Method and Paradigm

A method does not, of course, get you anywhere. A scientific method might give you clues as to where you might find the next step in your research. If you have just done an experiment, then the method might suggest you analyse the errors, or consult the theory. It is not a matter of turning a handle or blindly attempting the next step. The method is not really for that, and nor does it replace creativity in research.

Given that, we can ask what, exactly, is a method for? This is not an easy question to answer. In practice, a lot of people in research do not explicitly follow a method. They do experiments, consider the errors and so on not because they have the steps of scientific method in mind, but because that is how they are trained; that is how the subject ‘works’ for them.

So a method, while possibly useful for introducing how the subject might be tackled, is not, in fact, that widely used. It might be a useful teaching tool, recognising that there are generic similarities between projects in the same subject. Hence, for example, there are a plethora of courses in research methods in assorted subjects such as the social sciences, history and so on. In part, these are practical, covering things such as how to get started, how to find suitable material, get ethical approval and so on. In part, though, they cover the sorts of things you need to do to do research in the subject.

Research is the process of starting from a known position and finding something out which was not known before. Despite a lot of media hype about scientific breakthroughs and the like, most research advances the subject incrementally. Each research paper published in the sciences is a little advance over what went before. Thomas Kuhn, a Twentieth Century philosopher of science, observed that most of the time scientific research was conducted within the remit of what he called ‘normal science’, that is, the core understandings of the science (the paradigm is physics, because that was the most developed at the time) are known, understood and largely unquestioned. The research that happens occurs around the edges; it is almost filling in the gaps.

Another way of looking at a subject is as a web. There are core assumptions at the heart of the web, and these are spun out into more and more tenuously held assumptions until you get to the edge. This, perhaps is where ‘normal’ science takes place. Changing the nature of these links in the web does not disturb the web as a whole.

Every once in a while, Kuhn argues, someone comes along and sweeps the whole of the central, core, assumptions of a subject away and replaces them. This is the paradigm shift (I think Kuhn coined the phrase), a sudden change in the basic assumptions of a topic that leads to a completely different web, a completely different direction for the subject.

The paradigm shifters in physics are fairly well known: Galileo, Newton, Einstein for example. Whether they actually single-handedly changed physics is a bit more controversial. They certainly did not act in a vacuum, as is often assumed. That they thought differently about a subject and bought new things into physics is not disputed, but in all things context is important: the time was right for a breakthrough; the problems of the normal paradigm were becoming obvious, if not pressing.

Similar changes can be seen in other subjects, although I am not sufficiently an expert to be able to say. Something happened in theology, for example, around the fourth century AD, when the Patristic Fathers were forced into using non-Biblical, philosophical language to describe God, His Son, Jesus Christ and the Holy Spirit. Not all of them were happy with this shift in language, however, and it still causes a degree of difficulty today. Again, something happened in the Middle Ages to enable a shift to Scholasticism, and again at the time of the Renaissance and Reformation to shift away from Scholasticism. I dare say that a variety of similar shifts could be identified both in theology and physics and in other topics.

A shift in paradigm is not a shift in the subject as it is. Mostly, the new paradigms encompass the knowledge and understandings there were before. For example, Einstein’s relativity theories (for there are two) encompass the results of Newtonian mechanics and gravity as low energy cases. While the way of looking at the universe changed as a result of Einstein’s work, the fundamentals of rolling billiard balls around the place did not. Einstein’s theories are useful in high mass, high speed and long distances. Similarly, the Reformation did not instantly abandon all that had gone before – the Reformers, mostly, would have been shocked by the argument that they had. The insights of the past still informed the thinking of the present, as mass and momentum are still fundamental quantities in physics.

Has any of this to do with method? Mostly, the people who started the paradigm shifts were trained in the methods of the subjects as it was at the time. Einstein, for example, knew quite a lot of fairly obscure mathematics which he put to good use in General Relativity. The mathematics is now rather less obscure, of course, but it still takes a fair bit of getting your head around. Galileo was trained in the Aristotelian school of physics which he subsequently had a hand in overturning. If we are unable to sweep away totally what has gone before (and we cannot), then in order to extend it we have to be experts in the subject.

So the methods with which we have been brought up are fundamentally useful. We might not think about them explicitly, but they are around and do inform how we undertake even the most revolutionary of paradigm shifts. Our intellectual history does constrain the past, no matter how much we might have thought we have left the past behind.

