08 December 2016

Facts And Theory

Facts and Theory

Your correspondent, Mr. Porter, asks what is the difference between a Fact and a Theory. This was not a question much asked in the 19th century, when the difference was clear, but the certitude with which many Theories have been repeated in the Late Modern Age give them many of the appearances of Facts, so the question does now need some clarification.
Basically, there is a three-layer cake in science: Facts, Laws describing regularities in the Facts, and Theories that provide a narrative explanation from which the Laws may be deduced and the Facts predicted. (Especially, New Facts.) 

1. Facts.
Mr. Heinlein once said that Facts are “self-demonstrating; but this isn’t true. Fact comes fromfactum est, “that which has the property of having been accomplished,” “something done”; cognate with feat. This is clear in German: Tatsache, “deed-matter.” Down to Jane Austen’s time, the expressions “in fact” and “indeed” were used interchangeably.
In modern terms, a Fact is a product produced by a measurement process and in general two distinct processes will produce two distinct sets of results. For example, there are at least two ASTM-approved methods for measuring the coefficient of friction of packaging materials. One uses an inclined plane and translates the tangent of the angle at which the package begins to slide into its CoF; the other employs a dynanometer to pull the package and translates the Force at which the package begins to slide horizontally into the CoF. The same package, tested by each of the two methods, will in general return two different values. In other words, there is no such thing as the coefficient of friction. There is only the result of applying a specified method of measurement.
I recollect a situation, lo, these many years ago, when we discovered that the thickness of an aluminum can depended on the technician who measured it. Tech B consistently obtained thinner sidewall measurements, even when measuring the same can. The reason, as it turned out, was that she thought the micrometer was a C-clamp and screwed the barrel as tight as she could. But unlike steel, aluminum is compressible; so….
Dictionary definitions are often of little help in the practical problem of actually producing the measurement; and whether a measurement meets a requirement or not may depend on how that measurement has been defined operationally. In another case, a dimension on a beverage can lid was measured differently by ourselves and by our customer. Both gauges gave the same result on the gage block, but different results on the lids. The customer’s gauge was hand-held and the part dangled vertically from the pin. Our gauge was mounted vertically on a granite block and the part sat in a “nest” holding it at a certain angle. We were not actually measuring the same dimension, and the difference was enough to put one set of measurements out of specification and the other set in.
Even so simple a problem as determining the diameter of a pipe is fraught with questions. A pipe has infinitely many diameters, so in practice we can only take a sample of them. So how many diameters will we measure? At which locations on the pipe? Shall we use a pair of calipers or some other instrument? Will we report the mean of these diameters? The median? The extremal average? Far too many folks show a touching faith in the reliability of measurements. Hence the straight-faced reporting of political opinion polls and who has gained or lost ground since yesterday. What does the GNP mean when it includes not only the tons of steel poured but also the gallons of martinis poured? It’s not that combining these figures means nothing, John Lukacs once wrote, but that it might not mean what you think it does. Can we legitimately add values for manufacturing and for service? What about popular vote totals for States with different rules for eligibility? Or temperatures for Anchorage and New Orleans?
Now throw in questions of accuracy, precision, linearity, reproducibility, and stability of the measurement process. 

2. Laws.
Regularities in the Facts are called Laws, preferably stated in the privileged language of mathematics — Euclidean geometry in the case of Newton, or differential equations in the case of Maxwell. For example: that a body moving under uniform acceleration will cover the same distance as a body moving at the mean velocity during the same time was demonstrated by Nicholas Oresme using Euclidean geometry in the 14th century. But the thing to remember is that Laws are descriptive, not causative. Objects do not fall because of the Law of Gravity; rather the Law of Gravity simply describes how they fall. 

3. Theories.
A Theory finally is a story we tell ourselves so that the Facts and Laws “make sense.” From the story you can deduce the Laws and predict the Facts. More importantly, you can predict New Facts that were not used in developing the Theory in the first place. To the instrumentalists, that is all they need to do. They need not be True in any cosmic sense. In fact, any finite body of facts can support multiple theories that can account for them. There are today several theories that account for the facts of quantum mechanics: Copenhagen, standing wave, multiple worlds, transactional. (They are called “interpretations” for some reason.) This Duhem-Quine Theorem in Logic is what lies at the root of falsification mania. There is always more than one way to skin a cat, and more than one theory to explain a fact. Sometimes a new Fact can blow a well-established Theory clean out of the water. The Ptolemaic model explained the motions of the heavens tolerably well since the second century. (Motion around an epicycle around a deferent is mathematically equivalent to motion on an ellipse.) And the Aristotelian physics on which it was based had stood even longer. But when the phases of Venus were discovered by Lembo and others (all within the same month!) Ptolemy went down the tubes and his model was replaced with Tycho’s model. (Both Tycho and Copernicus explained the same data. They were mathematically equivalent, given only a shift in the center of the coordinate system.) It was only with the discovery of stellar aberration, Coriolis effects, and stellar parallax between the mid-1700s and mid-1800s that geomobility was proved in fact.
So we might say that Falling Bodies are the Facts while Gravity is a Theory meant to explain them. To Aristotle, this was a tendency inherent in the bodies themselves by which they moved toward the center of gravity. To Newton, it was a mysterious action-at-a-distance by which bodies reached out (somehow) and “attracted” other bodies (somehow). To Einstein, it was a property inherent in mass that “bent” the space-time manifold so that other bodies would move along geodesics toward the minimum gravitational potential. Each of these narratives (in of course greater detail) pushed our understanding of mechanical motion forward.
Similarly, the Evolution of species is a fact, and Natural Selection is one theory put forward to explain it. Sexual selection, neutral selection, natural genetic engineering, et al. are other theories.
This may be more explanation than the question wanted, and we are overlooking

4. Models.
In the third phases of Modern Science, ofttimes data itself is actually model output masquerading as data. For example, when some of the measured data is missing or if the instrument is broken or out of calibration, the missing data may be replaced by kriging or some other model output and then treated as if it were data. Or Something Else might be measured, such as tree rings, and translated to temperature by means of a statistical correlation model. A Model is sort of a hybrid of Facts, Laws, and Theories, partaking in many cases of the worst flaws of each.
--Mike Flynn

Quoted in its entirety and stolen from Jerry Pournelle's Blog Daybook

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