Diagonals revisited

[Midknightsun]

After reading this thread. . .

I feel like Cthulu just beat me with a big Rod of Neverending Nerd Rage+5

I think I need to sleep now.

 

[Thyrwyn]

It is logically, not merely physically, impossible for Pythagorus' Theorem to be false.

Einstein and Hawking disagree.

And I do insist that my characters, assuming they have Intelligence scores of at least 10 or so, notice glaringly obvious features of the physical world around them. I can't wrap my head around how someone could fail to do so, or expect me to play a character who failed to do so with any sense of immersion whatsoever.

Yet, you were upset that I could not see your side.

I read the post you linked to. The biggest of my problems with it is - why would the admittedly many and complicated variables being abstracted away ... systematically favour movement in some directions (on a grid which is in the first place completely arbitrary) over movement in others?

The grid is arbitrary - but fair. It affects all characters/monsters/agents/actors in the scene the same. In mathematical terms, we replaced all instances of a given variable with a given constant, on all sides of the equation. The 1-2-1-2 rule systematically penalizes movement on the diagonal. Why isn't that "glaringly obvious" and why doesn't it prevent "any sense of immersion whatsoever"? My point is that character's wouldn't notice that, either, because a) there are too many other variables clamoring for attention, and b) while the grid is constant within a given scene, it is not a world constant. You could not travel around the world "on the diagonal", for instance, because the grid does not exist outside of any given encounter.

(all of which are, by the way, firmly on the physical side of my distinction)

Your distinction has bearing on neither the argument at hand, nor my point that gridded world of D&D is non-euclidian regardless of the presence of the 1-1-1 rule. This is logically irrefutable. If I want to move to a space that is 3 spaces straight ahead and then 2 diagonals ahead and to the left, there is no straight line I can move that will get me there. Furthermore, if I were to move as described I would end up just over 26' (assuming each square=5') from where I started; if I were to move 2 spaces straight ahead and then 3 spaces diagonally ahead and to the left I would have covered more than 29'!

 

[Doug McCrae]

Other forums are going to point at this thread and laugh at us.

 

[Geron Raveneye]

The 1-2-1-2 rule systematically penalizes movement on the diagonal. Why isn't that "glaringly obvious" and why doesn't it prevent "any sense of immersion whatsoever"?

How do you get to that conclusion? There is no penalty. Either way, you cover 30' per round. On the other hand, the 4E rule penalizes orthogonal movement, because you only get to move 30' per round, while you get to move 42' diagonally. At least that's how it looks to me. Or are we talking from different understandings of the word "penalty"?

As for the fact that there is no straight line to describe mixed movement across the grid...that is an artifact from using a grid in the first place. If you use a string/ruler and chuck the grid out the window, you can move in staight lines, curves, and always stay within geometrically safe margins. But string/ruler and no grid wouldn't sell virtual tabletop gaming, even though that should be the best environment to calculate exact movement ranges, areas of effect and threat ranges in real time without a silly grid.

Other forums are going to point at this thread and laugh at us.

Maybe so...but who cares what other forums are doing, huh?

 

[Wormwood]

Other forums are going to point at this thread and laugh at us.

Waaay ahead of you.

 

[Steely Dan]

Other forums are going to point at this thread and laugh at us.

There is already mass pointing of fingers and giggling from the gallery.

 

[Ilium]

How do you get to that conclusion? There is no penalty. Either way, you cover 30' per round. On the other hand, the 4E rule penalizes orthogonal movement, because you only get to move 30' per round, while you get to move 42' diagonally. At least that's how it looks to me. Or are we talking from different understandings of the word "penalty"?

I hesitate to enter this discussion, but I think he means that 1,2,1,2 isn't exactly correct either. By counting the diagonals as 1.5 x 5 feet when they are really 1.41 x 5 feet, you are slightly penalizing diagonal movement when compared with orthogonal movement. So if you move 4 square diagonally, you actually only moved about 28.2 feet instead of the 30 feet you would move orthogonally.

The 4E method of counting results in a bigger "error" but both would be evident to a character who actually investigated it.

Is that right, Thyrwyn?

 

[Thyrwyn]

exactly. It began (pages ago) as a refutation of the use of "non-euclidian" to refer to the 1-1-1-1 move rule. The 1-2-1-2 rule fails to live up to the "euclidian" standard as well.

My point, again, is that any difference between the two rules is one of degree, not of kind. You can dislike one or the other all you want, but neither of them are models of geometric purity.

Either would be noticeable, or neither would be. I can happily exist in the latter camp.

for the record - I am laughing. But I am also having fun

 

[Plane Sailing]

Einstein and Hawking disagree.

Why do you think that?

I only ask because just last week I was listening to an eminent mathematician explaining how Pythagoras's theorem works perfectly well in n-dimensional space, even when talking about 197,883 dimensional objects

Source: http://www.bbc.co.uk/radio4/science/thematerialworld_20080207.shtml

Scientists: Marcus Du Sautoy, Professor of Maths at the University of Oxford and author of Finding Moonshine and Prof Robert Curtis, Deputy Head of Research, School of Mathematics, University of Birmingham.

They referred to Robert Griess at Princeton who ''constructed'' a sort of snowflake like figure in 196883 dimensional space which had over 10^53 symmetries

The ability of the theorem to function in n-dimensional space is fundamental to the construction of n-dimensional hyperspheres in spaces with an arbitrary number of dimensions.

I don't recall anything by Einstein or Hawking that particularly disagreed with this, and the current cutting edge of dimensional mathematics still holds that Pythagoras's theorem remains logically true and probably supercedes their opinion on the matter anyway.

Unless you know different?

Cheers

 

[Carnivorous_Bean]

I still haven't changed my mind. I'm very disappointed that 4E is going with 1/1 diagonals.

Ken

And yet your avatar contains a perfect solution to that problem if it bothers you.

And using a ruler to move your minis is another. 5 squares = 5 inches, in any direction. Simple, neat, effective. If the grid isn't doing anything for you, why continue to use the grid?