri, and that both manes and balors comprise some percentage of the total amount of tanar'ri, then there are an infinite amount of both manes and balors. All three infinities are equal - the number of manes is equal to the number of balors, and the number of balors is equal to the total number of tanar'ri. Transfinite mathematics is particularly bizarre and counterintuitive.
Tue, 2007-10-16 22:26
#5
Infinite Tanarri?
This is why the whole 'infinity of the Planes' always made my head hurt. Sounds nice in theory, until you realize that a lot of things stop making any kind of logical sense.
Wed, 2007-10-17 07:16
#6
Infinite Tanarri?
To Hell with this game. If Planescape isn't going to be about making sense in a logical fashion, and if the tanar'ri can't at least follow the rules of modern mathematics, then I'm not playing it anymore.
Wed, 2007-10-17 07:33
#7
Infinite Tanarri?
Crazy Theory Time: 
What do you think all those infinite layers of Abyss come from?
Anwser: they are created from infinite number of tanar´ri who dont hawe anyplace to live so they are used as building blocks for new layers of Abyss.
That would explain fact that tanar´ri are sometimes formed out of Abysall planar soup and just sorta pop into existance. They are something like loose bricks that eventualy fall out wall.
There is point to be learned from this: Even great planar races have housing problems.
Wed, 2007-10-17 10:37
#8
Infinite Tanarri?
The argument that all types of tanar'ri would also imply that there are an infinite number of unique tanar'ri, since unique tanar'ri represent a percentage of the total tanar'ri population. That's a frightening thought. The value of 1/x as x approaches infinity is zero. Inifnity minus 1 is still infinity. Bangs head against table. Maybe the Abyss is filled the rational people who go mad when trying to wrap their heads around things like this.
My questions about infinite manes and balors were meant to be rhetorical. My apologies for not making that clear from the outset. I have to agree that the entire issue is indeed bizarre and counterintuitive. Then again, that would imply that we are Guvner's at heart and trying to apply order and reason to what is given to us as a chaotic system.
The question of why there are so many tanar'ri is an interesting one, though. I don't have my books from 1st edition any longer, but I seem to recall that the Monster Manual had a disproportionate number of chaotic evil entries. Additionally, the majority of the bad guys that I encountered or ran as a DM were chaotic evil. I've noticed that many other gamers where I grew up had similar experiences. Honestly, I don't think that I was well-suited to trying to run lawful evil characters, nor were my players prepared to deal with an organized threat. It was simply a matter of convenience, and it supported a group working together to overcome a single, though powerful, foe- kinda like dealing with a bully. I feel like I just returned to the early 80s.
I don't know if this holds true for all those involved in the game early on, but with the sheer bulk of chaotic evil foes faced then, it seems only naturally that the Abyss would house a seemingly infinite supply of dispatched bad guys from my youth. Then again, this is representative of the sort of groupthink that has plagued the intelligence community until forced to face further scrutiny. Additionally, the infinite layers of the Abyss are the result of all those failed worlds that my friends and I created. That also explains why so many make no sense (pre-teen chaos).
Wed, 2007-10-17 16:54
#9
Infinite Tanarri?
Bah you lawful types and your Piking Mathematics! I would say that the reason why Tanar'ri seem to number more and do is because Evil of a Chaotic nature seems to, more often than not, stems from a more primal selfishness and sin, where as lawful evil is mainly tyrrany and oppression as well as the advantages that come from tyrrany and oppression. Giving in to a primal nature shouldn't be hard seeing as the primes seem to be flooded with being whose intelligence isn't really big enough to grasp basic morals. Hence evil of a more primal and chaotic nature ensues. Add that to violent criminals, drow, abyssal god worshippers and downright darstedly villians and you've got yerself one big vat o' tannarric potential.
Wed, 2007-10-17 18:29
#10
Infinite Tanarri?
Uh, my understanding was that Baatezu selected 'only the best larvae to 'promote' (although this is actually screed it's basically a random process but no Baatezu would admit to that) whereas Tanar'ri would convert as many as they could shove down to the appropriate layer. I believe that this is outlined in 'faces of evil'.
As far as sheer numbers go, remember that there could also theoretically be an infinite number of prime worlds to draw souls from.
So in summary- The Baatezu could, in theory, match the Tanar'ri in sheer numbers but that would mean changing their system, re-ordering their ranks, sorting out a new pay structure, sending the proposal to project review committee to have it stamped in triplicate, and generally going against their very nature. The Baatezu honestly believe that their system is already absolutely perfect and that that this will be proven in the long run so why instigate change?
Wed, 2007-10-17 23:21
#11
Infinite Tanarri?
