Scientific Method

Science, Scientific Methods and Mythologies By Belal E. Baaquie Department of Physics National University of Singapore

(Natural) Science A Google search yields over 260 million results for science, and over 8 million for the scientific method; it would seem that not much new can be said on these subjects. A working definition of science is the following: ‘ Science is knowledge and study of the empirical (qualitative and quantitative) aspects of nature ’ Empirical properties are those that can be verified/falsified by experiment.

‘ Hard Sciences’ ‘ Hard sciences’ or the ‘exact sciences’ refer to the sciences that have a mathematical formulation, and in which a mathematical calculation is performed to make predictions. Physics is probably the most ‘hard’ of all the sciences, and in this talk Physics will be used to illustrate the general principles of science and of the scientific method.

Scientific Truth A statement about nature, be it qualitative or quantitative is said to have the following scientific criterion for its validity: ‘ The sole criterion of scientific truth is experiment’ If, and only if, a hypothesis (and its predictions) is validated by experiment, it is true. Experiment refers to observing nature through instruments, that can include our physical senses. Human opinion does not count as experimental data.

Scientific Hypothesis Only a hypothesis that can be empirically validated or rejected qualifies as a scientific hypothesis. In other words, a scientific hypothesis in principle should be empirically falsifiable . For example, ‘energy is conserved’ is a scientific hypothesis, whereas ‘van Gogh’s paintings are beautiful’ is not.

Empirical basis of Energy Conservation In 1935 it was observed that in beta decay a neutron disintegrated into a proton and an electron. n  p+e - (energy not conserved: incorrect) Energy was not conserved in this process. Some physicists proposed theories for beta decay that violated energy conservation. However, Pauli predicted the existence of a hitherto unknown particle called the neutrino (little neutron) based on energy conservation. n  p+e - +  e (energy conserved: correct) The neutrino was soon detected providing empirical evidence for the conservation of energy.

Process of Hypothesis Testing

Scientific Method How does one go about finding out new patterns in nature? What approach does one adopt when faced with a new and unknown problem? The scientific method refers to the procedure, the means, the process, the technique, the way and so on that a problem is addressed in science. Most scientific discoveries are made is a chaotic and disorderly manner; scientists do not consciously follow any specific procedure and have only an intuitive understanding of how they themselves solve problems in their own work.

Scientific Methods in Physics Reductionism Structuralism ‘ Universalism’ Metaphorical Reasoning

Reductionism The procedure to ‘reduce’, that is, to explain a complicated phenomenon at one level by a simpler phenomenon at another ‘deeper’ level. Most materials can be reduced to the atoms that compose them and the interaction between these atoms. Many of the established branches of physics ‘reduce’ a complicated phenomenon to simpler structures, usually called ‘constituents’, of which the atom is the leading exemplar.

Newton’s Mechanics: Reductionism In Newton’s second law of motion, force causes acceleration. This is a classic example of reducing (explaining) motion to the force that causes it. The idea of an underlying mechanism , the generalization of the idea of force, is fundamental to reductionism. One is always looking for a mechanism to explain the apparent phenomenon. The Universe viewed as a machine, with inter-locking components, is a paradigm for the reductionist point of view.

Reductionism Works! Recently a famous physicist visiting Singapore claimed that reductionism is completely wrong and asked: “Does the property of rigidity lie in the properties of atoms? Is superconductivity the property of individual atoms?” His answer was ‘ No ’; and he went on to claim that all physical laws were the result of the ‘emergent’ (collective) properties of matter. The answer of ‘No’ does not mean reductionism is incorrect. Rigidity is explained by ‘reducing’ the (rigidity) properties of materials as resulting from the inter-atomic bonding of atoms composing the material. A superconductor is ‘reduced’ to the existence of Cooper pairs of electron that have undergone condensation, and resulting in the bulk property of zero electrical resistance. The entire field of materials science is based on ‘reducing’ the observed bulk properties of matter to their inter-atomic properties.

Structuralism When a phenomenon is too complicated to be ‘reduced’ to phenomena at a lower order, scientists look at the phenomenon as an original system. The inner relationships of the system are studied from first principles and lead to new structures. An example of structuralism is the black hole , the explanation for which is geometrical, and is not ‘reducible’ to atoms or anything else. Superstrings is a new structure at the most microscopic level. The DNA molecule is a structure at the macromolecular level that needs to be studied as an original structure, instead of only as a collection of about 10 12 atoms.

