Reductionism

A Beginner's Guide

Alastair I. M. Rae

• Publisher: Oneworld Publications
• Year: 2013
• ISBN:
  9781780742557
• Topic: Biowissenschaften
• Subtopic: Wissenschaftliche Forschung & Methodik

An unparalleled introduction to how the science of the small explains the biggest phenomena of life From the atom to our societies, this is an unparalleled introduction to how the science of the small explains the biggest phenomena of life. Ever since the ancient Greeks conceived of the atom, humans have sought the smallest ingredients of existence. In the past century, the use of reductionism to understand behaviour has gained momentum as the quantum universe and the workings of the human mind have been uncovered in particle colliders and fMRI scanners.Acclaimed physicist Alastair I.M. Rae spells out how the powerful tool of reductionism works, from the level of subatomic particles, up through molecular chemistry, and beyond to our neural networks. How does physics explain consciousness? Can quantum mechanics be applied to the brain or mind? What can economists learn from reductionism? Rae's exploration is an indispensable guide to one of the most fundamental ideas of science.

1

I reduce

Pigs might fly. This phrase is commonly used to describe something that is impossible and will never happen. But what would we conclude if we looked up into the sky and actually saw a pig flying past? Our first thought might be that it is a lighter-than-air balloon in the shape of a pig or that there must be some other ‘natural’ explanation. Why do we believe that flying pigs (and indeed flying carpets and broomsticks) are impossible, while objects such as most birds, some insects, aircraft, and rockets do indeed fly? The scientific answer is that all objects are subject to the law of gravity but the latter entities are constructed so that this force is countered by their ability to flap wings, spin propellers, or emit powerful exhausts. The first of these statements follows from the fact that gravity is a universal force that acts on the bodies’ component atoms independently of how they are arranged to create their external shapes. This is an example of reductionism, the fundamental principle that underlies all scientific reasoning and is the main subject of this book. Put simply, it states that the fundamental physical laws governing natural phenomena are the same as those applying to their basic constituents. Thus, for example, the total gravitational force on an object is the sum of the forces acting on the individual atoms, whether the object is a stone, a pig, a carpet, or even an aeroplane.

The principle of reductionism plays an important role in the scientific process, forming a central, if often unstated, assumption underlying almost every scientific statement. Reductionism means that the properties of something being investigated can be understood as emerging from the properties of its component parts and an understanding of how they interact. Thus, a biologist may explain a phenomenon such as the movement of a limb following a muscle contraction in terms of the properties of the biological cells that form the muscle – so ‘reducing’ the limb movement to the behaviour of its component cells. A biochemist may study a typical muscle cell and describe it in terms of the properties and behaviour of the molecules that make it up, hence ‘reducing’ the cell properties to those of the molecules. A chemist may examine one of the molecules and find that it is composed of atoms, and an atomic physicist might describe an atom as composed of a nucleus surrounded by a number of electrons which obey the laws of quantum physics. In this way, it could be said that biology can be reduced to atomic physics. Indeed, the physics of the nucleus and electrons can be further reduced to that of its constituent particles and these, in turn, emerge from the laws of what is known as quantum field theory. Beyond that some believe (or hope) that there is a ‘theory of everything’ waiting to be discovered. Attempting to understand what is happening at this most basic level is a major aim of some scientists and has motivated the building of the multibillion-pound Large Hadron Collider in Switzerland, where a long-predicted but never previously detected particle known as the ‘Higgs boson’ was discovered in 2012.

Further applications of reductionism relate to the behaviour of human beings as individuals and to society as a whole. Can our thinking can be reduced to the properties of our brain and can social behaviour be reduced to that of individuals? I shall be discussing these sometimes highly contentious ideas, as well as the less controversial applications of reductionism to the physical and biological sciences. Three important ideas form a tool-kit that will be used in tackling this task; these are the principles of falsification, simplicity, and emergence.

Falsification

What would be the logical conclusion to draw if we actually saw a flying pig, assuming that all natural explanations – such as it being a lighter-than-air facsimile – have been eliminated? The only alternative would be to conclude that the law of gravity could not have been acting on the pig at the place and time we observed it, so there must be something wrong with the laws of physics as they are presently understood. This would be an example of the principle of falsification, where a general proposition (the universal law of gravity) is shown to be false if one of its consequences (the impossibility of flying pigs) is found to be untrue. A classic illustration of falsification, from the world of biology, is the statement ‘all swans are white’. For centuries Europeans believed this to be true, because every swan they had ever observed was white. Soon after Europeans discovered Australia, however, they encountered black swans, which immediately disproved the general proposition.

