Letter to Peter

Chapter 3: Science and Reductionism

This Chapter looks at the way that science describes the "real world", how we can tell between good and bad science, and how different parallel scientific descriptions of the same event relate to each other.

What is Science?

As a word, "science" tends to have positive connotations. It sounds modern, and the sort of thing that parents feel their children should master, to ensure their success in the world! For this reason, the word "science" is used all over the place, covering many different activities (computer science, domestic science, political science, experimental science, forensic science; the list is diverse and endless). We may wrinkle our noses at some of it, but that is how the word is used.

In amongst this huge range of activity we want to get at two important aspects. First, whether we can "define" the word science or not, we have to be able to tell the difference between good and bad science. Secondly, for a variety of reasons, some people feel that science has "disproved" or superseded religion in some manner. We would like to understand why they feel this to be the case and what bit of science may have done this.

With these two aspects in mind, I think we can restrict the conversation to "scientific description" and "scientific laws". I think that most of those people who feel that science has taken the place of religion, feel that science and religion both claim to give descriptions of the world. The scientific description, they think, is steadily replacing the religious one. Some people might go further, feeling that the scientific descriptions have proved themselves accurate in progressing humanity from fig leaves, to cars and computers. All this progress in mastering our world is the demonstration that the description is valid. Religion, to such people, is about irrelevant folk in dusty churches who talk about God, but don’t even produce a decent morning’s entertainment, let alone a new BMW.

Science describes things. Science has developed a language that tells us about a lot of what is happening in the universe. It allows us enough understanding to design and make machines to perform particular complex tasks (e.g. go to the Moon, collect soil, take pictures and come back again). The language is a consistent characterisation, which allows us to notice patterns of behaviour in the universe.

Scientific laws are summarised patterns of behaviour of the world around us, for example; "things accelerate proportionately to the force applied".

What is Mathematics?

I think Maths is roughly the process of describing or relating many different situations at the same time. This perspective breaks into three branches:

1) problem solving (describing a situation in terms of another one you already know),

2) theory (setting up definitions, corresponding to generic situations, and proving things about them, to allow problem solving later) and

3) people who have lost the plot.

It was not obvious to me when I started studying maths that problem solving is just relating a new situation to one that you already know. It was also not obvious that the point of building definitions (of set theory or matrices or whatever) was to allow prove properties of many things at the same time. I am confident however that if you think it through you will agree with this claim. I have said I reckon scientific laws are about observing patterns in the universe: the simplest patterns are based on near repetition of very similar situations. The more complex ones come from maths relating the patterns to each other. That is what formulae actually do. Nevertheless, this understanding, this description did not just appear, it was built up over thousands of years

Where does Science start?

My father used to say that, when he was under pressure from a patient demanding a diagnosis, he used just to translate one of their symptoms into Latin (e.g. "erythema" is a rash). Then he would tell the patient that the Latin for the symptom was the disease (you have a rash, because you have "erythema"). Most patients were satisfied and reassured by the answer. Clearly, that isn’t science, but we can build this up in stages to modern medicine.

Medicine, at its most primitive, starts being descriptive of illness or abnormality, symptom by symptom. This goes with knowledge of the effects of a few herbs, or chemicals, or simple surgical measures (letting blood, say). Then medicine starts grouping the symptoms into patterns, and calls each pattern the same "disease" or "syndrome". The patterns are noted, together with their description, their likely outcome and effects of any treatments. It is all a way of building up knowledge. Then, with the microscope and other equipment, (and after some grave robbing to get some knowledge of anatomy), medicine builds a better picture of normality. For example, a doctor starts to know what the "normal" result is, in a blood test. Medicine starts linking the patterns of symptoms with particular "abnormal" things which go together with them; for example, linking a sore throat with finding bacteria on a throat swab.

