The Scientific Method

Conversation 10, Socrates Worldview 7/22

SOCRATES. Well, here we are Adeimantus and Critobulus. Are you ready to be enlightened about science, Critobulus?

CRITOBULUS. I admit that as a possible, if unlikely, outcome, Socrates.

S. Good man. You come with a mind that is not entirely closed. That’s all I ask. Now then, we are going to discuss science. Shall I propose a definition of science?

ADEIMANTUS. It would seem to be good to agree on the subject of our discussion.

S. Very well. When I talk about science, I mean the endeavour of pursuing knowledge via the scientific method, and the knowledge gained thereby. Will that do?

C. It might, provided we agree on the meaning of ‘scientific method’.

S. Quite so. What is your understanding of ‘scientific method’, Critobulus?

C. I think it is a grandiose name for an activity that when boiled down is nothing more than fairly random delving into the way things work, in order to make incremental improvements to technology. Advancement by trial and error, if you like. I don’t think there is any grand scheme behind science. Theories and hypotheses are merely window dressing for the sake of persuading people for the advantage of the proposer. The motives are usually sordid, money and power, although I will admit that some science, like medical research, might have more humane motives.

S. A dim view indeed, Critobulus, but one that I think you are not alone in holding. You discount scientific theories and hypotheses completely?

C. These theories and hypotheses are just myths designed to bolster the scientific establishment. They are a product of Western culture and have no more validity than the myths of any other culture. Anyway, it seems that scientific theories are always provisional. Scientists change them at the drop of a hat when it suits them, or when a rival group gets the upper hand.

S. Your view is straight from the postmodernist cannon, Critobulus. You confuse technology with science. Although they have a symbiotic relationship, they are not the same. Science is a far more intellectual pursuit. I see that my challenge is to convince you that the scientific method is more noble than you suggest, and that it is not tied to one culture, thought it found fertile soil in Western culture for reasons we might discuss another time.

C. Fire away!

S. So, I begin. Firstly, science presupposes a Realist¹ view of the world. Science regards the world as ‘out there’, regardless of whether you or I are looking at it or thinking about it. Remember what the ancient Greek Democritus famously said in around 400 BC: ‘By convention sweet is sweet, bitter is bitter, hot is hot, cold is cold, colour is colour; but in truth there are only atoms and the void.’

A. Amazingly prescient!

C. A lucky guess. He could not possibly have known that was true. It illustrates my point about random delving.

S. Yes, it is only in the last century that the atomic theory of Democritus has been shown to be correct. I quote Democritus for two reasons. The first is to illustrate how the idea often precedes and guides the scientific delving, which is far from random. The second is to emphasise the Realist view that science deals with things that have objective reality, not with the qualities of things which are in the mind of the beholder.

A. Are you saying that mind is outside the scope of science?

S. Not at all, Adeimantus. I do believe that most scientists of the 17th and 18th centuries would have regarded mind as being distinct from matter and of a different order of reality. I imagine they thought of the mind of God and their own mind as being aloof from the mechanistic workings of the material world that was the subject of their study. In a sense, they imagined a ‘God’s eye’ view of the material world. It is only much more recently that the idea of mind as a manifestation of the working of a physical process has gained wide acceptance, including among lay people, especially in the West.

A. Is this not a fundamental shift in viewpoint, Socrates?

S. Indeed it is, Adeimantus. Once upon a time, the scientist was happily outside the world he contemplated. Today he is very much inside and part of that world. As it happens, this distinction does not matter for our discussion of the scientific method, although it does place a limit on how far science can go. I am talking about quantum mechanics, which I propose to discuss at another time. It was, and still is, an important principle of science that we could observe the world without disturbing the very processes we were trying to measure and understand. In days gone by, it was assumed that measurements of space and time could be made with arbitrarily fine precision, at least in principle. Now we know it is not so. Quantum mechanics tells us that there are things going on in the universe that are too small or too fast for us ever to observe or measure them without disturbing them. The problem is that our minds, as we now think, cannot exist without our bodies, and our bodies and the tools we employ to observe and measure are macroscopic things which cannot make precise measurements of the quantum world without messing up what we are trying to measure. It is a fundamental limitation. The word of God might be able to ‘seek out the place where soul is divided from spirit, or joints from marrow’ (The New Jerusalem Bible, 1985, p. Hebrews 4:12), but our body-bound minds cannot.

