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20110215, 04:16 PM (ISO 8601)
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 Dec 2010
Ways to generate irrational/transcendental numbers in D&D
This is a very strange question, but due to the nature of a campaign I'm in, I'd like to try to combine abilities in weird ways in order to generate an irrational or transcendental number of hitpoints, xp, stat boosts, whatever (before rounding). Can anyone think of ways to do this?

20110215, 04:25 PM (ISO 8601)
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Re: Ways to generate irrational/transcendental numbers in D&D
Have the weirder monsters have imaginary HP. (Just multiply by i)
Then, some attacks could do imaginary damage and be the only ones that worked against said monsters.Last edited by Christopher K.; 20110215 at 04:27 PM.
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20110215, 04:31 PM (ISO 8601)
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 Mar 2008
Re: Ways to generate irrational/transcendental numbers in D&D
As far as I know the rules don't use anything but addition, subtraction, and multiplication of integers. Even division and exponents are very rare and don't use the operations themselves, simply using lists of results and tables that would have been generated by such operations on the design side, but not performing any on the playing side.
Last edited by FMArthur; 20110215 at 04:34 PM.
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20110215, 04:43 PM (ISO 8601)
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 Dec 2010
Re: Ways to generate irrational/transcendental numbers in D&D
I should note that I'm a player in the campaign, not DM. My character has a mathematicscontrol power, which is the origin of my desire to create this weirdness. Imaginaries have already come up (though not as damage), and they don't quite do what I'm aiming for. They basically invoke either lovecraftian beings (of which my character is one, so its less impressive than it sounds), or they invoke true fae.

20110215, 04:48 PM (ISO 8601)
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 Jan 2007
Re: Ways to generate irrational/transcendental numbers in D&D
I do know for sure, there are ways to achieve some interesting cardinal numbers, but irrational or complex numbers might be tricky if not impossible by RAW. You could use fractional BAB and saves without rounding and do other things like that, but it will all be only rational. If it's somehow possible to trigger an infinite chain of division, then you can get irrational. Unfortunately the only division, that is readily available is connected with saving throws against spells. I don't know of any way to carry over the result to another person (preferably with some other operations to be done on the number at hand), who would be forced to save again.
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20110215, 04:51 PM (ISO 8601)
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 Dec 2010
Re: Ways to generate irrational/transcendental numbers in D&D
When in doubt, divide by zero.

20110215, 04:56 PM (ISO 8601)
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Re: Ways to generate irrational/transcendental numbers in D&D
Use a lot of cone spells, maybe? The hypotenuse might often be irrational.

20110215, 05:03 PM (ISO 8601)
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Re: Ways to generate irrational/transcendental numbers in D&D
It's not possible with hit points. We define hit points as the number of points of damage that a being can take before being incapacitated. All weapons do damage in natural numbers. So hit points are defined as starting in the natural numbers, and only being able to go down by natural numbers, so they can only be integers.
An imaginary number of hit point means you need a concept that is orthogonal (at right angles to) hit points.
Irrational numbers? They exist anywhere there's geometry. What's the longest line you can draw on the floor of a 10x10 room? 10 times the square root of 2. What's the circumference of a thirty foot diameter round tower?
Irrational stats? Easy as pi, as long as you're willing to keep rolling dice. Suppose somebody hits on a pi or higher. He rolls 4 or higher, he hits. Two or lower, he misses. If he rolls a 3, roll the next digit on a 10sided die, marked 09. If he rolls 2 or more, he hits; 0 he fails; 1 he keeps rolling, to see if he rolls above or below 3.14159265358979323846264....
Transcendental hit points only have meaning if something can do a transcendental amount of damage. Since even the entire universe being destroyed would do a finite amount of damage, an entity that could survive that would still not need a transcendental number of hit points.
But I can give you one example of an implicit transcendental number. Assume you could define a potion that could cure one hit point, and a spell that could increase a potion by 1 additional hit point. How many kinds of potions could you create? Alephnull, of course, since you could have a potion that cured 1, 2, 3, etc. (Note that each potion can still only cure a finite number.) Now, put a 1potion in a bag of holding, a 2potion in another bag of holding, a 1potion and a 2potion in another, etc. You can put any number of potions in a bag, as long as no 2 potions in the same bag are identical.
How many kinds of bags can you create? Aleph1. So you now have defined two theoretical transcendental numbers. (It's only theoretical because it would take an infinite amount of time to prepare the potions.)
But this is backwards  an improper use of these number concepts. We use the system necessary to solve the problems in front of us; we don't use them where they are not necessary.

20110215, 05:04 PM (ISO 8601)
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 Dec 2009
Re: Ways to generate irrational/transcendental numbers in D&D
Math in college was such a long time ago....use matrices? Use a graphing calc with a sine wave or some such. Then "roll" along that point.

20110215, 05:08 PM (ISO 8601)
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20110215, 05:23 PM (ISO 8601)
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20110215, 06:53 PM (ISO 8601)
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 Dec 2010
Re: Ways to generate irrational/transcendental numbers in D&D
Its clearly not easy, but things like Empower spell for instance can generate a spare 1/2 hitpoint of damage (that is then rounded away).
An imaginary number of hit point means you need a concept that is orthogonal (at right angles to) hit points.
Irrational stats? Easy as pi, as long as you're willing to keep rolling dice. Suppose somebody hits on a pi or higher. He rolls 4 or higher, he hits. Two or lower, he misses. If he rolls a 3, roll the next digit on a 10sided die, marked 09. If he rolls 2 or more, he hits; 0 he fails; 1 he keeps rolling, to see if he rolls above or below 3.14159265358979323846264....
Transcendental hit points only have meaning if something can do a transcendental amount of damage. Since even the entire universe being destroyed would do a finite amount of damage, an entity that could survive that would still not need a transcendental number of hit points.
But this is backwards  an improper use of these number concepts. We use the system necessary to solve the problems in front of us; we don't use them where they are not necessary.
Originally Posted by SurlySeraph
So a 2person loop taking 1 damage looks like:
Person 1 takes sum[j=0..inf] 2^(2*j) = 1 and 1/3 damage
All the straight Nperson loops are going to give rational numbers I think.

