Are you left-handed, as I am? Then you are in a minority, somewhere between 4 and 30 percent of the human race. Most tools are designed not for you, but for right-handers. Also, society has long regarded left-handedness as odd, or actually evil. The words "sinister" and "gauche," which simply mean "left," both carry unpleasant overtones in English, and in the Arab world the left hand is "unclean" and avoided in normal human contact.

Other animals do not seem to have a preferred side. Humans, so far as we know, are the only creatures with a right-hand bias. No one can say why this is so. Also, it is extraordinarily difficult to define left and right in general terms.

To see this, imagine that you are in communication with a race of aliens, and that you can send word messages but not pictures. You want to describe for them a bolt with a right-hand spiral thread (the usual kind). You explain that a bolt is a metal cylinder, and on its outside runs a long continuous groove which steadily moves up the cylinder as it goes around it. The name for such a spiral form is a helix, and it is easily described mathematically.

So far, so good. But now, how are you to distinguish a bolt with a left-hand thread from one with a right-hand thread? This property of handedness, which is technically known as "chirality" or "helicity," seems impossible to describe without reference to other objects. Also, chirality is a basic part of the nature of a bolt. In the real world a right-handed bolt, no matter how you turn it, cannot be converted to a left-handed one.

Is this true for everything, that right and left handed spirals cannot be converted into each other? It is a valid statement for all rigid objects, but not for ones that can be deformed. For example, consider the toy known as a Slinky, best known for its curious ability to "walk" down a flight of stairs. A Slinky has a definite handedness. However, a Slinky with right-handed chirality can be converted to a left-handed one, simply by reaching down into the Slinky, grabbing the far end, and pulling it through itself. The Slinky resists, but if you keep pulling the result will be another Slinky, with the opposite handedness.

I demonstrated this a few weeks ago with the aid of paper, scissors, and sticky tape, seated at a corporate conference table in upstate New York and cutting out neat spirals while the friend of mine who runs the company was busy elsewhere. The result was entirely to my satisfaction. However, it later occurred to me that employees who looked in may have had suspicions as to my mental condition.

It probably seems self-evident that the universe itself will have no preference for left or right handedness. Oddly enough, at the microscopic level this is not true. In 1956, the physicists Lee and Yang proposed that certain processes governed by the weak law of force might sometimes not have left-right symmetry. This was confirmed by experiment in 1957. The result, known as the non-conservation of parity, surprised almost everyone, and it led naturally to the idea that some of the other "obvious" symmetries of Nature might not be obvious at all.

One of those symmetry failures had been known and noted for a long time. Every kind of sub-atomic particle has its own "anti- particle." For example, corresponding to the electron is the positron, identical to the electron in every way but possessing a positive rather than a negative charge. The anti-proton is just like a proton, except that it has a negative charge, and each other particle has its own type of anti-particle. If Nature were truly symmetric, positrons should be as abundant as electrons, anti-protons should be as common as protons, and "anti-matter," built up from these anti-particles, should occur in the same amounts as ordinary matter.

In fact, although anti-matter can be created in our laboratories, it seems to be rare to the point of non-existence in the world at large. No one knows why this is the case, but the imbalance must have been established very early in the history of the universe. Explaining the anomaly is one of the central tasks of modern cosmology.

The most puzzling symmetry of all, or the lack of it, comes when we look not at space but at time. If we hold a mirror up to time, we produce a universe which runs backward. All the equations which describe Nature at the sub-atomic level are symmetrical with respect to time; in other words, the equations have no preferred time direction, and they appear just as valid with time running backward as forward. In our everyday world, however, the idea that there is no preferred time direction is obvious nonsense. Stars condense from clouds of gas, begin a fusion reaction, and proceed through a well-defined stellar evolution. Chicks emerge from eggs, and no one ever manages to re-assemble Humpty-Dumpty. In the world at large, time has a well-defined arrow which goes in only one direction.

How do we explain the inconsistency between the laws that govern the world of the very small, and the everyday world we see around us? The best answer that science can offer is that the universe in its early days -- long before the time when the imbalance arose between matter and anti-matter -- was in a highly organized state. As organized as, say, a beautifully made vase. Drop that vase to the ground, and the number of ways that it can break into bits and pieces is very large. If you pick up all the bits and drop them again, the chance that they will re-assemble themselves to form the original is minutely improbable. The universe is like this, on a vastly larger scale. It is not theoretically impossible that events could run backwards, from disorder to the original order, but it is enormously unlikely. Ever since the beginning, despite local evidence to the contrary, the degree of organization of matter has decreased. The universe is running down. Eventually everything will become a random mess.

If you feel that this simply pushes the problem of the direction of time, like the problem of the absence of anti-matter, back so far that we can say next to nothing about it, I am forced to agree. Despite all our efforts, the nature of time and space remains as mysterious as ever.

Actually, I wish that time did run backward. Then I could look forward to that beautiful, organized, original state, rather than to a universe resembling my children's rooms.