A. Then is our quest to understand the world hopeless, Socrates?

S. Yes and no, Adeimantus. The quantum limit is very far removed from the scale of our everyday experience. There is an awful lot of space and time both bigger and smaller than ourselves that science can illuminate, so it is worth pursuing the scientific method to see where it takes us in our understanding of the world. But the limit to our knowledge does exist, and that fact has the profoundest consequences for what we are to make of the discoveries of science as they affect our lives and our ‘worldview’. I should also add that the idea of our minds being an outgrowth of our bodies, while widely accepted, is far from being assimilated into our understanding of the consequences for our lived experiences, society, and morality. We are presently in a kind of limbo where the old worldviews no longer work and no new one has emerged that is universally satisfying. We shall return to these questions in our later conversations. For now, let us continue with our examination of the scientific method.

C. Please do. I hope to get out of here before lunch time.

S. I will propose a few more guiding principles for the scientific endeavour.

C. Hang on, Socrates. How did we define the scientific endeavour?

S. I suggested it was pursuing knowledge via the scientific method. I should have gone further and added that we hope through this endeavour to discover a small number of laws that govern the complexity of the physical world that we see around us. To put it another way, we hope the apparent complexity of the physical world can be ‘boiled down’ to a few laws that govern the processes going on in the physical world.

A. You are saying that we hope to discover the order behind the chaos, supposing that there is order there.

S. You could put it that way, Adeimantus. We are looking for the laws, supposing that there are laws. Firstly, let me state the principles² and then we can talk about how we are to regard them philosophically. Firstly, we suppose that the laws are universal, that is, they apply everywhere and at all times. Are you happy with that?

C. We will go along with it for the sake of the argument, Socrates.

S. Secondly, the most important laws describe change, how one physical state transforms into another over time.

C. Fair enough.

S. Thirdly, the laws are precise and admit no exceptions. This means that they can be formulated as mathematical equations and used to make precise predictions about the future states of the world.

C. Just spare us the equations, Socrates.

S. Fourthly, the laws are local. This means that if a body in one place is to influence a body in another place, a physical signal must travel from the first body to the second and modify the local physical conditions around the second body. The physical signal is also subject to the laws.

C. Hopefully four principles are enough!

S. Four are enough, Critobulus, as far as the physical world is concerned. But let me propose one more guiding principle for the way we go about scientific enquiry. This is sometimes called ‘Occam’s razor’. Einstein is credited with saying it this way: ‘Everything should be made as simple as possible, but not simpler.’ The intent is that we do not introduce ad hoc assumptions to explain away observations that appear to violate our laws. We have to consider that the law itself may be wrong and need to be modified in some way.

C. So, we don’t invoke a miracle or act of God to explain away a discrepancy between theory and observation?

S. Especially that, Critobulus! Now we come to a very important question. What is the philosophical status of our guiding principles? Are they assertions we must regard as true? Are they axioms from which other laws are to be derived? No, they are merely suppositions. We suppose that they are true and then we see where this takes us. If we find some observations that violate one or more of these principles after eliminating all other explanations, we must be prepared to modify or abandon the principles. So far in the scientific endeavour, this has not been necessary.

C. But you didn’t disagree with me when I said that all scientific theories are provisional and that scientists seem to change them at the drop of a hat.

S. Scientists sometimes modify the laws to accommodate new data, without invalidating agreement with the old data, but so far they have not found the guiding principles to be invalid. And you are correct when you say that the laws are always provisional. This brings us to the vital question of scientific proof. Have you heard of the method of induction, Critobulus?

C. I can’t say that I have.

S. You use it all the time, whether you know it or not. Every time an aeroplane fails to fall out of the sky, your confidence that aeroplanes are safe increases. You think that the probability of an aeroplane crashing while you are in it is so small that you are prepared to risk your life in it, even though you have no proof that the aeroplane will not crash.

