More Bent Light...

From: Dane 'Danger' Johnson (dane@frame.com)
Date: Thu 22 Feb 1996 - 03:49:37 EET


The esteemed (or, in Lunar cooking, I suppose that might be 'steamed') Ian
Gorlick said, in relation to my comments on Bent Light in Glorantha:

>I believe that is why Greg (and Nick) originally proposed that light does
curve.
>It was so there would be a horizon on a flat planet. I merely extrapolated
from
>that proposition. Nick seems to feel that I have extrapolated beyond
reasonable
>limits.
>
>Please check your assumptions about people's feet coming into view on the
>horizon while their heads aren't. Raising an object above the ground should
have
>a symmetrical effect with raising the observer above the ground.

As to reasonable levels of extrapolation, I don't think I'm qualified to
say. IMHO, if the extrapolation adds MGF to your campaign, go for it, but
of course the more you do that the farther from established cannon you get.
<Shrug> It's an old problem and I don't pretend to have any special insight.

As to the horizon provided by bent light, I fear it will behave somewhat
differently than the horizon we all know and love. I'm afraid this is long
and not entirely on topic, so if you don't want to see more, skip past this
all and/or I can take this to e-mail.

Here on Earth, where light travels (more or less) in straight lines, the
horizon is provided by a combination of "straight" light and a bent surface.
It looks like we are standing on a convex surface (ie, on the top of an
inverted bowl).

On Glorantha, with a flat surface and bent light, the appearance will be, I
think, different. Instead of appearing to be on the top of an inverted
bowl, it will appear that the observer is at the BOTTOM of a bowl oriented
in the usual fashion...

I could make this clearer with a small sketch, but since this is ASCII, bear
with me. The 'O' marks the observer, the equals signs mark the surface of
the planet, and the line of periods will be the line of sight. So, on
Earth, looking straight ahead, we look "off" the curvature of the planet,
like so.

        O...............
     =======
  === ===
 = =
= =

Light from around the bend of the planet can't get to us because it moves in
straight lines, so it's out of sight.

On Glorantha, we look parallel to the surface, of course, like so.

        O.........

==================

Light, if it moves in straight lines, comes directly to the eyes and we can
"see" forever, although distance will cause things to be too small to make out.

However, with bent light, something odd happens.

  
              ..O
           ...
       ....
.......
=====================

Assuming the O to be the head of someone standing on Glorantha, the light
will now follow a bent path from the object and up towards the Sky Dome.
Our line of sight, then, is no longer straight, but curved. If we
straighten out the Line Of Sight to be what we'd thing of as "normal", it
virtually bends the ground.

==..............O
  ===
     ====
         =======

Also, something odd happens to stuff in the distance. Going back to the
real picture, with the bent light, we introduce a wall we're looking at,
standing right at the horizon, made up of }:
               ,,
            ,,,
        ,,,,
},,,,,,, ..O
} ...
} ....
}.......
========================

Now, ignoring for the moment that the closer to the Sky Dome you are the
more attraction it will presumabely have on the light (thus bending the
light's paths into parabolas), we can see that if our head is at O, then the
light from the Horizon, where the Wall stands, is just visible to us. This
light is coming off of/coming from the very bottom of the wall. Light from
the top of the wall is moving in a path parallel (or perhaps a little more
steeply curved, because of the parabola effect I mentioned earlier), marked
by ',' and it misses the top of the head.

If we somehow raise the wall up off the ground, then all the light coming
off of it misses us. Merely making the wall taller doesn't allow it to
become more visible.

If our vantage point is raised, however, then we will be able to intercept
the light from the top of the object and/or which is coming from a source
farther away on the plane and we'll be able to see a bit "over" the horizon.

This implies, unless I've goofed up my (admittedly Earth-based) geometry,
that instead of things rising up head first over a convex horizon they will
drop down into a convex horizon feet first.

Which is weird, nonintuitive, and not at all the sort of Horizon I want.
<Shrug> So I'm going to ignore it. But it is (I think) what happens when
you take the bent light supposition to it's painful conclusion, assuming
generally Earth-like behavior of everything else involved (like mechanisms
of vision and physics and whatnot).
Dane

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