CHAPTER TWO
The Science of Nature and
the Nature of Science
Preliminaries
WHAT, THEN, IS SCIENCE, which I claim to be the most nearly objective means we have for comprehending the real world? The rest of this book is devoted to answering that question. In the following we’ll see what science is and how it operates. We’ll discover the objective nature of science. Yet we’ll learn why, nevertheless, some degree of subjectivity can’t be avoided in doing science. We’ll also look into what lies beyond science, into some of the general intellectual framework of which science forms a part. And we’ll consider the limits of science, what science can and does deal with and what science cannot deal with.
Many people, among them a large number of scientists, believe science is the fountainhead of understanding of, if not everything, then at least everything of material nature. They are mistaken.
Granted, science is usually not expected to probe or comprehend the nonmaterial, subjective aspects of the universe, such as morals, beauty, love, and faith. Most of us realize that, and we limit our expectations accordingly. (Even so, it appears that considerations of evolutionary advantage can shed light on matters such as altruistic behavior, perception of human beauty, and morality.) And there are aspects of the universe, such as life, consciousness, mind, and intelligence, whose materiality (or lack thereof) is the subject of heated debate. Although many people, and I among them, take a materialist position with regard to these aspects, not everyone thinks science is able to deal productively with such issues.
But even in its handling of the material universe, science, by its very nature, has intrinsic limitations. One such limitation is that it cannot comprehend the material universe as a whole. Science does indeed give us understanding of various aspects of the material universe and the phenomena within it. But science can go only so far. In principle, the material universe as a whole remains beyond science’s grasp.
Nonscientific modes of comprehending and understanding, such as feeling, intuition, and religion, have, with the coming of the age of enlightenment and the rise of rationalism, become largely relegated to those aspects of the universe that lie outside the domain of validity of science. And I fully concur with that. In dealing with all those aspects of the universe that science does successfully comprehend, or is potentially capable of comprehending, nonscientific modes of comprehending should indeed be rejected as sources of objective understanding.
As an example, consider the multicolor effect obtained when sunlight passes through a glass prism or through drops of water. Science offers an explanation of the phenomenon in terms of the wave nature of light, the dependence of the speed of light in glass and water on the frequency of the transmitted light, and so on. Moreover, the explanation offered by science holds through myriad observations and experiments. A nonscientific explanation might be that the spectrum is the direct result of God’s will to enrich our lives with the beauty of the colors thus manifested, or is a sign of God’s promise to humankind that there will be no repetition of the devastating flood of eons past. The scientific explanation is objective, and we can all agree on it. It is also useful in that it enables us to control the prismatic effect with advantageous results. In this case, the nonscientific explanations do not clash with the scientific one. Because they are subjective, one can take them or leave them. They do not enable any control. I’m ever anew full of wonder and delight at the sight of a spectrum, especially as manifested in a rainbow, and the sight of a rainbow can even remind me of a certain biblical narrative. But it is the scientific explanation that comes to my mind when I am in explaining mode, both for myself and for my students.
Those who prefer explanations involving feeling or belief, rather than scientific explanations, in those domains where science is valid are welcome to them. That’s their personal business. But the encroachment of nonscientific modes of comprehension on the domain of validity of science, as a matter of public policy, is another matter altogether. Science, where valid, offers by far the most nearly objective comprehension and understanding available, and is thus the only mode of comprehension suitable for general public recognition. It’s a unifying factor for humankind and a firm foundation for a world culture. Nonscientific modes of comprehension, for their part, are subjective. They’re best left to the individual, or to like-feeling and like-believing groups of individuals, and should not be allowed to become public policy in any domain where the validity of science has been demonstrated.
Imagine what might happen if a country did base public policy on nonscientific modes of understanding in a domain where science has a firm grasp. Say a country is in need of a petroleum exploration policy in order to make the most effective use of the few small petroleum deposits in its territory. One option would be the usual, science-based one, involving gravity, magnetic, and seismic surveys to pinpoint the most promising locations for drilling. An alternative, initially cheaper option might be to identify promising locations by having the Supreme Leader throw darts at a wall-mounted map of the country.
