HEAD

Chapter 2
Reproducibility.
What is nature?

Michael Faraday is a fascinating character in the history of science. Born the son of a poor blacksmith, his formal education, such as it was, ended by age 13; but it ended by his becoming apprenticed to a bookbinder and bookseller; his informal self-education was beginning! This unconventional background left him knowing practically no mathematics. But he was an incredibly insightful experimentalist and he had an intuitive way of understanding the world in mental pictures. No less than five laws or phenomena of science are named after him. His experimental discoveries came to dominate the science of electricity, and of chemistry too, for the first two thirds of the nineteenth century. His conceptualization of the effects of electromagnetism in terms of lines of force laid the foundation for Maxwell's mathematical electromagnetic equations, and for the modern concept of a "field", in terms of which much fundamental physics is now expressed. ²⁴

Figure 2.1: Michael Faraday as a young man

It was said of Faraday that whenever he heard of some new result or phenomenon, reported in a public meeting or a scientific journal, the first thing he would do was to attempt to reproduce the effect in his own laboratory. The reason he gave for this insistence was that his imagination had to be anchored in what he called the "facts". He understood in his bones that science is concerned with reproducible phenomena which can be studied anywhere under controlled conditions and give confirmatory results. "Without experiment I am nothing," he once said.

Faraday's attitude is a reflection of what is often taken for granted in talking about science, that science deals with matters that show reproducibility. For a phenomenon to be a question of science, it had to give reproducible results independent of who carried out the experiment, where, and when. What the Danish Professor Hans Oersted observed during a lecture demonstration to advanced students at the university in Copenhagen in the spring of 1820 ought to be observed just the same when Faraday repeated the experiment later at the Royal Institution in London. And it was. Here, by the way, I am alluding to the discovery that a compass needle is affected by a strong electric current nearby, demonstrating for the first time the mutual dependence of electricity and magnetism. According to the students present at his demonstration, this discovery was an accident during the heating of a fine wire to incandescence using an electrical current. But Oersted's own reports claim greater premeditation on his part²⁵.

2.1 The meaning of experiment

Imagine a family trip to the Australian beach. The youngster of the family, three-year-old Andrew, is there for the first time. He is fascinated at all the new experiences. He idly, perhaps accidentally, kicks the gravel on the way down to the sand, and pauses to hear it rattle. When seated in the sun he grabs handfuls of sand, and throws them awkwardly over himself, and anyone else who strays too near. He is fearful and wondering at the unexpected waves, even the gentle ones that surge up the smooth sand towards him. Sarah, the eight-year-old is more deliberate. She is on a trek down the beach to find treasures: smooth pebbles of special shape or color, sand dollars, shells, seaweed, and maybe a blue crab. She returns with her bucket full, and she proceeds to sort her collection carefully into different kinds and categories. Cynthia watches both with motherly affection; her gaze shifts to the surf. She delights in the almost mesmerizing rhythm: rolling in and out. She wonders, at an almost subconscious level, what makes the waves adopt that particular tempo. Dan, the husband, chooses a spot well up from the water for their base, to avoid having to move as the tide comes in. He erects the sun-shade, trying a number of different rocks till he finds the ones that best keep it upright in the soft sand. He lies alongside his wife where the shadow will continue, even as the sun moves in the sky, to protect his fair skin from excessive ultra-violet radiation caused by the antarctic ozone hole.

Humans experiment from their earliest conscious moments. They are fascinated by regularities perfect and imperfect, and by similarities and distinctions. In children we call this play. In adults it is often trial and error devoted to a specific purpose, but sometimes it is simply a fascination that seeks no further end than understanding. We are creatures who want to know about the regularities of the world. And the way we find out about them is largely by experiment.

Induction is often touted as the defining philosophical method of natural science. It takes little thought and no detailed philosophical analysis to recognize that the deductive logic of the syllogism is inadequate for the task of discovering general facts about the natural world. All boggles are biggles, no baggles are biggles, therefore no baggles are boggles, is the stuff of IQ tests, not a way to understand the universe. By contrast, induction, the generation of universal laws or axioms from the observation of multiple specific instances, is both more fraught with logical difficulty and also vastly more powerful. But as a practical procedure it is hardly more than a formalization of the everyday processes of discovery illustrated by our Australian beach.

Figure 2.2: Francis Bacon

Francis Bacon (1561-1626) is often credited with establishing the inductive method as primary in the sciences, and thereby laying the foundations of modern science. Here is what Thomas Macaulay, in his (1837) essay thought of that viewpoint.