Modern science, in its efforts to understand the universe and the processes underlying it, embraces the principle of falsification. It is often believed that science has developed theories which truly describe many aspects at least of the physical world. There is no way, however, that this can be proved absolutely because, however much evidence is found that supports a theory, it is always possible that it will be falsified by some future observation.

The question of how a general conclusion can be drawn from a series of repeated observations is known as the ‘problem of induction’ and has been studied over the ages. The principle of falsification was introduced into this debate by the philosopher Karl Popper. Born in Austria in 1902, into a family that had converted to Lutheranism from Judaism, Popper worked in Austria until 1937, when he became a refugee from Nazism. After a stay in New Zealand, he settled in London in 1946, where he remained until his death in 1994. Popper made a number of significant, though sometimes controversial, contributions to philosophy but he is probably best known for his contribution to the philosophy of science, which is set out in The Logic of Scientific Discovery. First published in 1934, this work proposed that the problem of induction could be resolved by emphasizing the role of falsification. In Popper’s view, the purpose of a scientific investigation is not to look for evidence that supports a theory but to carry out experiments that might disprove it. Thus, at any stage in the development of the scientific understanding of a physical phenomenon, there is a provisional theory (such as ‘all swans are white’) which has not yet been disproved. When further observations are made (like visiting Australia and seeing a black swan) the results should be examined to see if they are consistent with the proposed theory. If they are not, a new theory has to be devised that explains the new result and also accounts for all the earlier observations that were consistent with the old theory. The new, more sophisticated theory is then accepted as true unless and until it is in turn disproved by further experiments. Popper summed this up in the aphorism ‘Good tests kill flawed theories; we remain alive to guess again’.

Popper developed these ideas further to propose a definition of scientific knowledge: ‘In so far as a scientific statement speaks about reality, it must be falsifiable; and in so far as it is not falsifiable, it does not speak about reality’. This means that to qualify as scientific, a statement’s content must be falsifiable in principle. This does not mean that it has already been falsified – because then it would be known to be false – but there should always be a possible test which would falsify the statement if it came up with a particular result. For example, ‘the sun rises every morning’ would be falsified if one morning this did not happen. Similarly, ‘pigs do not fly’ could be tested by observing the behaviour of pigs. In contrast, a statement such as ‘grass is always bright red unless someone is looking at it (either directly or indirectly), when it turns green’ is unscientific because, whatever the reality, it could never be falsified.

As an example of how scientific understanding employs the falsification principle, consider how the theory of gravity evolved. Isaac Newton, who lived from 1642 until 1727, was allegedly inspired to propose his theory of gravity after observing an apple falling from a tree, showing that there had to be an unseen force attracting the apple to the Earth. He generalized this idea by postulating that this same force acted between any two massive objects, including astronomical bodies, and that this is the reason why the moon moves round the Earth and why the Earth and other planets move in regular orbits about the sun. He was able to express his ideas mathematically to make precise predictions of this orbital motion, which agreed with the results obtained by observations made by astronomers.

Newton’s theory of gravitation held for around two hundred years, during which time increasingly precise measurements of planetary motion were made. The only observations that did not quite agree with Newton’s predictions related to some fine details of the orbital motion of Mercury, the planet closest to the sun. Various proposals were made to explain this discrepancy without abandoning Newton’s theory; these included the suggestion that another planet (provisionally named ‘Vulcan’) moved in an orbit that was even closer to the sun and that its gravitational force affected Mercury’s motion. However, no direct evidence of Vulcan was found and, indeed, later observations have shown that no such planet exists.

