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Truth and Non-Trivial Prediction

Several powerful truth-evaluating proce­dures are basic and widely used in science. They could be construed as general principles of truth detection. The first is non-trivial prediction; the second is convergent validation.

Every truth claim can be seen as proposing a model about reality. The word model indicates a theory or claim about the structure of some objectively existing system.

As argued on the page Defining a System people can (and do) propose theories about non-existing things. In that case, the model exists in their heads, but it does not correspond to any system in the "outside world" (the world outside that person's nervous system).

This implies a difference between (1) the world as people perceive or conceive it and (2) the world as it exists independently of our perceptions. This difference is taken for granted by scientists, including cognitive scientists.

Amateur philosophers like to jump to the conclusion that we know nothing about the real world. Or the world is all an illusion. Or (an ancient religious position) consciousness comes first and then the world is formed by it.

None of these are implied by the distinction between internal represent­ation (the brain's processes of representing the environment) and the external environment. Cognitive scientists simply realize that perception or conception of the world is itself a process that must be explained.

It must take place in some system (inside the brain, in the case of humans). In that sense all our know­ledge of the world is a construction. To capture a thought in language or other symbols is to make a representation of it in our cognitive networks.

All Knowledge is Schematic

A model of a system may be embodied in an external diagram, equation, or physical model of a system. The model is intended to capture relationships be­tween components of a system.

On the page about networks we argued "all knowledge is schematic," meaning that representations of reality in the cognitive system are never as detailed or complete as the real objects themselves. Mental models are like maps.

On that same page, the map metaphor was developed a bit. (I also used the map metaphor to explain how science works, in my introductory psychology textbook.)

Maps are a useful metaphor for scientific theories (or internal represen­tations of things) because people are familiar with road maps and weather maps. We have accurate intuitions about them.

Scientific theories (and models in the head) have several features in common with maps:

All those things are also true of maps or models in our heads: representations, as cognitive scientists call them. To evaluate the truth of a representation, claim, or belief about reality, one must test it. (And that is true of maps, also.) The best way to test a model is to use it to make a risky or non-trivial prediction.

Non-Trivial Predictions

The phrase non-trivial means surprising or unusually precise. If a model only predicts things that are unsurprising or vague (the earth will rotate once in the next 24 hours) nobody will be impressed.

If a model predicts something surprising (UFOs will land in Washington D.C. tomorrow, based on signals received from a mysterious craft orbiting the earth) then fulfillment of the prediction validates the claim. If the prediction comes true, we know the signal really was from aliens.

The principle of non-trivial prediction: Scientific theories or models are tested by using them to generate non-trivial (surprising or unusually precise) predictions.

Thousands of people make predictions about the stock market every day. Some get lucky. But if a person successfully predicted, with precision, how a stock would move, day after day, the world would take notice, and that person might become very wealthy.

That person might also be the focus of an insider trading investigation. The only obvious explanation for such a prediction would be that the person was using secret information provided by an insider at the company, which is illegal.

The example shows that making risky predictions that come true is powerful stuff. It is presumed to reflect some sort of special knowledge.

In science, the special knowledge allowing non-trivial predictions comes from a theory or model telling us some­thing we did not know before. If a risky prediction based on it comes true, it is powerful support for the new model.

A single successful prediction must be followed by others. Replication (repetition of research) is necessary whenever scientific research shows a surprising effect. Replication is necessary to make sure a surprising result is not a fraud or a fluke caused by unknown and unrepeat­able factors.

Einstein used his theory of relativity to predict that very strong gravity would cause light waves to bend. That was surprising to physicists. Nobody had considered the possibility that light would bend due to gravity.

Einstein's theory implied that light from a faraway star, passing close to our sun before reaching earth, would bend a little bit if it came very close to the enormous gravitational pull of the sun. Normally this cannot be noticed because the glare of the sun prevents observation of light passing close to it.

However, during a total eclipse, such an effect might be observed. Einstein predicted it would be.

On May 29, 1919, Sir Arthur Eddington went to the island of Principe, off Africa, to view a total eclipse of the sun. The constellation of Taurus was positioned behind the sun on that day.