C. It seems reasonable to take that risk.

S. Well, the laws of science are even more certain than aeroplane flight. You know that aeroplanes sometime crash, but no-one has ever seen a violation of the law of conservation of momentum. It would only take one verified violation of the law of conservation of momentum to invalidate the law, but no-one has ever seen one. So, although we cannot prove that the law will never be violated, we are extremely confident that the law of conservation of momentum will hold the next time we observe a collision between billiard balls. The law has been tested literally billions of times in all kinds of situations. This is the nature of induction. Although we cannot prove a law about the physical world, our confidence that the law is true grows every time we make an observation that is consistent with it, and while we have no observations that negate it. What is more, our confidence in the guiding principles grows while our laws remain consistent with them. Do you agree that induction is reasonable, Critobulus?

C. I do, it’s just common sense. But scientists are very adept at moving the goal posts whenever they encounter an observation that disagrees with their pet theory. What about these ‘paradigm shifts’, like throwing out Newton’s laws of motion and replacing them with Special Relativity. For years we were forced to swallow something that was proved wrong in the end!

S. It is postmodernist propaganda that you have swallowed hook, line, and sinker, Critobulus. Newton’s laws of motion were not ‘wrong’ outright. What happened was that the laws were shown to be an approximation that was very good for objects moving at low speed relative to the speed of light, but to become progressively more inaccurate as the speed got closer to the speed of light. Einstein’s Special Relativity did not replace Newton’s laws so much as subsume them. At the low speeds of everyday life, Special Relativity and Newton’s laws give the same predictions within the accuracy of our observations. It is only when we look at sub-atomic particles that are moving close to the speed of light that we need the corrections introduced by Special Relativity. You can still confidently predict the path of a space vehicle on its way to Pluto using Newtonian mechanics. There was no paradigm shift in the ability to make accurate predictions, more of a gradual improvement.

A. But did not Special Relativity represent a paradigm shift in our understanding of space and time, Socrates?

S. That is so, Adeimantus. Newton naturally accepted the naive concept of universal time because he had no reason to think otherwise. Experiments like that of Michelson and Morley led Einstein to realise that time was bound up with space in a way that makes all observers see the same speed of light, regardless of their motion. I think it is fair to say that nobody really ‘understands’ that, although the resulting equations of motion enable us to make precise predictions that have never been found to be inaccurate. The revelation is that the universe is stranger than everyday experience told us it was.

A. I suppose you are going to say more about that, Socrates.

S. I intend to at another time³. I must firstly point out a rather obvious implication of the method of induction. Are you aware of what I am alluding to, Critobulus?

C. I might be.

S. Clearly, science can only deal with phenomena that are repeatable. We must observe the phenomenon as it occurs many times in order for our confidence to grow that the observed behaviour is consistent with a universal law. That is how induction works. Preferably, the experiment should be repeated by different observers to reduce the possibility of bias or cheating. As a corollary, science has nothing to say about historical accidents.

C. What do you mean by ‘historical accidents’?

S. Let me give you a frivolous example. Suppose I, Socrates, walk under a balcony and a piano that is being lifted on the balcony slips and falls on my head. A philosophical observer might ponder whether there is a universal law which says: ‘Whenever Socrates walks under a balcony, a piano will fall on his head.’ The event in question could be counted as an instance of the class of repeatable experiments designed to test the law: ‘Objects fall towards the earth when released from on high’, but the philosopher’s proposed law refers particularly to Socrates, balconies, and pianos. This particular event is presumably not repeatable because Socrates is unlikely to walk under a balcony, or anywhere else for that matter, once the piano has fallen on his head. It is an event that can occur only once in history. That is why I call it an historical accident. No general law can be deduced from it about Socrates, balconies, and pianos.

C. I understand.

S. Now, we have talked about the methods of science. The next question is, ‘How do we decide what to apply it to?’ Unlike Critobulus, I am convinced that science rarely indulges in ‘random delving’.