All the time, as more and more things are linked (e.g. as all being due to a bacteria), the speed and sophistication in building cures accelerates. The bank of accepted knowledge keeps getting re-tested, statistically, to ensure that is it "evidence-based". In this whole process of medicine developing, when exactly did the "science" start? Recall:

We have done all of the steps above, but we still feel there is something missing, until some attempt is made to explain links between the intervention, the symptoms and the test results. What is missing is evidence of "explanatory power". Describing and recognising patterns is not enough. We can make conjectures about, say, the links between bacteria and symptom, and test them. For example, we could conjecture that the bacteria cause the disease, rather than results from it. We test this by deliberately infecting someone who is well with bacteria; to see if they become ill. Explanatory power suddenly accelerates the speed with which you establish patterns; you start being able to predict patterns rather than use the patterns to predict results.

Perhaps then Science starts with explanatory power? However, not all explanation is useful.

Good and Bad Science

Animists (who were the majority of the population where I lived in West Africa) have their own descriptions, which are different to ours. For example, according to Souleymane (who was a close friend), his grandfather was killed by a spell cast by someone else in his village. The day his grandfather died, the latter had washed in the morning in his charmed jar ("fetiche") which would protect him from death. However, the grandfather still died, and an explanation was sought. "It turned out" that the charm had not protected the grandfather from death, because his protective spell had been undermined by one of his wives, who had told him a lie. Souleymane’s description looked like it was going to predict something, but when the prediction went wrong, another rule was added. In this sort of description, apparent counter-examples are easily explained by adding a new part of the theory. It was easy for Victorian missionaries to dismiss this kind of belief as primitive paganism, but it is harder today, as Souleymane was a university graduate of remarkable ability (until his own early death). His beliefs were absolutely sincere, and shared by every one of his contemporaries. Do we just say he has a different outlook, and accept it (now that cultural broadness, alternative medicine and so on are socially desirable)? This would be easy where I worked with Souleymane, since we still agreed on things like retail outlet design, and debt collection. Whilst I was in the office, however, Carrie was in the eye clinic at the local hospital. She saw endless people who had been left unnecessarily blind or disfigured, because their local witch doctor had rubbed their eyes with a bark extract, instead of sending them in to the hospital earlier. One person I knew, was, as far as I could possibly tell, frightened to death by the religious leaders. We have to correct this, but how can we do so? Description that does not conform into the science-maths pattern makes every situation a one-off and prevents integration into a common perspective.

As an approach to this problem, let us think for a moment about how both our "normal scientific descriptions" and descriptions like Souleymane’s come about. Both have evolved from a long history of earlier beliefs. They started with a similar knowledge base but the science-maths approach has got somewhere and Souleymane’s stories have not. The science-maths approach was perpetuated and improved by its success, but another mechanism perpetuated the animist views. This was an unintended statistical process which moulds descriptions:

We can understand how parts of Souleymane’s beliefs survived. The beliefs were flexibly structured, to be able to fit in with anything that actually happened. There is no evidence imaginable which would prove his beliefs false. Where they did predict things, their credibility as not on the line if the prediction failed, since additional theory could be added. In competition between beliefs, this sort of "resistance to contradiction" clearly gives an advantage; the belief set has mutated and found an evolutionary niche.

The two most famous people who have commented on the evolution of scientific beliefs are called Karl Popper and Thomas Kuhn . Both discussed how scientific models evolved by analogy with Darwinian evolution of species. I understand Popper as trying to dictate what the rules should be and Kuhn as trying to work out what they actually are or were in practice (the second is obviously better).

Popper insisted that any theory must be composed of only predictions which could be proved wrong, and that the predictions must be a significant extension to what we already know (i.e. not "one day this old man will die"). From this perspective, Souleymane’s beliefs were "unfalsifiable" they "could not be proven false". Popper’s rules would however have been useful to eliminate Souleymane’s theory.