When the sun was darkened, Eddington recorded the positions of the stars. Sure enough, they appeared closer to the sun than they should have been. The light passing by the sun had been bent.

1919 headline says Einstein Triumps
A 1919 New York Times headline

On November 10, 1919, the results of Eddington's observa­tions were released to the public, producing the New York Times headlines shown here. Einstein's theory of relativity was proven true.

Similar observations were made during several eclipses, replicating the finding. That is important because critics alleged that Eddington fudged his results, interpreting ambiguous statistics as verification of Einstein's prediction. Repeating the observation during other eclipses eliminated such doubts.

Convergent Validation

In addition to the non-trivial prediction about light bending as it passed near the sun, Einstein's theory of relativity made other non-trivial predictions. One was the claim that time runs at different rates in systems that are moving at great speeds relative to each other.

This effect has not only been verified; it must be taken into account in order for a GPS (global positioning system) to produce accurate results. Einstein's theory of relativity predicts that atomic clocks on satellites speeding around the globe will fall behind clocks on the ground by about 7 microseconds per day.

This is due to the speed with which satellites are moving, relative to the ground. The 7 microseconds must be added back in so GPS units can accurately determine the location of a GPS unit. Combined with other non-trivial predictions, this provides very strong proof of Einstein's theory of relativity.

When two or more risky predictions based on the same model all come true, it is strong evidence for the model. When independent forms of evidence support the same conclusion, that is called convergent validation.

Things converge when they come together. Convergent evidence is evidence from a variety of sources, all supporting the same model or truth claim.

Ideally, the evidence that converges should be from independent sources. If evidence supporting a theory comes from a single experiment, or a single investigator, that is not as powerful as evidence from multiple sources, not influenced by each other, agreeing on the same conclusion.

In general, when evaluating convergent evidence, the more independent are the sources of information, the better. In science, if two totally different forms of evidence both support a theory (like the bending light and differences in time measurement, in tests of relativity) that is powerful support for a model.

Converging evidence is used in crime scene investigations. In the case of an unsolved crime, the problem to be solved is whodunit? To answer the question, crime scene investigators must gather many forms of evidence.

When the truth becomes known, every­thing falls into place. The evidence converges on a single conclusion, and the guilty party is revealed.

Convergent evidence must exist if a theory or model (or explanation of a crime) is true. Why? Because there is only one reality out there. If a model accurately describes that reality, all the evidence should be consistent with that model.

For this reason, all the evidence at a crime scene must point back to the same source, once it is properly interpreted. A single serious inconsis­tency can spoil the case and prevent a conviction. If the suspected killer has an airtight alibi, having been photographed at a remote location by a security camera at the moment of the crime, a jury is unlikely to convict.

If there is one true model, all the evidence must be consistent with it. If not, there is something left untold, some element yet to be explained.

This implies that a single anomaly (unexpected result) could disprove a scientific theory. Mathematics works that way; a single proof is sufficient to estab­lish a theorem as true, and a single error invalidates a proof.

However, in evaluating models of complex natural systems, proofs are generally not so sudden and decisive. Scientists know that errors can occur in gathering and interpreting evidence, so they do not throw out a well-established theory because of one anomalous observation. Results cumulate over time, and the truth becomes known as surprising results are replicated and additional tests are performed.

Scientists are keenly interested in unexpected findings. Anomalies that withstand investigation (i.e. can be replicated) are clues about defects in a scientific model. That was an important theme in Thomas Kuhn's classic, The Structure of Scientific Revolutions.

Models are proved by being continually tested. The word proof means test, as in proving ground: a place where cars are tested. A model of a natural system must be tested in multiple ways to be validated.

Even then, a good theory is only an approximation of nature. A good theory is much like an accurate map. It might be the best available alternative when constructed, but it can usually be improved as time goes on.

Scientists, if speaking carefully, will say a theory that passes many tests is provisionally true. That means it appears to be true with the evidence now available. It will be regarded as true until an improved model comes along.

The principle of convergent validation: A model supported by multiple independent sources of evidence is provisionally true.

This is a very practical way of defining truth. It is not a metaphysical claim about pure truth, never to be challenged. Scientific models are always open to challenge. Creative scientists test Einstein's theories every year.

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