Science and the Scientific Method

We briefly discuss the epistemology of science and the method(s) adopted in the practice of science.

Method

Method, or methods, usually refers to procedures and prescriptions that are applied for finding solutions to new and unsolved problems. Hence, before discussing the more specific case of the methodology of science, a brief discussion on the general question of method is in place. Social theorists have analyzed various methods that can be used in obtaining knowledge, and have come up with a classification of the procedures followed in the creation of new theories and ideas. The inductive method goes back to Aristotle and Newton, and consists of inferring the universal rule by looking at many specific examples. For example, if the earth attracts the apple, one concludes by induction that the earth also attracts all bodies that have mass. In contrast, the deductive method starts from a universal postulate, and then proceeds to ``deduce'' what the workings of the universal rule should be in particular examples. For example, if it is true that cholesterol can cause heart disease in all individuals, then one deduces that a patient with high cholesterol also will have the same disease. In other words, one can go from particulars to the universal using the inductive method, as well as from the universal to the particulars using the deductive method. Karl Popper has the well known definition of what is a scientific hypothesis, namely, it is a falsifiable hypothesis in that under some circumstances the hypothesis could have been false, and only if it survives such a test, can it be taken to be valid. For Popper, scientific theories progress through conjectures and falsifications. Thomas Kuhn proposed the idea of ``paradigm'', in which a theoretical framework - called a paradigm - is accepted to be valid. Scientists then apply the paradigm in all sorts of new and novel circumstances to find out where the paradigm breaks down. This ``paradigm-breaking'' method is taken to be an explanation as to how new scientific theories emerge. Day to day and routine research in science can be partially understood using the categories described above. For example, most physicists accept the validity of quantum theory - a so-called paradigm - and work within its framework to find new, novel and unforeseen consequences. Research proceeds both inductively and deductively, and in practice, scientists will use any and all modes of inquiry in attempting to solve a problem. All the methods above can be applied with varying degrees of relevance to both the sciences and to the humanities, although the applicability of these methods is more well established in the sciences.

