What is a Theory?

Steven Dutch, Natural and Applied Sciences, University of Wisconsin - Green Bay
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On April 13, 2007, the Associated Press ran a story on the successful isolation of proteins from dinosaur bone, including the following quote:

"The fact that we are getting proteins is very, very exciting," said John Horner of Montana State University and the Museum of the Rockies.

And, he added, it "changes the idea that birds and dinosaurs are related from a hypothesis to a theory."

To scientists that's a big deal.

In science, a hypothesis is an idea about something that seems probable, while a theory has been tested and is supported by evidence.

It is a big deal. It's also a big steaming pile of coprolite. Not the protein isolation, which is really an exciting advance, but the bogus definition of "theory."

Consider the following usages of the word "theory."

The Ptolemaic Theory of the solar system, of course, was the ancient notion that the earth was at the center of the solar system and that the annual looping motions of the planets were due to their moving around the earth on circles attached to larger circles. The Phlogiston Theory of combustion was the idea, popular in the 1700's, that combustion was caused by a chemical substance called "phlogiston." These usages are current today in many histories of science, despite the fact that the theories were wrong. So immediately we are forced to conclude that a theory is definitely not something that "has been tested and is supported by evidence," but can even refer to something that is known to be false. We can even talk about the theories of Immanuel Velikovsky, using the term to describe something that is obviously false from the very beginning.

The Theory of Relativity was Einstein's discovery of the way bodies behave near the speed of light. Although we now regard the theory as solidly established and tested, it was called "Theory of Relativity" right from its first appearance, and long before any direct experimental proof had been obtained. In those days, its status was much like Grand Unified Theories of physics today, theories that physicists hope will eventually connect all the forces in nature. Here we have "theory" used to mean ideas that are by no means established. Indeed, in the case of a Grand Unified Theory, we're talking about something less well established than a hypothesis. If somebody were to develop a specific line of research that might contribute toward the development of a Grand Unified Theory, say unifying gravity and quantum mechanics, we'd call that research line a "hypothesis," and regard it as an improvement on the present state of affairs.

The Theory of Continental Drift, like Relativity, was called a theory by supporters (a few) and detractors (many) long before persuasive supporting evidence appeared. When the crucial evidence did appear, it turned out that the theory was a misnomer. All the action takes place in the oceans, and the moving parts of the earth's outer shell consist of slabs made up of both oceanic and continental crust. So we no longer use the term "continental drift" except in a historical or informal context and the theory is now called Plate Tectonics. Here we have the odd case of a theory that became obsolete by being proven.

Stress Theory in engineering refers to a combination of experimental and theoretical results that enable engineers to calculate loads in structures. If you're inclined to dismiss evolution as "only a theory," better stay off bridges and out of airplanes and tall buildings. You wouldn't want to risk your life on a mere theory, now, would you? Stress theory is a simplification of insanely complicated physics. We couldn't begin to calculate the stresses at every point in a slab of concrete, given the varying mechanical properties and random distribution of the cement and aggregate, but we can approximate construction materials with simple, ideal materials that do obey neat theoretical laws. Here "theory" refers to formulas derived from simple laws that we know nature doesn't obey exactly, but does obey closely enough for us to use the results with high assurance. So Stress Theory is indeed "tested and is supported by evidence" but not in the same way as relativity.

Number Theory isn't a scientific theory at all in the sense of hinging on experiment. It's the collection of mathematical concepts dealing with what numbers are and how they behave. Music Theory is even less like science than Number Theory. It's the rules we use for making and describing music. If you regard evolution as "only a theory," then this is great news. All that boring stuff you learned about sharps, flats, demisemihemiquavers and chords? You can forget it - it's only a theory! Just hammer the keys any old way you like. The reason Japanese music sounds so different from ours is that they have a different theory.

Neither Number Theory nor Music Theory are entirely arbitrary. Most mathematicians say that mathematics is not science because it doesn't rely on experiment or observation, but some branches of mathematics are "richer" than others, that is, they lead to more interesting results. In the 19th century there was a whole branch of mathematics called "triangulation geometry" that dealt with increasingly complex properties of triangles. That turned out to be a pretty limited area of research, and is now regarded as a historical backwater. Not only has it been pretty well explored, but none of it led anywhere else. There are branches of mathematics that flourish and then sputter out, and the only way to tell what's rich and what's not is to explore and see. So there is an empirical element to mathematics. Similarly, between the physics of sound and the way our brains are wired, there are some combinations of sound that work for us and some that don't. We split an octave into seven intervals and Oriental music splits an octave into into five, but not too many musicians generate wholly random frequencies with wholly arbitrary rhythms.

