D&D 4E Non-Euclidean Geometry in 4E?

[Puggins]

sqrt(18) = ???

I had to look at it for a minute, but you're right that ainatan's been warping space a lot more than WotC is: the only "reasonable" conclusions are that people can actually move quite a bit faster along diagonals, or that squares of distance are more like polar than normal coordinates. Your math is wrong unto the devil, though.

EDIT: Or "it's all an abstraction, you really should relax", of course - I suggest hex grids or free movement for your home games if you can't.

I'm pretty sure my math is correct- it's my presentation that probably needs some help. Let me rephrase.

Take the first picture. The wizard and the monster are orthogonally 30 feet apart. If you assume that the path is the "hypotenuse" of a room, connecting opposite edges, then each side of the room is 30 divided by sqrt(2), or 21.3 feet. The area of that room is (21.3)^2, or 450 square feet. Since each 5'x5' square consists of 25 square feet, there would be 18 squares in that room- yes, I know that they'd be chopped up on the actual map, but the total square area is roughly 18 map squares.

Now take the second picture. This one is a ton easier, since the hypotenuse is actually diagonal. They are standing in opposite ends of a 30'x30' room. I actually did this on my calculator the first time and got a rounding error, but I didn't need to do that. a 30x30 room consists of 36 map squares and 900 square feet, and is twice the size (in area) of the 1st room.

Hopefully that makes things more clear.

 

[Puggins]

Nitpick: the scientific definition of the meter is the distance light travels in a vacuum in a (very small) fraction of a second.

So there is some precedent for judging distance based on how far something can travel in a certain length of time.

I knew somebody would bring that up

Yes, you're absolutely right. But there is a difference between a mathematical constant of the universe (c) and a D&D character. You can be confident that one won't change as of tomorrow. The other might be in the trash can within an hour or two.

 

[WhatGravitas]

I'm sorry, but you are trying to explain the unexplainable. The rules are simply wrong, and they create bizarre situations due to the nature of the square grid.

Actually, the rules only break the rotational invariance of the room. 4E world is simply an anisotropic space. The problems stem from transferring geometry tailored to isotropic, euclidean space to it.

Cheers, LT.

 

[Imban]

I'm pretty sure my math is correct- it's my presentation that probably needs some help. Let me rephrase.

Take the first picture. The wizard and the monster are orthogonally 30 feet apart. If you assume that the path is the "hypotenuse" of a room, connecting opposite edges, then each side of the room is 30 divided by sqrt(2), or 21.3 feet. The area of that room is (21.3)^2, or 450 square feet. Since each 5'x5' square consists of 25 square feet, there would be 18 squares in that room- yes, I know that they'd be chopped up on the actual map, but the total square area is roughly 18 map squares.

Now take the second picture. This one is a ton easier, since the hypotenuse is actually diagonal. They are standing in opposite ends of a 30'x30' room. I actually did this on my calculator the first time and got a rounding error, but I didn't need to do that. a 30x30 room consists of 36 map squares and 900 square feet, and is twice the size (in area) of the 1st room.

Hopefully that makes things more clear.

Hmm... okay, your math *is* right, then, I just didn't get what you were talking about. But ainatan was positing that the hypotenuse was the same length in both, so...

 

[HeinorNY]

Actually, the rules only break the rotational invariance of the room. 4E world is simply an anisotropic space. The problems stem from transferring geometry tailored to isotropic, euclidean space to it.

Cheers, LT.

But if you were playing the wizard, wouldn't you prefer to set the minis on the grid like in the second diagram?

 

[HeinorNY]

Hmm... okay, your math *is* right, then, I just didn't get what you were talking about. But ainatan was positing that the hypotenuse was the same length in both, so...

In the 1-1-1-1 rules they are.

 

[Geron Raveneye]

Actually, the rules only break the rotational invariance of the room. 4E world is simply an anisotropic space. The problems stem from transferring geometry tailored to isotropic, euclidean space to it.

Cheers, LT.

You know...if I see ANYbody complaining about WotC "dumbing down" D&D with 4E again, I'll point them to your post here. THIS is certainly not dumbing down D&D, not by a long shot.

On the other hand, it'll make planehopping to the Far Realm no big deal anymore.

On a tangent, can anybody think of an equally simple rule that will fix angles > 360° in a circle into D&D without breaking a sweat? I'm getting a lovely lovecraftian feeling by now.

 

[WhatGravitas]

But if you were playing the wizard, wouldn't you prefer to set the minis on the grid like in the second diagram?

If I'd play the wizard, I'd prefer to have more of my party colleagues around me! Or a defensive spell! Or not having a monster there. Or a wall in front of my character. And the second picture is exactly like the things I have listed - a completely different situation. Like having a wall in front of you. Or more friends.

The two pictures, under 4E space, are simply non-comparable, because they show entirely different situations, that have nothing to do with each other, unless you cling to the idea of rotational symmetry.

But I give you that: It's a weird idea to give that up. And I prefer the 2-1-1-1-1 rule from this thread. And I wish I could see a Escheresque projection of 4E space into our euclidean space - basically a square grid warped into a circle.

On a tangent, can anybody think of an equally simple rule that will fix angles > 360° in a circle into D&D without breaking a sweat? I'm getting a lovely lovecraftian feeling by now.

Hmm... I wonder it that's not already the case... That's why I want to see that projection - it's too late to think about it without a pretty picture!

Cheers, LT.

 

[Sir Sebastian Hardin]

But if you were playing the wizard, wouldn't you prefer to set the minis on the grid like in the second diagram?

If I were thw wizard, that is, a player. I couldn't decide how the grid is placed. Its the DM's call.

I still don't like the 11 rule. I'll go with hexes or 1.5 diagonals. I am, like you, against 11:1, but your reasoning is ruining our case.

 

[ruemere]

I'd like to point out that simplifying diagonal movement to 1-1-1-1 is likely to remove a portion of fun factor which has to do with manoeuvring in combat. My parties often performed intricate flanks, piled AoOs on opponents or simply enjoyed using spring attacks to pick out select targets.

Still, we're pretty oldschool in our approach, with most simple combats being resolved through initiative order and GM adjudicating distances (sometimes making dots on simple paper to make notes of everyone's position), with battlegrid reserved for special cases. Also, we often use circles (to find out reaches of various effects) and cords. For example:

Softie

Toughie

Meanie

Drop a 5' circle on a Toughie, to find out area he threatens. Put a cord (with 1' increments marked) starting from Meanie and ending at Softie, have the Meanie owner decide on exact path and find out, if the Meanie may reach Softie without Toughie having it with Meanie.

No battle map necessary, pretty exact distance and no need to count. And all you need is a cord with marked 1' increments and several circles for 5, 10' and 15' reaches. Oh, and a paper cone.

But, as I said. It's old school solution invented in times when you had to be able to GM in small rooms, without tables, on moving trains and in other, less than comfortable, places.

Regards,
Ruemere