C. I am convinced you will answer the question for us, Socrates.

S. Indeed I shall, Critobulus, if only for your sake! We can take history for a guide. In pre-scientific days, people ‘delved’ in alchemy, and astrology. You would not be entirely wrong, Critobulus, to describe their motives as base, at least some of the time. The alchemists wanted to get gold from cheaper materials, and the astrologers wanted to predict the future to the advantage of themselves or their clients. More charitably, some of them may have been seeking to understand the wonder of God’s creation. Whatever their motives, in the process they amassed a lot of useful observations about chemical reactions and the motions of the heavenly bodies. Meanwhile, philosophers from the ancient Greeks onwards worried about the motion of bodies. They argued about whether or not there was a void between objects. They asked how a body could move if there was not an empty space for it to move into. Some maintained, rather in opposition to common observation, that everything was one, nothing ever changed, and motion was an illusion. Others, like our friend Democritus, thought that there had to be a void for his atoms to move around in. But he must have wondered, I suppose, why moving bodies tended to slow down and stop if there was nothing in the void to bump against them and stop them. Galileo, I also suppose, took up this line of thinking. Galileo, being a modern man at the beginning of science, decided to do experiments into the question. He was building on the thoughts of those who had gone before him, not delving at random, Critobulus.

C. All right, Socrates, I accept that.

S. There is more to learn from the example of Galileo, Critobulus. In your opinion, does science deal with complex things, or simple things?

C. Complex things, of course. Everyone knows that. It is part of the mystique that scientists like to cultivate.

S. Your answer does not surprise me, Critobulus. Many people are under the misconception that science deals with complex things. In fact, at its base, science deals with simple things. Let’s continue with Galileo. As we were saying, he decided to investigate the motion of bodies to see if he could discover laws governing motion. He realised that he had to isolate, as much as he could, the things he was studying from extraneous influences. So, in the case of moving bodies, he had to eliminate friction. Thus, he found by rolling balls down a slope and across a level surface that if frictions were reduced, the bodies would keep moving for longer. He speculated that if friction was eliminated entirely, a body would keep moving at a constant velocity forever, that is, in the same direction with constant speed. We say that its momentum is constant, or ‘conserved’. You do know what momentum is, don’t you?

A. The product of a body’s mass and its velocity.

S. Well done, Adeimantus, you were paying attention at school! You know that a body’s momentum remains unchanged unless a force acts on it. The force may be friction, or perhaps the impact of a collision. And we know that if two bodies collide, the total of their momentum before and after the collision is unchanged, or as we say, conserved. This law allows us to play billiards, or to reconstruct the path of vehicles before and after a road accident, or to estimate the masses of subatomic particles from the angles they fly off at after a collision. When I was a young fellow in the first-year physics class at university, we did experiments on air tables, as well as playing billiards.

C. Air tables?

S. An air table has a flat surface penetrated by thousands of tiny holes through which air is pumped. Little pucks float on the cushion of air and move around with very little friction. We used stroboscopic cameras to study collisions between pucks and did indeed confirm that momentum was conserved in every collision. It is good training to actually observe these things with real objects.

C. It’s all very well to play with marbles and pucks, Socrates, but what about collisions between big things, like asteroids for example.

S. The wonderful thing is, Critobulus, that we can usually ignore the complexity if it is not essential to the law in question. So, for the purposes of conservation of momentum, we can ignore the complexity of an asteroid and consider it as a point mass located at the ‘centre of mass’ of the object. When we do that for extended objects like asteroids or billiard balls, we find that momentum is conserved. You have played enough billiards to understand conservation of momentum, I believe Critobulus? When you hit a straight shot, your white ball stops dead and the red ball goes off with the same direction and speed as your white ball.