The vulgar notion about Bacon we take to be this, that he invented a new method of arriving at truth, which method is called Induction, and that he detected some fallacy in the syllogistic reasoning which had been in vogue before his time. This notion is about as well founded as that of the people who, in the middle ages, imagined that Virgil was a great conjurer. Many who are far too well-informed to talk such extravagant nonsense entertain what we think incorrect notions as to what Bacon really effected in this matter.
The inductive method has been practiced ever since the beginning of the world by every human being. It is constantly practiced by the most ignorant clown, by the most thoughtless schoolboy, by the very child at the breast. That method leads the clown to the conclusion that if he sows barley he shall not reap wheat. By that method the schoolboy learns that a cloudy day is the best for catching trout. The very infant, we imagine, is led by induction to expect milk from his mother or nurse, and none from his father²⁶.

Bacon thought and claimed that his analysis of Induction provided a formulation of how to obtain knowledge. That's why he named what is perhaps his crowning work, the "New Organon", meaning it was the replacement for the old "Organon", the collection of Aristotle's works on logic, which dominated the thinking of the schoolmen of Bacon's day. Bacon did not invent or even identify Induction. It had in fact already been identified by Aristotle himself, as Bacon well knew. Bacon thoroughly analyzed induction. He offered corrections to the way it was mispracticed, emphasizing the need for many examples, for caution against jumping to conclusions, and for considering counter-examples as importantly as confirmatory instances. He advocated gathering together tables of such contrasting instances, almost as if by a process of careful accounting one could implement a methodology of truth. These methodological admonitions are interesting and in some cases insightful, but they fall far short of Bacon's hopes for them. Scientists don't need Bacon to tell them how to think. And they didn't in 1600. What it seems philosophers did need to be told, or at any rate what is arguably Bacon's key contribution, is captured in his criticism of prior views about the ends, that is purposes, of knowledge. He says that philosophy was considered "... a couch whereupon to rest a searching and restless spirit; or a terrace for a wandering and variable mind to walk up and down with a fair prospect; or a tower of state for a proud mind to raise itself upon; or a fort or commanding ground for strife and contention; or a shop for profit or sale; and not a rich storehouse for the glory of the Creator and the relief of man's estate."²⁷ For the schoolmen and generations of philosophers before them, all the way back to Aristotle, true learning was for the development of the mind, the moral fiber, and the upright citizen, not for practical everyday provisions. The Christianized version was, everyone agreed, for the glory of the Creator. Bacon's innovation was that science must also be for the relief of man's estate; that it must be practical. This insistence on the practical transformed speculative philosophy into natural science. Macaulay's summary is this.

What Bacon did for inductive philosophy may, we think, be fairly stated thus. The objects of preceding speculators were objects which could be attained without careful induction. Those speculators, therefore, did not perform the inductive process carefully. Bacon stirred up men to pursue an object which could be attained only by induction, and by induction carefully performed; and consequently induction was more carefully performed. We do not think that the importance of what Bacon did for inductive philosophy has ever been overrated. But we think that the nature of his services is often mistaken, and was not fully understood even by himself. It was not by furnishing philosophers with rules for performing the inductive process well, but by furnishing them with a motive for performing it well, that he conferred so vast a benefit on society.

What Bacon was advocating was knowledge that led to what we would call today technology. This emphasis has drawn the fire of a school of modern critics of science as a whole (part of the Science Studies movement) whose argument is that science is not so much about knowledge as it is about power. Despite Francis Bacon's many failings of legal and personal integrity, there seems little reason to question the sincerity of his avowedly humanitarian motivation towards practical knowledge. He lived in the court of monarchic power and rose to become the most powerful judge in England before his conviction for corruption and bribery. So he was no naive idealist, and is a natural target for the suspicions of the science critics. But he was at the same time a convinced Christian who would not have been insensitive to the appeal of a philosophy motivated by practical charity, especially since it supported the escape from scholasticism that he also yearned for. Whatever may have been the sincerity of Bacon's theological arguments in favor of practical knowledge, there can be little doubt that they furnished a persuasive rationale that helped to establish the course of modern science, and that persists today.

Technology demands reproducibility. Technology has to be based upon a reliable response in the systems that it puts into operation. Technology seeks to be able to manipulate the world in predictable ways. The knowledge that gives rise to useful technology has to be knowledge about the world in so far as it is reproducible and gives rise to tangible effects. These are precisely the characteristics of modern science.

When we talk about experiments, however, we normally conjure up visions of laboratories with complicated equipment and studious, bespectacled, possibly white-coated scientists; not a day at the beach. The practical experimentation at the beach which is our symbol for the acquisition of everyday knowledge does not draw strong distinctions between the levels of confidence with which we expect the world to follow our plans. At any time we hold to a vast array of beliefs with a wide spectrum of certainties from tentative hypothesis to unshakable conviction; and most often we draw little conscious distinction between them. In most cases, we have no opportunity to do so, since the press of events obliges us every moment to make decisions about our conduct based on imperfect and uncertain knowledge. Establishing confidence in reproducible knowledge, certain enough for practical application, and meeting our expectations for natural science, requires a more deliberate approach to experimentation. This (capitalized) Experiment is a formalization of the notion of reproducibility.