But as we’ll see, the material universe as a whole lies outside the domain of science. Thus cosmological schemes—schemes offering descriptions of the birth, evolution, and possible death of the universe—as useful as they are for science—are beyond the competence of science. They are no more and no less valid than analogous descriptions given by religion (one’s own) or by myth (the other guy’s religion). Because science cannot speak authoritatively about the universe as a whole, we have an opening for the legitimate entry of nonscientific modes of comprehension into the business of explaining the material universe. Here, one’s feelings and beliefs can be just as valid as the scientific-appearing descriptions espoused by scientists. They might be even more valid to their holder than those of science, if, for instance, they’re more satisfying or aesthetically pleasing.
My own background as a physicist inclines me to cosmological schemes couched in scientific terms. Even so, I do realize the intrinsic lack of scientific validity of such schemes and avoid taking them as seriously as I take genuine science. But more about that later. In any case, if someone prefers the biblical description of the coming into being of the universe, for example, or any other description couched in mythic terms, science cannot object. Even with all its tools and procedures, it really can do no better.
To understand some of the intrinsic limitations of science, in particular its inability to comprehend the material universe as a whole, we must first understand just what science is (and is not). That’s what the present chapter and the next are about. The “scientific method,” that oversimplification taught us in school, involving observation, hypothesis, experiment, and theory, is only part of the picture. This chapter and the next convey only part of the picture as well, but it is the part I need as groundwork in support of my presentation, and in making my points. So let’s get to work, and since we should know what we’re talking about, we start with some definitions.
Science
Consider the following definition of science:
Science is our attempt to understand objectively the reproducible and predictable aspects of nature.
Each element of that definition also needs definition. First, look at our. This seemingly innocuous qualifier carries a heavy load of implication. It tells us that the source of science lies within ourselves, that science, although having to do with nature, is a human endeavor. Nature would presumably go its merry way, whether we were around or not, or whether we tried to understand it or not. But without our curiosity and our urge to understand, science would not exist.
Now for attempt. This is our admission that we forgo a priori any claim for assured success. Thus science, in spite of its amazing successes, might not yet have the final word (if indeed there is a final word to be had), and might not yet be capable of handling everything within its domain.
We dealt extensively with objectively in the preceding chapter. What we mean is that everything that science does must be as objective as possible. Any evidence used must be objective: available and accessible to everyone who makes the effort. All considerations must be based on reason, which is accessible to everybody, rather than on the likes of intuition, emotion, and faith, which are private.
Next consider understand. We take “understand” to mean “be able to explain.” That’s fine, but what is meant by “explain”? Here we use the dictionary definition: give reasons for. We consider a phenomenon to be understood if we’re satisfied that we know the reasons for it.
Nature
Now consider nature. For the purpose of our discussion:
Nature is the material universe with which we can, or can conceivably, interact.
The universe is everything. The material universe is everything having a purely material character. To interact with something is to act upon it and be acted upon by it. That implies the possibility of performing observations and measurements on it, and of receiving data from it, which is what we’re actually interested in. To be able conceivably to interact means that, although we might not be able to interact with that something at present, interaction is not precluded by any principle known to us, and is considered attainable through further effort and further technological advance. Thus the material universe with which we can, or can conceivably, interact is everything of purely material character that we can, or can conceivably, observe and measure. That is what we mean by nature.
“But nature is surely more than that!” many would exclaim. “What about beauty, love, etc.? Aren’t they part of nature too?” They, and other such subjective concepts, are certainly part of the universe, but whether they are of purely material character or not remains an open question. So, for the purpose of our presentation, we exclude subjective concepts such as mind, idea, feeling, emotion, and so on, and confine ourselves to the narrow, strictly materialist definition of nature. Thus “nature” serves us as a convenient, concise term for the subject of our present investigation, which is the material universe with which we can, or can conceivably, interact. The universe might very well possess other components too, but if so, they’re not of concern to us here.
That leaves reproducible and predictable aspects to look into, and this too involves some discussion.
Reproducibility
Reproducibility means that experiments can be replicated by the same and other investigators, thus providing data of objective, lasting value about particular aspects of the phenomena of nature. Reproducibility makes science a common human endeavor (rather than, say, an incoherent collection of private, incommensurable efforts). It allows investigators to communicate meaningfully, across space and time, and to progress through joint effort. Reproducibility makes science as nearly as possible an objective endeavor of lasting validity. There seems to be no necessity a priori that nature be reproducible at all, but the fact that science is being done (and redone) proves that nature does possess reproducible aspects. The reproducible aspects of nature form the objective real world that science deals with.