[Digression: if you look up the defined frequencies of musical notes, you'll find a fascinating balancing act. Sing the scale, and you'll hear that "fa" and "la" fall kind of flat. There are actually five full intervals in the Western scale and two half intervals, or a total of six whole intervals. Wave phenomena tend to follow exponential scales, so ideally each whole interval should represent a frequency ratio of 6(2), and the half intervals 12(2). The intervals over a whole octave multiply out to a factor of two. That's what an octave is: one note has twice the frequency of another.
    Except that notes harmonize when they're rational multiples of each other, say one note has two thirds or four fifths the frequency of another. That has to do with the mechanics of how things vibrate, both the strings and reeds in instruments and the membranes in our ears. And the sixth root of two won't allow rational multiples.
    So, the musical scale is a carefully fudged system that allows rational multiples while approximately maintaining constant intervals. For example, A4 is defined as 440 hertz and B4 as 493.88. The ratio 493.88/440 = 1.12245454, whereas 6(2) = 1.12246205. Very close, but not quite the same. You can't hear the frequency difference, but you certainly would hear if notes weren't rational fractions.
    Okay, go back to what you were doing.]

The Theory of Evolution was called a "theory" in Origin of Species itself. If the work that proposed evolution for the very first time referred to it as a "theory," we can hardly go claiming that the word refers to something "tested and ... supported by evidence."

So What's Wrong With The New Definition?

It's Historically Inaccurate

As the above examples show, restricting "theory" to something "tested and is supported by evidence" flies in the face of centuries of usage.

It's Intellectually Dishonest

The redefinition of "theory" seems to be largely driven by the abuse of the term "theory" at the hands of creationists. In response to the intellectual dishonesty of creationists, who equated "theory" with "hypothesis" or "conjecture" in regard to evolution, some scientists have begun trying to make an end run by redefining "theory" to mean something with a high degree of confirmation. But you don't counter scientific illiteracy and intellectual dishonesty with your own scientific illiteracy and intellectual dishonesty.

"But It's In The Literature"

So is the term "myth," as applied to science, as in "science is the myth of modern man."

Sorry, Humpty Dumpty, this is not Wonderland and words mean what they mean, not what you choose them to mean. Redefining a term with widespread understood usage to a specialized usage that is quite different doesn't make the usage legitimate scholarship. It marks the user as an incompetent scholar.

So What Is A Theory?

A theory is any systematic and coherent collection of ideas that relate to a specific subject. It's easy to see that this definition applies to every single example of theories above. There's no requirement that the collection be demonstrated, and it can even be false, especially if we're speaking about the history of science. String Theory in physics is highly speculative, but it's still a theory.

A lot of the confusion about theories arises from the fact that all hypotheses are theories. You have a disconnected collection of observations, and you generate an idea that connects and explains them. You now have a theory - a systematic and coherent collection of ideas that relate to a specific subject. Hence the common claim "I have a theory about that." But it's still not demonstrated, so it's a hypothesis. All hypotheses are theories, but all theories are not hypotheses, just like all residents of Muncie are residents of Indiana, but not the other way around.

In the case used at the beginning of this page, the idea that birds are related to dinosaurs was always a theory. It was also a hypothesis, although a well supported one. The recovery of dinosaur protein, and its similarity to bird protein, makes the idea a better supported hypothesis - there are still too many possible twists and turns the data may take for us to regard the hypothesis as solidly proven.

Below the level of hypothesis we have speculation and conjecture. These terms refer to concepts that may be supported logically or by some evidence, but are too far from testability even to be hypotheses. Generally a hypothesis refers to an idea that is testable, if not now, perhaps in the future. Speculations and conjectures are ideas that either have no known tests, or the tests are so far from being practical that they may as well not exist. The idea that the sun will become a red giant is a hypothesis. True, the actual test is a long way in the future, but we can test the hypothesis by applying our theories of stellar evolution to other stars and seeing how well we can explain what we actually observe. Extraterrestrial intelligence is a speculation. Until, and unless, we actually receive a signal, we have no information whatever on which to base a conclusion. (Some of the searches now in progress have turned up enough negative evidence to rule out some of the more wildly optimistic speculations. There's nobody close by.)

The term "conjecture" is often used in mathematics almost in the sense of "hypothesis." For example, the idea that there are an infinite number of prime pairs like 41 and 43, or 101 and 103, is a conjecture. It seems likely to be true, but nobody knows how to prove it. Some conjectures turn out to be wrong. For example,  consider the sums 32+42= 52 , 33+43+53= 63 and 304+1204+3154+2724=3534 . The mathematician Leonhard Euler proposed Euler's Conjecture, that for sums of nth powers, there had to be n terms in the sum. Computer searches have shown that the conjecture is wrong. For example, it only takes three fourth powers to sum to another fourth power. The smallest known example is 95,8004+217,5194+414,5604 = 422,4814 (any questions on why this needed a computer?).

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Created 12 March 2007;  Last Update 30 August, 2011

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