A formal Experiment is generally conducted in the context of some already-articulated theoretical expectation. It can be considered the opposite end of a spectrum of different degrees of deliberateness in experimentation. The idle play of the beach is the other end. And in between are random exploratory investigations, fact and specimen gathering, systematic documentation and measurement, the trial and error of technique development and instrumentation, and the elimination of spurious ideas and mistakes.

At its purest an Experiment is devised specifically to test a theoretical model or principle. Isaac Newton's famous demonstration that white light is in fact composed of a spectrum of light of different colors is often cited as an illustration of experimental investigations leading up to a "crucial experiment". In his letter to the Royal Society of February 1672 he relates in a personal story-telling style his initial experiments with the refraction of light through a prism, and his demonstration by careful measurement that the greater than two degree spread of the refracted colors could not be caused by the angular size of the sun's disc. He talks about various ideas he ruled out as possible explanations of the observations and then says: ²⁸

Figure 2.3: Newton's drawing of his Experimentum Crucis, published much later in his Opticks (1704) .

The gradual removal of these suspitions, at length led me to the Experimentum Crucis, which was this: I took two boards, and placed one of them close behind the Prisme at the window, so that the light might pass through a small hole, made in it for the purpose, and fall on the other board, which I placed at about 12 feet distance, having first made a small hole in it also, for some of that Incident light to pass through. Then I placed another Prisme behind this second board, so that the light, trajected through both the boards, might pass through that also, and be again refracted before it arrived at the wall. This done, I took the first Prisme in my hand, and turned it to and fro slowly about its Axis, so much as to make the several parts of the Image, cast on the second board, successively pass through the hole in it, that I might observe to what places on the wall the second Prisme would refract them. And I saw by the variation of those places, that the light, tending to that end of the Image, towards which the refraction of the first Prisme was made, did in the second Prisme suffer a Refraction considerably greater then the light tending to the other end. And so the true cause of the length of that Image was detected to be no other, then that Light consists of Rays differently refrangible, which, without any respect to a difference in their incidence, were, according to their degrees of refrangibility, transmitted towards divers parts of the wall²⁹.

Even this report and Newton's conclusions were not without controversy. Others seeking to reproduce his results observed different dispersions of the light, presumably because of using prisms with different angles. There followed a correspondence lasting some years, but in a remarkably short time the acceptance of this demonstration became practically universal because the key qualitative features, and by attention to the full details even the quantitative aspects, could be reproduced at will by experimenters with only a moderate degree of competence.

2.2 Is reproducibility really essential to science?

Observational Science

Most thoughtful people recognize the crucial role that repeatable experiments play in the development of science. Nevertheless, there arises, an important objection to the view that science is utterly dependent on reproducibility for its operation. The objection is this. What about a discipline like astronomy? The heavenly bodies are far outside our reach. We cannot do experiments on them, or at least we could not in the days prior to space travel and we still cannot for those at stellar distances. Yet who in their right mind would deny to astronomy the status of science?

Or consider the early stages of botany or zoology. For centuries, those disciplines consisted largely of systematic gathering of samples of species; cataloging and classifying them, not experimenting on them. Of course today we do have a more fundamental understanding of the cellular and molecular basis of living organisms, developed in large part from direct manipulative experiments. But surely it would be pure physicist's arrogance to say that botany or zoology were not, even in their classification stages, science.

In short, what about observational sciences? Surely it must be granted that they are science. If they are exceptions to the principle that science requires reproducibility then that principle rings hollow.

Some commentators find this critique so convincing, that they adopt a specialized expression to describe the type of science that is based on repeatable experiments. They call it "Baconian Science". The point of this expression is to suggest that there are other types of science than the Baconian model. What I suppose people who adopt this designation have in mind is observational sciences. They think that observational sciences, in which we can't perform experiments on the phenomena of interest at will, don't fit the model of reproducibility. There is some irony in using the expression with this meaning, since actually Bacon was at great pains to emphasize the systematic gathering of observations, without jumping to theoretical conclusions, so he certainly did not discount observational science, even though he did emphasize the motivation of practicality.

