Theory in Natural Science, Seen Through Chemistry

Theory in Natural Science, Seen Through Chemistry

Author: Dclean
Reviewers: 黍离, 白書, and 一毫秒的永恒

  Human understanding of nature begins with the observation of natural phenomena. The immediate impressions formed by those observations became some of the earliest “knowledge” in human history. In pursuit of deeper understanding, people gradually classified, organized, and connected that knowledge through logic. Out of this process came the first rudiments of “theory.”

  This article discusses how science understands theory, the place of theory in the natural sciences, and its relationship with practice.

Part I | How Disciplines Differ: Subject Matter and Method

  We often ask what really distinguishes physics from chemistry. We also encounter claims that chemistry is merely a branch of physics. To think clearly about such questions, we must first identify what makes one discipline different from another.

  The most obvious distinction is subject matter. The humanities, for example, study patterns in the development of human society, which plainly differs in a fundamental way from the natural sciences’ study of how the natural world operates. Yet subject matter is not the whole story. Once a discipline has an object of study, it also needs methods suited to that object. Subject matter and method, in fact, select one another. The separation of physics and chemistry provides a useful example of this mutual selection.

  Physics and chemistry are both natural sciences concerned with nonliving systems, and at first glance their subject matter does not look very different. In secondary school, you may have read a statement such as: “Chemistry studies the properties of matter from the atomic level up to the supramolecular scale.” But this definition invites an obvious question. Why should physics cover both the very large—from macroscopic to cosmic scales—and the very small, below the atom, while chemistry is assigned only the region in between?

  Let us introduce a concept called the “unit of observation”: the most basic part of the objective reality involved in a problem that can be treated as a whole. What are the usual units of observation in the problems studied by elementary physics and elementary chemistry?

  In the microscopic realm, elementary physics studies interactions among particles. Individual particles are plainly our units of observation: we can write equations for a particle or a system of particles and solve for its behavior. The same applies at cosmic scales. We treat individual celestial bodies as wholes, study their interactions, and write equations for a body or system of bodies to determine its behavior.

  In a chemical reaction, however, no comparable unit of observation can be found. A molecule cannot serve, because it does not remain unchanged through the reaction. Nor can an atom, because atoms gain and lose electrons. In a chemical reaction, there is simply no unit that remains unchanged while also having an internal structure that can be ignored for the problem at hand. That means the mathematical equations describing a chemical system cannot be reduced to the simplicity of elementary physics. Early in the history of science, this was the highest level of complexity that available mathematics could handle. For the same reason, secondary-school chemistry cannot treat its problems with the rigorous mathematical methods familiar from physics. It must remain at a macroscopic level and rely on comparatively empirical theories.

  In this sense, the fundamental difference between physics and chemistry arises from the characteristics of their objects: subject matter determines method. From the perspective of scientific history, however, the direction can also be reversed. As people observed nature, they gradually developed scientific methods of inquiry. Once a method suited to a certain kind of object had emerged, investigation shifted from unstructured observation to observation guided by that method. Human observation is necessarily limited, yet methods derived from a finite set of observed objects must later be applied to objects never seen before. In that process, each distinct method finds the subject matter to which it is best suited. Selection then runs in the opposite direction. This two-way selection between subject matter and research method is the embryo of disciplinary differentiation.

Part II | The Birth of Theory and the Development of a Discipline

  In the natural sciences, the first theories arose by making observational results logical and systematic. Theory raised knowledge from a level of simple, intuitive recognition to one of organized logical structure. Its central property is logical coherence, and that is what distinguishes a theory from an empirical conclusion.

  The earliest theories were induced from experimental findings, and their validity was tested against further experiments. The reasonableness of this approach is obvious, and it has run through research in every field and period. Consider the training set and testing set used in today’s popular field of machine learning. To find a relationship between input variables and a target variable, an algorithm fits the training data. Whether that fitted relationship works across a broader range must then be evaluated on the testing set. If inputs from the test set pass through the fitted relationship and produce target values close to reality, the learning has been comparatively successful. The fitted relationship produced by machine learning is not itself a “theory,” however; it is an “empirical conclusion,” even if its mathematical or logical form is clear and rigorous. The relationship was fitted by a computer algorithm. It has no inherent physical meaning, nor can one necessarily use it as a starting point for logical deduction of new conclusions. Theories, by contrast, can serve as major and minor premises for one another, logically generate new theories, and be derived from or corroborated by others within the same system. That is what their “logical character” means. If researchers move from a mathematical relationship to a clear physical picture, obtain a formula with definite physical meaning, and integrate it into an existing theoretical system, then the result has risen to the level of theory.

  Later theories need not arise directly from experimental data; they can also be deduced logically from theories already in place. This route is especially important in the abstract sciences, most notably in mathematics and its “axiomatic systems.” A mathematical axiomatic system still differs fundamentally from a theoretical system in natural science because the two study different kinds of objects. This is why the logical character of theory was emphasized above.

