I have to be honest. Of all 13 episodes of Cosmos, this may be my least favorite. I loved the story of Milton Humason, but so much time on the cosmology of India seemed to me unnecessary, as if Sagan couldn’t think of anything else to say. But he recovers nicely in the final three episodes, so I guess it’s ok to let this one partial clunker slide.

One section of the episode, besides the Humason biography, that I very much enjoyed was the description of how the Doppler shift is used in cosmology. To me this is Sagan at his best, using his narrative as an excuse to teach an exciting science idea. The Doppler shift is not only an interesting effect that shows the deep analogies to be made between sound waves and light waves, but it is also an example of human ingenuity. The tiny clue to be found in the shifting of dark spectral lines, like the tiny clues provided by the spectral lines themselves in discovering the makeup of the stars, reveals so much when human beings put that clue to work.

I think the thing that makes science teaching unique, special, and worthwhile is the way it can link to our everyday lives. We are all of us surrounded by the mystery of the cosmos every day. For instance, everyone has had the experience of flipping on and off a light switch. You flip the switch up, the light comes on. You flip the switch down, the light goes off. But therein lies a deep mystery.

If you look inside any switch, you find wire connected to metal. When the two separate pieces of metal join, electric current flows and the light comes on. When the two pieces are pulled apart, the electric current stops and the light goes off. But the connection between the pieces of metal is a problem.

Most metal, such as the copper of many electrical connections, is covered with a layer of oxidation. This layer is not good at conducting electricity. And yet electric current can flow through this layer. Why? Because of a bizarre effect known as quantum tunnelling. On a macroscopic scale, we’d be very surprised if, while pounding a hammer against a wall, our hammer suddenly disappeared and rematerialized on the other side. It is possible, but highly unlikely. On an atomic scale, however, such things happen quite often, and it is exactly this sort of tunnelling that allows a switch to turn on. Electrons tunnelling through the non-conducting oxidizing layer and appearing on the other side are precisely the electrons that cause the switch to turn on and off.

Why can electrons do this? Because, unlike hammers, electrons are so tiny and so relatively energetic that their wavelengths are much larger than their particulate sizes. A hammer’s wavelength at ordinary speeds is so tiny that for all practical purposes the hammer is the size of, well  a hammer. But an electron, with a wavelength much larger than its own pinpoint size, is like a cloud of probability. And every once in a while, quite by accident, the electron finds itself in a part of the cloud that allows it to jump over an apparently impassible gap, such as the gap between two pieces of metal in an ordinary light switch.

The Doppler effect is at work every time we look into the night sky. Quantum tunnelling is responsible for every flip of a switch. The wonder and mystery of science is around us every day. We are all of us on the edge of forever.