We don’t claim that nature is reproducible in all its aspects. But any irreproducible aspects it might be found to possess lie outside the domain of science, by the very definition of science that informs our present investigation. Parapsychological phenomena, for example—extrasensory perception (ESP), telepathy, telekinesis, clairvoyance—if, as some claim, they exist, would nonetheless be irreproducible aspects of nature.
For a detailed view of reproducibility, let’s express things in terms of experiments and their results. Reproducibility is then commonly defined by the statement that a given experiment, when replicated, always gives the same result. But what is “the same” experiment? Each experiment, and we’re including here all of the runs made on the same experimental apparatus, is a unique phenomenon. We try to avoid all possible changes, but no two experiments are identical. They must differ at least in their calendar and clock times (where the experiment, is repeated in the same laboratory) and/or in their locations (where the experiment is duplicated in another laboratory). And they might (and always do) differ in other aspects as well, such as in their orientations in space. So when we specify “same” experiment and “same” result, we actually mean equivalent rather than identical. We can’t even begin to think about reproducibility without permitting ourselves to overlook certain differences, such as those that involve time and location as well as various other aspects of experiments.
Consider the difference between two experiments as being expressed by the change that must be imposed on one experiment if we are to convert it into the other. Such a change might involve a change of time, if the experiments are performed at different times. It might (also) involve a change of location, if they are (also) performed at different locations. If the experimental setups have different orientations in space, the change will involve rotation from one direction to the other. If they are in different states of motion, a change of velocity will be involved. We might replace a brass component of the apparatus with an equivalent plastic one. We might bend the apparatus somewhere. Or we might measure velocity rather than pressure. And so on.
But not all possible changes are associated with reproducibility. Let’s list the ones that are. We certainly want to include change of time, to allow the experiment to be repeated in the same laboratory, and rotation and change of location, to allow other laboratories to duplicate the experiment. Since almost all laboratories are attached to Earth, the motion of Earth—a complicated affair compounded of its daily rotation about its axis, its yearly revolution around the Sun, and even the Sun’s motion, in which the Earth, along with the whole solar system, participates—requires rotation and changes of location and velocity, both for experiments repeated in the same laboratory and for those duplicated in other laboratories. Then, to allow the use of different sets of apparatus, we need to add replacement by other materials, other atoms, and other elementary particles. Owing to unavoidable limitations on the precision of experiments, we must also include minute changes in the conditions of running the experiments. And there are changes of a more technical nature, which we needn’t go into here.
Thus the reproducibility-associated changes that might be imposed on experiments include: change of time, change of direction (rotation), change of location, change of velocity, replacement by other materials, and small changes in the conditions.
As an example, imagine some experiment whose result is a particle appearing at the center of the apparatus one second after we turn on the switch. Repeat the experiment with the same apparatus, in the same direction and state of motion relative to Earth, but eight and a half hours later and at a location 2.2 kilometers east of the original location. If the particle now appears where we expect it eight and a half hours later than, and 2.2 kilometers east of, its previous appearance—that is, if it still appears at the center of the apparatus one second after the switch is thrown—we have evidence that the experiment might be reproducible. (Evidence, but not proof of reproducibility. By the rules of logic, a single negative result disproves reproducibility, but no finite number of positive results can prove it. A few positive results make us suspect reproducibility; many convince us; great numbers of additional positive results confirm our conviction.) In other words, if we ignore when and where the experiment is performed, and we nonetheless obtain the same result every time—a particle appears at the center of the apparatus one second after the experiment starts—then it’s looking as if changing time and shifting position don’t matter.
So let us define reproducibility. Consider two experiments that differ only by one or more of the reproducibility-associated changes mentioned above (such as change in the time or place the experiment is carried out). For these experiments to be considered essentially “the same,” even though they are truly different, the intrinsic experiment-result process must be identical for both experiments, and thus unaffected by the difference between them. This means the results of the experiments must differ in exactly the same way the experiments differ. In the example, the experiments are 2.2 kilometers apart and so are the results, with the particle appearing at the center of the apparatus in both cases. The experiments are 8.5 hours apart in time, and so are the results: in both cases the particle appears one second after the switch is thrown. The intrinsic process—a particle appearing at the center of the apparatus one second into the running of the experiment—is unaffected by the experiments’ different locations and times. If this holds true for some experiment, and for its replicas that differ from it by all reproducibility-associated changes (that is, all changes of time, direction, location, velocity, and so on), we then declare this experiment reproducible.
