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Re: [Phys-L] Where is the sky?



On 08/18/2013 07:50 PM, Bob Sciamanda wrote:

How is it that the blue sky of scattered sunlight appears to come
from a highly localized source confined to a distant hemispherical
surface? Does not the entire atmosphere participate in this
scattering?

When you ask about "appearance" you are asking about the
eye, mind, and brain; you're not really asking about
the sky.

The retina is two-dimensional, and a great deal of what
goes on in the brain is two-dimensional. The convolutions
of the cerebrum are a way to pack more two-dimensional
processing into the skull. It is only with difficulty
that the brain can represent the third dimension.

For objects that are nearby, you can perceive the distance
using binocular parallax. For slightly more distant objects,
you can get a clue about the distance from motion parallax.
For far-away objects, it's all but impossible to determine
distance. A few hundred million years ago we figured out
that a two-dimensional representation works just fine for
far-away objects. Theory says that the reality is three
dimensional, but projecting it onto two dimensions is
more efficient and has no downside. The information it
throws away is information we didn't really have anyway.

The blue sky by day is one question, and stars by night
is an even more interesting question. The default mental
representation is stars on an abstract far-away two-
dimensional sphere. However, if you use computer graphics
to /rotate/ the star field a little bit, the brain
immediately switches to a three-dimensional representation.

Similar remarks apply to drawings. Architects, artists,
etc. have lots of tricks and conventions that they use
to suggest three-dimensional perspective in a two-
dimensional drawing ... but if you can use stereopsis
or motion parallax, it's a whole different perception.
The image leaps off the page.

Again: The vertebrate brain is capable of representing
three-dimensional configurations, but it won't do it
unless there is a good reason. Fighter pilots have a
strong incentive to learn to visualize rapidly-changing
three-dimensional configurations. Contrast this with
sports (except quidditch), which mostly involve people
running around in two dimensions.

Do you consider clouds to be part of the sky? If
you're not clever, a big cloud far away looks an
awful lot like a small cloud up close. So the
default mental representation is two dimensional,
with the cloud painted on the dome of the sky.
However, pilots have an incentive to judge how
far away a given cloud is. You can use motion
parallax, based on the motion of the airplane, to
figure out how far away each cloud is. Given a
minute or two of data, you can build up a three-
dimensional picture of what is going on in the
sky, valid out to distances of tens of miles in
every direction.

Some people are verrry much better than others at
visualizing three-dimensional configurations. I
reckon it's sorta like playing the piano: Some
people have greater or lesser amounts of innate
talent. The ones who /practice/ get better.

Most people have a hard time visualizing things
in two dimensions, let alone three. Over lunch
sometime, try asking somebody how many stars
there are in the top row of stars on the US flag.
Most people have no idea.

If you want to practice in 3D, you might start
with small models of the Platonic solids. Run
through the symmetry group for each one, rotating
it in your hand. Then put down the object. Close
your eyes and /imagine/ the object. Imagine
various possible rotations. Pay special attention
to subgroups of the symmetry group. It's a good
way to keep yourself amused during boring meetings.
I'm making two complimentary points here:
a) It's hard.
b) It's doable if you work at it.