Mind Wandering

I recently found myself in a church, the one two blocks from the house I grew up in. The one where my mom sang in the choir. And where I spent many a Sunday bored to tears for about an hour.

While trapped in a pew I would spend time looking around, day dreaming, and wondering about an optical illusion.

This is the alter as it is today, a bit more open and bright than when I was a school kid.

The illusion has to do with the brown arch at the top of the image.

Or is it a white arch?

At either end of the arch is a corner piece. Sometimes it appears brown and concave. And others, white and convex. At least to me. And has since I was in grade school. How does it appear to you?

🕯  🕯  🕯  🕯  🕯

There was another optical puzzle to occupy my time on this visit.

Look at the candle shadows in the image below (bigafy for best results).

The shadows for the right three candles appear "solid" while those for the left three have a dark center with lighter edges. Curious. The key for me to solve the puzzle was the leftmost candle on the right side. It has a shadow lighter than the other two.

That's because it is only one shadow, from a light to its right, whereas the other two are shadows from two lights, on on the left and one on the right, and from two candles. It just so happens that the geometry of the situation, for the candles on the right, is such that the shadows overlap. So for the shadow to the left of the middle candle, it is the shadow of the middle candle from the light source to the left and the shadow of the right most candle from the light source on the right. The leftmost candle on the right side does not have a candle to its left, so the leftmost shadow is from only one candle.

If you look at the base of the candles on the right, you can see the double shadows as the back wall juts out a bit, and the geometry is no longer such that the shadows overlap.

Here is a text based schematic diagram:

                                                  Double

                         Shadow             Shadow

                                \                      /\

                                  \                  /    \

                                    \              /        \

                                      \          /            \

                                        Left              Middle

                                      Candle            Candle

                          

                   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

                            ^            

                            |    gap between lights and candles

                            v

                   ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

                Left Light                                                Right Light 

                   Source                                                       Source

For the three candles on the left, the lights and candles don't quite line up, so the overlap of the shadows is not complete. Thus the dark center to the shadows, that's the overlap.