While I am aware of this theory. I've no doubt that the Baatezu are just lying to make themselves appear as equally powerful as their Chaotic counterparts. I find highly unlikely that the baatezu would be given a great disadvantage if they did have a few more in their ranks. Unless...
What if the baatezu find transforming larvae into fiends more difficult? After all a polymorphism is rather a chaotic kinda spell. ugh more larva debates! The blood war continues on a crappier level!
Thu, 2007-10-18 02:25
#12
Infinite Tanarri?
To Hell with this game. If Planescape isn't going to be about making sense in a logical fashion, and if the tanar'ri can't at least follow the rules of modern mathematics, then I'm not playing it anymore.
I propose that both, Tanar’ri and Baatezu are infinite, but that the Baatezu are countable while the Tanar’ri have the cardinality of the continuum. (Maybe their number is even fractal - chaos theory.)
This means that you can assign a number out of 1,2,3,… (nonnegative for convenience’s sake) to each and every Baatezu (standing neatly in ordered rows), so that two different Baatezu never share the same number and if there is Baatezu n there is also Baatezu n+1.
(I daresay Baatezu are doing this all the time.)
Tanar’ri on the other hand are uncountable. Whenever you assigned your numbers you will find Tanar’ri that you missed, hanging around between the ones you numbered.
(See Cantor’s diagonal argument for this. It’s easy, but I don’t want to write this down here. Ok. I’ll give a clue. The numbers look like this: 1000…, 2000…, …
Take the first number and change the first digit. Take this digit for the new number. Generally go on to the n-th number and change the n-th digit. Take this n-th digit for the new number. Your new number is different from all numbers you assigned. Damn, missed that one 
How many angels fit on the tip of a needle?
Thu, 2007-10-18 03:16
#13
Infinite Tanarri?
How many angels fit on the tip of a needle?
Depends on the kind of Aasimon used, the size of the needle, it's material, the plane you do this on and of course whether polymorphing magic is allowed.
But most of the time three, of course.
Thu, 2007-10-18 03:42
#14
Infinite Tanarri?
Rabenaas wrote:
How many angels fit on the tip of a needle?
To quote Terry Pratchett and Neil Gaiman and their book "Good Omens": It is not the point how many angels or devils can dance on the tip of the needle, it is the cracks on the electrons that bother´s them. 
Thu, 2007-10-18 06:47
#15
Infinite Tanarri?
I just like the irony of the idea that either side could 'win' the blood war - the Baatezu if they shed some rules and just promoted every larvae in sight up to pit-fiend or the tanar'ri if they stopped squabbling long enough to concentrate their attacks in an effective overall strategy. However in doing so the winning side would truly be the loser because they compromised their philosophy in a war which is fundamentally about two warring philosophies regarding the nature of perfect evil.
Thu, 2007-10-18 08:04
#16
Infinite Tanarri?
To Hell with this game. If Planescape isn't going to be about making sense in a logical fashion, and if the tanar'ri can't at least follow the rules of modern mathematics, then I'm not playing it anymore.
I propose that both, Tanar’ri and Baatezu are infinite, but that the Baatezu are countable while the Tanar’ri have the cardinality of the continuum. (Maybe their number is even fractal - chaos theory.)
And I propose to hell (whichever) with all this rant about infinity. If "it doesn't make sense" is not a valid argument (though I'll argue it is) than take "style". As subjective as it is I think every fantasy world should have its own logic coherent with itself. So if devils and demons are brought up from souls or breeding they can't be infinite but in definition. And the latter is nothing but the whim of any author (cannon or not) who thought it'd be cool to make things infinite. I could give a similar argument on that divine loco having no rails, but I don't want to discurage anyone (partly because I think the concept is cool, partly because I know I'm too much of a doomsayer).
Oh yes, and I always thought the Tanar'ri would outnumber the Baate'zu because they can actually breed... beats me. (I for myself think lawful evil peeps are just as common - maybe more - than chaotic ones.)
Thu, 2007-10-18 16:25
#17
Infinite Tanarri?
I propose that both, Tanar’ri and Baatezu are infinite, but that the Baatezu are countable while the Tanar’ri have the cardinality of the continuum. (Maybe their number is even fractal - chaos theory.)
So the Baatezu are aleph-null in number and the Tanar'ri are aleph-one? That could work out. Maybe. I don't really know enough about different cardinalities within transfinites to make any kind of analysis, though.
Fri, 2007-10-19 06:21
#18
Infinite Tanarri?
