Diagonal wonkiness scenarios

[Ourph]

To summarise: Even if your room is actually honest-to-goodness a circle that you portray as a square, the 4E diagonals still don't work mathematically past a first order movement. Or in other words, what 4E is doing is not just the same as transforming circles into squares. You still may be okay with this, and that's fine.

Exactly. However, the thing to note is that there can be appropriate triangle inequalities within the "battlemat geometry", there's just no way for someone who is not also subject to those rules to actually draw that triangle on the battlemat.

In the battlemat universe, both people moved exactly the same distance and both moved in a non-straight line (perhaps to avoid some obstacle), even though, as viewed from our geometry, one moved in a straight line and one moved along two straight diagonals. How do we know this? Because in the battlemat universe, both people moved the same distance and both ended up in the same spot. This couldn't happen if one path was straight and the other non-straight, ergo neither path was straight.

 

[Nytmare]

Many of you "11:1 guys" act like zealots defending this wonky rule.

No, we act like the people who understand what it is that the new rules are trying to describe.

 

[Rystil Arden]

Don't worry, I speak math.

Care to explain what a 180 degree angle looks like in a non-Euclidean space?

To requote for emphasis:

Chebyshev space is the L-infinity space.

Would you agree that Manhattan distance does not violate the triangle inequality? Manhattan distance is the L-1 space. The points (0,0), (0,1), (1,0) form a triangle. The lengths of these sides in Manhattan distance are 1, 1, and 2. This gives equality for the condition "the measure of a given side must be greater than or equal to the difference between the other two sides". These points are clearly not on a "straight line" when viewed in Euclidean space.

A straight line in a space is defined as the shortest distance between two points, so actually (1,0), (0,0), (0,1) is on a straight line in Manhattan distance. Manhattan distance cannot be easily mapped into Cartesian coordinates--it would involve squaring circles as for 4e Chebyshev/Minkowski, but then when you go 3D, you get something that looks sort of like an octahedron rather than a sphere.

 

[Nytmare]

As a side note, when 3rd Ed came out, everyone in the circle of gamers I played with was awestruck with the innovation brought on by the 1-2-1 convention. Prior to that, when using minis and a quad-mat, we would either do orthoganal only movement, or 1-1-1.

I think it's funny that it took my gaming group almost ten years to realize that it wasn't actually doing anything special for us.

 

[Ourph]

At it's heart, both are problems with mapping the world onto a battlemat, and playing on the battlemat.

According to 3e, and presumably 4e, you don't occupy either diagonal square. If you (the editorial you, not you specifically ) have no problem with one world-to-battlemat distortion, why should another be a problem?

Which is why I say it's not a movement problem, it's an "occupation" problem. If two creatures standing adjacent to each other (i.e. "shoulder to shoulder") can impose certain penalties or restrictions when another creature attempts to move between them, it should apply to creatures oriented both orthagonally and diagonally. The only time the movement rules come into it is to determine whether you have the movement necessary to reach the unoccupied square beyond the adjacent creatures. If a creature has the necessary movement, the difference between orthagonal and diagonal alignment should become moot. In both cases, the creature doing the moving is still passing between two adjacent creatures. The only way to justify freely moving diagonally is, as you correctly point out, if the creature in question miraculously becomes 2 dimensional during his diagonal movement. If that were possible, then there shouldn't be any penalty for moving orthagonally through an occupied square either. A 2d creature shouldn't have any problem slipping between 2 creatures, no matter how they are oriented.

 

[Rystil Arden]

Exactly. However, the thing to note is that there can be appropriate triangle inequalities within the "battlemat geometry", there's just no way for someone who is not also subject to those rules to actually draw that triangle on the battlemat.

In the battlemat universe, both people moved exactly the same distance and both moved in a non-straight line (perhaps to avoid some obstacle), even though, as viewed from our geometry, one moved in a straight line and one moved along two straight diagonals. How do we know this? Because in the battlemat universe, both people moved the same distance and both ended up in the same spot. This couldn't happen if one path was straight and the other non-straight, ergo neither path was straight.

