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<blockquote data-quote="Thyrwyn" data-source="post: 4071119" data-attributes="member: 12354">Einstein and Hawking disagree.Yet, you were upset that I could not see your side. The grid is arbitrary - but fair.&nbsp; It affects all characters/monsters/agents/actors in the scene the same.&nbsp; In mathematical terms, we replaced all instances of a given variable with a given constant, on all sides of the equation.&nbsp; The 1-2-1-2 rule systematically penalizes movement on the diagonal.&nbsp; Why isn't that &quot;glaringly obvious&quot; and why doesn't it prevent &quot;any sense of immersion whatsoever&quot;?&nbsp; 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.&nbsp; You could not travel around the world &quot;on the diagonal&quot;, for instance, because the grid does not exist outside of any given encounter.Your distinction has bearing on neither the argument at hand, nor my point that gridded world of D&amp;D is non-euclidian regardless of the presence of the 1-1-1 rule.&nbsp; This is logically irrefutable.&nbsp; 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.&nbsp; 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'!</blockquote>

[QUOTE="Thyrwyn, post: 4071119, member: 12354"] Einstein and Hawking disagree.Yet, you were upset that I could not see your side. 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 [i]systematically[/i] 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 [I]world constant[/I]. You could not travel around the world "on the diagonal", for instance, because the grid does not exist outside of any given encounter.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 [I]no straight line I can move that will get me there[/I]. 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'! [/QUOTE]

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