The Doctor's Dilemma
Is orthodontics predicated on greater mathematical precision than is inherent in the system?
In 1965, Professor Lotfi Zadeh published a paper he called "Fuzzy Sets", after which what used to be called "vague" was now called "fuzzy". Zadeh said, "There are some who feel [there is a] fundamental inadequacy of the conventional mathematics--the mathematics of precisely defined points, functions, sets, probability measures, etc.--for coping with the analysis of biological systems, and that to deal effectively with such systems, which are generally orders of magnitude more complex than man-made systems, we need a radically different kind of mathematics, the mathematics of fuzzy or cloudy quantities."
The idea of a fuzzy world was hinted at by the multitalented Jan Christian Smuts in a 1926 book entitled Holism and Evolution, with words that orthodontists could well ponder. Smuts said the initial mistake lies in interpreting the world as a collection of bivalent data that are purely artificial and not in accordance with the shading-off continuities that are the nature of science and philosophy.
We live in a world in which some things have a "yes" or "no" answer, and they are called bivalent. Other things do not have a simple "yes" or "no" answer, and they are called multivalent. Computers, by their very nature, are bivalent. To a computer, everything is either "0" or "1". As Bert Kosko points out in a book called Fuzzy Thinking, the computer doesn't exist that replies "more or less" to a question. We would probably throw such a machine out the window, because that is not what we want to hear from a computer.
If binary units--0 or 1--are "bits", Kosko calls "fuzzy units"--somewhere between 0 and 1--"fits". They are the kind of thing that bothered Zeno the Eleatic. He worried that if you had to traverse half the distance from A to B, and then half again, and half again, you could never get all the way from A to B. If we see science as black and white, we are making a fundamental mistake. Between the extremes of black and white are an infinite number of shades of gray.
Orthodontists have been using classifications of malocclusion as if they really exist, whereas there are an infinite number of individuals stretched out among the classes. Somewhere between Class I and Class II are Class I and a half, a quarter, an eighth, and so on to infinity. Orthodontists' acceptance of classifications has obscured rather than clarified our understanding.
We have sought to make orthodontics more scientific by means of mathematical accuracy, but have only produced more inaccuracy. Listen to Kosko: "Scientists try to find the math that best fits the world or the world that best fits the math. They build exact math models to describe some little piece of the universe or to describe the whole thing. They spend their professional time arguing that the few drops of data someone has measured support their models better than they support the competition's models. Or they argue that their math fits with the math of the current champ's model or the math of the competition does not fit. They work in math and trust in math and shoot in math but can never achieve the logical certainty of math."
Preferred facial appearance varies from race to race, from place to place, and from time to time. Even in one race at one place at one time, there will be a range of opinions about the most pleasing facial appearance. No measurement or group of measurements I know of will necessarily satisfy two people, and those two could be the orthodontist and the patient.
If the stomatognathic complex were a room, orthodontists would be rearrangers of furniture. Some of the rules would be logical--you don't put tables and chairs on ceilings or walls. Some of the rules would be mensural--you don't put a 12-foot sofa in a 10-foot room, without changing the dimensions of the room first. Some of the rules would be practical--you don't put chairs on top of tables. With all of that, there is no precisely correct positioning of the furniture. What looks good to one person might not look good to another, and if the floor is seriously off-level it might require some help to keep the furniture in place.
In the trip from etiology to malocclusion, from cause to effect, there is a lot of fuzzy stuff going on that we don't quite understand, or else we wouldn't let it take its course. That is why we are so inadequate at prevention.
Luckily, the human genetic code develops the teeth within a somewhat elastic mask of lips and cheeks, and orthodontists rearrange the teeth within that relatively small area. But when a classification is used to describe the occlusion--looking to interdigitate the upper and lower posterior cusps according to a certain formula--things begin to get fuzzy, because Nature is often pretty good at creating matched sets. This is one of the ideas that Dr. Jan De Baets was getting at in last year's series of JCO articles on the Pseudo-Class I (February-April 1995). It could be called the Doctor's Dilemma. If the molars interdigitate in textbook fashion, the bicuspids and cuspids might not. In such a circumstance, if the cuspids interdigitate in textbook fashion, the molars and perhaps the bicuspids might not. Is either of these relationships going to be stable? Does the situation call for some upper or lower posterior stripping, or for occlusal equilibration? Will either of these contribute to stability?
I guess the message is: Let's not get so involved with precise numbers that we fail to fully evaluate each individual. Without neglecting scientific research, let's keep in mind the essential role of understanding and intuition in orthodontic correction--the art of orthodontics, if you will.