Black Holes and Superstrings A black hole is represented by a three dimensional sphere in space, with it’s surface called the black hole’s horizon . To observers outside the black hole, a particle falling through the horizon can never return. The falling particle, on crossing the horizon, is transformed from atoms into a more general mode of superstrings: ten dimensional entities thought to compose all of physical reality. Outside the Black Hole: Ordinary Matter Inside the Black Hole: Superstring states

Superstrings: Fundamental Postulate All of physical reality is made out of different states of the superstring that can be open or closed. Each vibration of the string is equivalent to a point particle. One superstring gives rise to infinitely many fermions and bosons.

Superstrings can exist only in 10-dimensional spacetime Quantum superstrings, due to combination of the quantum principle with relativity, can only exist in 10 dimensional spacetime . Quantum string is massless with each piece of the string traveling at the speed of light, and undergoing quantum fluctuations. For the quantum string not to ‘fall apart’ it can only exist consistently in 9 space and 1 time dimension.

How Long is the Superstring? Superstrings contain the theory of quantum gravity. Gravity becomes comparable in its strength of coupling at the Planck distance. Superstrings’ size is about 10 -35 m ( Planck length ), and has string tension of 10 39 tons! The size of a superstring is as much smaller than the atom as the atom is smaller than the size of the solar system!

Black Hole Evaporation Three structures, namely atoms , black holes and superstrings give rise to new quantum phenomena, called Hawking radiation. Hawking showed Black holes evaporate due to the quantum fluctuations of the vacuum In string theory black holes evaporate since they are emitting open and closed strings; these strings appear as ordinary massless particles once they are outside the horizon.

What is a Prediction? Some physical phenomena cannot be explained by either reductionism or structuralism, for which the concept of predictions needs to be re-examined. Given the initial position and velocity of a golf ball, its future position can be ‘exactly’ predicted by Newton’s equations of motion – and tested empirically. Quantum mechanics and statistical physics (eg. kinetic theory of gases) force us to broaden our view of predictions: we can only predict the likelihood of events, with the outcome of any particular experiment being completely random (undetermined).

Classical Particle in a Box : position is deterministic Suppose a particle is placed inside a box with velocity v =0 Classical Description: Position of particle unique for all time ; on measuring its position it will be always found at say x 0 . x0

Quantum Uncertainty: Position of Particle in the box is Random We repeat an experiment N times by placing an electron inside a box, and then measuring its position . Its position is found to be random: it is found n times to be near x. We conclude the probability of being near x is P(x)=n/N, for N very large. x P(x) Particle at rest is simultaneously everywhere in the box, since it has a finite probability P(x) of being found near all points x.

Statistical Ensemble Another kind of uncertainty arises from the sheer complexity of the problem, and from our inability to exhaustively describe it. C onsider the atoms in this room, of which there are approximately 10 23 ! Can we predict the motion of every single atom? – or more importantly do we need to do so for determining the air’s pressure, density, temperature and so on? The answer is ‘No’ – we don’t need so much information. Since we have no information about the state of the atoms in the room, one replaces the state of the gas in the room, one assumes that the positions and velocities of all the atoms are completely random , with every possible configuration of the atoms having an equal likelihood of occurrence. Hence, the gas is now described by an ensemble (collection), technically called the micro-canonical ensemble, whose elements are all possible configurations (positions and velocities) of the 10 23 atoms comprising the gas.

Statistical Predictions What can we predict about the atoms of air in this room based on the idea of the ensemble? We can make statistical predictions that result from a large number of measurements. For example we can compute the average energy of every atom by averaging the energy of an atom over all its possible configurations. The result of such averaging procedure is the energy of every atom is proportional to the room’s temperature, that the pressure, volume and temperature of the gas obey the ideal gas law and so on.

Universality Class: Collection of Systems We can go further and consider, instead of an ensemble (collection) of atoms, we can construct a collection of physical systems, called a universality class . An example of such a collection is all the proteins in a particular living system; note the human body can make up to 300,000 proteins. Entire systems, like a protein, are elements of a universality class , which in turn can be described by statistical laws similar to the statistical laws that describe the behavour of an ensemble of atoms.