C. That’s true, Socrates.

S. When an accident investigator examines the wreckage from a collision of vehicles, he is able to calculate the trajectories of the vehicles before the collision from their motions after the collision, even though the vehicles have disintegrated to some extent. He assumes that the law of conservation of momentum holds and applies to all the bits treated as simple masses. If he has trouble making the momentum add up, he considers that he might be missing a bit. He does not conclude that the law of conservation of momentum has been violated because he believes in induction and knows that in billions of collisions that have been observed the law has never been shown to be invalid. My point in saying all this, Critobulus, is to impress on you that science starts by examining simple things.

C. All right, Socrates, but it seems a long stretch from little balls to planets and solar systems.

S. Scientists following Galileo soon discovered two more conservation laws that help us to understand the motion of bodies. One is the law of conservation of angular momentum, which is related to the spin of a body. The second is the law of conservation of energy. Do you know what energy is, Critobulus?

C. Certainly, it is the buzz I feel when I am in tune with the universe.

S. I perceive that you are only half joking, Critobulus. Scientists define energy rigorously. They can write down equations for it and can calculate it precisely. Energy comes in various forms, like kinetic, potential, and chemical. The marvellous thing is that these forms can be transformed into each other, but always in a way that conserves the total amount of energy.

A. What about transforming mass into energy, Socrates?

S. You are thinking about E=mc², Adeimantus. You are correct as usual. That is a refinement from Special Relativity that applies to bodies moving at close to the speed of light, and in nuclear reactions and in the creation and destruction of sub-atomic particles. The scientists of the seventeenth century did not encounter those conditions and in everyday life we find that energy is conserved.

A. Agreed.

S. Let us go back to Galileo. You know that he is famously said to have conducted an experiment by dropping objects made of different materials from the leaning tower of Pisa and concluded that all objects fall at the same rate. Indeed, if we drop a feather and a lead weight inside a vacuum chamber where the friction of air is eliminated, they do fall at the same rate.

C. So I have heard.

S. Do you think you would notice the difference, Critobulus, between the feather and the lead weight landing on your head, even though they are falling at the same speed?

C. I expect I might, Socrates. Even I am not so insensitive as to fail to perceive the difference. How would you explain that?

S. I can’t explain your insensitivity, Critobulus, but I can explain the difference in sensations. It is to do with the amount of kinetic energy possessed by the falling objects. Kinetic energy, as the name suggests, is a result of motion. The kinetic energy of a body is proportional to its mass and the square of its speed. Our falling feather and lead weight have the same speed, but the lead weight has the greater mass and, therefore, more kinetic energy with which to deform your hair, if not your skull. Now, if energy is conserved, where does the kinetic energy of the falling bodies come from?

C. Please enlighten me, Socrates.

S. We say that a body suspended in the air has potential energy because, if it is released, it will fall and its potential energy will be converted into kinetic energy as it picks up speed. The higher the body is, the more potential energy it has. The potential energy comes from lifting the object against the pull of gravity. You have to do work, that is, put in energy, to lift the body. Then, when it falls, you get the energy back in the form of kinetic energy. Conservation of energy is always at work.

C. You never get anything for nothing.

S. Spot on, Critobulus. Likewise, you can have potential energy due to the electrical attraction between things. The electrical forces of attraction between atoms and molecules give rise to electrical potential energy. We call this chemical energy, which I mentioned earlier. Thus, if the atoms rearrange themselves into a state having lower chemical energy, some energy is given off, usually in the form of heat or light. We will talk about heat in a minute. A common way of releasing chemical energy is to burn something, which is a chemical reaction in which a substance reacts with oxygen.

A. It sounds like conservation of energy is a very useful concept.

S. Indeed, Adeimantus. But let’s return to the laws of motion and gravity. Newton conjectured that the force of gravitational attraction between two bodies is proportional to the product of their masses and the inverse of the square of the distance between them. A fascinating insight proceeding from Galileo’s observation of falling bodies is that the mass we use to calculate the force of gravity is the same as what we call the inertial mass, which is the mass we use in calculating the momentum and kinetic energy of a body. Later, Galileo’s observation formed the basis of Einstein’s theory of General Relativity, which generalised Newton’s law of gravity in much the same way as Special Relativity generalised Newton’s laws of motion. Anyway, armed with his laws of motion and of gravity, Newton was able to use mathematics to show that the planets move in elliptical orbits around the sun. Thus, he was able to verify Kepler’s earlier conjecture about the planets moving in elliptical orbits. Kepler had arrived at his conjecture by painstaking analysis of the collected astronomical observations made by astronomers and astrologers over the centuries. The remarkable thing is that the observation of the motion of simple bodies was able to make sense of the tremendously complex observations of the heavenly bodies.

