Predictive power
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The predictive power of a scientific theory is its ability to generate testable predictions. Theories with strong predictive power are heavily valued, because these predictions can often encourage the falsification of the theory. It is different from explanatory or descriptive power, by which already-known phenomena are explained by a given theory, in that it presents a new and novel test of theoretical understanding.
One of the famous cases of predictive power usually cited by scientific textbooks was in Albert Einstein's theory of general relativity, which predicted that if photographs taken of the stars near the edge of the sun during an eclipse were compared to photographs of the same stars not near the sun, a "bending" of their light would be perceived. Einstein put forward this prediction, a logical outcome of his theory, in 1915, but it could not be tested until 1919. The reporting of its accuracy was heralded publicly throughout the world as a revolution in physics, as its results would not have been expected through the previous theory of gravitation. As a contrast, an example of Einstein's explanatory power was his theory's ability to explain the strange perihelion of the planet Mercury's orbit. Though this aided in its acceptance by scientists (as the current theories could not explain the phenomena), this was not considered sufficient evidence of its accuracy, as the phenomena to be explained was known before the theory was formulated.
The historical reality of the eclipse experiment is a bit more complicated than the textbook explanation, though, highlighting some of the problems with retrospectively applying a notion such as predictive power. For a variety of reasons, the scientific results of the eclipse observations were far from clear, and though the results were given tremendous prominence both inside and outside of the scientific community, there were many scientists at the time who felt there were good reasons to doubt whether the prediction had been accurately fulfilled, or whether or not the results (even if observed correctly) truly had no alternate interpretation. The field of science studies has, for many years, pointed out that all scientific facts are in various ways constructed through a variety of assumptions, institutional forces, and interpersonal relations, and are rarely without expert dispute in their day, and the philosopher/historian Thomas Kuhn famously pointed out that "textbook" histories of science tell the story of the current theory as a linear set of triumphs, when in reality the historical record is much more complicated. The example of the 1919 eclipse is often used as an example of selective interpretation of evidence and the ambiguity of observations.
Other examples of predictive power of theories or models include Dmitri Mendeleev's use of his periodic table to predict previously undiscovered chemical elements and their properties, and Charles Darwin's use of his knowledge of evolution by natural selection to predict that because there existed a plant (Angraecum) with a long spur in its flowers, a complementary animal with a 30 cm proboscis must also exist to feed on and pollinate it (twenty years after his death, a form of hawk moth was found which did just that).
Scientific ideas without any predictive power are known as "conjectures", or, at worst, "pseudoscience". Because they cannot be tested or falsified in any way, there is no way to determine whether they are true or false, and so they are not afforded the label of "scientific theory". More philosophically murky is when theories have predictive power but only in respect to technologies not currently possible. For example, certain aspects of string theory have been labeled as predictive, but only through the use of machines which are not yet built and some of which it is not sure could ever be built. Whether or not this makes it truly predictive or not is a matter of dispute among scientists and philosophers.
References
- On the problems with the eclipse observation, see: Harry Collins and Trevor Pinch, The Golem: what everyone should know about science (Cambridge, England: Cambridge University Press, 1993).