In this blog post, we explore what the essence of science is and where its beauty stems from, based on the philosophies of science by Karl Popper and Thomas Kuhn.
It was a long time ago. As a first-year high school student, I was faced with the first situation in my life where I had to make a decision on my own. It was the choice between the liberal arts and science tracks. My parents left the decision entirely up to me, telling me to choose what I liked and not to regret it. Despite the unspoken convention among people that “those who dislike math go into liberal arts” and the reality that all my close friends were heading into liberal arts, I ultimately chose the science track. Because, for me, natural science is the most beautiful discipline.
More than any grand reason about contributing to human civilization or changing our lives, I found it beautiful that planets move in elegant circular orbits governed solely by universal gravitation (though gravity isn’t the only influence), that throwing a stone into the air follows the trajectory of a quadratic function graph derived from mathematics, and that in chemical reactions, molecules transform into products through random effective collisions.
As you can see here, I am arguing that beauty is one of the properties of natural science. However, science possesses properties that are too different from traditional beautiful disciplines—art, music, literature, and so on. The latter disciplines might even have been born with the purpose of pursuing beauty. Natural science, which describes nature, has a character distinct from other disciplines.
Regarding the question “What is science?”, 20th-century philosophers of science engaged in fierce debate. First, the Vienna Circle, which swept through early 20th-century philosophy of science, proposed a logical positivist view of science, arguing that science is formed through induction. Specifically, it held that scientific knowledge is generated and justified through induction via three stages: first, unbiased data collection; second, generalizing from collected facts to derive hypotheses; and finally, testing these hypotheses through new observations and experiments. This view was highly plausible as it aligned well with the common image of research activities discovering natural laws from objective facts. However, induction always involves an extension of content, leading to a critical flaw: even if the premises are true, the conclusion’s truth is not guaranteed. Furthermore, the feasibility of unbiased data collection sparked significant controversy.
At this juncture, Karl Popper (1902-1994) proposed falsifiability instead of verification, arguing that principles in natural science cannot be perfectly proven but only falsified. Specifically, Popper defined scientific activity as follows:
1. Propose a hypothesis that appears to explain the given problems well.
2. If empirical evidence is found that contradicts the hypothesis, discard it immediately. If not, retain the hypothesis. At this point, one must not claim the hypothesis has been proven. One can only say it has withstood several rigorous empirical tests.
In other words, he argued that the nature of science is falsifiability, and if something cannot be falsified, it is not science. From this, astrology, creationism, and the like can all be classified as pseudoscience, and one can even conclude that mathematics, which constructs its system through perfect premises and deductive reasoning, is not science. However, falsificationism, which pursued perfect logic and described scientific progress in an extremely rational manner, also encountered difficulties. First, there are indeed scientific theories that cannot be falsified. For example, statements asserting the existence of certain entities, such as “black holes exist” or “genes exist,” are impossible to falsify. More critically, falsification is harder than one might think. Consider judging the truth or falsity of the proposition “All crows are black.” Suppose there actually existed a gray crow. Could we then immediately conclude that not all crows are black? To reach this conclusion, we would need additional premises such as ‘our color vision is accurate enough to distinguish colors precisely’ or ‘we possess the ability to distinguish crows from other birds’. For scientific theories, the hypotheses required for falsification are more numerous and complex, making it even harder to declare a theory false based on a single counterexample.
This gap between the ideal and reality of scientific theories led to the emergence of Thomas Kuhn (1922-1994), who emphasized historical facts. He defined the development of science as two processes: “normal science” and “scientific revolution.” Normal science expands the application of knowledge within an existing paradigm, while a scientific revolution replaces the paradigm itself. A notable point here is that when a scientific revolution occurs, the paradigm shift differs from Popper’s claim—that through trial and error using the methodology of conjecture and refutation, science moves toward a more objective and rational direction. Kuhn argued that when a paradigm shifts, not only does our worldview change, but the world itself changes. The truth of nature is not something possessing an original form like rubber clay; rather, it changes according to the interpretation of the observer—that is, the scientists. Ultimately, this led to the theory of incommensurability. The existence of a common denominator is a precondition enabling two numbers or polynomials to be compared; incommensurability means, quite literally, that theories belonging to different paradigms cannot be compared with each other. Here, it shatters Popper’s theory that scientific theories develop cumulatively into more fundamental and better theories, asserting that no hierarchy exists between paradigms.
The greatest divergence between Popper and Kuhn lies in the gap between ideal and reality. Popper showed no interest in the actual history of scientific development, instead presenting an ideal of science concerning which science is more desirable. He proposed a rational, objective scientific norm that approaches truth through constant trial and error, undergoing the baptism of falsification. In contrast, Kuhn presents the reality of scientific development, arguing that while it may seem irrational, it has functioned successfully, making it difficult to find a more ideal methodology than the actual operating principles. Perhaps these two theories themselves are incommensurable. In terms of presenting the nature of science, these theories can be seen as equally valid.
Among these theories, where might the special nature of natural science emerge? Is it in the methodology of scientific development, or does it arise from the existence of paradigms as Kuhn argues? I believe both claims are correct. The use of a distinct “scientific” methodology, or the existence of such paradigms, stems from the fact that science is underpinned by nature. Science directly engages with nature and attempts to understand it. While nature may sometimes appear in different guises, the existence of a universal and consistent natural world is likely the most crucial factor making science special.
I believe the beauty of science stems precisely from the nature of science discussed above. The characteristics of generality, unity, and simplicity inherent in nature constitute the fundamental aesthetic qualities of natural science. Or, according to Kuhn’s theory, these aesthetic qualities are values universally accepted by scientists. He argued that because contemporary scientists share these values, paradigms form, and paradigm shifts occur when the weighting of these values changes. Aesthetic characteristics not only lend science its appeal but also significantly contribute to its development. Indeed, when constructing scientific theories, we approach them and formulate hypotheses using methodologies that consider this generality, unity, simplicity, and precision. A prime example is Dirac’s establishment of quantum electrodynamics by unifying classical electromagnetism and quantum mechanics. He mathematically described the complex quantum mechanics with perfect precision, guided by “mathematical beauty.” In this process, Dirac emphasized the beauty of nature and adopted the value of unity as his methodological principle. Simplicity also served as a core guiding principle in the development from Aristotelian mechanics to Newtonian mechanics.
Thus, beauty functions not only as an inherent property of science but also as a methodology for scientific advancement. Just as Popper adopted falsifiability as a scientific methodology, I believe that the methodology of pursuing beauty has actually driven scientific progress.