A. Wonderful, but what about systems involving vast numbers of particles?

S. Good question, Adeimantus. Consider gases for example. Suppose we have a billion atoms of some gas in a jar. What can our simple laws of motion say about it? Well, each of the atoms obeys the law of conservation of momentum as it collides with other atoms and with the walls of the jar. If we were able to follow the motion of the individual atoms, we would find that momentum is conserved in every collision, and we would be able to predict the path of each atom. Not only that, we could also calculate the kinetic energy of each atom and add up the total kinetic energy contained in the gas. But of course, it is not practical to do that with such a large number of atoms. What we do instead is calculate the probability distribution of the speed of the atoms. From the probability distribution, we are able to calculate quantities such as the average speed of the atoms in the gas. We find some interesting things. For example, the temperature of the gas and the pressure it exerts on the wall of the jar are both proportional to the average kinetic energy of the atoms. What do you think happens, Critobulus, if we heat the gas?

C. I guess the temperature increases. Again, doesn’t everyone know that?

S. I imagine they do, Critobulus. But how do they explain the transfer of heat. Let me explain. Suppose you hold a lighted candle under the jar containing the gas. Hot air is rising from the candle flame. Because the air is hot, the atoms in the air are jiggling quickly. When they collide with the bottom of the jar, they transfer some of their momentum to the atoms of the wall of the jar and make them vibrate more quickly. Now when the atoms of the gas in the jar collide with the wall of the jar, they pick up some extra momentum from the atoms in the wall. As a result, the average speed of the atoms of the gas increases, which means that the average kinetic energy of the atoms in the gas increases, and so the temperature of the gas increases. You see that the transfer of heat is really the transfer of kinetic energy from the candle flame to the atoms of the gas.

C. I see that.

S. And where did that energy come from in the first place.

A. From the chemical energy stored in the candle, which is a result of the electrical potential in the chemical bonds in the candle wax.

S. Good man, Adeimantus.

C. Now I can explain why my coffee is getting cooler.

S. I hope so, Critobulus. We are making progress.

A. Coming back to Newton’s law of gravity, Socrates, something is bothering me. You said earlier that the laws are local. How can a body in one place, like the sun, exert a force on a body that is far from it, like the earth?

S. Newton called this ‘action at a distance’, Adeimantus, and it troubled him greatly. These days we say that the forces are mediated by fields, which are essentially disturbances that travel from one point in space to the neighbouring, or local, points, and thence to their adjacent point, and so on until they reach some distant point where they locally affect an object located there. We now have a quantum-mechanical description of the fields, and we find that fields are associated with sub-atomic particles. For example, the electric force between two objects is mediated by an exchange of photons, which are the particles associated with electric fields. Likewise, gravity is associated with particles called gravitons. The disturbances of the fields travel outwards in waves, so the particles and waves are two aspects of the quantum-mechanical description of forces. We will talk about this another time. If you want to read about it, you could try the book by Wilczek (Wilczek, 2021), or one of the many other books on the subject of quantum field theory.

C. Entertaining bedtime reading, I am sure!

S. Science deals with simple things. Complex explanations are just compounded from a lot of simple things.

A. A gas composed of one type of atoms might be regarded as simple even though there are many atoms, but I thought that the motion of fluids, namely hydrodynamics, was something that science had not made much progress on.

