August 28, 2011 | 62
The concept of handedness—of left and right, say, or of clockwise and anti-clockwise—is deceptively simple. In fact, I think it is among the most subtle in all of science and mathematics. In this post I will pose a challenge that I hope intrigue my readers.
This will not be a test or a quiz: I have not yet completely worked out a solution myself. Rather, it is the opening salvo for what I hope will be an interesting discussion. For a follow-up post, I plan to interview some physicists to see what their take is. But first, some preliminaries.
Imagine that you had to explain the meaning of the words “left” and “right” to someone who had never heard those words before. And imagine, moreover, that you had to do so in a purely verbal manner, that is, without drawing pictures or pointing at things or otherwise making gestures.
After giving it some thought, you would perhaps start by appealing to some shared experience. For example, to an American you could say that if they were to drive cross country from New York City to San Francisco, their right side would be where Canada is, while their left side would be the side of Mexico.
But what if you were told to make no assumptions about where the person is coming from or how much geography he or she knows? You could hope that they knew something about the stars. You could explain, for example, that if one looks at the constellations of the Zodiac with their “up” side pointing north, then they would see the constellation of Gemini, say, to the left of Taurus and to the right of Cancer. (In the celestial sphere, the constellations of the Zodiac are those traversed by the sun in its apparent path in the sky during Earth’s yearly revolution.)
But constellations are purely conventional groupings of stars, and in fact the way they’re assembled is culture-dependent. Besides, how many of us can recognize them? In a dark, moonless sky I can perhaps spot the Big Dipper, Orion, and a couple more if I’m lucky.
Even if your friend had never learned about any constellations, though–or if they had never seen any because they spent their entire lives in L.A. or New York–you could still use astronomical references to explain left and right. Perhaps the simplest way to do so would be to tell them that if they’re facing north, “right” is where the sun will rise and “left” where it will set.
Of course, you’d first have to explain the word “north.” But that is easy to tell—at least if you live in the Northern Hemisphere—because the North Star is the only star that virtually doesn’t move during the Earth’s rotation. (There is no South Star.) In the long exposure below, where the stars form streaks in the sky over the Annapurna Range (Himalayas) as the Earth rotates, the North Star is the little dot in the middle.
Another way that you could introduce the concept of “left” and “right” could be by resorting to human anatomy. You could point out that that “left” is the side where the heart is, while the liver is on the right—and then you’d have to hope that your interlocutor is not among those rare people who have their entire bodies inverted, with their hearts on the right, their livers on the left and so on.
Or, you could take a biochemistry approach. Have your friend learn how to purify and crystallize DNA and analyze its structure. Ordinarily, the DNA’s double helix is twisted in such a way that it looks like a spiral staircase that goes up as it goes from left to right: think of a forward slash, “/”. It is what people call a right-handed screw. A left-handed screw, on the other hand, is like a spiral staircase that goes down, like a backward slash, “\”. (You would also have to make sure that your friend does the experiment properly, so that their DNA doesn’t curl up the wrong way, in the so-called Z-DNA conformation, instead of in the usual conformation, called B-DNA. The two conformations however look very different to a structural biologist.)
Perhaps you are beginning to see my point. To communicate or even establish a notion of left and right, you have to appeal to some common experience, some tangible object or phenomenon. Or, as a physicist might say, you have to define that notion operationally. Absent that, there is no a priori way to orient yourself. This, by the way, is reflected in the way mathematicians describe handedness, also known as chirality or orientation, in an abstract space: In geometry there is no a priori notion of left and right the way that there is an a priori notion of positive and negative numbers. It is purely a convention.
So here is my challenge to you, dear reader. How would you communicate the concept of left and right via radio signals to an alien civilization?
First, of course, the two civilizations would have to detect each other and decrypt each other’s languages, which could take some back and forth; and messages would take tens or hundreds of years to get from here to their star system and back, depending how far their star system is. But let’s say you’ve had a few centuries to practice interstellar communication.
To spice things up a bit, let’s revert the situation–so that it is the aliens who have to teach left and right to us–and let’s say that the future of humanity is at stake. We have discovered that in a few decades the sun will explode, and that the only way our species can survive is to abandon the solar system. Fortunately, the aliens possess the technology to build a sort of cosmic gate to cross wormholes. A specially-built spacecraft could take four men and four women on board, cross the cosmic gate machine and almost instantaneously travel across the galaxy. There, these pioneers could find a hospitable planet to settle. They could then go forth and multiply, ensuring the survival of the species.
There isn’t enough time for the aliens to send a cosmic gate and a wormhole spacecraft our way, so we need them to teach us how to build one. We need them to send us the blueprint. So they begin to beam information to us in the form of a 3-D technical drawing, encoded as a set of 3-D coordinates in space.
But there’s a snag. To work properly, wormhole traveling relies on a network of cosmic gate machines the aliens have placed around the galaxy. All of those machines are built in such a way that a ship must cross them in a corkscrew motion. That motion must be like what we on Earth would call a right-handed screw. Any attempt to cross the gates in a left-handed motion will result in disintegration of the gate machine and of the ship and everything inside it.
You see, we can reconstruct a detailed 3-D drawing from the coordinates–all those x’s, y‘s, and z‘s they sent us. We earthlings have a convention to set up coordinates in such a way that if you stand up in the positive z direction and look down to the xy plane, the positive-x axis will be to the right of the positive-y axis. But we have no way to tell if that is the same convention that the aliens use. Thus, we have no way to tell if model we build, and its corscrew motion, are the correct ones or their mirror images.
The aliens’ language does include words for “left” and “right” and for “left-handed screw” and “right-handed screw”. But in all our communications with them, we were never able to figure out which was which. We need them to explain to us which of their words corresponds to our word “left,” and which to our word “right.” To do so, they will need to appeal to some common point of reference or phenomenon. I shall restate the challenge as follows:
How can an alien civilization instruct us via radio signals on how to build a spaceship that flies with a right-handed twist?
I can think of at least a couple of “easy” solutions to this problem, one of which was suggested to me by my friend David Harris. I will describe those solutions in a subsequent post, but in the meantime I am curious however to see what ScientificAmerican.com readers—who are a smart bunch—will come up with. Remember, you have to save the human species!
Later, I will “cheat” and I will modify the problem a bit to make it harder, and also more interesting. At that point, some rather deep physics concepts should come into play.
Read the follow up to this post, Galactic Challenge, Part II: The Richard Feynman Files
The New Ambidextrous Universe: Symmetry and Asymmetry from Mirror Reflections to Superstrings: Third Revised Edition. By Martin Gardner. 2005.
The Handedness of the Universe. Roger A. Hegstrom and Dilip K. Kondepudi in Scientific American, Vol. 262, pages 108-115; January 1990.
Alien Pizza, Anyone? On other worlds, biochemistry could have taken a different turn. Davide Castelvecchi in Science News, Vol. 172, No. 7, pages 107-; August 18, 2007