Dr. Hoi Fung CHAU
Department of Physics, The University of Hong Kong

Please read the following passage carefully. I am sure you will find it interesting!

You may notice that more and more people, including a few movie stars, wear crystal jewelleries. Do you know why? It is because crystals, especially purple crystals known as amethyst, can change your life in a subtle way. Amethyst is crystalline silicon dioxide (common name is quartz) with trace amount of manganese and iron (III) oxide. Its refractive index is about 1.55. Amethyst is known since the ancient times in various civilizations. They thought that amethyst protects the owner against drunkenness. In Tibet, amethyst is regarded a sacred gemstone. Leonardo Da Vinci once also claimed that amethyst was able to dissipate evil thoughts and quicken the intelligence. The secret power of amethyst comes from the manganese and iron it contains. Manganese and iron are ferromagnetic and hence will alter nearby magnetic and Qi fields. The nature of these fields is very different from the usual magnetic field we study in physics. In particular, they are not detectable by any physical instruments. The presence of these magnetic and Qi fields can only be confirmed by the effect of continual exposure to these fields. Upon weeks of exposure to these fields, the behavior of living things around it can be altered. As reported occasionally in major newspapers, both physical and mental health of people can be improved by wearing amethyst jewelleries. These newspaper reports convincingly show the advantage of wearing amethyst.

(Amethyst)

Do you think what you have just read is science? What is the reason behind your choice? Please take a few minutes to think about these questions carefully before reading further.

Before I tell you the answers, let me ask you what science really is. Quite a number of high school students in Hong Kong think that science has two characteristics. First, science must be correct; and second, scientific writing must contain equations and/or scientific terms. Judging from these two criteria, you may conclude that the above paragraph on amethyst is science.

Unfortunately, these two criteria are not the defining characteristics of science. Science need not be 100% correct: every scientific theory has its own limitation. All secondary school mechanics experiments show that Newton’s three laws of motion are highly accurate to describe the motion of bodies in daily life. These laws are so accurate and useful that engineers use them to design houses and trains. Nonetheless, experiments involving high energy particle collision conclude that our familiar Newton’s three laws of motion break down when the speed of the particle involved is close to the speed of light. Thus, Newton’s laws limitations are not 100% correct; and yet Newton’s laws of motion is science. Moreover, it is perfectly possible to write down a scientific theory without using equations and scientific terms. Careful use of equations and scientific terms merely aim to make the discussion clear and precise. For instance, saying “F = ma” and saying “the net force acting on an object is equal to the product of mass and the rate of change of velocity of that object” convey the same message although the former one is easier to remember. Yet, the latter statement contains no equation and scientific term.

If science need not be 100% correct and can be expressed without equations or scientific terms, then how one distinguishes between science and non-science. Actually, scientific theory must satisfy a number of criteria. The more important ones are falsifiability, predictive power and simplicity. Let me explain these three conditions one by one.

A theory is falsifiable if in principle one may show that the theory is wrong by the result of an observation or experiment. In this respect, the statement "F = ma" is falsifiable because we can, in principle, prove that the statement is wrong if you can find an instance clearly demonstrating that the net force is not equal to the product of mass and acceleration of the object. In contrast, the equation “ ” is not falsifiable because we cannot disprove the validity of this equation for any angle. In other words, no angle could make the above equation incorrect. In this respect, although mathematical techniques are vital tools in the study of science, theorems in pure mathematics are not falsifiable. Hence, mathematical theorems are not scientific statements. An important consequence of falsifiability is that a scientific theory may be revised from time to time as more and more experiments are performed. For example, the high energy collision experiments we have just mentioned falsified Newton’s law of motion. In order to explain the results of these experiments, Einstein put forward his theory of relativity. And if someone finds an experimental result contradicts the theory of relativity, we have to replace Einstein’s theory by something else.

A theory has predictive power if it makes specific prediction on situations that no one has encountered before. For instance, the statement "if you throw a ball today with a force F, you will experience an reaction force - F acting by the ball" has little predictive power. It tells us nothing about what will happen if we throw the ball tomorrow. In addition, the prediction should be sufficiently specific. For example, the saying "the number thirteen will bring you bad luck" is not sufficiently specific and hence has limited predictive power because different people may have different perception of what bad luck is. Similarly, the statement "Fma" has limited predictability.

A theory is simple if it involves only a few assumptions and/or parameters. If two theories can equally explain all the experimental results available, we tend to accept the one that is simpler. This principle is known as Occam's razor. Let me give you an example. Suppose one of your classmates does not come to school today. One possibility is that she is sick. The other possibility is that she takes a bus to school but the bus breaks down. She has to get out of the bus and takes a taxi. Unfortunately, the taxi driver is caught by a policeman for speeding. The policeman therefore invites your classmate to the police station as witness. Although both possibilities can equally explain why she is absent from school, but without any further information, we believe that the first possibility is more likely to be true in comparison to the second possibility because the first one is simpler. By the same token, the statement "F = ma" is simple as it involves only three parameters, namely, force, mass and acceleration; and yet it is able to precisely predict all known mechanical systems at sufficiently low speed so far. In summary, a scientific theory must be detailed enough to precisely explain all relevant observations and to predict the outcomes of similar experiments. But at the same time, the theory must also be simple enough to be comprehensible. In this respect, you may begin to appreciate the beauty lies in Newton's three laws of motion.

After knowing the three important characteristics shared by all scientific theories, you can convince yourself that the amethyst passage above is not science. First of all, the assertion toward the end of the amethyst passage is extremely imprecise and not specific. One does not know in what way the magnetic and Qi fields can alter the behavior of living things. Does it mean that the fields affect the motion of an animal or the mood of a human? We are not sure from what is given in the passage. Second, it is impossible to falsify the claim in that passage. The claim that these special kinds of magnetic and Qi fields can somehow alter the behavior of living things is so vague that it is not possible even in principle to set up an experiment to unambiguously disprove. Therefore, the amethyst passage above is not scientific.

As a matter of fact, many pseudo-science writings and commercials share the same feature as in the above amethyst passage. Namely, they use many scientific terms to indirectly convince people that what they are saying is correct. Besides, they try to mix science and facts with pseudo-science. In the passage above, the facts about the chemical composition, physical characteristics and historical believes on amethyst are told before telling you the non-sense Qi field. Besides, the physical meaning of "magnetic field" used in the passage is completely different from the usual definition of magnetic field in physics. (How come we cannot detect the "magnetic field" no matter how sensitive our measurement apparatus is?) Next time, think carefully before you believe in a television commercial or popular scientific writings.

In summary, science can be regarded as a consistent story telling exercise. Like a detective, scientists tell you the simplest version of the story (that is, a scientific theory or hypothesis) that is consistent with all known observations and experiments. Unlike an ordinary story in a novel, a "scientific story" has a number of precisely stated predictions. When new evidence is found which contradicts with its predictions, one may have to revise the story (that is, the scientific theory) again. This mechanism ensures that the story becomes closer and closer to the truth. This is one of the most important reasons why scientific methodology is so powerful.