To love our children well, we must equip them with a strong education in the sciences as well as the liberal arts.
In recent years, there has been withering criticism of liberal arts education. Perhaps this is because those most concerned about a meaningful university education work in liberal arts fields. Perhaps it is because what passes for the liberal arts has, in many places, been reduced to adolescent chatter, prompting a heated response by those who wish to avoid a descent into barbarism. But let us not forget that those of us who specialize in the sciences also have an important role to play in helping to preserve civilization.
Modern humans rely on a vast array of technology and depend upon science for its maintenance and extension. The impoverishment of scientific education is of great concern, because it will lead to a decline in scientific capability and will deprive students of exposure to some of the greatest creations of the human mind.
The Aim of Education
Any serious discussion of education must commence with a clear statement of its aim. In the conclusion of her 1954 essay, “The Crisis in Education,” Hannah Arendt asks two basic questions. First, do we love the world sufficiently to take responsibility for saving it from ruin by bringing forth a vibrant new generation? And second, do we love our children sufficiently not to leave them to their own devices, unprepared to face challenges unforeseen by us?
Sadly, it was not long after the publication of Arendt’s essay that American colleges and universities rushed headlong to abandon their educational responsibilities by eliminating their core curricula and weakening basic courses in mathematics and science. They decided that they did not love their children enough to equip them with the fundamental tools of intellectual inquiry.
The Nature of Scientific Knowledge
No matter one’s field of study, to be a serious scholar one must possess a deep appreciation of the kind of knowledge with which the field is concerned. Scientific knowledge concerns quantitative (geometric, numerical, and logical) relations among physical phenomena. The form of scientific knowledge is mathematical, but the epistemology of science does not stop there. For a mathematical model to constitute scientific knowledge, it must be validated. This is accomplished by performing experiments whose quantitative outcomes are predicted by the model and deciding whether the results justify acceptance of the model. Acceptance or rejection is always relative to a choice of predictions and validation criteria.
It is one thing to make this kind of general statement; it is quite another to make it operational. Indeed, there is no universal validation method, nor are there criteria that would be agreed upon by all knowledgeable parties. Science is not objective; it is inter-subjective. This means that those with sufficient mathematical expertise and knowledge of the experimental apparatus can agree on whether or not the theory should be accepted (relative to the criteria), but this does not mean that all agree on the criteria. Moreover, all theories are contingently accepted and always open to rejection based on similar criteria should new phenomena be observed, say, by superior instrumentation. What is not at issue, however, is the general epistemological structure, in particular, the requirement of quantitative predictions made prior to validating observations.
Much more is required of a scientist than simplistic notions of scientific method and falsifiability as an epistemological criterion. Method is a contextual issue, depending on the mathematical statements constituting the theory, the phenomena under investigation, and the experimental apparatus. Validity is far more subtle than determining whether some particular observation agrees with some particular prediction; indeed, scientific validation is necessarily probabilistic, so that deep statistical issues are always at play.
The History of Scientific Inquiry
Science has a rich history. Its ground has shifted from its totally empirical Egyptian-Mesopotamian beginnings to its twentieth-century formulation in terms of a mathematical-experimental duality.
To appreciate the full meaning of this duality requires a deep appreciation of the evolution of epistemology. At minimum, one should be familiar with the following concepts: Plato’s distinction between true knowledge in metaphysics and empirical shadow knowledge, as well as his theory of forms; Aristotle’s four types of cause and his requirement that knowledge be causal; Bacon’s insistence on designed experiments; Galileo’s bracketing of causality and focus on mathematical description of behavior; Newton’s systematic formulation of scientific knowledge grounded on deduction from basic laws; Descartes’s attempt to reduce science to rationalism; Hume’s demolition of induction and causality as being neither logically nor empirically demonstrable; Kant’s reinterpretation of causality as a category of understanding necessary for thinking about the phenomena; and the twentieth-century recognition of the statistical characterization of predictions as the ground of validity in the light of nature’s unintelligibility.
Just as a weak historical grounding leaves a liberal arts student prey to popular ideologies, a scientific education devoid of the great perspectives leaves a science student prey to contemporary prejudices. “Data mining” and “big data,” for example, are two pre-Galilean approaches that have surfaced with a vengeance today. As Albert Einstein astutely observed,
A knowledge of the historic and philosophical background gives that kind of independence from prejudices of his generation from which most scientists are suffering. This independence created by philosophical insight is—in my opinion—the mark of distinction between a mere artisan or specialist and a real seeker after truth.
What Makes a Good Scientific Education?
Beyond philosophy, a good scientific education includes a solid base in mathematics and statistics. For the most part, today’s physicists get a good mathematical education. This is not so for most engineers, even though modern engineering is characterized in terms of mathematical operations. The situation is far worse in biology, whose complexity dwarfs that of physics and engineering, so that its mathematical requirements are even greater. Absent the requisite mathematical training, one is left to mere storytelling or to the generation of multi-colored visualizations from unstructured data using canned computer software. To those in the liberal arts, this might be compared to analyzing the “works” of the latest talk show literati.
