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View Full Version : Ways to generate irrational/transcendental numbers in D&D



NichG
2011-02-15, 04:16 PM
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?

Christopher K.
2011-02-15, 04:25 PM
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.

FMArthur
2011-02-15, 04:31 PM
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.

NichG
2011-02-15, 04:43 PM
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.

I should note that I'm a player in the campaign, not DM. My character has a mathematics-control 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.

Radar
2011-02-15, 04:48 PM
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.

Kobold Esq
2011-02-15, 04:51 PM
When in doubt, divide by zero.

Telonius
2011-02-15, 04:56 PM
Use a lot of cone spells, maybe? The hypotenuse might often be irrational.

Jay R
2011-02-15, 05:03 PM
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?

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 10-sided die, marked 0-9. 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? Aleph-null, 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 1-potion in a bag of holding, a 2-potion in another bag of holding, a 1-potion and a 2-potion 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? Aleph-1. 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.

randomhero00
2011-02-15, 05:04 PM
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.

SurlySeraph
2011-02-15, 05:08 PM
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.

Shield Other or Share Pain chains should do it.

Goober4473
2011-02-15, 05:23 PM
Use a lot of cone spells, maybe? The hypotenuse might often be irrational.

I bet you could get some interesting numbers out of Shape Spell (I blieve it's called).

NichG
2011-02-15, 06:53 PM
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.


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.


We haven't met this guy in hitpoints yet, but we've met (and become) creatures whose 'information density' was imaginary.



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 10-sided die, marked 0-9. 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....


Thats how you'd run it, but generating it in the first place is tricky if you're starting from integer stats. Also, see below:



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.


Transcendental is numbers like e and pi. I think you're thinking of ordinal numbers (cardinalities), which I'm not trying to mess with since in this campaign thats a good way to get permakilled.



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.


So the point here is to mess with some of the information-theoretic aspects of this campaign's universe by combining a math manipulation power with things extant in the D&D rules that would resolve strangely if you could actually see the numbers.



Shield Other or Share Pain chains should do it


Good call! I guess you'd need an infinite loop with some sort of well-defined fractal branching to make it actually go irrational? It might be a bit of a pain to set up with a finite number of creatures though...

So a 2-person loop taking 1 damage looks like:

Person 1 takes sum[j=0..inf] 2^(-2*j) = 1 and 1/3 damage

All the straight N-person loops are going to give rational numbers I think.

Kami2awa
2011-02-15, 07:23 PM
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.

*!Head explosion!

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.

The Deej
2011-02-15, 09:06 PM
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
------
N-1

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

Urpriest
2011-02-15, 09:16 PM
You've said it's ok to use numbers pre-rounding. 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.

NichG
2011-02-15, 09:29 PM
You've said it's ok to use numbers pre-rounding. 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.

So any explosive spell should do it then for the irrationals at least. And even better, its an irrational number of dice worth of damage. Great, I think that'll do the trick.

dob
2011-02-15, 09:30 PM
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 real-imaginary plane.

Safety Sword
2011-02-15, 09:47 PM
I think negative energy and planar protection spells are about to take on a whole new meaning.... or perhaps more correctly, definition.

randomhero00
2011-02-15, 11:45 PM
Wow...its been way too long since I studied math...

Kurald Galain
2011-02-16, 03:35 AM
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?

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.

Radar
2011-02-16, 04:43 AM
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? Aleph-null, 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 1-potion in a bag of holding, a 2-potion in another bag of holding, a 1-potion and a 2-potion 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? Aleph-1. 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.
There is an easier way to achieve Aleph-1. 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 Aleph-1. 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.

John Campbell
2011-02-16, 01:27 PM
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.
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'.


What's the circumference of a thirty foot diameter round tower?
120', same as a 30'x30' square tower. But their areas are different...