As a student of mathematics, I have begun to understand the importance of axioms, self-evident ideas on which conceptual structures are based, and I regard the act of establishing or agreeing with axioms as courageous, in the knightly sense of the word. Taking on an axiom is a naked and vulnerable commitment to an idea which may, at a later date, be proven completely wrong, but it is a necessary commitment for all scientific inquiry and advancement.

Scientific Courage

I am not alone in this appreciation for scientific grit.

In his book “The Structure of Scientific Revolutions,” the American physicist Thomas Kuhn distinguishes between two types of scientific research: normal science, and revolutionary science. He defines “normal” science as research conducted in a framework of existing rules, called a “paradigm,” wherein progress adds to the accuracy and precision of measurements, like adding pieces to a puzzle with an established border. When novel observations or anomalies are discovered, normal scientists will justifiably dismiss them as outliers, so that new questions do not challenge the existing paradigm, but rather strengthen it. “Revolutionary” scientists will instead look closely at novel observations and use anomalies as a basis to devise alternative paradigms, boldly exploring uncharted territory, with the possibility of discovering that earlier assumptions were wrong. In contrast to normal science, revolutionary science is not cumulative, and leads to a revision of existing beliefs. In both cases, scientists must take the risk that their research will return contradictory results or fail to supply rigorous evidence.

Kuhn discusses the necessity for scientists to “focus attention on a small range of relatively esoteric problems,” so that they may reach otherwise unattainable depths. This focus implies a sacrifice in cross-disciplinary understanding; if they are wrong at square one, specialization can result in a researcher’s life’s work being a failure. We see that scientists must also have the courage to specialize, which always carries the largest risk.

When this small range of problems becomes limited, or the paradigm stops producing functional results through normal scientific research, scientists must change and sometimes completely abandon older research methods.

A “paradigm shift” is a change in axioms and has occurred at almost every major scientific breakthrough over the past centuries. As a famous example, in the 18th century, it was believed that “phlogiston,” a fire-like element, was a substance present in all combustible material, and which was necessary for combustion. By 1777, Antoine Lavoisier had proven this theory to be false by using closed vessels to demonstrate that certain metals gained mass when burned, despite the idea that they were supposed to lose the mass of phlogiston. In its place, Lavoisier contributed the “oxygen theory of combustion,” and launched a much more strict and rigorous era of chemical research. During each shift, it follows that where one paradigm fails, another paradigm succeeds. Revolution is consistent across the history of science, because we cannot get rid of one idea without finding something better.

Looking at the state of modern science, with computing power growing at Moore’s exponential rate, paradigm shifts are occurring much more frequently than in the past, with the major exception of theoretical physics, which is stuck on Einstein’s theory of relativity — despite major progress in the mathematics of theoretical physics, researchers have made very little addition to the physical dimensions of the discipline. Modern scientists will need to be prepared for massive axiomatic changes heralding entirely new disciplines and fields of study. Damasio’s own field, neuroscience, is only in its adolescent stage compared to long-running disciplines like physics, astronomy, chemistry and biology, but its novel insights into the inner workings of the mind are beginning to have profound consequences in medicine and artificial intelligence, among many other fields.