The idea is that when any reproducibility-associated change is imposed on a reproducible experiment in its entirety—that is, the same change is imposed on both the experiment and its result—the changed result will always be the actual result of running the changed experiment. One could then say that for such an experiment nature is indifferent to reproducibility-associated changes; they are unessential changes. Impose such a change on a reproducible experiment, and you get an experiment that, although it might differ from the original one in location, orientation, time of execution, and so on, is still essentially the same experiment in the sense that its result is essentially the same the result.
To put things a different way, imagine some reproducible experiment whose result is an explosion occurring at the edge of the apparatus 2.5 seconds after the switch is turned on. If we repeat the experiment with the same apparatus, in the same direction and state of motion relative to Earth, etc., but three hours later and at a location 1.6 kilometers west of the original location, we’re assured the explosion will occur three hours later than and 1.6 kilometers west of its previous occurrence. That is, it will again pop up at the edge of the apparatus 2.5 seconds after the start. And that will happen no matter when or where the experiment is performed. So ignoring when and where, the experiment always gives the same result.
Predictability
Predictability means that among the natural phenomena we choose to investigate, order can be found, from which laws can be formulated, laws that predict the results of relevant new experiments. Predictability makes science a means both to understand nature and to exploit nature. Just as for reproducibility, there seems to be no necessity a priori that nature be predictable at all, but the fact that science is being done, in countless laboratories and other circumstances, proves that nature indeed possesses predictable aspects. And just as for reproducibility, we do not claim that nature is predictable in all its aspects. But any unpredictable aspects it might possess lie outside the domain of science by the definition of science that informs our present investigation. Parapsychological phenomena, for example, if they exist, would be such an unpredictable aspect.
In order to view predictability in detail, let’s again express things in terms of experiments and their results. Predicting the results of new experiments doesn’t often come about through pure inspiration, but is normally attained by performing experiments, studying their results, finding order among the collected data, and formulating laws that fit the data and consistently predict new results.
Imagine we have an experimental setup, and we run a series of, say, fifty experiments on it. We have experimental inputs exp1, . . . , exp50 and corresponding experimental results res1, . . . , res50, res pectively. Thus we obtain the fifty data pairs (exp1, res1), . . . , (exp50, res50). We study these data, apply experience, insight, and intuition, perhaps plot them in various ways, and, perhaps with a bit of luck, we discover order among them. (There’s no standard operating procedure for finding order!)
Suppose we find that all the data pairs obey a certain relation, such that all the results are related to their respective inputs in the same way. This relation is then a candidate for a law predicting the result res for any experimental input exp: simply apply the relation that works so well for the data pairs already obtained to any other input exp and thus find the predicted result res. Imagine further that this is a valid law. Then additional experiments will confirm it, and we’ll find that data pairs (exp51, res51), (exp52, res52), and so on, also obey the same relation, as predicted. Predictability is the existence of such relations for experiments and their results.
For an example, consider the experimental setup of a given sphere rolling down a fixed inclined plane. The experimental procedure consists of releasing the sphere from rest, letting it roll for any time interval t, and noting the distance d the sphere rolls during the time interval. (Here t and d are playing the roles of exp and res, respectively.) Suppose we perform ten experiments, giving the data pairs (t1, d1), . . . , (t10, d10). Or, to be more specific, say we obtain the following ten numerical data pairs, where the time interval t is measured in seconds and the distance d is in meters:
A half-second roll from rest covers 0.025 meter. In one second the ball rolls 0.100 meter from rest, in two seconds 0.400 meter from rest, and so on.
We study these data and plot them in various ways. (The example is idealized, since in the real world there are always experimental errors that must be dealt with. But to avoid unduly complicating our presentation here, we ignore such difficulties.) Most of the plots show nothing especially interesting. But lo and behold! In the plot of the distance d against the square of the time interval t2, it looks as if all ten points fall close to a straight line:
A plot of the data from the rolling-sphere experiment. The distance the sphere rolls from rest is plotted against the square of the time interval, and the data points tend to fall close to a straight line.
The fact we just discovered, that the ten data points all fall near a straight line in the plot of d against t2, suggests the relation that the distance traveled from rest is proportional to the square of the time interval: d1 = bt12, . . . , d10 = bt102, where b is the coefficient of proportionality. This means that when we double the time we allow the ball to roll, for example, the distance it goes is qua dru pled. Check that. The distance covered in a two-second roll, 0.4 meter, is four times the distance of 0.1 meter the ball rolls in one second. And similarly for other data pairs.
