In times past, Enlightenment scientists conceived of the whole Universe as a game of billiards. On the smallest scale, matter was understood as made up of solid, indivisible atoms described as being like billiard balls by British chemist John Dalton in the early nineteenth century and Dmitri Mendelev, the Russian chemist who organized atoms into the Periodic Chart of Elements in 1869. According to Dalton and Mendelev, the movement of billiard-ball-atoms is governed by deterministic laws of cause and effect. If force is applied to an atom of carbon, it will react in a completely predictable way, just as when a player like current Worldcup title holder Dick Jhtmlers strikes a ball with an exact amount of force and spin at a precise angle, the ball will follow a completely predictable trajectory and thus score the point. On the largest scale, British mathematician Isaac Newton established in the late seventeenth century that all the stars and planets in the Universe, as well as all objects on Earth, are governed by a universal force of gravity. The laws of motion governing stars and planets follow from the geometry written by Euclid in the third century BC, in which parallel lines never cross. Thus from the smallest atom to the largest star, mankind lived in a billiard-ball universe, governed by cause and effect and Euclidean geometry.

All this changed with the scientific revolutions in the early twentieth century. In the 1890s, British physicist J. J. Thompson discovered the first subatomic particle, the negatively-charged electron, proving that the atom was not solid. With the subsequent discovery of the positively-charged proton (1914) and the neutron, scientists realized that the atom was composed of minute charged particles held together by electrical forces, and unlike a billiard ball, an atom was mainly empty space! Then in 1927, German physicist Werner Heisenberg proposed the indeterminacy principle, which stated that the location of subatomic particles cannot be determined with exact precision, but only within a range of probability. Thus, the determinism of classical physics was undermined at the most fundamental level of matter and energy. Surrealist painter Man Ray captured this change in our modern understanding of the Universe in his 1938 painting La Fortune (Chance), in which the billiard-ball model of the universe is set askew with the introduction of chance.

Just as physicists were determining that nature is not deterministic at the smaller scale, astronomers were discovering the mathematical laws governing the Universe are not the plane geometry of the billiard table, but laws of a non-Euclidean spherical geometry. In the General Theory of Relativity (1919), Albert Einstein stated that a line in the Universe - the shortest distance between two points - is not straight but curves, because all light waves moving through outer space are bent as they pass through the gravitational fields of massive bodies such as stars and galaxies. In other words, the space of the Universe is non-Euclidean and curved - in outer space, parallel lines, if extended indefinitely will cross!

What is a billiard player to do in this new non-deterministic, non-Euclidean Universe_! Fortunately, we do not play billiards in the subatomic realm or on a cosmic scale, but on a scale in-between - in the terrestrial realm of planet Earth. Although at the subatomic level probability rules, when atoms join to form solid billiard balls, their motion is guided by cause and effect. Also, the gravitational forces acting on billiard balls are so weak from a cosmic perspective, that on the billiard table, Euclid's laws of plane geometry remain in force and parallel lines never cross. So although we no longer live in a billiard ball Universe, on Earth, it's still a billiard-ball planet. But in actual play, although the precision of the geometry is predictable, one must develop an intuitive sense of the motion of the balls. Along with the ability to calculate the path of the ball it is important to feel the motion of the balls, particularly given the subtle changes in force, stroke, spin, and friction encountered in advanced level play, and to intuit how the ball will respond when varying those parameters. A feeling for the nature of the balls as they hook, roll, or slide coupled with an understanding of the geometry that governs the game will provide the clearest picture.

But, in billiards, the elusiveness of the game continually asserts itself declaring that Man Ray may well have the most complete picture. Just when we begin to understand our game, something happens on the table to skew our view. Although the billiard balls are governed by the laws of geometry and physics, often the predictability of their trajectory seems a random event. At times, it is as if the table is tilted and the simple forces which govern the game seem uncontrollable and we come up empty. But somehow, in this skewed perspective, (possibly with fortune's guidance) you regain a feel for the motion of the balls and with renewed confidence can transcend the governing forces in a given position. One need only to watch how the balls behave under the hands of a Blomdahl or a Sang Lee with their masterful understanding and control to believe that in the universe in which they play, surely parallel lines could cross if they so desired.

This first appeared in the January/February 2000 issue of Carom News, the newsletter of the USBA.