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Treebeard's Stumper Answer
8 March 2002

Over The Rainbow

Rainbows are an ancient symbol of hope, and it's my hope we get to see one soon. We really need more rain before summer. Rainbows are caused by the "transit of light through particles of water," but they are unusual objects that not even bluebirds can fly over. Stumpers abound. When I try to fit a full rainbow into a photograph, why doesn't it help to step back? Why does light reflecting from millions of raindrops add up to just one rainbow? Do two people standing side by side or many miles apart really see the same rainbow? (Thanks Cynthia!)

Above are two rainbows I photographed in the Santa Ynez Valley last fall. Note how different the shapes are. If you look close at the top-right photo, you can see that it is a double rainbow with the colors reversed so that the two red bands face each other.

Right is a close shot of the end of the rainbow, and another question. Does that rainbow pass in front of the tree or behind it? It seemed far away at the time, but now I'm not sure. If you look close, you can see a few streaks of rain in the foreground as I took the picture.

Below are some other rainbow-like objects I've managed to photograph lately. These rings and sundogs look more like bright clouds than rainbows, but there is a hint of color even in the moon ring at night. It's interesting that the reddish color is on the inside of these bows rather than the outside like normal rainbows. I'm still waiting to capture halos, pillars, and a perfect fogbow!

Partial ring around the sun at sundown. Ring around the full moon at night.
Sundog on the left side of the sun. Sundog on the right side of the sun.

It's an ancient tradition that rainbows are a symbol of hope, and I was glad that some DMS students knew the original story. (What?) I have to think of the wonderful song "Over The Rainbow" by Harold Arlen and E.Y. (Yip) Harburg written for the Wizard of OZ movie (1939). Judy Garland soars over the rainbow in the first two notes ("some-where"):

Somewhere over the rainbow, way up high
There's a land that I heard of, once in a lullaby
Somewhere over the rainbow, skies are blue
And the dreams that you dare to dream really do come true
Some day I'll wish upon a star,
And wake up where the clouds are far behind me
Where troubles melt like lemon drops
Away above the chimney tops, that's where you'll find me
Somewhere over the rainbow, bluebirds fly
Birds fly over the rainbow
Why then, oh why, can't I?

If happy little bluebirds fly
Beyond the rainbow
Why, oh why, can't I?
  Original sheet music from the
Library of Congress OZ collection.
There's another collection here.

What is it about rainbows that makes them such a perfect symbol for hope and fantasy? It is a fun scavenger hunt to track down as many cover versions of "Over the Rainbow" as you can find in all music genres! Amazon and CDNow are useful research tools. Napster and Morpheus have fallen, but Grokster and Kazaa and Limewire/Gnutella (etc.) are acceptable if you clean out the spyware. How many different cover versions can you find?

Rainbows are a pattern of light reflected by all the raindrops at a particular angle between eye and sun. Each falling drop sends a single color to my eye at its exact angle, but there are many drops, near and far. If I step back, I'll see light coming from different drops, but the angles will stay the same, so the rainbow's size stays the same as well. We all see the rainbow colors reflected from different drops, so I'm not even sure if I see the same rainbow! It's a rich symbol. You can easily walk (or fly) through my rainbow, but your own will always be out of reach.


My fellow DMS teacher Cynthia Carbone suggested this stumper in an email. She also gave me this beautiful rainbow photo taken at Hollister Ranch near Point Conception. This photo is a fine example for my stumper on The Perfect Light (08 Feb 2002). Note how everything is brighter inside the rainbow, but not over it!

There is a Chumash Native American story about going over the rainbow at Point Conception, with many different versions. In one version, the Rainbow Bridge goes from the Santa Cruz Island to the mainland:

Hutash had an idea of making a bridge out of a rainbow. She made a very long, very high rainbow, which stretched from the tallest mountain on Santa Cruz Island all the way to the tall mountains near Carpinteria. Hutash told the people to go across the Rainbow Bridge, and fill the whole world with people.

So the Chumash people started to go across the bridge. Some of them got across safely, but some people made the mistake of looking down. It was a long way down to the water, and the fog was swirling around. They got so dizzy that some of them fell off the Rainbow Bridge, down, down, through the fog, into the ocean. Hutash felt very badly about this, because she had told them to cross the bridge. She didnít want them to drown. Instead, she turned them into dolphins. So the Chumash always said that the dolphins were their brothers.

Another version of the story has the bridge going the other direction as the path for departing souls traveling from the "Western Gate" at Point Conception to the afterlife beyond the Channel Islands.

Hidden away on San Marcos Pass not far from my home is this interesting Chumash rock art site. Protected underneath the rainbow-shaped rock arch is a rainbow-shaped fragment of red lines. Unfortunately, the sandstone is badly eroded and only this fragment remains. This was a foggy day.