Given the discrepancy between theory and experiment, a new theory was needed and this was produced in the early twentieth century by Albert Einstein. Einstein was born in Ulm (which is now part of Germany) into a non-practising Jewish family. His reputation was first established by three papers published in 1905, before he had acquired a position as a professional scientist. These papers made major contributions to several fields of physics, some of which we will return to in later chapters. Einstein is generally regarded as the greatest scientist of modern times and he has certainly acquired a fame that vastly outshines that of any possible rival. His greatest work is probably the General Theory of Relativity, which was published in 1916, when he was Director of the Kaiser Wilhelm Institute for Physics in Berlin. This set out an alternative theory to Newton’s law of gravitation, which had been falsified by the observations made on the planet Mercury. Einstein’s theory proposed that gravitational attraction is the consequence of the distortion of space itself by the presence of massive bodies. In nearly all practical circumstances, the predictions of the new theory are indistinguishable from those of Newton but in the case of the orbit of Mercury, Einstein’s, rather than Newton’s, predictions agree with the experimental observations. The general theory of relativity also predicted the results of some other experiments that had not been performed at that time. In particular, it predicted that the path followed by a light beam would bend as it passed through the gravitational influence of the sun. This was confirmed by a joint British-German expedition to observe a solar eclipse shortly after the end of the First World War.

Newton’s theory was generally accepted until the discrepancy in Mercury’s orbit was identified, which was correct, as all its previous predictions had been experimentally confirmed. So far, general relativity has survived all experimental tests, which include explanations of the behaviour of ‘black holes’, where the gravitational forces are so large that all matter has been crushed into a point. Theoretical difficulties, however, arise when general relativity is combined with quantum theory. At present, experimental study of situations where the quantum nature of gravitation is significant is not practicable, but if and when they are, both general relativity and quantum theory may well have to be replaced by an even more sophisticated theory. Until then, the general theory of relativity should be accepted as a true – but provisional – explanation of the motion of objects under gravity and the predictions of any future theory will have to agree with those of general relativity in all the areas where it has been successfully tested.

Simplicity

Another important principle that underlies any scientific explanation is that it should be as simple as possible. This idea is often attributed to William of Occam, a Franciscan friar who lived in Surrey in the fourteenth century. When Occam first proposed that ‘entities must not be multiplied beyond necessity’, this was primarily a theological statement connected to Occam’s belief that the only fundamental entity was God. Today, however, this principle is applied to the scientific process. In this context, his statement, which is often referred to as Occam’s razor, means that a good theory should involve no more assumptions (entities) than are necessary to explain all the known facts. As an example of a bad theory, one could postulate that the force of gravity depends not only on the mass of an object but also on its colour – perhaps that a red object would be subject to a stronger gravitational force than a blue one. As it has been observed that otherwise-identical red and blue objects fall to the ground in the same way and take the same time to do so, an additional force would have to be postulated to explain why the motion is exactly the same as in Newton’s ‘colour-free’ theory. Occam’s razor says that this more elaborate theory should be rejected because it contains additional entities – gravity plus another colour-dependent force – instead of gravity alone.

Another illustration is the development of our understanding of the solar system. It is often said that the first person to suggest that the sun rather than the Earth sits at the centre of the solar system was the Polish astronomer Copernicus, who worked in Krakow early in the sixteenth century. The idea had, however, been proposed by the Greek philosopher Aristarchus of Samoa as early as the third century BCE. It was dismissed at the time – which was probably correct since there was then little or no evidence to support it. When, about two hundred years later, Ptolemy devised a detailed model of the solar system that had a stationary Earth at the centre, this was actually the simplest model capable of explaining the available observations. By the time Copernicus came along, more data on the nature of planetary motion was available. He also had the key insight that the orbits of the planets were ellipses, with the sun located at one of the foci, rather than circles with the sun at the centre, as Aristarchus had suggested. Copernicus’s resulting theory was able to account for all the known facts. Nevertheless, this heliocentric theory only came to be fully accepted after the invention of the telescope enabled greatly improved measurements of the motion of the planets. Given the context of their theories and the nature of the experimental evidence available, it can be argued that both Ptolemy and Copernicus applied Occam’s razor correctly (though not consciously) in reaching their conclusions.

One simplifying assumption, made in all scientific work, is that the fundamental physical laws, such as gravity, are the same everywhere at all times. Thus, although when Alan Shepard played golf on the moon in 1971 he could hit the ball very much further than the best professional golfer on Earth, the same law of gravity applied in both cases. Because the mass of the moon is much less than that of the Earth, the force of gravity on the golf ball is smaller. Similarly, if I measure the time it takes for an object to fall from my hand to the floor today, I will get the same result tomorrow – provided, of course, that I release it from the same position each time. One of the consequences of the assumption that the fundamental laws do not change with time is that magic or miracles, in which the laws of physics are temporarily suspended while some otherwise impossible process is assumed to occur, are not part of science.