However, we need to think carefully whether observational sciences are really exceptions to reproducibility. Let us first consider astronomy. It is an appropriate first choice because in many ways astronomy was historically the first science. Humans gazed into the heavens and pondered on what they saw. The Greeks had extensive knowledge of the constellations and their cycles. And it was the consideration of the motions of the planets, more than anything else that led to the Newtonian synthesis of gravity and dynamics. But astronomy, considered in its proper historical context, is not an exception to the scientific dependence on reproducibility. Far from it. Astronomy was for the pre-industrial age the archetype of reproducibility. It was just because the heavens showed remarkable systematically repeated cycles that it commanded the attention of so many philosophers in attempts to explain the motions of the heavenly bodies. It was because the repeatability gave astronomers the ability to predict with amazing precision the phenomena of the heavens that astronomy appeared almost mystical in its status.

What is more, the independence of place and observer was satisfied by astronomy with superb accuracy. Better than almost all other phenomena, the sky looks the same from where ever you see it. As longer distance travel became more commonplace, the systematic changes of the appearance of the heavens with global position (latitude for example) were soon known and relied upon for navigation. And what could be more common to the whole of humanity than the sky?

Far from being an exception to the principle of reproducibility, astronomy's success depends upon that principle. Astronomy insists that all observers are going to see consistent pictures of the heavens when they observe. Those observations are open to all to experience (in principle). And those observations can be predicted ahead of time with great precision.

One way to highlight the importance of reproducibility in the context of astronomy is to contrast Astronomy (the scientific study of the observational universe) with Astrology (the attempt to predict or explain human events from the configurations of the heavenly bodies). Many people still follow assiduously their daily horoscope. Regarded as cultural tradition, that is probably no more harmful than wondering, on the feast of Candlemas, if the groundhog Puxatawney Phil saw his shadow; and recalling that if so, by tradition there will be six more weeks of winter. Astrology, for most people, is a relatively harmless cultural superstition. But surely no thinking person today would put forward astrology as a science. Its results are not reproducible. Its predictions appear to have no value beyond those of common sense. And its attempts to identify shared particular characteristics of people born in certain months simply don't give reliable results. Once upon a time there was little distinction between astronomy and astrology. Their practice in the pre-scientific age seems to be a confusing mix of the two. A major success of the scientific revolution was the disentangling of astronomy and astrology. The most important principle that separates the two activities is that astronomy is describing, systematizing and ultimately explaining the observations of the heavens in so far as they are reproducible and clear to all observers.

There are, of course, unique phenomena in astronomy. Supernovae, for example, each have unique features, and are first observed on a particular date. In that sense they are observations of natural history. On 4th July 1054, astronomers in China first observed a new star in the constellation of Taurus. Its brightness grew visibly day by day. During its three brightest weeks it was reported as visible in daylight, four times brighter than the evening star (Venus). It remained visible to the naked eye for about two years. It is thought that Anastasi Indian art in Arizonan pictographs also records the event. Surprisingly, there seem to be no European records of the event that have survived.³⁰

If this were the only supernova ever observed, then we would probably be much more reticent to regard the event with credence. But there are approximately twenty different recorded supernovae (or possibly novae) in our galaxy during the 2000 years before 1700. And with modern telescopes, supernovae in other galaxies can also be observed fairly frequently.

The SN1054 supernova is probably the best known because it gave rise to the beautiful Crab Nebula discovered in 1731. That gas in the Nebula is expanding was established in the early 20th century by observing the line splitting caused by the Doppler effect. The nearer parts of the Nebula are moving towards us and the further parts away from us. In 1968 a new type of pulsing radio emission was discovered coming from the center of the Nebula. This Crab Pulsar is also observable in the visible spectrum. It is now known to be an extremely compact neutron star, rotating at an astonishing 30 times per second. ³¹

Figure 2.4: Photograph by the Hubble Telescope of the Crab Nebula.

One can get readily accessible reproducible evidence of the date of the SN1054 supernova. The expansion rate of the Crab Nebula can be established by comparing photographs separated in time. One can then extrapolate that expansion backward and discover when the now-expanding rim must have been all together in the local explosion. This process, applied for example by an undergraduate at Dartmouth College to photographs taken 17 years apart, gives a date in the middle of the 11th century. In 100% agreement with the historic record.³² [For technical precision we should note that, since the nebula is 6000 light years away, the explosion and the emission of the light we now see took place 6000 years earlier.]

Notice the following characteristics. First the Crab Nebula's supernova, though having its own unique features, was an event of a type represented by numerous other examples. Second, the event itself was observable to, and recorded by, multiple observers. Third, the supernova left long-lived evidence that for years could be seen by anyone who looked, and still gives rich investigation opportunities to experts from round the world, who simply have to point their telescope in the right direction. These are the characteristics of reproducibility in the observational sciences.