Oh i'm pretty sure the baatezu can breed as well. BUT the real answer here is that the only good kind of evil is pure evil! Them loths're just playing both sides while they reign over both! It seems that lawful evil and chaotic evil morals are ultimately stagnant as you end up entering a war to which their will be no winner. Then again dying a neutral evil sure as the waste is grey doesn't land you anywhere pretty either. hmm... But the loths're probably making damn well sure that no side has an advantage. That just leave the ultimate puppet masters the GEHRELETHS MWahahahahaa! Join the dots it all makes sense!!!! Then again..
Fri, 2007-10-19 07:08
#19
Infinite Tanarri?
Now that you say it.. had the Gehrheleths ever did something useful or interesting? Though this is outoftopic...
Fri, 2007-10-19 08:40
#20
Infinite Tanarri?
Now that you say it.. had the Gehrheleths ever did something useful or interesting? Though this is outoftopic...
Well, the Yugoloth tower on Carceri is still unfinished mostly thanks to their efforts. Aside from that, they muck around and smell horrible.
Mon, 2007-10-22 16:39
#21
Infinite Tanarri?
Thats just what they want you to think!
Sat, 2007-10-27 06:44
#22
Infinite Tanarri?
What abotut such a solution:
The planes and their denizens are infinite. However, the known parts of the planes are finite. Ergo, only a finite number of Baatezu and Tanar'ri has even heard of the blood war. In other words, the infinity of planes means only that there is always one more nation, continent, world to discover.
The rulers of the planes onlu proclaim themselves as such. They rule only the parts they know about. Asmodeus' dominion may be nine times the size of our galaxy, but is still finite.
Sat, 2007-10-27 09:49
#23
Infinite Tanarri?
What abotut such a solution:
The planes and their denizens are infinite. However, the known parts of the planes are finite. Ergo, only a finite number of Baatezu and Tanar'ri has even heard of the blood war. In other words, the infinity of planes means only that there is always one more nation, continent, world to discover.
The rulers of the planes onlu proclaim themselves as such. They rule only the parts they know about. Asmodeus' dominion may be nine times the size of our galaxy, but is still finite.
That's sort of what I always assumed. There's the finite parts of the planes that everybody's heard of and where all the action happens, but then there are infinite expanses of hinterlands. On the Outlands the hinterlands are nicely beyond the inner ring, but on other planes they could be large expanses of countryside between various locations. Ironically, it's also how I integrate the Fiendish Codex finite lower plane theory. They only describe the notable locales, whereas the hinterlands inbetween are unchanged and infinite.
Sat, 2007-10-27 09:51
#24
Infinite Tanarri?
schpeelah's way is how I handle it. Aliens need thier own versions of Heaven, Hell, etc. 
These would be based on thier ideas of alignment.
Sat, 2007-10-27 21:22
#25
Infinite Tanarri?
One thing to remember is that the planes aren't places. They're ideas. The other thing people sometimes forget, exemplars aren't individuals they are expressions of those ideas. The nature of chaotic evil is to be an unending tide of destruction trampling over everything in its path, so the exemplars of chaotic evil, the Tanar'ri, are an unending tide of destruction. The nature of Lawful Evil is to be an organized front that moves precisely and purposefully and rules with an iron fist, so that's what the Baatezu do. Neither philosophy is clearly better than the other, so neither group of exemplars is clearly better than the other. They fight because they both think that they're philosophy is just a little bit better, just a little bit more right, and some day, if they just keep fighting, they'll prove it.
That's basically the entire key to the Blood War. Anything beyond that, and you're just over thinking it.
Sat, 2007-10-27 22:39
#26
Infinite Tanarri?
One thing to remember is that the planes aren't places. They're ideas. The other thing people sometimes forget, exemplars aren't individuals they are expressions of those ideas. The nature of chaotic evil is to be an unending tide of destruction trampling over everything in its path, so the exemplars of chaotic evil, the Tanar'ri, are an unending tide of destruction. The nature of Lawful Evil is to be an organized front that moves precisely and purposefully and rules with an iron fist, so that's what the Baatezu do. Neither philosophy is clearly better than the other, so neither group of exemplars is clearly better than the other. They fight because they both think that they're philosophy is just a little bit better, just a little bit more right, and some day, if they just keep fighting, they'll prove it.
That's basically the entire key to the Blood War. Anything beyond that, and you're just over thinking it.
Don't forget the NE goal of extracting as much profit as possible from both sides.
Sun, 2007-10-28 07:05
#27
Infinite Tanarri?
A little bit better? They think their friggin philosophy IS all that really matters!!!
Mon, 2007-10-29 05:43
#28
Infinite Tanarri?
