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View Full Version : So I was Watching ViHart and Numberphile...



Chimera245
2014-12-15, 02:04 PM
I had a neat Idea! But it takes some explaining...

For a while now, I've been using a specific kind of idea of what gods are like in my games.

Basically, that gods have a stat that is literally infinite. A god of strength, for example would have infinite strength, a god of the arts might have infinite ranks in Perform, and a god of fire would have, um... infinite fire...or something...

Anyway, that worked all fine and well in all my games and stories, as it led to gods being "above" mortals, no matter how strong or high level they got.

But also raises the Blob-Juggernaut conundrum...What happens when an unstoppable force meets and unmovable object? What happens when two gods with infinite strength armwrestle? Basically, I just arbitrarily decided that whoever had higher Divine Rank would win, and if they were equal, they roll for it with their divine rank as a modifier.

But then I watched ViHart and Numberphile and learned there are different kinds, sizes, and general flavors of infinity...(who knew?)

In a nutshell, (mostly because I don't know how to post links...) it goes like this:

The weakest, smallest, least awesome infinity is Countable infinity, called Aleph Null. It's the number of numbers that can be counted. (not that you can actually count all those numbers without spending infinity time doing it, but anyway...) In my mind, I see this as "Divine Rank 0".

Then there's Uncountable Infinity, which is the number of numbers between any other two numbers. Like between 1 and 2 is 1.5, between 1.5 and 2 is 1.75, between 1.5 and 1.75 is 1.625, etc. you can always add more decimal places and get more numbers inbetween.

Anyway, math stuff happens, and you basically have Omega-Null (which is the same as Aleph Null, i think), then Omega-1, Omega-2, Omega-3, etc., each one more "Infinity-y" than the last. And you can still do ordinary math to these numbers.

And I'm thinking, maybe they could match up to Divine Rank in D&D. And then we have a way to actually pseudo-quantify Divine rank in a way that lets game stats use it.

And I'm thinking that MIGHT bring up a sort-of balanced way to play a game where the PCs were gods. In a way where they don't just feel like Really Strong People with Really Intimidating Responsibilities.
But there would have to be rules for what different parts of a character sheet replaced with infinity would actually MEAN in gameplay...

I was thinking:
-A character's Divine Rank, (arbitrarily set by DM during character creation, to determine power level of the game) would determine which Omega-number you have. For examples, we'll say DM says DR 10.
-You could either have a single stat at Omega-10, or you could split it up, and have two stats at Omega-5, or one at Omega-6, and two at Omega-2, or you could have ten stats at Omega-1, etc.
-Math can be done to Infinite numbers, but it gets kinda weird. Apparently "1+infinity" is infinity, but "infinity+1" is one more than infinity... or so says the videos I watched. So would a god with Omega-4 STR, wearing a Belt of Giant Strength(+6) have Omega-4 or Omega-4 + 6 strength? Such rules would have to be worked out for the game to work, 'cuz that would matter...
-If two gods with different rank oppose each other in some way, (like hide vs. spot), do they roll for it? If the hider has more divine rank than the spotter, meaning he is more well hidden by a magnitude of infinity, does the spotter have a chance to see him when the dice can only possibly add 20? Or are the dice on another "scale" when it comes to divine rank/infinite rolls?
-Also, what kind of challenges await PC gods with infinite stats? One with infinite strength could kill unkillable creatures, one with infinite speed could go to the end of endless planes, one with infinite constitution could eat the Infinite Plane of Candy... So what sort of things could a clever DM do to them?

Any thoughts on the whole idea?

qwertyu63
2014-12-16, 09:23 AM
I have no thoughts ATM, but... *jaw drop*

I really like this.

I might be back later with more thoughts.

Amechra
2014-12-16, 01:02 PM
I was thinking:
-A character's Divine Rank, (arbitrarily set by DM during character creation, to determine power level of the game) would determine which Omega-number you have. For examples, we'll say DM says DR 10.
-You could either have a single stat at Omega-10, or you could split it up, and have two stats at Omega-5, or one at Omega-6, and two at Omega-2, or you could have ten stats at Omega-1, etc.
This is not how the different cardinality of infinity work. Omega-1 would have a number of members equal to 2 ^ Omega-0. Just thought you should keep this in mind.


