In a previous post, “My Journey from Theory to Reality“, I explained how converting my ‘worldly’ profession of teaching economics to an act of worship required working on intentions: (both mine and the students). I made the intention to study “useful” knowledge, in order to provide service to the creation of God, for the sake of the love of God. I also asked my students to make the same intention.
Our Prophet Mohammad SAW made dua for beneficial knowledge, and also made dua for protection from useless knowledge. This distinction does not exist in Western epistemology. In fact, there is an explicit argument made that there is no such distinction. Apparently useless knowledge we acquire today (for example about how bats navigate without eyes) may become useful tomorrow (as in the discovery of the sonar). It is clear that Islam does make a distinction, and so it became necessary for me to make the effort to find out the nature of “useful” knowledge. At the outset, I defined the term solely in terms of the ability to use this knowledge in order to solve some real world problem. Later, I learned much more about ‘useful’ knowledge. In this post, I will describe some basic and elementary facts that became clear to me in my search for useful knowledge to teach my students.
My first introduction to the huge gap between theory and practice came when I wrote my first book: “Statistical Foundations for Econometric Techniques“. When I submitted the first draft to Academic Press in 1990, one of the reviewers wrote that the author is an expert on theory, but has no grasp of real world problems. The theory of knowledge that we had absorbed in Graduate School taught us that applications were trivial. We took our theoretical models, and plugged in real data sets to get the results. So I was irritated by this criticism; I decided to add one real world application to each chapter of my book. To my great surprise, this process took six years, delaying the publication of the book to 1996! I ran into great difficulties when I tried to find serious and realistic applications of the theory I was describing in the book. It was not a matter of just plugging in data and producing results. Most data did not fit the assumptions made in our theoretical models. Eventually, I did manage to add a lot of realistic examples, almost one per chapter as I had decided. But in the process I learned a lot about the gap between theory and practice in Econometrics. I could find real examples only by choosing the very few realistic problems which provided a rough match to the theoretical assumptions. I learned that the vast majority of complex real world problems did not fit the simplified assumptions we used to set up our theoretical models.
As one example, Chapter 5 of my textbook was an introduction to robust regression techniques. When I surveyed the literature, I found more than 25 different techniques had been suggested in the theoretical literature. This was too many to cover in one chapter. While trying to decide what to cover, I decided to look at techniques which had actually been applied to the analysis of real world data sets. That immediately reduced the number under consideration to only 5 or so, which was possible to cover. This was just one among many examples which showed me the great divide between theory and practice. Theoreticians would happily work out solutions to problems which never occur in practice, making assumptions which lead to nice mathematical solutions. In contrast, real world problems would have structures which were too complex to express in elegant mathematical forms, and hence were never dealt with by the theoreticians.
The simple idea of converting the theoretical knowledge that I had been taught, into practical ideas which were relevant to solution of real world problems, made my life an exciting process of continuous discovery — every abstract theoretical idea acquired new life when it was translated into the context of a real world application. Many theories and skills that I had been taught died a natural death — I learned that they could not be applied. For example, I discovered that the mathematical theorems and proofs that I had spent years learning had no practical real world applications. The few theories that could be applied acquired new meanings, depth, and complexity, when viewed in the light of real world applications. This led me to what I have called the ‘forest and tree’ principle. The forest is a theory about how a collection of trees can be grouped together — this collectivity exists in minds, and is subjective. At the same time, the trees are out there, and an objective part of external reality. Understanding the world requires simultaneous work on the theories which organized the complex external reality into simple patterns (the forest) , and on the objects (trees) which have been collected into a pattern by ignoring a huge amount of details regarding the particulars (like size, type, distances from other trees, age, etc.). The forest and tree principle involves looking together at the forest and trees: the general and abstract theories, and the particular and special trees. I found this principle of great importance in developing “useful knowledge”.
The Forest and Tree principle: Any abstract theory, philosophy, or concept, can only be understood in context of its application to a particular, specialized, concrete, and unique real world problem. The converse is also true: we cannot understand particular, special, and unique real world problems without the help of abstract theories.