The Scientific Method

The scientific method encompasses both the mathematical and empirical sciences, and we briefly discuss why it is necessity that drives science and determines what we mean by the scientific method. By necessity we mean iron laws of nature and of human thought that scientific theories have to try and explain. By the statement that science is driven by necessity, we mean that the discipline of science as such addresses aspects of reality that are governed by necessity. This is not to say that scientists are driven by necessity. To the contrary, scientists are driven primarily by curiosity and the desire to know how the natural world functions. Scientific research is open ended and exploratory, and finding new and unexplained phenomena is the main objective. On the other hand, inquiry which is motivated by other criteria such as fulfilling human or social objectives usually falls under the category of engineering and technology. Mathematical sciences - which include mathematics, computer science, simulations and so on - consist of purely symbolic structures that are freely produced by the human mind. Of course all of language consists of signs and words as well, in that the word is not a thing but can only signify (point to) to what it represents. However mathematical sciences are symbolic systems with a difference, in that they are constrained and driven by necessity. A mathematical theorem necessarily follows from the axioms of the subject. It does not depend on the subjectivity of any mathematician, since all mathematicians will be able to reproduce the same (universal) result. Mathematical investigations and explorations are subject to the iron laws of necessity. Evidence in mathematics consists of the derivation of the result. There are instances when there are plausible theorems for which no such evidence is available, and such theorems are called conjectures. Only when a proof is offered is the matter resolved. Mathematics is that component of human thought that is entirely and completely determined by necessity. Mathematical theorems are unconditionally valid - in all circumstances and for all time. Empirical sciences - which include physics, chemistry, biology, astronomy, geology and so on - are theories and explanations of nature based on empirical verification. Such verification entails producing evidence - for or against the theory - in the form of data which is presented to sense perception, and is external to the mind. Scientific data cannot be something that is produced by the human mind, for example, a personal opinion and so on. Once empirical evidence - namely, data - has been procured, the mind can then analyze such data to interpret, verify or falsify various scientific theories. Data is the result of the process of experimentation, in which some natural phenomenon is studied. There is a view that experiments should be differentiated from observations, in that experiment is taken in the following narrow sense. Namely that experiment implies procedures - in a laboratory or controlled environment - in which the degrees of freedom can be isolated from the environment and restricted, and that the process under study can be repeated time and again, and so on. Observations, on the other hand, are taken to be procedures in which the experimenter plays a passive role, as in the collection of data in astronomy, geophysics and so on. We use the term experiment for both procedures, since in both cases the underlying logic of both endeavors is the same, namely to obtain data regarding the phenomenon of interest, and for empirically testing the relevant theory in question. The hallmark of all empirical science is the following: The sole criterion of scientific truth is experiment. Experiments in turn are closely guided by theory as well. One of the hallmarks of science is the ability to identify mathematical symbols of the theory with certain physical phenomenon, and then go out and measure these physical quantities. For example, we define velocity as the rate at which the position of an object is changing. We can then go out and measure the velocity of the object. Very abstract and subtle properties of nature are defined by advanced scientific theories, and which in turn indicate the manner by which they can be experimentally tested. For example, an atom is incredibly small, but once its physical properties have been understood, precise experimental tools can then measure these properties. At the advanced levels of science, theory has to guide experiment on what to look for, and one can often find new phenomenon because of this guiding role of theory. Experiments in turn react back on theory with new findings. It is this dialectic of experiment and theory which has for the last four hundred years driven scientific knowledge. Scientific theories address only those aspects of nature that can be empirically tested. Scientific imagination is free to create and invent whatever it fancies. However, scientific imagination has to face the acid test of nature, and is subject to necessity imposed by nature. Nature imposed necessity puts severe restrictions on the possible forms of scientific thought. The power of scientific knowledge originates from this very compulsion of experimental validation. Conforming to nature provides science - and in effect man - with the ability to control and manipulate parts of nature. In making nature act and react based on the inherent laws of nature, scientific reason fulfills its own objectives. This ability to gauge the laws of nature has, in turn, led to myriad forms of technologies that have become vital for human survival. Empirical science is driven by necessity, but to a lesser extent than mathematics. The laws of nature are taken to be exact, universal, immutable, unconditional and eternal. The human understanding of these natural laws, however, is partial, limited and contingent. Consequently, truths in the empirical sciences are conditional and contingent: they are valid only in certain well-defined domains and in circumstances that are limited. Any and every scientific law is open to being challenged, and is sometimes completely replaced by laws that have a greater domain of validity. Hence the changing and evolving nature of scientific truths: scientific laws - as realized by the practitioners of science - grow and change to encompass increasing domains of phenomenon and with a greater degree of accuracy. An explanation with only a limited range of applicability is usually called a model. A postulate that receives some experimental verification is called a principle. Explanations of greater validity are termed as theories, and these tend to be more detailed than models and have greater predictive power. The term law is usually reserved for those theories that have been experimentally verified, such as the law of energy conservation and so on. What is common to both the mathematical and empirical sciences is that the particularity of an individual scientist plays an inessential role. A mathematician or a physicist may be recognizable by the style of his or her thinking, and in the choice of what he or she chooses to study. However, the results of these deliberations are valid only if they are independent of the individual's particularity in that other scientists can reproduce the results. It is hence consistent to group mathematical sciences together with the empirical sciences, since they are both driven by necessity, and we will use the word science to encompass both of these disciplines. The methodology of science, it's so called mode of inquiry, is determined by necessity. In particular, the need to produce scientific evidence, be it in the form of a proof of a theorem or in the form of experimental data needed for verifying or falsifying a particular theory, guides this mode of inquiry. The mode of inquiry is vertical, in that discoveries and results of previous generations are the basis of further explorations. One can revisit earlier conclusions, but in general, the domain of scientific knowledge encompasses more and more layers of phenomena, and accumulates more and more ``facts'' and data. For some people, there is no such thing as ``the scientific method'' and they see as many methods as there are divisions in science, namely, a different method for physics, another for chemistry, and yet another for biology and so on. For us, these are all empirical disciplines based on the same assumptions, namely, that nature is intelligible and yields to a rational and mathematical analysis, and that experiments are the sole gauge of what is true and what is false. From this point of view there is only one scientific method that subsumes all of the empirical sciences. The most powerful aspect of the sciences is its ability to predict how nature will behave in the future, or in new and unknown circumstances. Technology is rooted on devices and instruments that are made based on scientific principles, which can then successfully manipulate nature. A jet plane flies because the design of the plane conforms to the laws of fluid mechanics. Science can even predict the existence of phenomena that were hitherto unknown. For example, the mathematics of quantum physics predicted in 1929 that an electron would have an anti-particle as its counterpart. Anti-particles had never even been thought of until then, let alone having been detected. And sure enough, when guided by this theoretical prediction, anti-electrons were experimentally found in 1935. There are numerous such examples in science. Science has many precise, unexpected and counter-intuitive predictions that follow from the mathematical structure of scientific theories. The question naturally arises, are there mathematical structures essential for theory that do not have any measurable manifestation? Richard Feynman has the following to say. ``It is not true that we can pursue science completely by using only those concepts which are directly subject to experiment. In quantum mechanics itself there is a probability amplitude, there is a potential, and there are many constructs that we cannot directly measure.'' In other words, Feynman candidly acknowledges the presence of constructs in scientific theories that have no direct experimental consequence, but are nevertheless essential for understanding nature. Are there theoretical constructs in physical theories that have absolutely no physical consequence, but are nevertheless required by the mathematical structure of the theory? One can only make some conjectures. In quantum mechanics, the answer to this question, in principle, seems to be yes. The predictive power of science is completely based on the universality and ``objectivity'' of mathematics. The result of mathematical calculations yield new symbols and structures that are then identified, by a leap of imagination, with physical objects and processes. The incorrect view of dividing the world into the ``subjective'' and ``objective'' realms is fundamentally false, as is illustrated by the example of mathematics. A most ``subjective'' of all forms of human thought - namely a system of symbols and relations created entirely by the human mind - is the most ``objective'' of all human constructs as evidenced by its power to predict the properties of that most ``objective'' of all things - namely nature!