What about botany and zoology, in their collection and classification stages? Again, careful consideration convinces us that these do rely on reproducibility. If only a single specimen is available, it remains largely a curiosity. Who is to say that this not simply some peculiar mutant, or even a hoax? But when multiple similar specimens are found, then it is possible to detect what is common to all specimens and to discount as individual variation those characteristics that are not. Indeed, in the life sciences the best option is to have breeding specimens, which guarantee the ability to establish new examples for which the reproducible characteristics are those on which the scientific classification is based.

All right, what about geology then? Its specimens don't reproduce. But again the observation of many different examples of the same types of rock, or formation, or other phenomenon, is essential to its scientific progress. In its earliest stages, before geophysics had more direct physical descriptions of its processes, geology progressed as a science largely by the identification of multiple examples of the same processes at work, that is by reliance on repeatability. As the scientific framework for understanding the earth's formation was gradually built up, the systematic aspects of the rock formations began to become clear. Events could be correlated to produce an ordered series of ages. Then additional techniques such as radioactive dating enabled geologists to assign a quantitative date to the different geological ages, based on multiple assessments of the time that must have elapsed since the formation of rocks identified as belonging to each period. All of this process requires the ability to make multiple observations, observe repeatable patterns, and perform repeatable physical tests on the samples.

So observational science requires multiple repeatable examples of the phenomenon or specimen under consideration. It does not require that these can be produced at will in the way that a laboratory experiment can in principle be performed at any hour on any day. Observations may be constrained by the fact that the examples of interest occur only at certain times (for example eclipses) or in certain places (for example in specific habitat), over which we might have little or no control. But it does require that multiple examples exist and can be observed.

Randomness

A second important objection to the assertion that science requires reproducibility concerns the occurrence in science of phenomena that are random. By definition, such events are not predictable, or reproducible, at least as far as their timing is concerned.

If science is the study of the world in so far as it is reproducible, how come probability, the mathematical embodiment of randomness, the ultimate in non-reproducibility, plays such a prominent role in modern physics? Here, I think, it is helpful to take for a moment a historical perspective of science. Pierre Laplace is famous (amongst other things) for his encounter with the emperor Napoleon. Laplace explained to him his deterministic understanding of nature. Bonapart is reported to have asked, "But where in this scheme is the role for God", to which Laplace's response was "I have no need of that hypothesis" . Regardless of his theological position, Laplace's philosophical view of science was rather commonplace for his age. It was that science was in the process of showing that the world is governed by a set of deterministic equations. And if one knew the initial conditions of these equations for all the particles in the universe, one could, in principle at least, solve those equations and thereby predict, in principle to arbitrary accuracy, the future of everything. In other words, Laplace's view, and that of probably the majority of scientists of his age, was that science was in the business of explaining the world as if it were completely predictable, subject to no randomness.

This view persisted until the nineteen twenties, when the formulation of quantum mechanics shocked the world of science by demonstrating that the many highly complicated and specific details of atomic physics could be unified, explained, and predicted with high accuracy using a totally new understanding of reality. At the heart of this new approach was a concession that at the atomic level events are never deterministic; they are always predictable only to within a significant uncertainty. Heisenberg's uncertainty principle is the succinct formulation of that realization. Quantum mechanics possesses the mathematical descriptions to calculate accurately the probability of events but not to predict them individually in a reproducible way. Perfect reproducibility, it seems, exists only as an ideal, and that ideal is approached only at the macroscopic scale of billions of atoms, not at the microscopic scale of single atoms.

Where does that leave the view that science demands reproducibility? Did 20th century science in fact abandon that principle?

It seems clear to me that science has not at all abandoned the principle. The principle is as intact as ever that science describes the world in so far as it is reproducible. For hundreds of years, science pursued the task with spectacular success. Quantum mechanics, shocking though it seemed and still seems, did not halt or even alter the basic drive. What it did was to show that the process of describing the world in reproducible terms appears to have limits, fundamental limits, that are built into the fabric of the universe. The quantum picture accepts that there are some boundaries beyond which our reproducible knowledge fails in principle (not just for technical reasons). Even as innovative a scientist and supple a philosopher as Albert Einstein was repelled by the prospect, famously resisting the notion that the randomness of the world is in principle impenetrable with his comment "God does not play dice". Einstein, like scientists before and after him was committed to discovering the world in so far as it is reproducible, not arbitrary. The overwhelming opinion of physics today, though, is that Einstein was wrong in this epigram. God does play dice, in the sense that some things are simply irreproducible .