S. Yes and no, Adeimantus. When referring to the gas in the jar, I avoided mentioning the detail that the gas is assumed to be at thermal equilibrium. This means it has been allowed to settle down, so it does not contain any significant swirls and eddies. Swirls and eddies are a sign of a gas or fluid that has not reached equilibrium. When the gas is at equilibrium, it is quite uniform and we can easily calculate the probability distribution of the speed of its atoms, from which we deduce its macroscopic properties, like temperate and pressure. But in other cases, we may be interested in the details of the swirls and whirls, for example if we want to study how the flow over a wing generates lift. Scientists consider a little parcel of the fluid. It can be treated as a particle and obeys the same laws of motion as any particle, except that the forces on it are generated by the pressure of the parcels adjacent to it. Thus, we have equations of motion that can be used to calculate the motion of any parcel to arbitrary accuracy. The problem is that these equations are very difficult to solve in a general way. Now that we have supercomputers at our disposal we can, given an initial state of the fluid or gas, use the equations to calculate the state of the fluid or gas at any time in the future. Sometimes the calculated flow is chaotic and sometimes a surprising order appears, just as it does in nature. So, while some mischievous persons have said that science cannot provide a good theory of fluids, in a way we know everything about the fluid, it is implicit in the equations, but we have to do the calculations to find out what happens in particular circumstances. Are you happy with that answer, Adeimantus?

A. Quite. Would the same apply to forecasting the weather?

S. Very much so, the laws of gas and fluid motion are central to predicting the weather, only the scale is larger and there are many more processes involved.

A. What sort of processes?

S. The diurnal heating and cooling by solar radiation, evaporation, and cloud cover, the release of energy by the condensation of water, just to name a few. Because of the huge size of the Earth, many more fluid parcels have to be considered than for a more limited hydrodynamical calculation. Massive supercomputing capability is required. Then there is the problem of adequately describing the starting state for the calculations. A tremendous number of weather observations are needed just to characterise the starting state at one time. If there are too few observations and the starting state is thereby too uncertain, the predictions rapidly diverge and one can have little confidence in them. This was the situation in the days when I was a weather forecaster.

A. You were a weather forecaster, Socrates?

S. I was for a time, Adeimantus, but that is another story. These days, meteorologists have many more sources of data, from satellites and remote sensing, for example. You might have noticed that forecasts out to one or two weeks are much more accurate than they used to be.

C. Fair enough, but what about climate models? Some people say that, ‘The science is settled’, and others say that climate models are junk.

S. There is truth and error in both points of view, Critobulus. For one thing, climate is a multi-faceted concept. It is one thing to predict the trend in annual rainfall in a given zone, and it another to predict the frequency of storms of a given strength. All the processes involved in predicting the weather are relevant, but it is not practical to run detailed weather models over the span of time needed to predict climatic trends. Approximations are required, and there are many ways of going about them. It is fair to say that the basic science behind each of the contributing processes is well understood, but balance and proper interaction between the various processes and approximations are much harder to get right. For example, there is no scientific doubt that ‘greenhouse gases’ like carbon dioxide absorb heat radiated from the earth and trap it in the atmosphere. You can do that experiment in the lab. That will tend to increase the temperature of the earth. But rising temperature could increase evaporation from the oceans, leading to increased cloud cover. Now, clouds reflect solar radiation and that tends to cool the earth. So, through these and other processes, we have multiple, interconnected feedback loops. Climate models have ‘parameters’, numbers that represent the strength of each process. Getting the values of the parameters right is a delicate business. Small changes can make a big difference to the predictions.

A. How can the modellers ever verify their results?

S. One way is to apply the models to the past, where we have some data. Another is to look for agreement between different models that use different techniques. Agreement in both cases tends to increase confidence. But the conditions in the past might be different from what is expected in the future, so testing on the past does not necessarily test a model in the ranges that might prevail in the future. And different modelling approaches can still suffer from the same biases. In summary, we might say that the science of the processes that influence the climate is well-understood and ‘settled’, but the predictions of models that combine all those influences to make prediction of the future climate are much less certain.

C. As I suspected, Socrates.

S. You will have noticed, Critobulus, that the weather and climate have taken us away from the simplicity of basic physics and into areas of great complexity. Where there is great complexity, there is great uncertainty. Some of the sciences, especially Social Sciences, economics, and some aspects of health such as diet, are inherently complex and in these fields drawing firm conclusions through the scientific method is problematic. I am not suggesting that non-scientific methods should be used, only that announced results must be treated with caution. Some scientists in these areas are prone to making dogmatic and dubious assertions. They do science great harm and damage the credibility of science in general.