-Math can be done to Infinite numbers, but it gets kinda weird. Apparently "1+infinity" is infinity, but "infinity+1" is one more than infinity... or so says the videos I watched. So would a god with Omega-4 STR, wearing a Belt of Giant Strength(+6) have Omega-4 or Omega-4 + 6 strength? Such rules would have to be worked out for the game to work, 'cuz that would matter...
The videos you were watching... either they're wrong, or you misunderstood them. 1 + ∞ and ∞ + 1 are both equal to ∞, unless you've redefined the binary operations to make them non-commutative (in which case, it isn't addition.) Omega-4 and Omega-4 + 6 would be the exact same thing.


-If two gods with different rank oppose each other in some way, (like hide vs. spot), do they roll for it? If the hider has more divine rank than the spotter, meaning he is more well hidden by a magnitude of infinity, does the spotter have a chance to see him when the dice can only possibly add 20? Or are the dice on another "scale" when it comes to divine rank/infinite rolls?
This one's up to you; at this point, you probably should be looking into Nobilis, because the poor D20 system was never intended for this.


-Also, what kind of challenges await PC gods with infinite stats? One with infinite strength could kill unkillable creatures, one with infinite speed could go to the end of endless planes, one with infinite constitution could eat the Infinite Plane of Candy... So what sort of things could a clever DM do to them?
A clever DM would go play Nobilis, since that's a system designed to deal with playing Gods and giving them challenges. In D&D? To be fair, there probably isn't any challenge you could give one character that wouldn't destroy other members of the party, assuming your character's focuses are different.

Oh, and you never said what would happen if someone with Str ∞ attacked someone with DR ∞/-. Remember, ∞ - ∞ = ∞.

Chimera245
2014-12-16, 09:50 PM
The videos I watched did indeed mention these terms for infinity being non-commutative. They didn't really explain WHY they were non-commutative, but I just decided to take their words for it.

As far as the cardinality of the defferent Omegas, I was just trying to be simple, and not scare anyone off with long math explanations. But it does serve as a simple way to mark these values on a character sheet to map the Omegas to Divine Rank directly, even if that means the value of increasing DR rises exponentially.

As far as Inf. STR vs. DR Inf./-, that's exactly why i was bringing the different values of infinity in. If one has STR Omega-2 and the other had DR Omega-3/-, then the attacker has failed to do enough damage to get past the DR. On the other hand, if it were Omega-3 str vs. DR Omega-2/-, then he would be doing damage in excess of the DR to the target's HP. If they were both Omega-2, I would say there would need to be a "Divine Rank Check" to see what happens.

Basically the way I saw this, even a weaker man can sometimes win at arm wrestling, if he gets better leverage or sits at a better angle. I saw this being true of the gods as well. If a guy with Omega-1 strength and a guy with Omega-2 strength compete, there's still a chance that the weaker guy can win if he puts his smaller infinity to better use. Thus the need for checks. I just need to figure out the rules for them...

That being said...

How do you write the little sideways-8 infinity symbol?
Is there a way to write the little-w Omega symbol?
Is there a way to put the number as a sub-script so it doesn't look like Omega-2 is saying "Omega minus 2"?
And I have never heard of Nobilis before. Where can I find more about it?

Amechra
2014-12-16, 10:13 PM
I think they might be using the + after the ∞ to refer to increasing the transfinite ordinal (ω0 + 1 = ω1). I mean, it's valid to do that, but then it isn't exactly addition (or, rather, they didn't define how they were doing their addition.)



All of the following are written by pressing CTRL + SHIFT + U, entering the listed symbols, then hitting the SPACEBAR.

∞: 221e
ω: 3c9

You see that symbol that says X2 up in the editing toolbars above where you write the posts? Click it. Or wrap the 2 in <sub></sub> tags, replacing the angle brackets(<>) with square brackets([]).

Nobilis is a diceless game by Jenna Moran where you play demigods that reign over anything from Hope to WMDs; it's literally designed for this kinda thing. You can find a quick review of the corebook for the newest edition here. (http://www.rpg.net/reviews/archive/15/15366.phtml)



Someone with higher Infinity should always win. The gulf between mortals and ω0 is the same relative scale as from ω0 to ω1; to use your examples, it's not that one guy's just stronger than the other, it's that one of them is a sickly toddler and the other is The Incredible Hulk.