But that does not stop science from proceeding to explore what is measurable and predictable. Science does that first by pressing up to the limits of what is reproducible. If individual events are not predictable, it calculates the probabilities of events. Quantum theory provides this reproducible measure in so far as reproducibility exists. The interesting thing about Quantum mechanics is that it is governed by deterministic equations. These equations are named after the great physicists Erwin Schrödinger and Paul Dirac. A problem in Quantum mechanics can be solved by finding a solution of these equations. The equations take an initial state of the system and then predict the entire future evolution of that state from that time forward. This is such a deterministic process that some people argue that Quantum mechanics does not undermine determinism. But such a view misses the key point. The function that is solved for and the future system state that is predicted are no longer the definite position or velocity of a particle, or one of the many other quantities that we are familiar with in classical dynamics (or the everyday world). Instead it is essentially the probability of a particle being in a certain position or having a certain velocity. This is an example of science pressing up against the limits of reproducibility. The world is not completely predictable even in principle by mathematical equations, but science wants to describe it as completely as possible, to the extent that it is. So when up against the non-predictability, science invokes deterministic mathematics, but uses the mathematics to govern just the probability of the occurrence of events. Probability is, in a sense, the extent to which random events display reproducibility. Science describes the world in terms of reproducible events to the extent that it can be described that way.

And science proceeds, second, by pressing on into the other areas of scientific investigation that still lie open to reproducible description: describing and understanding them as far as they are indeed reproducible.

The history of nature

A third important challenge to the principle of reproducibility lies in the types of events that are inherently unique. How could we possibly have knowledge of more than one universe? Therefore how can reproducibility be a principle applied to the Big Bang origin of the universe? Or, perhaps less fundamentally, but probably just as practically, how can we apply principles of repeatability to the origin of life on earth, or to the details of how the earth's species got here?

I think these issues all boil down to the question "What about natural history?" Is the history of nature part of science?

It is helpful to think first about the ways that science can tell us about the past. Today, our ability to analyze human DNA has become extremely important in legal evidence. It can help prove or disprove the involvement of a particular person in a crime under investigation. The high profile cases tend, of course, to be capital cases, but increasingly this type of forensic evidence is decisive in a wider variety of situations. Obviously this is an example of a way in which scientific evidence is extremely powerful in telling us something about history - not as overwhelming as it is often portrayed in the popular TV series such as CSI, but still very powerful. Important as this evidence may be, it still depends on the rest of the context of the case which is what determines the significance of the DNA test results. Moreover, the laboratory results themselves are rarely totally unimpeachable. We have to be sure that the sample really came from the place the police say it did. We have to be sure it was not tampered with before it got to the lab or while it was there. We have to be sure that the results are accurately reported, and so on. So science can provide us with highly persuasive evidence, in part because of its clarity and the difficulty of faking it. But when we adduce scientific evidence for specific unique events of history (even recent history) our confidence is, in principle, less than if we had access to multiple examples of the same kind of phenomenon.

To illustrate that difference in levels of confidence, ask yourself how successful a defense lawyer would likely be if they tried to defend against DNA evidence by arguing that it is a scientific fallacy that DNA is unique to each individual. Trying to impeach the principles of science would be a ridiculously unconvincing way to try to discredit evidence in a criminal case. Those principles have been established by innumerable laboratory tests by independent investigators over years of experience and subjected to intense scrutiny by experts. General principles of science, such as the uniqueness of DNA, need more compelling investigation and evidence to establish them than we require for everyday events. But they get that investigation, and the support of the wider fabric of science into which they are woven. So, once established, we grant them a much higher level of confidence. What's more, if there is reason to doubt them, we can go back and get some more evidence to resolve the question.

But notice that our confidence in scientific principles is not the same as confidence in knowledge of the particular historical question. We are confident that insofar as the world is reproducible, and can thus be scientifically described, DNA is unique to the individual. But that does not automatically decide the legal case. If in fact there is other extremely compelling evidence that contradicts the DNA evidence, we are likely to conclude that in this specific instance there is something that invalidates the DNA evidence and we should discount it.

In summary, then, for specific unique events of history, evidence based on scientific analysis can be important, but is not uniquely convincing.

However, even though it contains some questions about unique events, much of natural history is not of this type. Much is about the broad sweep of development of the universe, the solar system, the planet, or the earth's creatures. In other words, questions of natural history are usually about generalities, not particularities, about issues giving rise to repeated observational examples, not single instances. For these generalities, science is extremely powerful, but continues to rely upon its principles of reproducibility and clarity.