Scientific Method

How do we come to know something? That is, how do we move from ignorance to understanding, from knowing nothing to knowing something. We have suggested that there are three levels, at least so far, of meaning: common sense, where we relate things to us; theory, where we relate things to other things; and method, when we reflect on how we undertake the other two levels.

The levels of common sense and theory are both really problem-solving levels of meaning. I need to mow my lawn, and I have a choice of scissors, a scythe and a lawnmower. The problem is which to choose, and that might depend on the size and shape of my lawn, the length of the grass and whether I want to preserve the cuttings for straw or compost. These are common-sense issues, the question completed in the concrete aspects of the lawn itself.

At the level of theory I might want to know the trajectory of two billiard balls after they hit each other at such and such a speed and this angle. While I might apply the laws of conservation of energy and momentum to solve the problem, it is still a problem to be solved. In that sense it is much like the lawn cutting problem: it is a problem and we have an idea of how to solve it.

When we get to the level of method, however, we are asking a slightly different question. It is not ‘how do I solve this problem’ but ‘how do I solve problems?’ The question is general; the specifics of the actual problem to hand has dropped away. Put another way, the question at this level is something along the lines of ‘is there a general way to tackle and solve any problem that might face us?’

Reactions to the question are likely to be mixed. You might think ‘Of course not! A problem in physics is different from a problem in history.’ That is, of course, correct, the content varies, but does the approach? Alternatively, you might think ‘Every problem is the same in some way: I might have to think about a problem in history, and then think about one in physics. But it is still me doing the thinking.’ That too is correct, but in a different way. A human thinking is a human thinking, whether that thought is about history or physics or anything else.

We do have some paradigms of human thinking, some good examples where we can see intentional thought going on. By ‘intentional’ I mean actually determinedly thinking about a problem, sitting and thinking how I want to cut the lawn, not just grabbing the lawnmower because that is what I did last time. The best example, and probably the most obvious, is scientific method.

I have lost count of how many news stories start ‘scientists have discovered…’ whether that be exoplanets, new species or treatments for cancer. There are a number of issues at stake here which I shall ignore; the one I want to focus on is the ‘discover’ word. How is it that we go from something that we do not know to something that we do?

The usual answer is by a magical term ‘scientific method’, although that method itself is rather badly defined. If we ask ‘what is scientific method’ we do not usually get a simple, single reply. Method, it seems, varies between disciplines of science and even within a discipline. Normally, we fall back on such ideas as experiment and theory, repeatability, hypothesis and verification. Exactly how these fit together is a bit unclear.

Another objection is that method can start to sound a bit of a mechanical turning of the handle. Many years ago I recall my maths teacher telling us that he was going to teach us fractions in such a way that we understood what was going on. ‘Many of you,’ he said, ‘will have learnt how to do this in primary school by following some rules, such as “write it down, turn the book upside down and use red ink”…’ What he meant was that there are techniques to do things in mathematics, as in science, but just mechanically doing them does not give understanding, only the right answer.

The point is, as Feyerabend observed in Against Method, scientific breakthroughs are not made by those who follow the rules as a mechanical process. You will not find a ‘cure’ for cancer by following what everyone else is doing. The point is to do something different, something new and discover something that was not known when you started or even could be inferred from what was to hand. You might (and should) have good reasons for trying what you do, but you have no guarantee that it will work, or that it will show what you are hoping for.

The process of scientific method, then, is not as clear as we might think or like it to be, but it does give a fairly clear idea as to how systematic investigation works alongside creativity. There are ideas, hypotheses and experimental results. At some point in a scientific investigation you have to sit down and try to work out what is going on. What do these results mean?

The abstraction of these processes and questions could be a view of how human intentional thinking works. We have the data, we sit and stare at it, read around it, ponder it until we get an insight into what is going on. That only works for this set of data, so then we try to generalise it, to work out what happens beyond our data set – that might include theoretical work or more experiments. Then we have to make a judgement call: is this right? We weight the evidence from experiment and theory, we compare with what we already know and we have to decide.

Once we decide, of course, we have to verify the work, perhaps by communicating it in an article or conference report, and, if the scientific community agrees, we can be fairly confident that we have found something new. There is a lot more to the process than simply turning a methodical handle.