Science and "falsifiability"

Although it is attractive to inoculate our science with such a rigorous test as Popper’s, I am afraid that this medicine kills the patient, or in this case kills the science-maths approach too. Remember the two step process described earlier:

There is so much subtly embedded assumption in the characterisation step that I do not think you could significantly progress science without it (except possibly in bits of particle physics). Some people (I believe a small minority of scientists , but possibly a majority of philosophers) do think that the science is about the predictions/equations and the explanatory description is just an "aide-memoire". They think atoms are not a "fact" they are just an artefact of calculation, a dummy variable to be eliminated before the end). The world is data; why do we need words; can we not just handle data with equations? Does Popper’s approach not then work?

The problem is that in practice this scientific method is a complete non-starter, because the most powerful step in most science is the approximating "characterisation" of the problem in the first place. For example, it is the characterisation of water an incompressible viscous Newtonian fluid which does most of the work. There may be more than one way of doing this characterisation (other possible stepping-stones between the real world and the scientific prediction, e.g. the other levels mentioned later in this Chapter), but you cannot jump directly. Moreover, when you jump you have to resort to "everyone knows" arguments.

In science, we cannot rigorously separate subtle assumption from fact; but we need our eyes open about the existence of both in what we are doing. The way science has come about is not simple. Kuhn explores how science jumps between theories (paradigms), for complex reasons including strength of personality, rather than logically inching forward. We do however have to recognise that the evolutionary process will corrupt what people believe and we do have to try to compensate for it. An example of this evolutionary process is the tendency for people to adopt unfalsifiable beliefs such as Souleymane’s, of which we should be very wary (both Kuhn and Popper discuss bad examples in psychoanalysis). However, a belief is not necessarily wrong just because it has an "evolutionary" advantage, and sometimes we have to live with this.

Description is built around observations and a story evolves. If it is the only story that seems to explain something, it carries on being accepted until another theory appears. We do not know it is definitely correct, as I have said in Chapter 2, we actually know very little, but we accept it nonetheless. Odd things that do not fit cause adaptation, not execution. Often, two quite different ways of describing things end up as being shown not only both true, but equivalent (wave function versus matrix descriptions of quantum mechanics being an example). It was actually the conflict between Souleymane’s "medicine" and our own, which started the question about how to reject bad description. Only when two theories are in conflict, in a way which means they certainly disagree, do we generally invoke experimental tests as an executioner. When we have two pictures that cannot be consistent, we solve the dispute by finding out where they predict different outcomes, and then trying the experiment. The medicine which we believe, and Souleymane’s beliefs cannot be consistent. I am confident our version of medicine would win. Therefore, I can say with confidence Souleymane’s beliefs were bad medicine. His beliefs, as they stand are flawed science. Later, we will have to decide whether we think his beliefs were religion or not.

Science and Understanding

Science is, as far as our present discussion goes, about understanding our physical universe. This is characterisation not a definition.

We recognise scientific description will be distorted through time by the dynamics of how beliefs survive and spread. We continue to judge scientific description using common sense, based on the speed or simplicity with which it gives both pioneering scientists, and students, insight into physical phenomena. We consider whether that is because it is "true" (in the sense that we would still agree with our broad imagery "given full relevant information"), or for some other reason. We add a hygiene requirement that there should be a reasonable density of experimental evidence around the description, and occasional soul searching (illuminated by insight into the dynamics of belief evolution) to check we have not been deceiving ourselves about the whole story.

From a humble perspective (with a rather limited view of the history of science), I think sometimes everyone knows a theory is obviously true before it gives new results. This is because it sorts out known results in such an impressive way that, unless there is some other bizarre reason, it could only be because it is true. I think that the explanatory descriptions ("the stories around the formulae") are also validated by the speed with which students understand science (but I haven’t tried to teach it any other way than with the stories). Life is too short to find any bizarre reasons, so I will assume there is underlying reality in the descriptions. The alternative might be, for example, that I am a brain in a vat being manipulated by someone who finds it amusing to make me believe in atoms.