That suggests the law d = bt2 predicting the distance d for any time interval t, not only the ones we measured. For our numerical example, the suggested law is d = 0.10 t2. As it happens, this hypothesis is correct, and all additional experiments confirm it: d11 = bt112, d12 = bt122, and so on. Or to be specific, we might run the experiment for the additional time intervals t = 5.5 seconds, t = 6.0 seconds, and so on. By substituting these values of t in the relation d = 0.10 t2, we calculate the respective predicted distances the sphere is predicted to roll for the additional time intervals: d = 0.10 × 5.52 = 3.025 meters, d = 0.10 × 6.02 = 3.60 meters, and so on. When the experiment is run, these are the actual distances the ball rolls. The new data are found to obey the suggested law. Thus the relation of distance to time interval is a predictable aspect of the setup.
It should now be clear what we mean by the reproducible and predictable aspects of nature. They are those aspects of nature that are both objective (all investigators agree on them) and orderly (they exhibit sufficient regularity to allow prediction).
But note this. Since we don’t include the reproducible and predictable aspects in our definition of nature as the material universe with which we can, or can conceivably, interact, it follows that we’re leaving the door open to the possible appearance of irreproducible and/ or unpredictable phenomena in nature. Such phenomena could be fascinating, and we might, with good reason, attempt to understand them. But then we would not be doing science; we would be involved in nonscientific modes of comprehension and explanation, and that would belong to another story altogether.
Law
At this point we should be in a position to begin to appreciate the definition of science that forms the basis of our present investigation:
Science is our attempt to understand objectively the reproducible and predictable aspects of nature.
In our effort to understand, we first search for order among the reproducible phenomena of nature, and than attempt to formulate laws that fit the collected data and predict new results. Such laws of nature are expressions of order, of simplicity. They condense all existing data, as well as any amount of potential data, into compact expressions. Thus, they are abstractions from the sets of data from which they are derived, and are unifying, descriptive devices for their relevant classes of natural phenomena.
In the above example of the rolling sphere, the law d = bt2 is an abstraction from the data pairs (t1, d1), (t2, d2), . . . , thus a simplification of them. It expresses an order that exists among the different runs of the experiment. It offers a description and a unification of the rolls of the sphere down the plane.
As an archetypal historical example of a law of nature derived from observational data, let’s consider the case of Kepler and his three laws of planetary motion. Johannes Kepler (1571–1630) pondered the astronomical data available to him for the five planets that were known at his time—Mercury, Venus, Mars, Jupiter, and Saturn—and found this order. If Earth is considered as one of the planets, and if the motions of the planets (the six innermost planets of the solar system) are considered from the point of view of a hypothetical observer standing on the Sun (the heliocentric point of view), then the motions possess three properties. For our present discussion it’s not necessary to understand the properties in detail, and if you’re unfamiliar with the concepts involved, don’t worry. The properties are:
1. The path each planet traverses in space, its orbit, lies wholly in a fixed plane and has the form of an ellipse, of which the Sun is located at a focus. (Actually, the ellipses of these six planets are close to being circles, with the Sun located at their common center.)
2. As each planet moves along its elliptical orbit, the (imaginary) line connecting it with the Sun sweeps out equal areas during equal time intervals. These areas have the shapes of slices from an elliptical pizza. (Thus, from geometric considerations, a planet moves faster when it’s closer to the Sun and more slowly when it’s farther from the Sun. Since the orbits of these six planets are nearly circular, this property simply means that each planet moves with nearly constant speed.)
3. The ratio of the squares of the orbital periods of any two planets equals the ratio of the cubes of their respective orbital major axes. The orbital period of a planet is the time it takes to complete one revolution around the Sun, the planet’s “year.” The orbital major axis of a planet is the major axis of the ellipse formed by its orbit, which is the distance between the two ends of the ellipse, one end being the point of nearest approach to the Sun and the other the point of farthest departure from the Sun. (Since the orbits of the six planets are nearly circular, the major axis is practically the diameter of the orbit, so without much error one may read “orbital diameters” for “orbital major axes.” And since those lengths appear in a ratio so that a power of two cancels, one may also read “orbital radii.”) If we denote the orbital period of any one of the planets by T1 and that of any other by T2 and denote their respective orbital major axes (or diameters or radii of their orbits) by a1 and a2, then this property is expressed by the formula
or equivalently
As I mentioned just before presenting the three properties, it’s not necessary that you understand the properties in detail. The most important point is that Kepler formulated properties of the planets’ motions. It is of secondary importance that the properties concern (1) the form of the planetary orbits, (2) the speed of each planet as it moves along its orbit, and (3) the relation between the time it takes each planet to complete one revolution around the Sun (the planet’s “year”) and the size of its orbit.