Meaning, Meaning and Meaning

We have described so far two levels of meaning: common sense and theory. The first is the everyday thinking and acting we carry out. In some sense, common sense is only completed by the objects of the world around us. We do not, for example, change a car wheel in theory. We could, perhaps, describe what to do, but only when confronted by the flat tyre and spare in reality do we act. We know what to do not because of some abstract set of ideas, but because we have before us nuts, wheels, a jack and a spanner.

In a sense, the level of common sense is also Polanyi’s level of tacit knowing. This is not exclusive – there are many things that I know which are not related to the everyday world around me – but I might not be able to articulate, in the world of common sense, what to do without the spanner and jack before me. I can show you, but not tell you where to put the jack, perhaps.

Nevertheless, there is another level, the level of theory. In a modern motor vehicle, someone will probably have sat down with a pen and paper (or a computer) and worked out where the best lifting points for the vehicle would be, how sturdy the jack has to be for safety and so on. This is the level of theory: abstract thinking from first principles to get some results which are generally useful, such as ‘the metal of the jack has to be this thick’. This starts from the abstract, from the theoretical thinking about the forces and materials involved in jacking up a car.

The level of common sense is related to the objects around us, the objects of everyday life and their relation to us. We have a task, and we have some tools and we apply these to the task in front of us. The job may be easier or more difficult depending on the tools we have before us. Consider how much easier changing a wheel is for a mechanic at a fully equipped garage that it is on your own front drive. But the point is that these tools are focused on doing that job.

The level of theory relates objects to each other and themselves. We start with considering the weight distribution of a vehicle and the necessity of lifting a corner of it. This is more abstract thinking: the colour of the car, the precise nature of the puncture and so on are not interesting or useful in this problem. What we need here is an idea of the forces involved in lifting the car, not whether we might scratch the paintwork. The forces and objects interact with each other, not with us (at least, not directly).

As with this sort of abstraction, so with scientific theories. What counts in a scientific theory is the interaction of objects with themselves and with each other. Two billiard balls interact to have a collision and their behaviour is modified by the impact of one on the other. This has nothing to do with any human observer. At least, as far as we know, the interaction would be the same if no-one was watching it. The theory, in this case, the laws of motion, momentum and inertia, relate the bodies, the billiard balls, to each other, not to the human watching.

At this stage, we can develop our theories and then relate them back to the concrete world around us. We can both catch a ball, in the realm of common sense, and also calculate its trajectory given some initial conditions giving the velocity, angles and initial location, say the direction to the thwack that the ball receives from a cricket bat. This calculation may be less than helpful in actually catching the ball, but it allows us to understand the motion of the ball under a variety of circumstances, some of which may pertain to our situation.

The level of theory, then, gives us the tools to tackle questions of objects related to themselves, such as balls under a given impetus of energy and direction, or giraffes and how they have evolved to survive in a given environment. How we go about tackling these more theoretical problems is an interesting question in itself, however. There is another potential intellectual move from the theoretical, asking how things are related to themselves and other objects, to asking how we work out how those theories can be established.

The question of how theories are established is the level of method. The question is not ‘how do these balls interact?’ but ‘how do we establish how these balls interact?’ The relevant method here is that of the physical sciences. Scientific method supplies a framework for answering the question of how we go about solving theoretical questions. For many scientists, it is not an explicit question. While it may be that they do implicitly subscribe to ‘scientific method’, not too many practising scientists actually consider method per se. They get on with the business of science, using and developing theories and relating them to measurements.

Nevertheless, this third level, that of method, as a level of reflection on theoretical activity is an important one for the integrity of the sciences and, indeed, any other human activity. Human thought and activity is not permeated by relativism, subjectivity and a whole range of false claims, barefaced denials of the facts and evasion. If we have no means of reflecting on our activities, that is if we have no way of pondering how we go about thinking about some of these issues, then we have no way of establishing the falseness of some claims and the accuracy or authenticity of some others.

The problem is that reflection on theory, considering method and how it yields something looking like truth is hard work. Most of us feel, most of the time, that we have neither the time, energy nor information and understanding to establish the truth or otherwise of claims we hear. By the time we do manage any reflection, the world has moved on anyway and we look out of date and out of touch. That does not mean that such reflection is unnecessary, but it does mean that nailing down outright falsehood is a lot more difficult than it perhaps should be.