We believe the universe is expanding from an initial event, starting some 13 billion years ago, because we can observe the Doppler shifts of characteristic radiation lines that are emitted from objects over an enormous range of distances from our solar system. We see that the farther away the object is, the more rapidly it is receding from us, as demonstrated by the frequency downshift of the light we see. Anyone, anywhere can observe these sorts of effects with telescopes and instruments that these days are relatively commonplace. The observed systematic trend is consistent with a more-or-less uniform expansion of the universe. If we project back the tracks of the expansion, by mentally running the universe in reverse, we find that our reversing tracks more-or-less bring all the objects together at the same time: the time that we identify as the Big Bang, or the age of the universe. This picture is confirmed by thousands of independent observations of different stars and astrophysical objects. Thus, the Big Bang theory of the origin of the universe is a generality: that the universe had a beginning roughly 13 billion years ago, when all of the objects we can see were far closer together. And it is a generality confirmed by many observational examples that show the same result.

Figure 2.5: Temperature, atmospheric carbon-dioxide, and dust record from the ice cores from Vostok, Antarctica.

What about earth's history? The history of the earth's climate is a topic of great current interest. How do we know what has happened to the climate in past ages? This information comes in all sorts of ways from tree rings to paleontology. Perhaps the most convincing and detailed information comes from various types of "cores" sampled from successively deposited strata. Examples include ice cores, and ocean sediments. Ice cores as long as three kilometers, covering the last three quarters of a million years have been drilled from the built-up ice arising from annual snowfall in Antarctica. The resulting history of the climate is laid out in amazing detail. By analyzing the fraction of different isotopes of hydrogen and oxygen in the water, scientists can estimate the mean temperature. By analyzing trapped gases, the fraction of carbon dioxide can be determined, and by observations of included microscopic particles, the levels of dust in the atmosphere can be documented, in each case over the entire history represented by the core. Figure 2.5 illustrates the results from the core analyzed in 1999.³³

These results are reproducible. If a core is drilled in the same place, the results one gets are the same. Actually, the longer (3km) core was drilled more recently (2004) in a different place in Antarctica than the one I have illustrated,³⁴ but shows almost exactly the same results for the periods of history that overlap. Moreover, deep-sea-bed sediment cores from all over the globe show global ice mass levels deduced from oxygen isotopes that correlate extremely well with the ice-core data for their history, but stretch back to 5 million years ago. The rapid progress in these observations and analysis over the past decade has enabled us to build up a remarkable record of the climatic history of the earth. It enables us to construct well-informed theories for what factors influence the different aspects of climate, and to say how the climate varied through time. But these vital additions to our knowledge are still about broad generalities: the global or regional climate, not usually the highly specific questions that preoccupy historians. For example, the uncertainties in the exact age of the different ice-core samples can be as large as a thousand years or more. In the scheme of the general picture of what happened in the last million years, this is a negligible uncertainty; but on the timescale of human lives (for example) it is large.

2.3 Inherent limitations of reproducibility

We have seen some examples of the great power of science's reliance upon reproducibility to arrive at knowledge. These examples are not intended to emphasize science's power; such a demonstration would be superfluous for most modern minds. They are to show the importance of reproducibility. We are so attuned to the culture of science that we generally take this reproducibility for granted. But we must now pause to recollect both that this reproducibility is not obvious in nature, and that in many fields of human knowledge the degree of reproducibility we require in science is absent.

Of course, substantial regularity in the natural world, and indeed in human society, was as self-evident to our ancestors as it is to us. But the extent to which precise and measurable reproducibility could be discovered and codified was not. The very concept and expression `law of nature' dates back only to the start of the scientific revolution, to Boyle and Newton. And in its original usage, it intended as much the judicial meaning of a legislated edict of the Creator as the impersonal physical principle, or force of nature that now comes to mind. Indeed, a case can be made that it was in substantial degree the expectation that law governed the natural world, fostered by a theology of God as law-giver, that provided the fertile intellectual climate for the growth of science. As late as the nineteenth century, Faraday motivated his search for unifying principles, and explained his approach to scientific investigation, by statements like "God has been pleased to work in his material creation by laws". By referring to God's pleasure, Faraday was not in the least intending to be metaphorical, and by laws he meant something probably much less abstract than would be commonplace today.

In drawing attention now to disciplines in which the reproducibility expected in science is absent, I want to start by reiterating that this absence does not in my view undermine their ability to provide real knowledge. The whole point of my analysis is to assert that non-scientific knowledge is real and essential. So I beseech colleagues from the disciplines I am about to mention to restrain any understandable impulse to bristle at the charge that their disciplines are not science. I remind you that I am using the word science to mean natural science, and the techniques that it depends upon. If the semantics is troubling, simply insert the qualification "natural" in front of my usage. Let us also stipulate from the outset that there are parts of each of these disciplines that either benefit from scientific techniques or indeed possess sufficient reproducibility to be scientifically analyzed. I am not at all doubting such a possibility. I am simply commenting that the core subject areas of these disciplines are not most fruitfully studied in this way for fundamental reasons to do with their content.