So then, that means a few things. One, where is my real straight line then? If that wasn't a straight line, there must be a shorter path that neither of those people took. Where is it? Why can't I take it? Also, iif I have a spell that shoots in a straight line, it won't shoot in a straight line on the battlemap? I'm thinking even the other pro 1-1-1-1-1 people wouldn't want to wrap their heads around a straight line not being straight. If that doesn't make your head explode and 1-2-1-2-1 does, your brain is wired very differently from mine (admittedly possible)

 

[SlagMortar]

A straight line in a space is defined as the shortest distance between two points, so actually (1,0), (0,0), (0,1) is on a straight line in Manhattan distance. Manhattan distance cannot be easily mapped into Cartesian coordinates--it would involve squaring circles as for 4e Chebyshev/Minkowski, but then when you go 3D, you get something that looks sort of like an octahedron rather than a sphere.

Fair enough. Then in Chebyshev space there are multiple "straight line" (by that definition) paths between two points. Do you still claim 4E movement violates the triangle inequality?

Edit: Note there are also multiple "straight line" paths between two points in a Manhattan space, which makes sense. If you need to get to the NW corner of a city block from the SE corner, you can go W and then N or you can go N and then W. The distance is the same either way.

 

[IanB]

After playing about 30 games of DDM 2.0 with the new diagonal movement:

Yes it is weird at first. I thought I was going to be bothered by it forever - I *really* hated the idea at first - and was thinking "I will have to house rule this in my home RPG or we'll all go mad".

But honestly? I don't even notice it now. It really doesn't end up mattering at all for purposes of skirmish, and I am pretty sure for RPG the same will mostly hold true. It is only when you go to a 3rd dimension being involved that I think it gets ... complicated.

 

[Sir Sebastian Hardin]

In the battlemat universe, both people moved exactly the same distance and both moved in a non-straight line (perhaps to avoid some obstacle), even though, as viewed from our geometry, one moved in a straight line and one moved along two straight diagonals. How do we know this? Because in the battlemat universe, both people moved the same distance and both ended up in the same spot. This couldn't happen if one path was straight and the other non-straight, ergo neither path was straight.

Now, this is good a case.
Things like running and charging in straight lines could be counter-case, but they are gone, I think...

BUT...(here we go)
That valid asumption is invalidated by the way they handle Area effects. There's no movement there. No erractic non-straight movement. In spell areas all you get is: "Diagonal = Orthogonal. Deal with it!"

So then, that means a few things. One, where is my real straight line then? If that wasn't a straight line, there must be a shorter path that neither of those people took. Where is it? Why can't I take it? Also, iif I have a spell that shoots in a straight line, it won't shoot in a straight line on the battlemap? I'm thinking even the other pro 1-1-1-1-1 people wouldn't want to wrap their heads around a straight line not being straight. If that doesn't make your head explode and 1-2-1-2-1 does, your brain is wired very differently from mine (admittedly possible)

And this.

 

[Rystil Arden]

Fair enough. Then in Chebyshev space there are multiple "straight line" (by that definition) paths between two points. Do you still claim 4E movement violates the triangle inequality?

Edit: Note there are also multiple "straight line" paths between two points in a Manhattan space, which makes sense. If you need to get to the opposite corner of a city block, you can go left and then right or you can go right and then left. The distance is the same either way.

I said it violates the triangle inequality in Euclidian spaces. And it does. As I said, a Minkowski space would be fine. Chebyshev too. Both of them cause significant headaches as Minkowski is relativistic and Chebyshev is a quantum space. If you're cool with the fact that since the triangle inequality can never be broken in an applicable then we must be in one of these sorts of spaces, then I think we completely agree. I disagree with the people who think that we're in a Euclidian space (no quantum physics required!) and that the triangle inequality is preserved in that space.