Levels of Meaning

We suggested last time that there are different ‘levels’ of meaning. What I mean here is that we can describe a giraffe in different ways: the common sense way, whereby a giraffe is a four legged animal with a long neck and spots, and a more theoretical way, where it has adapted to a particular environment by finding an ecological niche whereby a long neck enables grazing on otherwise unreachable food.

I put the word ‘level’ in scare quotes because it is a metaphor, and we sometimes have difficulty with metaphors. In this case, ‘level’ does not mean necessarily that one is better than another. The problem with spatial metaphors is that a higher level can seem to indicate superiority. In this case it indicates difference, only, not necessarily the superiority of the theoretical over the common sense.

As an example, consider the cycle of day and night. From the common sense point of view the sun rises and sets, and moves around the sky. From the perspective of physical theory, of course, the Earth rotates. This does not actually cause us too many problems. We can quite happily talk about sunrise without finding any cognitive hiccoughs over the fact that we know, theoretically, that the Earth rotates. We can live in both the common sense and theoretical world quite happily.

What we do not, or should not, do is to attempt to live in both the common sense and theoretical worlds at the same time. This can lead to all sorts of difficulty and confusion, and often impedes the progress of theoretical (in the sense here of scientific) work. It is, after all, obvious that the Earth does not move. We cannot feel it moving, although there is some evidence, from the motion of the planets, that something more complex is going on than everything simply rotating about us. It took centuries to work out what, however.

That working out required a degree of separation of the theoretical and the common sense. The approach taken, in order not to upset the authorities, was to suggest the heliocentric solar system as a hypothesis, for the purposes of calculating things more easily. That was just about acceptable to a church, university and society which had accepted a form of the Aristotelian universe, so long as it was never said that the Earth went around the Sun. Of course, it did not take long before the common sense idea was replaced by the heliocentric solar system largely because the latter was a lot simpler mathematically.

The transfer from one level of meaning to another is, therefore, not straightforward, but thinking you are at one level when you are at the other is problematic. For example, Creationism, the idea that the world was created in seven days, following the first chapter of Genesis, is a common sense sort of idea. Accounts of the world such as that (or rather, those) in Genesis are common sense accounts. After all, no-one was witness to the events recounted (except God) and so we have to in fact look for a non-common sense, a theological, meaning to the stories. Exactly what these are is not the issue here. The issue is if we read the account in Genesis 1 as a theoretical account, we land up with a load of silly ideas about the start of the world, and a denial of a lot of accepted science. Concepts that are in that position are usually incorrect.

To transfer from one level to another can be difficult. As in the case of Creationism, as much has to be unlearnt as new has to be learnt. Modern science and theology of the natural world starts from a very different place than modern creationism, and reaches different conclusions. No amount of effort by ‘scientific’ creationists to bridge that gap will in fact achieve it. As a common sense world view it perhaps works, but as a useful one for technology and science it does not.

Primarily, then, moving from the level of common sense to the level of theory (or science) is a question of education. We learn about the evolution of giraffes and, once we have done so, we can appreciate the giraffe both as a four legged animal with a long neck, and as a highly evolved adaptation to a particular environment. Once we have understood the evolution of giraffes, however, we can move from the level of common sense – the four legged animal with a long neck – to one of ‘theory’ - the evolved creature - without much cognitive effort. The interesting question is, perhaps, how anyone managed it in the first place, or how we manage to make the transition when we learn about it.

Often the move is made, or suggested, by a model or a metaphor. In science the move from the Earth centred universe to the Sun centred solar system was made by diagrams and physical models of things going around a centre. From this the motion of the planets from the viewpoint of the Earth can be understood. Sometimes, the planets move backwards because the Earth overtakes them in orbit. This retrograde motion was a puzzle in the Earth centred universe, but was solved by the heliocentric one. But the move was from common sense to theory, and that move was enabled by a lot of observational data but made by a new model of the world.

Similarly (although I do not know this, not being a zoologist) the move from a common sense giraffe, as giraffe that just is as it presents, to the giraffe as a result of millions of years of evolution requires some sort of shift, achieved by the sorts of metaphors and models which we can learn as part of our biological studies. As with the cycle of day and night we can then live at both levels quite happily.

The question is then, of course, is there a further level beyond that of theory, as theory is beyond that of common sense. But that would be another post.