These properties express an order among the astronomical data. They offer a description and a unification of them. The motions of the six planets are not just any motions, but are related by their possessing the three properties.
The properties are called Kepler’s laws of planetary motion. They are laws of nature, in the sense that they correctly predicted the relevant properties of the motions of the additional planets that were discovered in the solar system in later years: Uranus, Neptune, and Pluto (no longer considered to be in the planet category). They are also laws in the sense that they are valid for any system of astronomical bodies revolving around a massive central body, such as the moons revolving around the planet Jupiter.
So now we have science proceeding by our (1) collecting reproducible, thus objective, data about nature and (2) finding, by whatever means, objective order and laws among the data. But laws are not explanations; they are descriptions. They describe the data in a concise manner and allow predictions. But they do not explain why things are as they are. To understand objectively the reproducible and predictable aspects of nature and not merely describe them, we must take an additional step. We must find objective explanations for the order and laws we discover. Such an explanation is called a theory. The next chapter deals with theories.
Science is our attempt to understand objectively the reproducible and predictable aspects of nature, where nature is taken to mean the material universe with which we can, or can conceivably, interact. The conduct of science involves searching for order among the reproducible phenomena of nature and then attempting to formulate laws that describe the collected data and predict new results.
Bibliography
For an idea of what physics, my model of a natural science, is about, see
R. K. Adair, The Great Design: Particles, Fields, and Creation (Oxford University Press, Oxford, 1987).
R. G. Newton, The Truth of Science: Physical Theories and Reality (Harvard University Press, Cambridge, Mass., 1997).
———. What Makes Nature Tick? (Harvard University Press, Cambridge, Mass., 1993).
J. S. Trefil, Reading the Mind of God: In Search of the Principle of Universality (Charles Scribner’s Sons, New York, 1989).
For more reading about the nature of science, see
H. Fritzsch, The Creation of Matter: The Universe from Beginning to End (Basic Books, New York, 1984).
R. Morris, Dismantling the Universe: The Nature of Scientific Discovery (Simon and Schuster, New York, 1983).
I. Prigogine and I. Stengers, Order out of Chaos: Man’s New Dialogue with Nature (Bantam Books, New York, 1984).
For the purposes of the present book, it’s not necessary to understand Kepler’s laws or even to be familiar with them. But if you’re interested, I suggest you look at any introductory college physics textbook. For a historical perspective of the laws, see
D. Park, The How and the Why (Princeton University Press, Princeton, N.J., 1988).
For the significance of the laws of nature, and for symmetry as an expression of the simplicity of those laws, see
R. P. Feynman, The Character of Physical Law (MIT Press, Cambridge, Mass., 1965).
See also Newton (1993) and Park (1988), above.
For introductory presentations of symmetry, see
G. Darvas, Symmetry (Birkhäuser, Basel, 2007).
J. Rosen, Symmetry Discovered: Concepts and Applications in Nature and Science (Cambridge University Press, Cambridge, 1975; reprinted with additions by Dover Publications, Mineola, N.Y., 1998).
More on laws of nature can be found in
J. D. Barrow, The World within the World (Oxford University Press, Oxford, 1988).
H. R. Pagels, The Cosmic Code: Quantum Physics as the Language of Nature (Simon and Schuster, New York, 1982).
V. J. Stenger, The Comprehensible Cosmos: Where Do the Laws of Physics Come from? (Prometheus, Amherst, N.Y., 2006).
Some books on irreproducible and unpredictable phenomena are
H. Broch, Exposed! Ouija, Firewalking, and Other Gibberish (Johns Hopkins University Press, Baltimore, 2009).
G. Charpak and H. Broch, Debunked! ESP, Telekinesis, and Other Pseudoscience (Johns Hopkins University Press, Baltimore, 2004).
M. Shermer, Why People Believe Weird Things: Pseudoscience, Superstition, and Other Confusions of Our Time (Freeman, San Francisco, 1997).