Anyway, we have our next belief, after belief in ourselves and after our belief in our abilities to observe, understand and decide. We decide to believe in the truth of (many) scientific descriptions because it is too complicated to believe in bizarre alternatives. The likely explanation is that the descriptions appear true because they are true.

The Parallel Nature of Scientific Descriptions

Systems (for example the computer on which I am typing) have, in general, different ways of being described and explained. Suppose I am playing a computer game, I "lose a life" and the screen goes blood red. Why does the screen go red? I could understand what is happening in terms of the game rules (the screen went red because my character died), in terms of the program source code the game is written in, in terms of machine instructions, in terms of the microcode level, in terms of the register transfer level (I might be out of date here), in terms of the electrical circuit (this base voltage then dropped below the threshold allowing current to pass...), or even in terms of quantum-electronics. The most general level of description is the quantum electronic description, "general" because we think it is "generally" applicable, (e.g. the governing equations of quantum electronics apply equally to a mouse digesting a piece of cheese). The most specific descriptions are the game rules because their logic is applicable only to that narrowly defined situation (playing that particular game on a computer).

More Specific to a limited situation

More General: covers most of the world as we know it


Each level in this picture gives you what, in principle, is a complete explanation of a situation (e.g. why the screen went red). The most important thing for this discussion is that every explanation is complete, in terms of its own rules. At each level, we have learnt many rules about how things happen and can understand things in terms of the rules.

The computer game example is a special case because it was actually built i.e. reasoned from a more general level successively to the most specific. Even so, for practical purposes you have to consider any given problem on the appropriate level of description. I do not deny that we lose information and flexibility by programming in C+ rather than directly in machine instructions, but it would be an unusual person who did not miss the point of what is happening completely if they only read the machine instruction version.

For comparison, let us take a human situation: I cried when my father died.

More specific to a limited situation

More general: covers most of the world, as we know it

Asked for an explanation of my tears:

Most specifically, a friend might probe the feelings of loss a little more and understand whether there were, say, feelings of regret over "things left unsaid", or feelings of guilt or loneliness, say, aggravating "normal" grief. Any explanation would be unique to this situation.

A historian would probably be content that this fitted into a typical pattern of human behaviour of grieving a parent. Any explanation might cover many bereaved people.

In more general terms, a doctor (say, talking to a medical student) might explain that a parasympathetic nerve was stimulating the tear duct, and could even prove it (somewhat anti-socially) with some local anaesthetic. Her explanation might apply to any watery eye.

More generally still, a cell biologist might explain how the tear duct responded to the tiny change in cell chemistry triggered by the nerve and consequently changed its behaviour radically to extract water from the blood flowing through it. This is not part of another description, it is a complete description in its own right in terms of its rules.

A quantum electronics professor might reply "don’t ask me I am still working on modelling an H2+ ion". This would apply to much of the world. The explanations at each stage use rules that apply to a wider range of situations.

There is a quite simple argument that religion is just a different level of explanation for the world to science and the two can explain the same things in different ways; like machine instructions versus game rules above. This simple argument is good from a high conceptual level, but before we accept or reject it, we should think a bit more about the way that the levels mentioned above interact. This subject is a bit complicated, but lets look at a couple of aspects.

First, which layer is the most fundamental? I have avoided calling the most general level of description "the most fundamental" because of the danger of confusing ourselves with what we mean. In Chapter 2, I explained that before we do any science at all we have to assume things (observation, understanding and decision) about us. In some senses therefore the "people" level of description contains things which are the logical building blocks on which even unified field theory is built. Even a boffin goes home and eats.

Second, why do we have these layers? I think it is an aspect of our brains only having a limited data storage bank, which means we zoom in and out on problems rather than try to analyse the whole. Why the world around us should obey consistent rules on so many different levels is another question, but we would never have got to quantum physics if there had been no consistency in the behaviour of the planets.