Mode of Inquiry in Physics

Since the idea of the scientific method, or the so called mode of inquiry of a discipline may be an idea unfamiliar to many, we analyze the case of physics to provide a concrete example of what a mode of inquiry addresses. In physics, there are two ways of ``attacking'' unfamiliar phenomena, namely using experimental methods, and the other being theoretical modeling. Theoretical physics uses mathematics as its tool of inquiry. However, unlike the discipline of pure mathematics that is characterized by symbol manipulation, the axiomatic method and rigor, theoretical physics creates new mathematics based on physical intuition, and seeks validation of its creations not in theorems, but rather in experiments. All theoretical models and laws of physics are approximate descriptions of nature, with well-defined domains of applicability. One of the distinctive features of the mode of inquiry in theoretical physics is the drive towards ``unification'', namely, the search for constructing and deriving all known theories to a deeper and more fundamental theory. This approach towards nature's laws has already paid rich dividends, as is evidenced by the establishment of the ``standard theory'' of particle physics in which all the known forces and constituents of matter have been unified into a common framework of quantum field theory. As shown in Figure 1.1, the standard theory has progressed by combining and synthesizing apparently unrelated features of nature's laws. The remaining puzzle of unifying matter and forces with gravity is thought to have been achieved in the proposed model of string theory. Some theorists criticize the drive towards unification in physics as being ``reductionist'' in that apparently complex phenomenon's explanation is sought in an underlying simplicity of constituents. While this approach is by itself not incorrect and has led to rich dividends in particle physics and in astrophysics, other branches of physics such as phase transitions, complexity theory, condensed matter physics and so on study large aggregates of matter and explain these with concepts that are more synthetic and ``holistic''. Only those theories of physics that successfully face the test of experiment are held to be correct. Similar to other empirical sciences, in physics experiment is the sole criterion of the truth or falsehood of a physical theory. Faced with inexplicable phenomena, theorists look for new combinations of known ideas to explain the problem, as well as symmetries and regularities that would simplify the problem. For example, faced with the phenomenon of the quantum evaporation of a black hole, theorists made an intuitive connection between the seemingly unrelated disciplines of thermodynamics and black hole physics. They made the hypothesis that a black hole has temperature just as an ordinary piece of matter does. And after years of research, using results from string theory, it was shown in 1995 that this conjecture was indeed a correct one. In the famous case of neutron decay, experiments seemed to show a violation of the conservation of energy and momentum. Physicists had the choice of either abandoning these hallowed principles, or of postulating the existence of a new particle, called the neutrino, that would restore the conservation laws. And sure enough, experiments soon found the elusive neutrino. Theoretical physics has created intuitive mathematics that lies beyond the formulation of rigorous mathematics, and has successfully made numerous predictions of new and novel forms of phenomena. The ability to predict the existence of hitherto unknown phenomena in nature is a distinctive hallmark of the scientific mode of inquiry.

