Theories and Reality
Dirk Roorda# 20-01-2006
Paper, written for the lecture series The Interaction between Science and Religion, by prof. Wil Derkse, Radboud University Nijmegen, dept. of philosophy.
The question: in what world do we live? has lead to many answers, from religion as well as from science. In this paper I want to explore the nature of the answers that come from scientists. I do not want to redo the basics of the theories of knowledge and scientific theories, as developed by Popper, Kuhn and Lakatos. I want to highlight certain limitations that occur in the scientific answers of today. Some of those limitations undermine certain expectations of science that one might cherish.
First I will argue that the self-inflicted limitation of reductionism combined with the apparent complexity of the real world, leads to the impossibility of a theory of everything.
Subsequently, that a relaxing of this limitation will lead to theories of more.
Finally we shall ponder about the interpretations of the world, in science, but also in religion. There I shall argue for the opinion that reductionism has a tendency to increase the conflict between science and religion, whereas a more mature scientific methodology allows some kind of integration between science and religion.
Reductionism leads to knowledge that is essentially incomplete.
Reductionism here is to be understood as a paradigm that sees the world operating according to a few basic laws that hold for the most elementary building blocks of the world. The program is twofold: 1. find those elementary laws; 2. deduce everything else that is worth knowing from those laws. If this succeeds, we have a theory of everything.
By the word essentially I mean to say: practically and theoretically, or: quantitatively and qualitatively, in short: in every possible way.
All our knowledge is incomplete, so what is so special about reductionism leading to incomplete knowledge? Reductionism lies at the heart of the scientific method, and science has provided us with many useful facts, patterns and theories, more than any other method, so it one might expect that all of our future knowledge will be obtained by this method.
It is tempting to follow a line of thought that seems to spread in our post-modern age: our values are not rational, we are not rational beings, there is more between heaven and earth than meets the eye. Hard core insights are discredited cheaply, tales of miracles are taken uncritically, the world is a place where everything is possible.
Clearly, in such a world there are no theories of everything. In such a world the thesis is indeed trivial. But in such a world the success that the reductionistic method does have, is taken for granted but remains unexplained.
The thesis gets spicy only in a world that is assumed to be firmly organized in patterns that are rationally describable. The thesis becomes surprising only there.
The main reason for the inadequateness of the reductionistic approach is complexity. The world is a complex phenomenon. The number of atoms in the universe is large, in fact, the number of atoms in a grain of salt is already nearly inconceivably large, as compared to number of brain cells we have. The number of ways that the building block of the universe arrange themselves is considerable, from quark to elementary particle to atom to molecule to biological macromolecule to cell to organism to population to ecosystem to planet to solar system to milky way to cluster of milky ways. At every level new phenomena occur, which are not violating the laws at a lower level, but which cannot be clearly expressed at the previous level.
In this complexity, there are theoretical and practical problems with reducing laws of one level to the laws of a more basic level, and so on until a bottom-level is reached.
The theoretical problems are related to the theorems of Gödel. The theorem states, in a restricted and precise context, that a formal system that has a certain expressiveness and proof-theoretical power, is not completely reducible to a formal system that is essentially simpler. One could say: there is no bottom-level of rock-solid knowledge!
The practical problems are those of computing. To compute the behaviour of a complex system, you need to compute the behaviour of its components together with all possible interactions between the components. In theory, one can compute such things if the laws are known, but in practice it might take too long. In some cases, you can compute the complexity of computing intricate systems, and one of the insights from is that there might be things that cannot be computed in any other way than watching it happen. The thing is its own computer. In other words: there might be patterns that are so complicated that they cannot be described in more concise ways than the pattern itself. This occurs in cases where a long history of evolution is coded in matter: living organisms. Here matter is ordered in such intricate ways, that they escape interpretation unless you take the history of the organism into account.
This proof outline might be refuted in several ways.
Here is a refutation of the theoretical argument: the theorem of Gödel is a result in a highly idealized setting. It deals with theories that have somehow a notion of infinitude in them, but in reality nothing is infinite. If we only deal with finite concepts and things, then there is no such limit to our understanding.
The practical argument might be refuted as follows: our capacities of computing and handling complexity are still growing fast, there is not yet an end in sight. As our computing power increases, the grid of our knowledge becomes finer and finer, approximating the ideal of total knowledge.
Alas, the situation is not good for those who believe in a steady progress towards total knowledge.
