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We briefly discuss the epistemology of science and the method(s)
adopted in the practice of science.
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 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.
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
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
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!
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
and deriving all known theories to a deeper and more fundamental
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
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.
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
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.
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
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
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.
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 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.
Relations between theories
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
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.
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