Figure 1.1: Relations between theories

Consider the phenomenon of Bose-Einstein condensation. At the unbelievably low temperature of a few millionths of a degree above absolute zero, where almost all thermal motion has ceased, pure quantum effects create the conditions for a new state of matter to come into existence. Although Bose-Einstein condensation had been predicted by quantum theory as early as in the 1920's, it was only in 1997 that this state of matter could be realized. There are also many cases of experiments leading to new theories, as in the fabrication of new materials such as high temperature superconductors. The use of experiment as an instrument of inquiry is a unique feature of the empirical sciences. Experimentally looking for states such as Bose-Einstein condensate or the neutrino has been compared to looking for a needle in a haystack. It is no exaggeration to say that without the guidance of theory, these states would be impossible to find. This close interplay of theory and experiment is another unique feature of the mode of inquiry in the empirical sciences.

Interconnectivity of the Scientific Disciplines

The study of nature has spawned a wide variety of scientific disciplines from physics and chemistry through biology and onto the study of the environment and so on. There is debate in certain quarters whether the various disciplines have at all a common methodology, and whether they form an interconnected whole. The various topics covered under Physical Laws focus on central ideas that run through all physical phenomena. A few key ideas, such as energy, entropy, light, atoms and so on permeate all physical phenomena, and provide the intellectual framework for the various scientific disciplines. The understanding of almost all physical phenomena requires the concept of energy. Almost every form of biological energy on earth has been derived from the Sun's radiation, and converted to other stored forms of energy through the process of photosynthesis. Entropy and free energy are fundamental for determining which chemical processes are possible. Atoms and molecules form the underpinnings of chemistry and biology. All of molecular biology consists of the study of macromolecules, and which in turn are described by energy and entropy considerations. All living organisms minimize their entropy by consuming energy from the environment. Mechanics explains the locomotion of animals. The list goes on and on. All aspects of nature are interconnected, and form a seamless whole. A handful of physical concepts cut across all disciplinary boundaries and explain diverse physical phenomena from subnuclear processes to the workings of living matter and out to planets and galaxies. The various scientific and disciplines can be also be characterized based on other criterion such as their degree of complexity. For example, in physics the focus is on explaining the properties of the simplest constituents, such as understanding what is an electron or a quark; in chemistry, complex combinations of atoms are of primary interest whereas in biology macromolecules consisting of millions of atoms form the foundation of the subject. Complexity itself has features which are universal and which in turn tie in with information theory and so on. Physics also studies such complex systems as bulk matter consisting of superconductors, semiconductors and so on as well as large bodies such as planets, stars, galaxies and the universe itself. The environment and ecology is another sphere where the synthesis of all the different sciences is needed to form a coherent understanding. Science is interconnected in many different ways, and it is the beauty of nature which shines through in all of one's studies in science.

Interconnectivity of Physics with other Disciplines

To illustrate the idea of the inter-connectivity of the various scientific and other disciplines, we briefly discuss this idea in the context of physics. Consider, for example, the water molecule, which is composed of one oxygen atom and two hydrogen atoms. Quantum mechanics leads to the conclusion that the angle between the average positions of the two hydrogen atoms in 105 degrees. One may think, so what, who cares, what difference does it make what the angle is? The result, however, has stunning and far-reaching consequences for biology. All life consists of chemical reactions taking place in the solute water. The ability of water to dissociate molecules crucially hinges on the angle between the hydrogen atoms being 105 degrees, since this allows the hydrogen atoms to ``get a grip'' on other atoms. The most symmetric configuration for $H_2O$ is with the angle between the hydrogen atoms being 180 degrees; in this case the two hydrogen atoms would lie along a line with the oxygen atom in the middle, and none of the biochemistry essential for the existence of life could ever have taken place. Another interesting connection is that of physics with finance. The price of a stock or a bond undergoes a random evolution in time in exactly the same manner as the position of a quantum particle does. Furthermore, the study of finance is also connected with the field of statistical mechanics, which studies the properties of a large collection of particles. In short, the study of physics correlates a vast diversity of phenomena, connecting processes at the nuclear and subnuclear level with the structure of stars, the properties of viscous fluids with the flow of blood in arteries and veins, thermodynamics with information theory, and so on.

Relevance of the Methodology of Physics to Other Disciplines

There are a few general results from the example of physics that are of some relevance for other subjects. 1. The distinction and inter-play of experiment and theory can be used as an analogy for the historical versus the formal approach to subjects such as literature, linguistics, sociology and so on. 2. The distinction between the intuitive mathematics of theoretical physics and the rigorous and axiomatic approach of pure mathematics can be used as a metaphor for the intuitive versus axiomatic approach in many of the subjects in the arts and social sciences.