Third, which layer gives the best explanation? In the case of human situations, it varies. Sometimes a piece of biochemistry will spiral upwards ("you are behaving like that because you have low blood sugar or a thyroid problem") and we have to go down to the biochemistry layer to understand it and fix it. There are other times when effects spin down; for example, if you were monitoring blood pressure you might see the effects of a heated argument. There will be insights from biology that we will lose if we move up to history. However, if we move down from history to quantum electronics we even lose the obvious distinction between a dead body and a living person (we struggle to define this precisely even in medicine).

Fourth, some layers can tell us definite things about other layers. It is rarely as clear-cut as with the computer game example but sometimes, say with powerful statistics, we can capture specific rules for a situation starting with the general ones. More often than finding a complete solution, we can put limits on what is possible. For example, the more general rules we believe scientifically can tell us some things about "causality" (more or less the impossibility of changing the past) which underpin our beliefs up into forensic medicine. More often, specific rules allow us to deduce the more general ones.

Fifth, and most obvious, to an incredibly accurate approximation, we know the rules governing the most general level; the equations for quantum electronics are known. They may not apply to the sun or a nuclear reactor, but they apply to virtually everything else you will ever come across. There are still questions like why electrons are the weight they are, but none of these would change the calculation needed to predict something. This does not make all scientists (or anyone else) out of work!

Why reductionism is dangerous.

By reductionism I mean the tendency to believe that the most general level of description (the bottom of our lists at the beginning of the chapter) is somehow better, truer or more important than higher level descriptions.

Since I have said that science is about understanding, you have probably already guessed that my next point. We judge the usefulness of scientific description on whether it helps us understand a situation (and get to a predictive stage).

To all intents and purposes, quantum theory does not explain why my Rhododendrons keep dying. However, "because they will not grow in soil with lime in" gives me a useful predictive tool for when I move house, and opens the choice of growing one in a pot of peat. In this we must be very clear: more specific levels of description can be truer, better and more valid than lower level ones. "Alive and well" has a real meaning, which cannot be captured in any number of megabytes of data. Furthermore, as we descend into more and more detail, where we expect to find precision we find precisely the opposite: imprecision, uncertainty principles and random probability.

Actually, suppose we did manage to get a quantum electronics description of my rhododendron onto a super-computer. At that the limit of current technology we cannot (or could not when I last checked, ten years ago) even simulate the exact quantum description of a hydrogen molecule, although a hydrogen ion, having one electron less, could be done. Maybe today we can do a bit more; it does not matter. As you know, there are around 10 to the 24 electrons per gram of matter (a million million million million). If RAM capacity doubles every eighteen months (which is currently, roughly, the rate of improvement) we may have a good enough computer to hold a description of the plant in around one hundred and twenty years. However, the problem is not holding the description, it is calculating the interactions (requiring processing power), which is far harder. If you insisted that the full equations were run without approximations, I estimate that even if computers doubled in power every eighteen months between now and the likely end of the universe (say, 15 billion years time), we might not make it. Of course, we could approximate or round up to make the sums doable. We could neglect interactions between electrons a millimetre away, rather than calculating each one to show it is negligible. Quite quickly, the numbers become more reasonable: but if we are allowed to use our brains as well as equations in approaching the problem, why not switch to a more appropriate description?

All this might mean is that, one day, I could find out if a soil was good for the plant, by feeding in the analysis to the computer. This might (one day) be quicker and cheaper than planting such a plant in the soil to try it. But even if it was, it wouldn’t help me understand what the problem was until I had simulated millions of soils, looked at the rough components and worked out the rule of thumb about lime! People living in a world where their computer told them exactly what would happen all the time would not be scientists: they would probably brain-rot and be worshipping the thing within a couple of generations!

