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Theory: How line of forbiddance width determines height of field


Shardlet

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I thought of this while posting in another thread.  So, the width of a line of forbiddance determines the height of the field generated by the line.  I could readily envisage that the field forms an excedingly acute triangle (in cross-section) with the width of the scribed line as the side opposite the smallest angle (wedge shaped).

 

In other words, a field generated by a line of forbiddance has two non-parallel sides which angle towards each other until they meet (forming the top of the field) and the angle of incidence between a side of a field to the line of forbiddance is constant from line to line.  This would result in the height of the field being precisely and calculably determined by the width of the line from which it is generated.  

 

What do you guys think.

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Perhaps. You do have to account for variable strength as well, though.

 

Myself, I'm inclined to believe that there is no definite "height" to the barrier a Line of Forbiddance creates, but instead a lessening of effect the farther you go from the base. The effect is described as a repulsive field, so I'd guess that, the wider the line, the stronger the "base" strength of the field, which strength weakens as you get farther and farther from the line. So you might be able to put your hand through a barrier 10 feet up while still feeling some resistance, but feel nothing at 20 feet. A grain of sand lightly tossed at the field, though, might need to get 30 feet up before it could get through. And some poor microscopic particle with no velocity might need to go 100 feet up before it could get through.

 

You could work such variable strength into a more geometric model, though: it could well be that the force required to get through any given Line of Forbiddance at an given height is governed by such angles.

Edited by Kurkistan
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Perhaps. You do have to account for variable strength as well, though.

 

Myself, I'm inclined to believe that there is no definite "height" to the barrier a Line of Forbiddance creates, but instead a lessening of effect the farther you go from the base. The effect is described as a repulsive field, so I'd guess that, the wider the line, the stronger the "base" strength of the field, which strength weakens as you get farther and farther from the line. So you might be able to put your hand through a barrier 10 feet up while still feeling some resistance, but feel nothing at 20 feet. A grain of sand lightly tossed at the field, though, might need to get 30 feet up before it could get through. And some poor microscopic particle with no velocity might need to go 100 feet up before it could get through.

 

You could work such variable strength into a more geometric model, though: it could well be that the force required to get through any given Line of Forbiddance at an given height is governed by such angles.

 

I got the impression that the strength of the line resulted from the precision with which it was drawn (i.e., the more perfect the line, the stronger the field).  If it was an effect of the width, then I would think that the Rithmatists would all have freaking thick chalk for drawing lines of forbiddance.

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The idea of a triangular shape is interesting, but after a bit of reasoning Kurkistan model seems more natural to me.

It seems more natural from a physics standpoint because most field effect have an intensity proportional to the inverse of the distance from the source. But also from a "Rithmatic" standpoint, it seems more natural to me that a rithmatch line can't create a define shape in 3D, but can only create a more vague field effect.

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I got the impression that the strength of the line resulted from the precision with which it was drawn (i.e., the more perfect the line, the stronger the field).  If it was an effect of the width, then I would think that the Rithmatists would all have freaking thick chalk for drawing lines of forbiddance.

 

I'm fairly sure it's both, but thickness is the real kicker. There's an illustration about Lines of Forbiddance that has this to say:

 

"Lines of Forbiddance have strength based on how straight the line is. Their stability is based on the material they are drawn upon, and the height their force wall extends is based on the width of the line." ("Line Strengths" illustration before Ch 18)

 

Fitch also specifies that only a "well drawn" Line of Forbiddance can stop a cannonball. So I'm guessing straightness works in conjunction with width, but width is what you really need at the end of the day. Joel even mentions the importance of width when he's going on his "why are pretty chalklings better!?" rant.

 

And they already use the equivalent of sidewalk chalk, so far as I know. They can't go too big because they need to be able to handle it delicately enough to draw chalklings and arcs. Thoiugh I suppose the truly committed Rithmatist could carry multiple pieces for different kinds of work simultaneously...

 

EDIT: That quote also casts some doubt on my own interpretation of force wall height. "Strength" could well mean that the force wall is of uniform strength all the way up until it stops, or that it has a known gradient based on straightness, but always stops at the same point based on thickness.

Edited by Kurkistan
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