  Logic also plays a vital role in the growth of theory and the maturation of a discipline. The history of natural science is the history of scientific theories being born, developing, and flourishing. Natural science is defined not only by its study of nature but also by the systematic organization of its theories, whose internal connections are logical. Only a systematic body of theory can produce a sound mechanism for detecting and correcting errors, and such a mechanism is essential to disciplinary progress. The opposite of systematic theory is the mere accumulation of facts. Knowledge assembled as disconnected scraps remains fragmented. It is difficult to learn and even harder to test for correctness; this is the weakness of an empirical discipline. Traditional Chinese medicine, a subject of longstanding debate, offers an example. Because it was established and developed so long ago, researchers had little ability to exchange information and could do little more than record what they saw, heard, and obtained from experiments. These records accumulated over centuries into a system. Yet every experiment is a chaotic system. At every link in such an empirical chain, individual variation or differences in conditions may make a result unreliable. Errors accumulated over a thousand years do not correct themselves; they grow larger. The result is what we see today: a medical book may contain hundreds or thousands of ineffective prescriptions, alongside many effective ones, because both correct and incorrect experimental conclusions accumulated with time. This flaw is fatal to a discipline’s future. A sound theoretical system cannot emerge while the body of knowledge contains too many practical errors. That is why modern science attaches such importance to reproducibility. If every experimental claim were accepted without independent replication, random errors would accumulate until the discipline’s theoretical structure collapsed.

  The systematic, logical character of theory also matters to learners. It determines how they grasp the core of a body of knowledge. Simply stating a theory in words has a very different effect from laying out the process by which it was established and guiding learners to derive it for themselves. In my view, the best way to learn a field is to follow the path by which its theoretical system was built. A few disciplines developed along peculiar routes that do not match ordinary patterns of cognition, but those cases are rare. This is the value of studying the history of science. Following the construction of a theoretical system partly exchanges the learner’s perspective for the researcher’s. The researcher sees far more: how a theory arose and how it generated new theories. Through this process, the learner can reach a much deeper understanding. Only a systematic logical structure makes this possible. A coherent body of knowledge resembles a branching tree. Begin with the trunk and grasp the core, and one can understand a field deeply enough to learn its branches more effectively. A heap of unrelated facts resembles a pile of bricks. Stacking them one by one reveals neither their deeper content nor their logical relationships.

  As an aside, the natural sciences may now possess highly developed theoretical systems, but learners meet those systems through learning resources. If a resource is written without logic and turns theory back into a pile of facts, the advantage of the theoretical system is lost.

  How approachable a discipline is to learners directly affects the speed of its development. This is one reason today’s flourishing natural sciences all have well-developed theoretical systems, while empirical sciences have gradually moved to the margins.

Part III | How Theory and Experiment Divide the Work

  A saying has circulated widely online in recent years: “Theory is when you know everything but nothing works. Practice is when everything works but no one knows why. In our lab, theory and practice are combined: nothing works and no one knows why.” A translation closer to the intended meaning would be: “Theoretical work understands every principle but has no practical value. Practical work produces results that work, but no one can explain why. Our laboratory combines theory and practice: none of our results is useful, and no one knows why.” The last line is pure self-mockery and can be set aside. The first two are exaggerated, but they contain some truth.

  My supervisor once told me that the ideal of computational chemistry is to guide experiment. How? With a sound theoretical framework and accurate calculations, theory can point out the right route before the experiment begins. Yet this ideal cannot always be achieved. Our research is often wholly disconnected from practice, but that does not make it meaningless. Accumulating such results adds brick after brick to theoretical science. A paper published several years ago in Science by my institute studied only the dynamics of a chemical reaction involving three atoms. The work was completely detached from practical application, but it was nevertheless excellent research worthy of Science. Theoretical work in every new field begins with the simplest cases and gradually develops until it can address real systems.

  Theory works through the reasonableness of its principles. I use “reasonable” rather than “correct” because no existing theory can be declared conclusively true. It is only reasonable at humanity’s current level of understanding; a sound approximation to a theory also counts as reasonable here. Only a reasonable theory can produce conclusions close to the facts, and that is the basis for testing a theory against reality. The requirement of reasonableness is both the strength and the weakness of theoretical research. The strength is that, given a sound theory, one can exclude every other interfering factor and obtain a completely “clean” result that is fully reproducible—something an experiment cannot achieve. The weakness is the point just made: a sound result requires a sound theory in advance.

  Experiment is almost the reverse. Its weakness is that no matter how carefully conditions are controlled, even the finest control-variable design cannot make every irrelevant variable identical. An experiment is therefore a chaotic system, and its results are less reproducible than theoretical ones. Researchers often publish a paper and then receive an email saying that its method cannot be replicated. Investigation may reveal a trace impurity on an instrument, or even a minute difference in impurities because the reagents came from another manufacturer. The strength of experiment is that any completed experiment produces a result. One need not know the reason beforehand, and the result is definite under the experimental conditions. The experimenters do not—and cannot—know those conditions completely or reproduce them exactly. They know only the few macroscopic variables they can control. In the examples above, they controlled many variables but did not foresee a tiny residue left on an instrument. Even without any understanding of the underlying principles, experiment can produce exciting and important discoveries. Theory cannot do that. Empirical conclusions differ from theories in this respect as well: many predict successfully even when their mechanisms remain unknown.

  The complementary qualities of theory and experiment naturally allow them to support one another in real research. If an experiment disagrees with a theoretical prediction and problems in the theory have been ruled out, the experimental conditions should be questioned. This is valuable when tracing experimental errors. Conversely, if a theory’s predictions consistently diverge from reality throughout a particular domain, the theory is probably not applicable there and should be improved or replaced.

  In general, a healthy discipline develops theory ahead of practice. Experimental science advances rapidly when guided by theory. In a discipline where applications run ahead of theory, the frontier often reaches a bottleneck and progresses slowly.

The author, Dclean, studied in the Department of Chemistry at Nanjing University and conducted research at the Institute of Theoretical and Computational Chemistry.