Lunar terminator paradox

There’s an optical phantasm recognized by names just like the “lunar terminator paradox”.
This has a lot dialogue and descriptions on-line, however none made sense in my
head, so I wrote this program to determine what was occurring. The paradox:

• The moon is illuminated by the solar
• After sundown, the solar is beneath, so we might anticipate the illuminated portion of
  the moon to level down, in direction of the place the solar is
• This is not what at all times occurs!

I used to be tenting within the mountains with a pal not too long ago. We had been trying up on the
sky, simply after the solar has set. The moon was clearly pointing up.

After enjoying with this program, I’ve readability: we’re trying up on the moon
from beneath. The most pathological case is a full moon. Let’s say the moon is on
the horizon: elevation=0. If we’re taking a look at this low moon, and the moon is
full, the solar is immediately behind us. The moon is totally illuminated, and we see
100% of the moon disc lit up.

Now, what occurs if the moon is just not on the horizon, however larger up on the sky?
Effectively, the solar is infinitely far-off, so the identical a part of the moon is lit
up. But we’re now trying on the moon from beneath, and we’d see among the
darkish aspect on the underside edge. I.e. the moon seems shiny on the prime, however has a
darkish slice lacking on the backside: it factors up! Even at sundown.

This is essentially the most clearly bizarre case. A half-moon has no paradoxical habits,
and the extra full the moon, the extra clearly we are able to observe the brilliant moon
pointing up regardless of the solar being down.

I produce two plots. At 3/4-full moon at sundown we take a look at the moon because it rises
from the horizon all the best way as much as the zenith:

If the moon is on the horizon (elevation = 0), we see the anticipated 3/4-lit disc.
As the moon rises, we see increasingly more of its backside, and thus increasingly more
darkish areas present up: It clearly factors up at sundown!

We may transfer the solar round. Let’s say the moon is 60deg up; let’s transfer the
solar from new-moon to a full-moon:

In the darkest configuration, we are able to nonetheless see a lit crescent on the underside: the
illumination is all on the other aspect, however we are able to see a slice of the
illuminated again aspect. As the solar swings round, we see increasingly more of the
moon. At azimuth = 90deg, we’ve a half-lit moon. Past that, increasingly more of
the moon is seen, at all times pointing up.

This was additionally an excellent fascinating examine of the present state of AI instruments. As I
was penning this and debugging, I might speak to Claude and Gemini about how this
labored and what I must be seeing. They had been each fully unable to
comprehend this, and would make infinite round arguments. Clearly they learn
some incomplete explanations on the web (as I’ve), and lack the reasoning
functionality essential to distill it into one thing resembling “understanding”.
AGI is just not right here but.