A. Are you saying that the scientific method is not applicable in these areas?

S. These so-called sciences employ some of the methods of science, such as doing experiments to test hypotheses. Done well, these methods can confirm with confidence that certain trends and correlations do exist. But what is lacking compared with more basic sciences is the traceability of the phenomena of interest back to causes connected with universal laws. There is nothing in the social sciences, for example, with the universality and certainty, as far as induction allows, of the law of conservation of momentum.

C. Are you saying that when you see a television advertisement featuring a scientist in a white lab coat, you need to be sceptical.

S. Especially then, Critobulus. Now, I have spoken at length and covered a great deal of ground. It is time I summed up.

A. One further question before you sum up, Socrates. Is it not a mystery that the physical world is governed by mathematics? Is God a mathematician?

S. There is no mystery, Adeimantus, for realists like you and me. Idealists might have a problem, because they tend to think that the things mathematics talks about, and which logic talks about for that matter, are somehow real. We realists think they only refer to words. So, an equation in mathematics only tells us that a certain set of words or symbols means the same as another set of words or symbols. When the words and symbols happen to describe a thing that exists in the real world, then we can expect the mathematical equation to tell us something true about the behaviour or qualities of that thing. There is no mystery, although I admit that I have brushed your question aside perfunctorily, and we might return to it another time for a fuller discussion.

A. I would like to discuss that topic further one day.

S. Now then, let me summarise what we have discussed about the scientific method. Science supposes that things in the physical world have objective existence independent of any observer, and that they behave according to a small number of laws which are discoverable by experimentation. All observers who do the same experiment are expected to get the same result. Scientific inquiry is guided by a set of principles which are supposed to apply, such as the universality of the laws, locality, and the precise description of change. The scientific laws can never be proven with absolute certainty, but through the method of induction, the confidence with which a certain law is held to be true increases with every experiment that agrees with it. A single verified experiment that does not agree with a proposed law is enough to disprove it, or at least limit the sphere of applicability of the proposed law. When a proposed law has its sphere of applicability limited in this way, it becomes inaccurate outside of its sphere of applicability, which indicates that there is a more general law which coincides with the original law in its restricted sphere, and which also works in the unrestricted sphere. Some of the laws of the basic sciences like physics and chemistry have been confirmed to such an extent that no reasonable person would base their actions on the thought that they might not be true. Science proceeds by working on simple things and eliminating all extraneous influences from experiments. Complex phenomena, like the climate, can be modelled as a combination of processes which are individually well-understood in terms of basic science, but the predictions are subject to uncertainties in knowing which processes are relevant and in describing the initial states of the systems. The method of scientific experimentation can be applied with some value to subjects that are inherently complex, like Social Sciences, economics, and some aspects of health, to confirm trends and correlations, but in those subjects there can be no expectation of discovering universal laws. Well, Critobulus, have I succeeded in enlightening you? Do you feel enlightened?

C. I confess that I feel somewhat enlightened in some aspects of science, but I still have a doubt about it being specific to Western culture.

S. If you will bear with me, Critobulus, it would be best if we address the cultural question at the end of our next discussion. With your forbearance, I will attempt to give a potted summary of the whole scope of science and our understanding of the physical universe. Then we will be in a position to compare the scientific story of the universe with that from other cultures.

C. I may have to fortify myself for that, Socrates.

S. Come along for a brisk bike ride before we talk, Critobulus. There is nothing better for clearing out the neural pathways and lifting the mood.

References

The New Jerusalem Bible. (1985). London, United Kingdom: Darton, Longman, & Todd.

Wilczek, F. (2021). Fundamentals: Ten Keys to Reality. Penguin.

1. See the conversation on Realism and Idealism.

2. Socrates is paraphrasing (Wilczek, 2021).

3. See the conversation on Space and Time.