The Silly, Wacky, Revealing and Useful Shadows

My daughter was jumping around, trying to separate from her shadow today. Probably inspired by Peter Pan's adventures of loosing his shadow, which had been found, washed, folded and magically re-attached. Shadows can be art, like a theater of shadows or a beautiful projection of tree branches on the wall or on a fresh carpet of snow.

Image courtesy of Funka Lalere, distributed under Creative Commons license

Shadows are surprisingly useful. Have you ever thought how to measure the height of an object that is much higher than you, like a skyscraper? It is believed that Greek philosopher and mathematician Thales went to the Egyptian Pharaoh and claimed that he found a way of measuring the height of pyramids. (This was 500 BC, way before HomeDepot). And Thales did it by using shadows! He deduced that at the moment that his personal shadow was equal to his height, the pyramid's shadow would be equal to its height. Using this very old math you can measure the height of your own skyscraper. Or you can impress your kids by measuring the height of any object under the sun, due to the fact that the relationship of your height to your shadow is the same as the relationship of your kid's height to his shadow, as is the relationship of any object to its own shadow. See toy illustration below.

When I worked in the movie special effects field, we paid special attention to the way artificially rendered objects were inserted into a movie sequence and how they cast shadows. For the movie 'Patriot', when shooting battlefield scenes in the vast fields of South Carolina, we used special technology to capture the direction of the sun, so that later, many artificial soldiers could be inserted into these movie sequences and their illumination looked realistic. Sophisticated computer programs were designed to carefully render new computer-generated soldiers, and simulate sunlight as well as soldiers shadows. Lack of shadows or incorrectly drawn shadows are easily detectable by our eyes and make scenes appear non-real. In fact, shadows help resolve the authenticity of video clips or photographs circling around the Internet and are used in digital forensics.

A friend and digital forensics expert, Prof. Hany Farid from Dartmouth, sent me this cover image of Angelina Jolie and Brad Pitt. Farid claims this to be a composite of two separate photographs, with shadow math serving as a proof. If you look at the shadows on Jolie and Pitt's heads, you can see that they are each looking into the sun, which therefore must be in two different places. Impossible!

Solar Eclipse, July 2009

Shadows can also be mysterious. A lunar eclipse, when the Moon passes through the Earth's shadow, or solar eclipse, when the Moon blocks the Sun and casts a shadow that brings night to day, had been mystically terrifying for generations. They have stopped wars, caused mass repentance and led to the silly rhymes about sun eaten by crocodiles. Eventually the geometry of planet motions and shadows they cast onto each other became understood. However, even with all this knowledge, let's admit that we have to frequently remind ourselves (and the Dream Works founders) that the Moon is not shaped like a banana.

Returning to frightening and spooky, who has never been scared by his own shadow at least once in their life? And does anyone know whether ghosts have shadows? Does it matter if you cannot see shadows in a dark room anyway? Nighty night and Happy Halloween!

Try it at home:

Mark your calendars for the next Total Lunar Eclipse that could be observed in North America on Dec 21st 2010. This is a great opportunity to share with your kids the geometry of planet configuration, motion and the mystery of a disappearing moon.

This Halloween, impress your kids by showing how to find any monster's height from her shadow. The only problem is that you have to dare stand next to the monster. Proportions of your height to your shadow's height should be the same as proportion of the monster's height to her shadow.

You can bounce off ideas on how one can separate from his/her shadow.


  1. My older son argues that ghosts do not have shadows since they are made of thin air and the air does not cast shadow.

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