I'm skeptical of this charming "over the rainbow" story, though it's been told many times. As far as I know, it's not included in Thomas Blackburn's classic book December's Child about Chumash oral narratives. But anthropologist Blackburn does mention some elements of the story in his narrative of the soul's journey to the paradise of Similaqsa after death. It's a darker vision:

On the fifth day after death the soul returns to the grave to oversee the destruction of it's property before leaving for Similaqsa The soul goes first to Point Conception, which is a wild and stormy place. It was called Humqaq, and there was no village there...

Just beyond... lies a body of water that separates this world from the next, with a bridge that the soul must cross to reach Similaqsa. The souls of murderers and poisoners and other evil people never reach the bridge, but are turned to stone from the neck down. They remain there on the near shore forever, moving their eyes and watching other souls pass. When the pole begins to fall the soul starts quickly across, but when it reaches the middle two huge monsters rise from the water on either side and give a loud cry, attempting to frighten it so that it falls into the water. If the soul belongs to someone who had no ?atiswim or who did not know about the old religion and did not drink toloache - someone who merely lived in ignorance - it falls into the water and the lower part of the body changes to that of a frog, turtle, snake, or fish. The water is full of these beings, who are thus undergoing punishment. When they are hungry they crawl out of the water and wander through the hills nearby looking for cacomites to eat. The old people used to say that someone who drank toloache always passed the pole safely for they were strong of spirit.

Once the soul has crossed the bridge it is safe in Similaqsa... Souls live in Similaqsa forever and never get old. It is packed full of souls. They harvest islay, sweet islay, and there is no end of it. Every kind of food is there in abundance.

At least this text shows that the idea of going "over the rainbow" appears in many cultures. It's an appropriate symbol for something that's always just out of reach.

Cynthia instigated this stumper with an email about something she read: said something to the effect that no two people see the same rainbow. I've been thinking about it ever since. Monte says I must have misunderstood it. He thinks the person standing next to me is probably seeing the very same rainbow.

My quick response (as a self-described philosopher-naturalist):

Of course those nutty philosophers also wonder whether we see the same tree, even standing side by side! I figure of course we see the same rainbow, but it's a funny sort of object. Are rainbows an exact distance away? Can we measure their size?

There are many Web sites and references that explain rainbows, so I feel no need to do it again here. I borrowed these charming illustrations from Beverly Lynds' About Rainbows, a good place to start reading.

Raindrops are an exact distance away, but a rainbow is formed from millions of falling drops at all different distances. They have an angular size of about 42 degrees, but no particular physical size that can be measured in meters or miles. When I walk towards a rainbow, I see light reflected from different raindrops, so the rainbow seems to move along with me. Stepping back does not help frame a photograph, d'oh!

Plato (in Cratylus 402A) reports that the enigmatic pre-Socratic Greek philosopher Heraclitus said you can't step in the same river twice:

Heraclitus says, you know, that all things move and nothing remains still, and he likens the universe to the current of a river, saying that you cannot step twice into the same stream.
Aristotle (in Metaphysics 1010a) shows where this line of thinking leads:
Observing that all this indeterminate substance is in motion, and that no true predication can be made of that which changes, they supposed that it is impossible to make any true statement about that which is in all ways and entirely changeable. For it was from this s upposition that there blossomed forth the most extreme view of those which we have mentioned, that of the professed followers of Heraclitus, and such as Cratylus held, who ended by thinking that one need not say anything, and only moved his finger; and who criticized Heraclitus for saying that one cannot enter the same river twice, for he himself held that it cannot be done even once.
Aristotles' short answer in the same passage is "Let it be granted that there is nothing permanent in respect of quantity; but it is by the form that we recognize everything." Good enough. On a micro-quantum level, maybe everything is "the stuff that rainbows are made of." But we can still communicate if we work at it.

I think of rainbows as an "emergent property" of how sunlight reflects and refracts through individual raindrops. It reminds me of the way sand ripples arise from the way individual sand grains bounce around in wind and water. But the usual explanations gloss over one detail that was first worked out by Fermat and Descartes (in an appendix to his Discourse on Method).

Every explanatioon of rainbows has a picture like this, showing how light enters a raindrop and refracts-reflects-refracts so that red light exits at an angle of about 42°. But what if light enters the drop a little higher or lower, won't it then exit at a slightly different angle? If every raindrop makes its own little rainbow, why doesn't the light recombine to make boring white light? (Something like that does happen with fogbows.)

The answer is that more red light emerges at about 42° than any other angle, no matter where the sunlight light hits the drop. And more blue light emerges at about 40°. I don't understand the math yet, but there's a JAVA simulator that allows you to send virtual lightbeams through a simulated raindrop at different locations and see what happens.

In these reduced screenshots, I circled the indicator to show how much light is bounced back to the viewer. The peak emission is close to 42 degrees, but it's not simple! I learned a lot by playing with this JAVA program. Mostly I learned there's still more to learn!

Whew! Now I can get to the fun part. I've been collecting cover versions of the song "Somewhere Over The Rainbow." Its a big list, so I moved it to my own Over The Rainbow page.

I'm not done with this. Here are some links for your own Web research on going over the rainbow:

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