We all learn Western epistemology (theory of knowledge), not because we take courses in philosophy, but by on-the-job training that an apprentice receives. The courses we take in chemistry, biology, physics, mathematics, history, economics, etc. etc. etc. define for us the nature of knowledge — knowledge is what we learn in our courses. Because it is never mentioned, we are taught that learning how to live, discovering the purpose of life, learning codes of conduct for our personal, family, and social lives — these are NOT part of knowledge. As I understood much later, real knowledge is about learning how to realize the potential for excellence that all human beings are born with. Knowledge of our internal world, which is required for this, is not part of the Western syllabus, but plays a central role in the teachings of Islam. The Forest and Tree principle applies to the knowledge of the external world, which is the sole focus of Western knowledge. But even when it comes to the study of the external world, Western theories of knowledge are seriously mistaken. This is especially surprising in view of the tremendous success these theories have achieved in terms of technological and scientific progress. The errors arise from the effort to prove that scientific theories are objective facts about external realities, when in fact they are subjective ways of organizing collections of facts into meaningful patterns. To understand this, it is useful to think more deeply about the forest and the trees.
Even though there is an external reality which is objective, out-there, and same for all, our only access to this reality is through our subjective senses. When we call an object in the external reality a “tree” – we have already added a lot of subjective information to the external reality. We have ignored a huge amount of information — how many branches, leaves, colors, wood density, age, molecular composition, roots, etc. etc. — in arriving at this classification. Philosophers of science have realized that observations are theory-laden. The tree is not an external reality out there; it is a product of our classification system which says that many details about the external Tree-object can be ignored, while certain special aspects must be taken into account. If we really took all details into account, then every tree would be a particular unique type of object which would have no other similar objects elsewhere. A fact of the type: there is an object O, at time T, which has characteristics C1, C2, … is not very useful because we cannot use it to say anything about the world in general. In order to learn from observations, it is NECESSARY to introduce THEORIES – These theories tell us what facts should be considered as important, and which ones can be ignored. It is after ignoring particular details of the tree, that we can create a collection of trees which share similarities, and are located in the same place. Thus the FOREST is a subjective meta-theory – it is theory which is built on top of our theories regarding what a tree is.
In general, whenever we collect an objective set of observations about the external reality, it is necessary to find some patterns in them, in order to learn something more about the real world. If we have a collection of facts F1, F2, F3, … these facts tell us nothing more than what they are themselves, UNLESS we construct a theory based on these facts. The theory is what allows us to LEARN from the facts, but the theory is ALWAYS subjective — it is based on our own judgments about how to organize the trees into a forest.
One very important implication of this way of understanding the world is that we DO NOT LEARN from EXPERIENCE. Experience is just a collection of facts that we observe in the process of engaging with the world. Learning comes from applying a THEORY to organize this experience. To give a very simple example, consider someone who struggles to achieve some goal, and fails 100 times. What can he learn from this experience? He may apply the theory that the goal is too difficult, that his capabilities are too limited, or some other similar lesson, which says that he should give up. Alternatively, he could apply the theory that his failure represents incomplete effort and insufficient experience, and therefore he should try harder, and learn more, in order to succeed. It is interesting that both theories can prove themselves by further experience. The one who gives up will say that yes, my theory is correct, and a 100 examples prove it. I have no need of further experimentation to prove my theory. The one who keeps trying may experience success on the 150th trial, can also conclude that his theory was correct. Identical people with identical experiences may apply different theories and learn different things from the same experience.
Let me summarize the key lessons of the forest and trees. Theories about the external world are based on collections of facts, but always involve subjective elements — theories are patterns in our mind which have some reflections in external realities as well. All facts are also theory-laden, which means that arriving at a “fact” always involves discarding large amounts of information as being irrelevant, and focusing on some small set of observables as being relevant — this classification is based on our theories about what matters and what does not matter. It is our higher level theories — like the forest — which determine how we define a tree (so as to fit into a collection of trees). So what we observe in the real world is based on the theories we use to look at the world. This is how our theories like “forest” can only be understood by looking at external realities represented by the “tree”. But also, the external reality can only be understood by applying theories which allow us to abstract from the particular and unique features, and put our experience in terms which can be shared across individuals because of the commonalities.
POSTSCRIPT: For a list of relevant posts to the project of creating new foundations for the study of statistics (and all subjects) see “Connecting Statistics to Reality“. Also, I recently saw a quote from Kant, which very succinctly summarized the essence of the Forest and Tree Principle: “Thoughts without content are empty, intuitions without concepts are blind. The understanding can intuit nothing, the senses can think nothing. Only through their unison can knowledge arise.” One must combine sense data (we see the tree) with the thought (forest) to create knowledge.