What abotut such a solution:
The planes and their denizens are infinite. However, the known parts of the planes are finite. Ergo, only a finite number of Baatezu and Tanar'ri has even heard of the blood war. In other words, the infinity of planes means only that there is always one more nation, continent, world to discover.
The rulers of the planes onlu proclaim themselves as such. They rule only the parts they know about. Asmodeus' dominion may be nine times the size of our galaxy, but is still finite.
I guess this is why they are always recruiting. Must be a slightly easier job for the devils than the demons. Which goes back to the "infinite resources, finite armies" theory.
Mon, 2007-10-29 11:21
#29
Infinite Tanarri?
I may be misremembering, this happens from time to time and from edition to edition, but I recall that only the Yugoloths breed and the others are recruited from larvae. No one knows the 'loths breed because they keep it dark but it is speculated since it is not known that they do not recruit up from larvae.
There is also the larvae trade in the Grey Waste. Not all Devils and Demons are culled from the larvae of their home plane. It is often preferred to use the NE larvae of the Waste for promotion. This leads to multudious hordes as both sides are increasing their base numbers from another plane.
Only so many Tanar'ri can go on an offensive because they often kill each other as the staging grounds become packed before the riverboats can even come.
Infinite recruits from infinite primes and larvae from other planes notwithstanding, unless the fiend 'dies' on their home plane, they just come back to fight again after one year and a day. This is primarily the reason the war is unwinnable until one side can totally invade the other's home turf and what, in my mind, the 'loth are preventing.
According to Guide to Hell, Nessus spawns Pit Fiends. The same phenomena might be happening in the Abyss.
20% of infinity, is infinity.
Strange but true.
Infinity can only be comprehended in the mind.
In terms of the Blood War, it does not really matter who has how many troops to throw at the other. The Blood War is a GM tool to use as campaign fodder, plot device, backdrop, or story arc.
Mon, 2007-10-29 12:12
#30
Infinite Tanarri?
Edited for lostness
Mon, 2007-10-29 16:19
#31
Infinite Tanarri?
One last update for this thread: Action finally won out over laziness and I have mailed out the prize. I've been informed that it has arrived at the intended destination intact, so everything is peachy in the world.
If I ever get my hands on some more cheap PS stuff (and it'll happen again eventually) we'll have to do something like this again. Thanks for all the contributions and help in getting this thing up and running.
Uhm... Hymneth... lost a little?
Mon, 2007-10-29 18:05
#32
Infinite Tanarri?
You betcha I am. I hate my browser. Let's try that again somewhere else. . .
:oops:
Fri, 2007-11-16 05:08
#33
Infinite Tanarri?
Well, technically, there's two ways of handling it that I've always felt were appropriate.
1. There's an equal number of Baatezu and Tanar'ri. However, the irony of it is that it just SEEMS like there's more Tanar'ri because there's more infinite layers of the Abyss than the Nine Hells. Except, because the Nine Hells are infinite then there's no possibility of there actually being less than infinity. So, the endless numbers keep on going on and on.
But what I use for simplicity in my games is against canon.
2. I stick with there being 666 Layers of the Abyss. They're constantly changing, getting remade, and destroyed but there's pretty much an even amount of matter there. Some of these are from the souls of petitioners while others come from Ancient Primordial EvilsTM like Tharizdun and so on.
There's A LOT more Tanar'ri than Baatezu (whom are also finite in number just like the number of humans are finite on an infinite universe like ours). However, the Baatezu tend to inflict disproportionate number of casualties on their enemies due to their organized tactics and strategy.
Still, the Tanar'ri would overwhelm the Devils if not for the fact they're fighting EACH OTHER as much as Asmodeus' gang
I think the point the author was attempting to make was saying that any given percentage of infinity is still infinite. Assuming that only 20% of tanar'ri are involved in the Blood War, for example, would be the same as saying there are an infinite number of tanar'ri fighting in the Blood War. If you take the subset of 'manes', then you could argue that there are an infinite number of manes. Similarly, would that also imply that there are an infinite number of balors? Is their infinity smaller than the manes' infinity?
You other assumption, on the other hand, would be correct. If it is decided that there are a half million hordes of tanar'ri (between 1 and 500,000 in each horde- I generally reserve unit descriptions like legion, brigade, and regiment for baatezu and the like), then there are a finite number of tanar'ri involved in the Blood War- they just have an infinite supply of potential recruits/draftees.
For me, the latter is far easier to deal with. The tanar'ri are constantly killing each other (war or otherwise). This ebb and flow of support for the Blood War is probably what allows the baatezu to fortify positions and consolidate forces rather than being overrun by an infinite horde of tanar'ri.