As to Gödel's theorem: indeed, our present day reality and all its objects seem to be finite. Yet in order to reason about them, we make generalizations, at least into potential infinity. The knowledge we obtain in that way, can no longer be controlled by us. And this knowledge may have its implications in the finite material world. Take, for instance, the theorem of Gödel itself. It has been proven in 1929. At that time it came as a big surprise. Another mathematician, Ackerman, had just finished a book, in which he founded the whole of mathematics on simple theories, contrary to Gödel's theorem. When the book was still being proofed at the printer, he discovered a small mistake, which he thought could easily be repaired. But he could not do it, the book was not published, and Gödel proved why the book could not be right. The upshot is, that somehow our minds are able to reason with generalised concepts, involving infinity, and the outcome of these insights have utterly material consequences in the everyday world. Any theory that claims to be able to predict the course of the universe, must contain a universal theorem prover!
As to the argument of our increasing computing power: the world as we know it now is organized in a way that at the smallest level events are under-determined. Things happen at random there, only statistical assertions can be done with accuracy. This fact alone is not sufficient to rule out a steady progress to complete prediction and control. The condition is that the random fluctuations at the micro level cancel each other out and cannot be felt at macroscopic levels. But here chaos theory comes in: it says that there is no barrier between the micro cosmos and the macro cosmos: small events may have big consequences. There are concrete physical systems that are sensitive to the initial conditions: given two initial conditions that differ only infinitesimally, the corresponding behaviours of these systems from these initial conditions will be miles apart after some time. More precisely: differences in initial conditions grow over time at an exponential rate with regards to the time elapsed. To predict the outcome after 1 second, you need to measure the initial condition with a precision of one decimal. To predict after 2 seconds, you need 2 decimals, to predict after 1000 seconds, you need 1000 decimals, to predict after a year, you need more than 30 million decimals. In practice, experimenters in physics have seen an increase in measurement accuracy of several decimals. Time can be measured now in at least 5 decimals more than around 1900. Maybe we can add 5 decimals within the next hundred years. But we know that it must stop way before 100 decimals because of quantum theory. We can also estimate the effort needed to add a decimal of precision. Often, we can see that the resources of the universe are not sufficient to add a hundred decimals more precision. But in order to predict we need thousands of decimals.
The practical points are acerbated by two recent theories: quantum theory and chaos theory. These theories ban the hope that in the future we will be able to overcome our practical limits of computation. Somehow, the practical problem has become fundamental.
Let us consider a theory that explains the basic building blocks of the universe in a complete way, a theory of everything according to the reductionist. Such a theory describes a lot about the world and has also implications about more complex elements of the world. But there will be some truths about the world that cannot be proved or refuted by this theory (Gödel). And there will be truths that can be proven by this theory, but only in a very inefficient way, not feasible to us humans, even with the fastest computers.
We as human beings stand somehow in the middle of the hierarchy of complexity levels, between the atoms and the milky ways. It is likely that we are now encountering lots of phenomena that are completely intractable by such a theory of everything. The weather, the human genome, the problems of war and peace, the stock exchange rates, the evolution of new life forms, cultures, and what not. Yet we can acquire some knowledge about all these phenomena. We could even reduce some of that knowledge to simpler theories. But such a reduction would not increase knowledge or insight. The reduction would lose the specific information that the higher theory provides.
Reductionism leads us to the study of the smallest building blocks of the universe. It tries to gather complete knowledge there, and hopes to deduce all other knowledge that is to be had from there. Deducing is a cheap and sure way to increase your stock of true propositions. Now we have seen that it cannot work ultimately, I want to give other an refutation of the reductionistic method.
Let me first remark that although a method might not work ultimately, it can still be very useful in non-ultimate cases. This holds for reductionism. But the overwhelming success of reductionism so far, has more or less wiped out other interesting concepts of, and roads towards, knowledge.
The phenomena of the world that people are interested in, exhibit a complex structure in multiple layers. There are layers of elementary particles, atoms, molecules, macromolecules, living cells, organisms, brains, societies, planets, solar systems, galaxies, clusters of galaxies. The elements of each layer behave according to rules. These rules are formulated in a science, corresponding to that layer. Various branches of physics, chemistry, biology, psychology, sociology. But this is not the whole story: elements also obey the laws at lower levels. For example, cells are also systems of macromolecules obeying the specific laws of macromolecules, which are also molecules, obeying chemistry, the laws of molecules, which are also compounds of elementary particles which obey the laws of physics.
