Facts and Theories

Due to a conversation regarding facts and theories on a message board I sometimes visit, I decided to write a short item for my students answering a simple question:

"If a fact is fundamentally true, isn't it better than a theory?"

At first glance, it may appear that a fact is more valuable than a theory because the former is, by definition, true and unchangeable. The reality is that theories are much more useful to us than facts. Consider the following. Suppose you hold out a stone at arm's length and let go. It drops to the ground. That's a fact. You saw it happen. Unfortunately, by itself, it doesn't tell you very much. Now suppose you repeat this several times and each time the stone drops in precisely the same way as it did initially. This is beginning to get useful because you're noticing a pattern, and patterns can be predictive. Now, suppose you pick up stones of differing sizes, say 100 grams, 200 grams, half a kilogram and a kilogram, and drop each of them in turn. You observe that they each hit the ground in the same amount of time. Further, you drop them from different heights and you notice that the higher up they are, the longer it takes for them to hit the ground, but they all take the same amount of time to reach the ground.

You might now formulate a hypothesis; namely that the mass of a stone doesn't have an affect on how fast it falls from a given height and that height and time are interrelated. Your hypothesis is predictive: although you used only four sizes and a few heights, your broadened hypothesis should apply to any stone dropped from any height. So now you (and a bunch friends) starting picking up random pairs of stones and drop them from random heights, and sure enough, you see the same effect again and again. If you do this enough and it is continually verified without exception, you might even make a "law of falling stones", particularly if you were able to quantify the times and heights through careful measurement and reduce the relation to a nice formula. It is useful because you can now predict what will happen with any stone dropped from any height.

But this law is rather limited. It only applies to stones because you may have noticed that stones drop much faster than a piece of cork. While you might then proceed to make a "law of falling cork", that would be the long way home. Instead, you could take a step back and try to figure out why stones and cork both fall, but not at the same rate. Eventually, you might discover that the difference has to do with air friction and you can now create a law governing falling bodies in a frictionless environment. That's even more useful than the original "law of falling stones".

But even this new and improved "law of falling bodies" doesn't offer a lot of insight into what is really going on in the larger scheme of things. Through repeated observations and experiments this could be extended to cover not just falling bodies on the earth, but the interactions between any bodies, including falling stones and cork on the moon, or the interaction between the earth and the sun, the sun and the other planets, the sun and other stars, and so on. What you'll have arrived at is a full-blown theory of gravitation (Newtonian Gravitation). Now that is an extremely useful tool. It helps us design airplanes, get satellites into orbit, even get people to the moon and back safely.

Note that this theory is not just predictive but also falsifiable. That is, there are observations that could render it moot. It is not true in the same sense as stating that the original stone fell when you released it, but clearly it is far more useful than that single observed fact. Indeed, we might find observations which do clash with the theory. That doesn't mean that we just throw the theory away though. It may simply require a tweak to accommodate a larger range of input variables. That is, we may have discovered a more extensive set of circumstances under which the theory fails, but within its original confines, it's a perfectly good approximation. An example of this is Einstein's relativistic take on gravity. It refines Newton's theory for certain extreme cases (predicting effects such as gravitational lensing, or the bending of light by massive objects) but Newton's version is perfectly acceptable for something as mundane as lobbing a dead cow over a rampart via a catapult.

In sum, while theories are not facts and while they are not true in the same sense that, say, two plus two is four, they are far more useful to us by offering both explanatory and predictive power bolstered by the weight of accumulated evidence.