Because statistics forms the bond between theory and phenomena, rigorous education in statistics is critical for scientific education. This presents a significant hurdle, since serious statistics requires substantial mathematical training and often is counter-intuitive, especially when dealing with complex systems. There is a temptation to simplify the analysis to a point where it is intelligible to one who has only superficial statistical knowledge, which often is more dangerous than no knowledge at all. Recognizing their own weakness in statistics, many scientists include statisticians on their research teams, innocently believing that the chosen statistician is competent—after all, he holds a PhD from some elite university. Frequently, that belief is misguided.
When Alain Dupuy and Richard Simon of the National Cancer Institute conducted a detailed analysis of forty-two studies published in 2004, they found that twenty-one of them (50 percent) contained at least one of three basic flaws. And, because Dupuy and Simon only considered an error estimate to be flawed if it was calculated incorrectly, the situation may actually be much worse. Many researchers use error estimation methods that are simply not applicable under their experimental conditions, regardless of whether they are correctly calculated. As might be expected, the vast majority of erroneous research findings are favorable to the authors’ claims.
Authority, Barbarism, and Truth
The resulting pseudo-statistical balderdash is symptomatic of a deeper cultural problem. In 1930, José Ortega y Gasset wrote:
Whoever wishes to have ideas must first prepare himself to desire truth and to accept the rules of the game imposed by it. It is no use speaking of ideas when there is no acceptance of a higher authority to regulate them, a series of standards to which it is possible to appeal in a discussion. These standards are the principles on which culture rests. . . . Barbarism is the absence of standards to which appeal can be made.
Scientific epistemology uses standards developed over centuries in order to ground knowledge within a functional, phenomenal, and inter-subjective concept of truth. These standards constitute science’s higher authority. But this authority must be manifested by human beings who are sufficiently educated to make judgments in accordance with that authority. If educators fail in their responsibility to educate, then the higher authority becomes vacuous, because there will not be enough people who can exercise it well.
Today, the higher authority of which Ortega y Gasset speaks is largely absent, because educators have shrunk from the burden of their responsibility. Educators—and, in particular, those educational administrators who are responsible for curricular design—must renew their commitment to giving students the tools they need to investigate and to take responsibility for the world in which they live.
Educational Formation: The Scholar and the Dilettante
The desire for truth is infused into a young person by the culture in which he is raised and by the persons of authority around him. If, as in Aristotle’s best-governed state, persons of authority extol the “realization and exercise of virtue,” with virtue being “the result of knowledge and purpose,” then one might expect many citizens to desire profound knowledge. However, if persons in authority provide an “education” based on childish relativism, then it is highly unlikely that men will thirst for truth. Indeed, such chatter breeds indifference to truth.
Until recently, the desire for truth was at the heart of scientific inquiry. Of the early scientists, historian Morris Kline writes, “The search for the mathematical laws of motion was an act of devotion; it was the study of the ways and nature of God and His plan of the universe.” Perhaps one cannot expect such devotion to science when it is no longer about the nature of God. Nevertheless, truth must still be the driving force behind the scientific enterprise—otherwise, it will degenerate into mere chitchat. To avoid such degeneration, students must be given a mature appreciation of the transformation of epistemology from Aquinas to contemporary quantum theory.
As long as technical advances continue, even if they represent negligible achievement—think of computer games and similar gadgets—the general public thinks that science is still vibrant. Even nonscientific intellectuals may be unaware of the degeneration. Every year, more “scientific” papers are published, with increasingly vacuous content. As long ago as 1974, engineer Thomas Kailath commented, “It was the peculiar atmosphere of the sixties, with its catchwords of ‘building research competence,’ ‘training more scientists,’ etc., that supported the uncritical growth of a literature in which quantity and formal novelty were often prized over significance and attention to scholarship.”
The key word in Kailath’s comment is “scholarship.” Its pursuit differentiates the authentic scientist from the dilettante. Scholarship in science involves rigorous mathematics, deliberate experimental design, and careful statistical analysis. These requirements do not block novelty; in fact, they are required for worthwhile novelty. When novelty is detached from significance, it becomes insubstantial.
The Vocation of the University
Regarding the catastrophe that befell the liberal arts in the 1960s, Allan Bloom pointed out that the university no longer believed in its higher vocation. He wrote, “The American universities in the sixties were experiencing the same dismantling of the structure of rational inquiry as had the German universities in the thirties. . . . The university had abandoned all claim to study or to inform about value – undermining the sense of the value of what it taught, while turning over the decision about values to the folk, the Zeitgeist, the relevant.”
Why would one expect science not to suffer a similar fate? Science depends on a most critical value: thirst for knowledge concerning nature. If the university no longer puts the satisfaction of that thirst first and foremost, then it undermines the teaching of science, mathematics, and engineering. In doing so, it abandons scientific rational inquiry and scholarship in favor of data collection, data crunching, dubious algorithms, and computer visualizations. If our culture becomes so depleted that Plato’s dialogues, Kant’s critiques, Newton’s laws, and Einstein’s theories do not quicken the pulse and fill the heart with awe, then I fear that our souls will have become too impoverished for us to be true men of science.
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