Now suppose we want to study cells. The reductionistic program leads us to the study of its components, and their components, and so on, until we reach the bottom. In a sense this is a depth-first search of facts. Another search is also possible: abstract from the laws of the lower levels, study the types of cells, describe the games that cells play which each other, without trying to found this knowledge on the level of elementary particles. Only when you have a complete insight in these games, descend to lower levels, and try to found the laws of the cell game onto the laws of the macromolecules. This is a breadth-first search.
Scientific enquiry comes in two flavours: analytic and synthetic. The flavour of analysis is this: analyse given complex things into their constituent parts, reduce, abstract, work top-down, make deductions from basic laws, search depth-first. The flavour of synthesis is: observe given things in their interactions, build them up into systems, add layers and properties, work bottom-up, use inductions from experience into theories, search breadth-first.
The success of the scientific is easily identified with its analytic flavour, but there would not have been results without its synthetic flavour. The synthetic flavour has always been there.
Real problem solving is always a keen interplay between breadth-first and depth-first methods. I think it is here that my deepest criticism against reductionism is located. I am not against reducing, against analysis. I am against the claim that only the mindset that favours abstraction, reductions, top-down, can give us the profoundest insights in the workings of the world.
The proof outline above has indicated that our tools to understand the world are far from perfect, and will remain so indefinitely. Reductionism assumes that there is a perfection somewhere in our reasoning that is not really there. The challenge is: how to advance our knowledge despite these imperfections?
A good example is Stuart Kauffman.
Life is the prime example of complexity. Systems of many elements, organized in many layers. The study of it requires all the intelligence and resourcefulness we have got. No single methodology will get us all the results. Cells play complicated games with each other. Macromolecules are constantly being assembled and disassembled. Big networks of richly connected elements perform real information processing. Terms as function and purpose can only be avoided at the price of missing generalisations and insight.
Yet, biology has been firmly in the grip of reductionism, ever since Darwin. A research program came into being with the purpose of explaining life and it forms by means of the same laws that are operative in the lifeless nature, using only efficient causes. Final causes, designers, God, it had to be removed from the picture of life. The problem is: life itself seems to be a mighty designer: every organism has designing capacities, in that they are capable of using tools (be it chemical reactions, organs, or external objects) for certain ends. The good thing about the program is that it eradicated terms that had no explanatory content. Invoking God or other designers to account for the existence of life, does not advance our knowledge of it. It covers up the deepest and most interesting questions. But somehow the God-explanations have left a trace: biology sought an explanation that replaced the term God in it by the term nature. But the explanation sought has still the structure of a deduction from first principles. Instead of God being in control, it is nature being in the same sort of control.
And there the program falters. The current explanation for the life forms is: DNA in the cells regulates the structure and function of cells, organs, and the organism as a whole. This DNA is constantly being mutated by influences of the environment (radio-activity, chemicals, other life forms such as viruses). This leads to variations in life-forms. The forms that have a survival advantage by the mutation, will develop further, and push the competing forms into the margin of existence and beyond.
But it is hard to see that mere random changes can accumulate to changes in function, to complex new organs and functions. It is conceivable that this happens, given enough time, but the time passed (3 000 000 000 years) is blatantly insufficient. There most be additional mechanisms and/or explanations.
Stuart Kauffman studies self-organization in complex systems. If people build complex systems such as computers, they always get broken if you modify them randomly, even a tiny bit. If I take my processor out, drill a screw through it, and put the damaged thing back, my computer is no good anymore. Kauffman researches other systems: systems that function still when you modify parts of it. These are systems that are evolvable, they continue to function through random changes. He is able to show in silico that genetic systems (systems of hundreds of thousands genes that turn each other on or off according to simple rules) have this kind of robustness. He also showed, that when you put sufficiently many different stuffs together, where the interactions between the stuffs are not too many and not too few, self-organization spontaneously occurs. It is just the most probable thing to occur.
The research program, started by Kauffman, might fill in the most notable gaps of the evolution theory. So, this is a point for reductionism, it seems. But it is not, due to the nature of the new explanations. Kauffman is not able to predict what exactly will happen if you put millions of stuffs together. He is only able to say things like: if the interaction level between the stuff is less than a certain value, nothing much will happen. If the interaction level exceeds a certain value, chaotic behaviour will happen, and somewhere in between, novel, more or less stable networks of reactions will be “created”. No control, only a little prediction. But a tremendous gain in qualitative insights in complex processes. Things can be seen for which new words are needed, characteristics that were meaningless for simple systems, must be defined.