Example: Protein Folding A protein is a biopolymer – a long linear chain of a few hundred amino acids (monomers) - which folds in a way that minimizes its (free) energy. Allosteric proteins can have many ways of folding, with energy differences  E that are close to zero. A small change of even one amino acid, or of the pH inside a cell, can cause the protein to flip from one folding to another one close by; this is the way for example how the bicep muscle can contract.

Re-formulation of Protein Folding To explain the change in protein folding from the reductionist point of view is a mathematically hopeless exercise; the smallest inaccuracy in the potentials could give a completely wrong result. The problem can re-formulated in the following manner. Consider a given protein as belonging to a universality class (collection of systems). We assume that the potentials of the systems are random , and then compute the probability P(  E) that a given system (protein) will have various folding states with energy differences given by  E.

New Genre of Predictions It is no longer meaningful to ask about the properties of a specific system. Instead new questions need to be asked that can be answered once P(  E) is known. This approach also expands our predictive power; although we may start our analysis by considering how systems of proteins behave, since they are biopolymers we can extend the validity of the results to other any biopolymer belonging to this universality class, including for example the RNA, since it will also have a behaviour governed by P(  E).

Laws for Systems of Biopolymers The f ollowing empirical laws can be addressed: # of cell types in an organism ~ (# of genes) 1/2 # species in island ~ (# of genes in island) 1/4 Universal quantities like the exponents ½ and ¼ could hopefully be computed from P(  E) that is the property of the universality class, and not of any particular system . # human cells~ 250; # genes ~ 30,000

‘ Universalism’ In this method, one groups a particular phenomenon in a class of systems, called universality classes. The probabilistic behaviour of the elements of the universality class is derived from the underlying fundamental (random) equations of motions of the system. In some cases the average properties of a universality class can be meaningful; these properties can be evaluated by averaging over the systems in a universality class, and are governed by the laws of the universality class and not by the laws of the individual systems.

Reductionism, Structuralism and ‘Universalism’ All methodologies coexist in scientific research. For example, to understand the double helix structure of the DNA the ‘reductionist’ concept of the covalent bond within a strand and Hydrogen bond between the two strands is employed. To understand how the DNA functions the structuralist method of the bases A, C, G and T as structures of information is used. And finally to understand the folding of the DNA the method of ‘universalism’ is used. To understand ‘emergent’ properties, such as cell replication, all methods including reductionism have to be used. Negating reductionism is like playing handball with one hand tied.

Transdisciplinarity of Science All scientific knowledge is subdividing into new specializations, and established specialized field such as Physics is further subdividing into even more specialized disciplines. The greater the specialization, there is an even greater need for transdisciplinarity, of connecting different scientific disciplines and of combining fields in new and novel ways. Scientific methodologies have to be synthesized in in order to advance transdisciplinary knowledge. The example of research into the DNA is an example of the new forms of emerging methodologies.

History of Scientific Methodology Modern science starts in 1600’s with Newton and reductionism. By the 1900’s the kinetic theory of gases introduces the idea of statistical ensemble. Quantum theory (1930’s) shows that nature is inherently random and only average values of physical quantities can be predicted. With the advent of biological and other complex systems, the idea of universality class of systems is introduced, further reducing our ability to predict but increasing the domain of phenomena for which we can make quantitative predictions. The 21 st century may lead to other types of methodologies that we have not yet even dreamt of.

Metaphorical Reasoning How does one arrive at a scientific hypothesis? There are many ways, and one which is particularly interesting is metaphorical thinking. Metaphors -- often called a ‘picture’ in physics – are also useful in creating scientific concepts that attempt to explain a phenomenon one is trying to understand. If a picture can lead to precise experiments or quantitative equations, then the picture may be said to have provided a metaphorical insight into the understanding of the phenomenon. It should be noted that if the picture does lead to a quantitative result, then the picture is by itself not sufficient for any scientific purpose. Science cannot be done by pictures alone – these have to graduate to a scientific statement. Some mythologies are discussed to see that they provide a most unexpected source of useful pictures for physics. Myth: A traditional, typically ancient story dealing with supernatural beings, or ancestors, or heroes that reflects the worldview of a people, and serves to explain aspects of the natural world.