20110215, 07:23 PM (ISO 8601)
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 Apr 2007
Re: Ways to generate irrational/transcendental numbers in D&D
I like the idea of Imaginary Damage. Imaginary Weapons (which are probably not imaginary in the literal sense, aside from being imaginary objects in an RPG*) deal only Imaginary Damage where Complex Weapons can deal Real + Imaginary damage.
Are you asking how to randomly generate imaginary/transcendental numbers? Imaginary ones just need extra dice rolls (e.g. different colours); your Complex Battleaxe deals 1d8+1d6*i damage, where i^2=1 .
Transcendental ones are harder. Irrational numbers are easy though for a given number of decimal places; just roll a d10 for each decimal place. How you can use irrational numbers in game is probably one of those famous exercises for the reader.
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On the other hand, could go for powers named after mathematical ideas. Imaginary numbers make illusion effects, Irrational ones cause confusion, transcendental ones allow you to go ethereal. You could also Transform, Construct, or use Chaos, Divide your foes or Multiply your allies. Your adventures could take you through the Matrix, Flatland and the dreaded Radiodrome, where you fight the Witch of Agnesi to reclaim Gabriel's Horn.Last edited by Kami2awa; 20110215 at 07:34 PM.

20110215, 09:06 PM (ISO 8601)
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 Oct 2008
Re: Ways to generate irrational/transcendental numbers in D&D
you might be able to do something with the number phi (1.618...) if some sort of division could be achieved in addition to something using the Fibonacci sequence. I can think of a general concept of a Fibonacci sequence in DnD if two people have an item/magical effect that can copy itself. Two commoners start with 1 of whatever. commoner A copies his thing onto commoner B. now commoner A has 1 and commoner B has 2. Commoner B then copies all of his things onto commoner A. Now commoner A has 3, and commoner B has 2. Repeat ad nauseum. As the terms in the fibonacci sequence get larger, the expression:
N

N1
approaches phi, where N is the current term. Now the trick is just to come up a selfduplicating item/effect/whatever, and a way to divide, or somehow emulate division.

20110215, 09:16 PM (ISO 8601)
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Re: Ways to generate irrational/transcendental numbers in D&D
You've said it's ok to use numbers prerounding. Then just find something distance based. If you're in 3.5, distances are real numbers, and many spell effects are circular. It's pretty trivial to get quite a few transcendentals. Regarding how to turn these numbers into stats, I believe the famous Chuck E. Cheese build uses a maneuver that deals damage based on how far you move. The Locate City Bomb similarly has distance traveled factor in to damage. Both gain this factor through means substantially less cheesy than the builds themselves.
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20110215, 09:29 PM (ISO 8601)
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20110215, 09:30 PM (ISO 8601)
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 Oct 2009
Re: Ways to generate irrational/transcendental numbers in D&D
Imaginary numbers map to incorporeal creatures nicely; incorporeal creatures have a positive imaginary component of their hit points. Weapons that can damage incorporeal creatures have a positive imaginary component of their damage dice. Spells can rotate weapon's damage vectors some number of degrees in the realimaginary plane.

20110215, 09:47 PM (ISO 8601)
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Re: Ways to generate irrational/transcendental numbers in D&D
I think negative energy and planar protection spells are about to take on a whole new meaning.... or perhaps more correctly, definition.
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20110215, 11:45 PM (ISO 8601)
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 Dec 2009
Re: Ways to generate irrational/transcendental numbers in D&D
Wow...its been way too long since I studied math...

20110216, 03:35 AM (ISO 8601)
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 Jun 2007
Re: Ways to generate irrational/transcendental numbers in D&D
Yes. A certain monster has a transcendent AC of 25+5i. This means that to attack him, you have to roll a regular d20 as well as an unreal die (bonus points for using the weirdest die you can find for that, such as 1d7). You only hit him if BAB + d20 >= 25 and iBAB + di >= 5i.
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20110216, 04:43 AM (ISO 8601)
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 Jan 2007
Re: Ways to generate irrational/transcendental numbers in D&D
There is an easier way to achieve Aleph1. You will need Arcane Fusion, Sanctum Spell metamagic, Twin Spell metamagic, bucketload of metamagic reducers to bring Twin Spell down to +0. The point is to squeeze Twinned Arcane Fusion into Arcane Fusion as a 3rd level spell (thanks to Sanctum Spell). As the 1st level spell you put any damage dealing spell  for example Shocking Grasp. Thanks to Twin Spell you establish a loop that with each step grows exponentially, which in the limit will give you Aleph1. The best part comes, when you look at the Shambling Mound  it gets temporary CON for electrical damage with no upper limit.
The other way AFAIK involved Lightning Maces or 1d2 Crusader and some other shenanigans. I don't know the details though.In a war it doesn't matter who's right, only who's left.

20110216, 01:27 PM (ISO 8601)
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 Jul 2007
Re: Ways to generate irrational/transcendental numbers in D&D
In 3.5, it's exactly 15'. More bizarrely, the diagonal of a 5'x5' room is exactly 5', and the diagonal of a 15'x15' room is exactly 20', so congruent triangles aren't, which kind of does a number on trig in general. What's sin(45°)? Well, it depends...
In 4E, it's exactly 10'.
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