It is as if the quality of such systems does not arise from the components of which they are composed, but from the interaction game they play. In fact, the same behaviours are seen in systems of molecules, cells, computer memory locations, humans, economic quantities. The regularities are not the laws of physics, but those of certain branches of mathematics: combinatorics, graph theory, chaos theory, fractal theory.
The new science of life takes seriously the fact that in order to study complex systems, we have to discover what is new at the specific level of reality in which the system expresses itself. The study of the parts of the system is of limited use for the understanding of the whole, and can largely be abstracted away. Instead of reducing the laws and concepts needed for complex systems to the laws and concepts designed for their elements, we have to come up with new concepts and new laws. We build a theory of more.
Mathematics has been the true and faithful companion of the reductionistic program. In a sense, mathematics itself can be seen as the bottom layer at the core of reality, even below the elementary particles. The success of mathematics is the success of reductionistic science.
But the picture is a bit more complicated than that.
Mathematics is the language to express patterns, structures, and to do so in generic, abstract ways. This language has been used to frame the deepest insights of mankind into the patterns of reality. Because of the genericity and abstraction of mathematics, it can also be used for patterns that have no counterpart in the as yet discovered reality. It can suggest the search for new patterns, not previously thought of. Sometimes, in this way, new real patterns are discovered. The loose connection with reality paradoxically increases the fruitfulness of math.
Mathematics is a human activity. It is carried out by people using mindsets that reflect a certain history and stage of thinking. Mathematics is old, and has flowered in many peoples minds, having very different mind sets. There is not much in mathematics, nor in the reductionistic program, that bind them to each other. The reductionistic program comes with certain abstractions and generalizations, but mathematics can equally well be used for other abstractions, and other methods of theorizing. The loose connection with specific mind sets paradoxically increases the fruitfulness of math.
Kauffman's work is an example how mathematics can be used to express flagrantly non-reductionistic theories about complex systems. His new laws and definitions have a highly mathematical character.
Mathematics performs the function of a sparring partner: it forces us to express what we think, it stretches the meaning of what we express in unexpected directions, it connects the depths of our insights with other deep insights.
The upshot is, that we live in a confusingly complex world, which still has something to offer to those who approach it with rational skills. Rather than mobilising one particular methodology, we need all the rational methodologies we've got, and mathematics will be the dialectic partner of all such methods.
The religious aspect of theorising about reality has been hinted at briefly in the section Explaining Life above. It occurs to me that where evolution theory and specific religions are in conflict, it is a religious conflict and not a scientific conflict. In cases where the two are in conflict, evolution carries a religious payload, and is not purely scientific. The religious payload is this: we, evolutionary scientists, understand the origin of life, and it is not your God, but nature itself. The answer from the religious side is: we do not understand the origin of life, but we ascribe it to God, and it is not purely nature.
If the conflict takes this form, the religious position is mostly right, or at least the most fruitful one, irrespective whether the evolution theory is wrong or not.
I see a remedy that involves a correction at both sides.
First of all, the evolution theory still has such big gaps in explaining the visible evidence of the evolution of life, that every suggestion of understanding the origin of life must be avoided. In the absence of this understanding, the phrase: it is not your God, but nature itself, has little meaning. It might be nature itself, but what a kind of nature is it where life is possible? It might lend itself to divine interpretation after all.
Secondly, believers in a God should not play the game “God versus nature”. The temptation is to take the things most dear to us, human life, mind, spirit, and put them in the sacred realm of God. There they are untouchable, not open to further scrutiny. All the other things are put in the realm of nature, where we are free to do what we want. The challenge here is to declare the realm of God to be profane, and the realm of nature to be sacred. Everything is open for research, but everything is sacred as well. So, even though evolution seems to be true, we keep a holy respect for nature, and we relate to it as to something divine.
It seems that the reductionistic paradigm is a conditioning factor for a conflict between science and religion. If the scientific debater as well as the religious debater accept a reductionistic paradigm, the following happens: the location of creative power is moved to the most elementary level of reality. The religious believer locates God at that level, and has not many options to see God elsewhere or otherwise. So he either clings to the power of God at that level, becoming a deist, or he succumbs to the temptation of magic: God is present everywhere, but through miracles and magic. The scientist deals blows to both of these positions: he knows the laws of the elementary particles, and does not need God as an extra hypothesis. And he does not need miracles and magic to explain the rest of the world, in due course the chain of explanation from first principles will be unbroken.
Once reductionism is no longer predominant, the view of the world will surely become less mechanistic. At all levels there is something interesting going on. There will be no single simple theory that accounts for everything. There is scope for continued wondering, pondering. Maybe something big is behind all this. Maybe not. Maybe the something big is within all this. And all this has such a richness in itself, that it commands respect. It will be no profanity to see all this as the locus of God.