I mean, you could institute a system where if someone rolls a Natural 20, they get to act as if they were one ω level higher.

qazzquimby
2014-12-17, 02:03 AM
I know about this, but not to the extent of Amechra.
To clarify ∞+1 = ∞ (practically, maybe not mathematically), because the one is so unbelievably insignificant in comparison. Same with ∞+1,000,000,000. Also, I thought ∞-∞ was indeterminate? Am I thinking of ∞/∞? What if you subtract a greater ∞ from a lesser ∞?

And I think if you were going to actually implement this, forget about fancy maths and just say Something with divine rank 2 will always beat something of divine rank 1 or lower. Something impossible for mortals (eating the plane of cotton candy) would be a divine rank 1 challenge. A die roll for D1, impossible for D0-, and effortless for D2+.

Any thoughts on that?

Thomar_of_Uointer
2014-12-17, 10:26 AM
Neat idea. This means that a God of Shadows would be infinitely stealthy, or invisible at will. A God of Wisdom would be clairvoyant (but not omniscient) and be able to see and hear everything. A God of Knowledge would have infinite spell slots and also be able to recall anything that has ever been written down.

It seems like a God of Life would be in a less-than-enviable position of being merely immortal and invincible. Your divine rank system should account for this and cover domain abilities and stuff like that.

You should probably consider what it means when any deity with infinite Strength can one-shot any other deity who doesn't have higher infinite Constitution.

Anyways, I think your "different levels of infinity" thing isn't the best idea. Instead I would assign divine ranks as points to the six ability scores, and wherever a comparison is necessary whoever has more divine rank assigned to that score wins.

qazzquimby
2014-12-17, 03:59 PM
Neat idea. This means that a God of Shadows would be infinitely stealthy, or invisible at will. A God of Wisdom would be clairvoyant (but not omniscient) and be able to see and hear everything. A God of Knowledge would have infinite spell slots and also be able to recall anything that has ever been written down.
That interpretation is more interesting than mine. I thought a level of godhood basically put +infinity on all stats, with differences only showing on the same divine rank, but only boosting some would make gods much more unique.

JBPuffin
2014-12-17, 10:02 PM
Yeah, this definitely wouldn't be very compatible with 3.5...on the other hand, it could work really well for something like FATE or something sort of light, where all you'd have to do is take a smallish die and add the Divine Rank to it.

So, a god has a generic Rank - say, Rank 1. A Rank 1 God has a single stat at ∞, while a Rank 2 God might have a single stat at ω1 or two at ω0 (∞). If you wanna have multiple Spheres of Influence, you can't have the same power as a god who has just as much total power but focuses more tightly. If you want to give some elbow room for the little guy, you could do something like 3 Fudge Dice + Stat, just to have some variety.

Of course, there comes the question of what a Rank 2 God of Fire can add his +2 to, although there's probably some metaphorical allowance in there. Same even with obvious ones like Strength, Speed, etc, because hey, GODS!


That interpretation is more interesting than mine. I thought a level of godhood basically put +infinity on all stats, with differences only showing on the same divine rank, but only boosting some would make gods much more unique.

That would rather defeat the point of gods having spheres whatsoever, really, but there are probably some common traits among them...ooooh, trap them in human forms, but they still have their Divine Stats. Awesomesauce :smallbiggrin:

Zale
2014-12-18, 02:31 AM
Funnily enough, I've seen this idea before: It's in the Immortals Handbook, well known for it's amusing neutronium golems.

IIRC it has infinity as a stat. Each infinity always wins but can be beaten by another infinity. (So infinite DEX is unhittable except by infinite STR, while infinite CON is canceled out by infinite STR. In the case of apposed infinities, they use their normal stats for determining things.)

It's an interesting idea.

Thomar_of_Uointer
2014-12-19, 01:36 AM
Yeah, this definitely wouldn't be very compatible with 3.5...on the other hand, it could work really well for something like FATE or something sort of light, where all you'd have to do is take a smallish die and add the Divine Rank to it.

In the case of FATE, it's probably better to just leverage the "Aspects Are Always True" rule. If you are A Mighty Warrior Who Cannot Be Bested In Single Combat, then you always automatically win duels. If you are A Scholar Who Knows Everything That Has Ever Been Written Down then it's as simple as that. The only time you would have to make rolls for such absolute aspects is when you're up against a similarly absolute aspect.