Another example of the application of scientific reasoning is the theory of evolution. Before this idea was developed in the nineteenth century, primarily by Charles Darwin, there was no scientific understanding of how living creatures had originated. The word ‘creature’ is itself a clue to the widely held belief that living beings must have been ‘created’ by some superior intelligence, generally known as God. That, at least, is the ‘creation myth’ of the Judeo-Christian monotheistic culture. Darwin’s theory has two main strands: first, the realization that living creatures change or evolve gradually from one generation to the next; second, the understanding that although these changes are effectively random, some will result in the off spring becoming better able than their parents to survive the challenges of their environment, while others will have the opposite effect. The offspring inheriting the beneficial changes are more likely to survive and produce further generations so that, over time, the species becomes better adapted to its environment. An increase in the complexity of the organism often results and this explains how the wide variety of living beings on Earth have evolved from very simple chemical molecules over a period of around ten billion years.

Evidence supporting Darwin’s theory was found by examining fossils, the preserved forms of living beings that existed in the past. It has also been fully supported by later, twentieth-century, research which identified the chemical processes associated with inheritance and mutation. There are still detailed questions to be answered about how evolution works in various contexts but nothing has been discovered that is inconsistent with the principles of the theory. Darwin’s theory is therefore an example of the application of both Popper’s falsifiability principle and Occam’s razor. An alternative model that requires the postulate of an additional unnecessary ‘entity’, comprising an all-powerful supernatural being, should, therefore, be rejected. Even if one believes for other reasons that God exists, the superficial simplicity of instantaneous creation has little or none of the explanatory power of Darwin’s alternative.

In these illustrations, the application of Occam’s razor is quite clear and uncontroversial but this is not always the case. If there had been no planet Mercury or any other evidence for the failure of Newton’s theory of gravitation, would Einstein’s theory of general relativity ever have been proposed or accepted? One might think not, because Newton’s theory appears much simpler and easier to understand than Einstein’s, which is mathematically complex and challenging. General relativity, however, is based on very general assumptions about the nature of space and time, while Newton’s theory is based on essentially ad hoc assumptions about the form of the gravitational force. It can therefore be argued that Einstein’s theory contains fewer of the entities that Occam says we should not multiply beyond necessity. Occam’s razor is an essential tool to be used in developing scientific theories but it is not always infallible, as there can be controversy as to which of two or more alternative theories is actually the simplest.

Emergence

Fundamentally, the principle of reductionism implies that no new fundamental laws are required to explain higher-level phenomena. New principles often emerge, which are sometimes described as ‘laws’ (Ohm’s law of electrical resistance is an example) but they are always consistent with, and in principle at least derivable from, the laws governing the lower level. The same fundamental physical laws determine both how an atom moves in a vacuum and how it behaves as part of a muscle.

Nevertheless, the question arises as to what, if anything, may be lost in the reductionist process. Does a description of the behaviour of its constituents tell us all that there is to know about an object or a process? Obviously not because, as we go from, say, a biological description of a living object to one in terms of atoms, we lose vitally important aspects of our understanding of the system at every stage.

Consider, as an example, a work of art – specifically, the Mona Lisa, painted by Leonardo da Vinci. When viewed from a distance, we see a depiction of a Renaissance woman offering us her famously enigmatic smile. If we examine the picture more closely, we can make out da Vinci’s separate brush strokes. If we look at the canvas through a microscope, we see each stroke is composed of small grains of paint of various colours. We might imagine that the reductionist process would entail describing the painting purely in terms of its smallest parts – the grains of paint. Is this all there is to it? Is the Mona Lisa just a collection of coloured spots? From one point of view there is nothing else. The grains of paint are the only reality – because, after all, the quality and intensity of colour that an individual grain produces is exactly the same as it would produce in another picture or on the artist’s palette. Nevertheless, everyone would surely agree that the painting as a whole possesses properties over and above those of its constituents: the whole is greater than the sum of its parts. This is consistent with the reductionist principle because the higher-level propertie...

Table of contents

• Cover 
• Half title
• Series Page
• Title
• Copyright
• Dedication
• Contents 
• Preface
• 1. I reduce
• 2. The building blocks of matter
• 3. Why water is wet and ice is hard
• 4. The chemistry of life
• 5. Neurons and the brain
• 6. Can we reduce the mind?
• 7. Society and the individual
• 8. Reducing the quantum
• 9. Conclusions
• Further Reading
• Index