My personal challenge is to interpret the world in such a way that our religious dimension has a fully acknowledged place in it and that at the same time the true results of science are welcomed heartily.
In my personal experience I feel an uneasiness with a world view containing a rigid hierarchy from elementary particles to life forms, regulated by the laws of nature. I have the feeling that it ignores things that are right in front of our noses. Moreover, this overlooking is so profound, that the awareness of overlooking something is wiped out.
Where does the awe, the wonder in our hearts, when we admire the world, come from? Where does our feeling of quality, of beauty come from? Our sense of mystery, our sense of belonging? Our bewilderment that we exist at all, that there is logic, that there are patterns? These things ask for a better explanation than the so-called anthropic principle: we are just what we are and that is why.
Science, and the predominant monotheistic religions all take a starting point far outside human experience. All the concepts of science are far-fetched abstractions without felt reality. A point in space has no dimensions, a point in time has no duration, a moving body is just a quantity of mass moving through space and nothing else, so that we can not hear it, see it, feel it. On such concepts we base the whole description of reality en find no meaning in it. On the other hand: God in the monotheistic religions is an absolute, not open to sensory experience, not to be identified with anything else, unthinkable. From such a God the whole of reality is derived, but we cannot really match the reality as given by this God with the reality as experienced by us.
I think we need a philosophy to overcome these defects. Not only a correction on scientific reductionism, but also a correction on monotheistic religion.
We need something that starts with ourselves and our experiences. What we experience should be most basic, things that cause these experiences are less basic, things that cause those causes, even less basic. This is reductionism turned upside down. It starts with meaning, so the concept of meaning cannot accidentally be lost. I have not read enough about process thought, but I found it interesting to read that process thought does not work with points in time in the mathematical sense. A point in time is a unit of experience, and it can be subdivided into smaller units of experience, but only if the experience itself can be subdivided into sub-experiences. So, when we have dinner with friends, we may have good moments, but these moments are not 3.5 nanosecond intervals in time. On the other hand, when we design computer chips, and use instruments to visualise what is going on, we can validly think in units of 3.5 nanoseconds, because in that context they correspond to real experiences. Not our own experiences, but the experiences of things that we experience.
A nice example is the computer. Right now I am typing this text, and I see the letters appearing on a white background. Now, analysing reductionistically, I just see black spots appearing on a white background. In order to understand which spots will show up, I shall have to build a theory of computers, and follow the intricate pathways that are built into it, in order to predict the movements of the electrons inside the computer. At best I find a predictable relationship between the key I press and the pixels that appear on the screen. But then I need also a theory of my own brain, how the neurons fire, how they are linked. At best I find a theory that predicts which keys I will press at the moment. In none of these theories is any account of the meaning of words, the meaning of programs, the notion of information. It is not a theory that explains anything. Moreover, now I am about to save the document, to close the computer, to mail this text to somebody, who finds it such a stunning text that he decides to burn this on CD. Years later, his child discovers this CD, inserts it in a computer, and reads it. He will see blue pixels against a yellow background, because his computer settings are different. How do we understand which blue pixels he will see? We have to understand the transformation of bits in memory into bits on the network into bits in another memory into bits on a CD into bits in yet another memory into pixels on a screen into words in a mind. Without the notion of information, meaning, programs we have to build whole new theories of amazing intricateness. We have to build a multiplicity of theories for every trivial event. I do not call that explanation. Ironically, without our human thirst for information, there would be no computers at all, the things simply would be non-existent, not heard-of because not worth-while.
I think so it is with us. We would be non-existent because not worthwhile, if there would be nowhere any concept of meaning, information, intent or purpose. We are the realization of some kind of intention. Intention exists, we have it, we manipulate it, it shapes our physical world more than anything else. In the foreseeable future it might shape our biological make-up as well. So why not take it seriously, as an all-pervading category throughout the universe and its environs? Maybe this turn of putting intention at the basis of a world-view, is an example of the integrating science with religion.
Davies, Paul about a common trait in monotheistic religion and modern science Taking science on faith
Gleiser, Marcelo about a common trait in monotheistic religion and modern science To Unify or Not: that is the Question
Kauffman, Stuart as he explains his vision on his own work in Beyond Reductionism and Breaking the Galilean Spell
Tudge, Colin about limitations of reductionism in The Omniscience and Omnipotence of Science
Whitehead, Alfred North founder of process thought, see wikipedia
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