In his (1997) graduate text Science Studies, introducing various philosophical and sociological analysis of science, David J Hess acknowledges without hesitation the difficulties in applying scientific analysis to other disciplines "Probably the greatest weakness in this position comes when the philosophy of science is generalized from the natural sciences to the human sciences". He says specifically "Many social phenomena are far too complicated to be predictable".³⁵ In other words, in my terminology, these phenomena are not science. Yet a few pages later he says. "One of the reasons social scientists lose patience with philosophers of science is that we are constantly told that we are in some sense deficient scientists - we lack a paradigm, predictive ability, quantitative exactness, and so on - instead of being seen as divergent or different scientists".³⁶ This is an argument about titles and semantics. Sociologists today acknowledge that sociology does not offer the kind of reproducibility that is characteristic of the natural sciences. They feel they must insist on the title of science, which I believe is because of the scientism of the age; without the imprimatur of the title they feel their discipline is in danger of being dismissed as non-knowledge. Yet they resent it when the essential epistemological differences between their field and science are pointed out. No wonder there are difficulties in this discussion. As a physical scientist, I need to keep out of this argument, but I will observe that if we disavow scientism, then the whole of this discussion becomes more tractable. It is no longer a problem for sociology to be recognized as a field of knowledge in which reproducibility is not available.

History is a field in which there is thankfully less resentment towards an affirmation that it is not science. Obviously history, more often than not, is concerned with unique events in the past that cannot be repeated. Here is a commentary by a historian on King James the Second's frequent remark to justify his intransigence: "My father made concessions and he was beheaded". Macaulay writes, "Even if it had been true that concession had been fatal to Charles the First, a man of sense would have remembered that a single experiment is not sufficient to establish a general rule even in sciences much less complicated than the science of government; that, since the beginning of the world, no two political experiments were ever made of which all the conditions were exactly alike ..."³⁷ Macaulay's typical, but confusing, use of `science' has already been noted, but the point he makes very clearly is that there is no reproducibility in history. No more than a small fraction of its concerns benefit from analysis that bears the stamp of natural science. Yet no thoughtful person would deny that historical knowledge is true knowledge, that history at its best has high standards of scholarship and credibility, and that the study of history has high practical and theoretical value.

Similarly the study of the law, jurisprudence, is a field whose research and practice cannot be scientific because it is not concerned with the reproducible. The circumstances of particular events cannot be subjected to repeated tests or to multiple observations. Moreover, the courts do not have the luxury of being able indefinitely to defer judgement until sufficient data might become available. They have to arrive at a judgement that is binding on the protagonists even with insufficient data. Consequently, the legal system's approach to decision-making is very different from science's.

In Britain in the early 1980s the government of Prime Minister Margaret Thatcher introduced policies in line with Milton Friedman's economic theories, which the press was fond of referring to as the `monetarist experiment'. Here was what an economist must surely dream about: the chance to see an experimental verification of his theory. What was the result of this experiment? Was monetarism thereby confirmed or refuted? To judge by current economic opinion, it seems neither. Economists don't really know how to assess the outcome unambiguously, because this was a real economy with all sorts of extraneous influences; and what is most important, one can't keep trying repeatedly till one gets consistent results. It may have been an experiment, but it was not truly a scientific experiment. Economics is an interesting case here, because economists have large quantities of precise measured data and usefully employ highly sophisticated mathematics for many of their theories, a trait that they share with some of the hardest physical scientists. Economics is a field of high intellectual rigor. But the absence of an opportunity for truly reproducible tests or observations and the impossibility of isolating the different components of economic systems means that economics as a discipline is qualitatively different from science.

Politics is to many a physical scientist baffling and mysterious. Here is a field, if there ever was one, that is the complete contradiction of what scientists seek in nature. In place of consistency and predictability we find pragmatism and the winds of public opinion. In place of dispassionate analysis, we have the power of oratory. And once again, nothing in the least approximating the opportunity for reproducible tests or observations offers itself to political practitioners. It seems a great pity, and perhaps a sign of wistful optimism, not to mention the scientism that is our present subject, that the academic field of study is referred to these days almost universally as Political Science.

We will discuss more, equally important, examples of inherently non-scientific disciplines later. But these suffice to illustrate that not only is science not all the knowledge there is, it may not be even the most important knowledge. And however much we might hope for greater precision and confidence in the findings of the non-scientific disciplines, it is foolishness to think they will ever possess the kind of predictive power that we attribute to science. Their field of endeavor does not lend itself to the epistemological techniques that underlie science's reliable models and convincing proofs. They are about more indefinite, intractable, unique, and often more human problems. In short, they are not about nature.