Science against Mythology Modern science, starting from its 17 th century founders such as Newton, Bacon and others, has considered mythologies to be unrealistic constructs about the world since it is often based on supernatural causes. For example a mythical Thunder God explains thunderstorms -- clearly unscientific. Many scientists today continue to reject mythologies as being misled by the appearance of nature, and feel that mathematical intuition is superior and a more accurate approach to nature. However, with the advance of science, we now realize that mythologies should not be read literally, but as metaphors and symbolic truths that need interpretation to be fully understood. Science maps phenomena into symbols that we can then grasp and think we understand. Myths like science also need to have an interpretation for the meaning of symbols that it uses. For example the Thunder God can be interpreted as a metaphor for forces of nature.

Myth and Meaning The word ‘meaning’ means the following: that we have rules for transcribing, for translating and mapping what we would like to understand to another level of language that is familiar to us. The very fact that mental rules exist to give meaning to mythologies makes it similar to science The inner logic of why mythologies and science ‘meet’ is, according to anthropologist Levi-Strauss, due to the manner in which our nervous system processes our experiences . Nature has only so many procedures and structures, and hence these may appear in consciousness first in mythology and then in science, and vice versa.

Science and Mythology Science reproduces some of the ideas of mythology in surprising ways. The ancient idea of the immanence of God postulates the presence of the Supreme Being everywhere in nature. The field, in particular the electromagnetic field, is a physical entity that is present at all points of spacetime – it is immanent in nature. All of physical reality is constituted by only a handful of (quantum) fields that are immanent in spacetime. Conversely the speed of light idea is a metaphor for an absolute truth, since it is an absolute (quantity) that is independent of the observer (inertial frame).

Black Holes, Superstrings and After life Recall a black hole is represented by a three dimensional sphere in space; anything that falls through the horizon can never escape from the black hole. To observers outside the black hole, a person falling through the horizon can never return – analogous to a person dying person never returning to the world. Death of a person is analogous to matter crossing the black hole’s horizon. The atom falling through the black hole has an ‘after life’ as a 10-dimensional superstring in a domain of reality inaccessible to ordinary matter outside the horizon. The person falling through the horizon is transformed and has an after life in another realm of reality (hopefully Paradise!) inaccessible to the living. Death Paradise

Interiority of Space and Inner Self In superstring theory the internal Calabi-Yau six-dimensional space -- one for each point of ordinary space -- is like the interiority of each person own inner self. Self-awareness seems to exist at a point, and within this point is an entire universe of consciousness of one’s inner self. It may be time for science to base itself on mythological ideas and then see if new phenomena can be discovered and new empirical predictions can be made.

Myths as a Resource for Science A fundamental myth of mankind is the existence of trans-physical entities and domains of reality – for example the realm of the spiritual world and realm of the after life. These trans-physical domains are not in spacetime as we know it, and entities are not made out of atoms and molecules. In 10-dimensional superstring theory, the extra dimensions of space can be thought of as metaphors of other trans-physical domains of reality.

Science: Going Beyond Empiricism All of science is empirical since experiment is the sole basis of all scientific truth. Empirical science has so far insisted on basing all its theories on measurable quantities, and has rejected myths as mere products of human imagination. Quantum physics has gone beyond simple minded empiricism by introducing the concept of the wave function that is not a thing, but rather information about the thing. Superstring theory has gone even further from empiricism by postulating a spacetime that is at least ten dimensions – and has dimensions that are not directly measurable. Science should now consider theories in which some of the ingredients are trans-physical realms that inter-face with physical reality – analogous to the domains inside and outside the black hole separated by the horizon.

Conclusions Science and its methods are evolving and change with the problems that it addresses. All methods are useful, and can be used by themselves or in combinations. The theories of physics are probably precursors to the shape that the other sciences will take in the future. To make new discoveries and further develop scientific methodology, deep mythological ideas can be a rich resource of metaphors for science. One of the main aims of science should be to have a theoretical framework that is a synthesis of the objective world of nature with the subjective realm of the Self .

References Giorgio Parisi, “Complex Systems: A Physicist’s Viewpoint” cond-mat/0205297 Claude Levi-Strauss, “Myth and Meaning”

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