We are human beings and scientific description is for us, and only us. When the scientific description is so detailed that a human could not possibly up-load into their brain all the data it gives (e.g. quantum theory and my rhododendron), it is only of use as an intermediate stage to something better. A perfect simulation is not a scientific description of a situation, any more than an experiment is. It might be cheaper (perhaps massively cheaper), or quicker than experiments, or it might give us numbers we could not easily measure by experiment. It might reassure us that on the micro-level, the equations we put in were working. But, as with experiments, its usefulness starts only when crunching the data comes out with something at the far end we can understand (e.g. we start noticing useful qualitative features, so we can think through improvements in design). I am not knocking experiments or simulations, and have spent a fair part of my life doing each. However, experiments and simulations are not ends in themselves. The interesting question is never so much "does the turbine melt" as "is it the tip vortex stripping the protective boundary layer?" It is the second line, not the first, which will help us to get the problem into our heads and hence to improve the design. The second line also gives us robustness in design against small variations in operating conditions.

To summarise, the advantages that a perfect simulator has over actually performing the experiment itself are potentially cost, speed and ability to measure everything. However, these are practical not philosophical gains... what is the ability to measure everything for? So that we can build concepts, gain insight and understand, intuitively, rough outcomes for similar situations. In short, to give us, humans, understanding.

So, why do I say reductionism is dangerous? It is dangerous because it leads to missing some obvious and important truths. A reductionist approach to man finds a $5 sack of chemicals, with no human rights and no meaning. The whole of those truths, which we would normally consider important, can be trivialised in this way. Some people (particularly A level science students) use reductionism to attack the basis for religions, while never apparently appreciating how the same argument, if taken to its logical conclusion, would devalue things they would not be prepared to lose.

I think that reductionism started (and starts, since we still learn science in a broadly historical order) in mechanics, where it is true that for a time descriptions become more satisfying because they become more general. "Apples fall" generalises to "all objects fall", generalises to include planets accelerating towards the sun, gyroscopes, fluids, the weather and so on. The general applicability of Newton's laws and their more fundamental equivalents gives us a feeling that, somehow, we are racing downhill toward the nature of everything, since at each step we gain understanding of more things around us. What a pity that, after a while, as we try to generalise behaviour into more and more cases (very small like quarks, very big like galaxies, very hot like suns, very dense like black holes) we forget that what we are now talking about is of less and less use in reality. We end up only predicting things we need a laboratory to test, or a bank of telescopes and computers to detect. We start having to use powerful statistical methods, just to recover things we already knew. Although I am well aware of the limitations of Newton's Laws, or of Schrodinger's Equation, they are in some senses better and truer than their more fundamental equivalents, since they are approximations which are easier to understand and use. Human or medical truths can be better than the corresponding chemical explanations in a similar way. You miss the point of the radical difference between the life and death of someone if you describe it too much in detail.

I warned you that I was going to include some of the poems that I wrote as a teenager. Here is the first! It is roughly relevant and rather autobiographical although written ten years before my father actually died, and before I met my "sweetheart".


Andrew's Dad would never read him stories;
"Best to keep his feet firm on the ground,
Confuse him, if you tell him tales of fairies,
When we know quite well that such things can't be found."

Still, the boy grew up a funny lad
"He lives in a different world", they said.
"Will Santa come and fill my stocking, Dad?"
Dad killed Santa, then and there, quite dead.

Though vexed, his father was a patient man;
Bought Andrew books on science in his youth,
Grew flowers in two pots, and, with a can,
Watered one -- the other flops -- "that's proof!".

One day; a simple fact; Andrew cried
To hear his father's fate; Dad's here no more,
But in his heart he could not quite decide
If "Dad" was fact or just folklore.

A sweetheart declared she loved him, but
No litmus test could tell him why,
Or whether it was true, or what ...
Red roses meant? ... What made him shy?

Andrew lived in scientific places,
But deep within he had another leaning;
To smile at smiles, and sorrow at sad faces,
And view facts from where he had a meaning.

Letter to Peter next chapter

If you have any comments please email:  book @ catesfamily.org.uk

Published on www.catesfamily.org.uk