My daughter Caroline sang the lead in her school concert last night. My wife and I were so scared for her, literally shaking in her seats, but she was brilliant. How a seven-year-old ever got that brave I’ll never know. I would have curled up under the bleachers at that age.

They sang “The Rainbow Connection.” I love the optimism of the song, its conviction that the world is a magical place.

It’s easy to read into the song an indictment of science as this dull, soul-crushing set of facts that takes the mystery out of everything, leaving it flat and dead. But that’s not how I see the song or science. Understanding rainbows reveals the real magic they possess, the deep and beautiful mysteries they contain.

Everything in the universe that makes its own light also makes a rainbow. Usually we can’t see the rainbow, because of an amazing thing: all the colors of light travel at exactly the same speed. Why? We’ll come to that.

Using special equipment like prisms or diffraction gratings, we can reveal the hidden, secret rainbow in all light beams. Sometimes we discover that the rainbow is made of just one color. Laser beams and sodium vapor lamps are like this, and tell us something deep about how that light is made. Other times there are just a few colors in the light beam. But most things, things that glow because they’re hot, things like incandescent light bulbs, campfires, and stars, give off every color of the rainbow.

We see stars because they’re so hot. They blast space with radiation, and a tiny bit of it reaches us, after traveling for tens, hundreds, thousands, even millions of years. Imagine that! Light that was formed before you were even born traveled through empty space, day after day after day, as you grew up. Then, one evening, you happened to glance into the sky and catch that little bit of light in your eye.

If you send that little bit of light through a diffraction grating before it reaches your eye, you discover something incredible. The light reveals the composition of the star that made it. What are stars made of? The same stuff you’re made of. In fact, the stuff you’re made of was made, originally, up there, in the stars. You are starstuff contemplating the stars. That’s only one of the things we learn by understanding rainbows.

What else? How about this? The rainbows we see are only a tiny bit of what’s actually there. I was recently writing for a textbook company, and a passage I’d written about “invisible light” was edited. They said they don’t discuss invisible light,  because all light is visible. They changed it to “invisible electromagnetic waves.”

Well, I’m their writer monkey, so OK. But they miss the entire point! Electromagnetic waves and light are no different, except for one thing. Our eyes react to light. To remove that connection is to take away one of the great unifications of science. Visible light is electromagnetic radiation we can see. Electromagnetic radiation is invisible light!

And some of that invisible light tells an incredible story. Watch the best thing on television. That would be the channel with no signal. You get nothing but static – noise. About 1 of every 100 bits of that static is the world’s oldest fossil. It’s radiation from the great fireball that began the universe. What’s on TV tonight? The Big Bang!

By studying this invisible light (there, I said it, nya nya!), scientists uncovered one of the most deep and meaningful things we’ve ever learned. The universe has a birthday. It wasn’t always here. It began.

OK, that’s two. One more for good measure?

Why can’t we ordinarily see the rainbows in light? Why do we need things like raindrops or spectrum glasses to break up the colors? As I said, that’s because under ordinary conditions all colors of light move at the same speed. But why? It’s because light (visible and invisible light) is something the universe does.

Over a hundred years ago, a scientist named James Clerk Maxwell was playing around with the equations of electricity and the equations of magnetism. He knew there were strange connections between these two phenomena, but neither he nor anyone else understood what those connections were. Maxwell noticed a missing symmetry in one of the equations. When he added that symmetry in, something amazing happened.

Maxwell recognized that he’d created a wave that spread out from the electric and magnetic fields. This wave carried the electric and magnetic fields through space. Its properties depended solely on the way empty space reacts to electric charges and magnetic fields. Change the properties of space, and you change the wave.

But here’s the magical part. Maxwell’s equations showed that the wave he’d just created moved with a single, unique speed. The speed didn’t depend on the size of the electric or magnetic fields, didn’t depend on how they moved or changed, didn’t depend on anything other than the properties of space itself. The speed of the wave was precisely the measured speed of light.

Maxwell had just shown that light, that mysterious substance that lets us see the ocean meet the sky, the Sun coming up over the horizon, or a seven-year-old girl singing before a crowd, is nothing more (and nothing less!) than wiggling electric and magnetic fields. Hold up a magnet and shake it – you’ve just created (invisible) light. Rub a balloon on your head. More invisible light. Light, the weaver of rainbows visible and invisible, is something the universe does.

And that’s The Rainbow Connection.