Tag Archives: Science

The Role of Imagination in Science, Part 1

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In Zen and the Art of Motorcycle Maintenance, author Robert Pirsig argues that the basic conceptual tools of science, such as the number system, the laws of physics, and the rules of logic, have no objective existence, but exist in the human mind.  These conceptual tools were not “discovered” but created by the human imagination.  Nevertheless we use these concepts and invent new ones because they are good — they help us to understand and cope with our environment.

As an example, Pirsig points to the uncertain status of the number “zero” in the history of western culture.  The ancient Greeks were divided on the question of whether zero was an actual number – how could nothing be represented by something? – and did not widely employ zero.  The Romans’ numerical system also excluded zero.  It was only in the Middle Ages that the West finally adopted the number zero by accepting the Hindu-Arabic numeral system.  The ancient Greek and Roman civilizations did not neglect zero because they were blind or stupid.  If future generations adopted the use of zero, it was not because they suddenly discovered that zero existed, but because they found the number zero useful.

In fact, while mathematics appears to be absolutely essential to progress in the sciences, mathematics itself continues to lack objective certitude, and the philosophy of mathematics is plagued by questions of foundations that have never been resolved.  If asked, the majority of mathematicians will argue that mathematical objects are real, that they exist in some unspecified eternal realm awaiting discovery by mathematicians; but if you follow up by asking how we know that this realm exists, how we can prove that mathematical objects exist as objective entities, mathematicians cannot provide an answer that is convincing even to their fellow mathematicians.  For many decades, according to mathematicians Philip J. Davis and Reuben Hersh, the brightest minds sought to provide a firm foundation for mathematical truth, only to see their efforts founder (“Foundations , Found and Lost,” in The Mathematical Experience).

In response to these failures, mathematicians divided into multiple camps.  While the majority of mathematicians still insisted that mathematical objects were real, the school of fictionalism claimed that all mathematical objects were fictional.  Nevertheless, the fictionalists argued that mathematics was a useful fiction, so it was worthwhile to continue studying mathematics.  In the school of formalism, mathematics is described as a set of statements of the consequences of following certain rules of the game — one can create many “games,” and these games have different outcomes resulting from different sets of rules, but the games may not be about anything real.  The school of finitism argues that only the natural numbers (i.e., numbers for counting, such as 1, 2, 3. . . ) and numbers that can be derived from the natural numbers are real, all other numbers are creations of the human mind.  Even if one dismisses these schools as being only a minority, the fact that there is such stark disagreement among mathematicians about the foundations of mathematics is unsettling.

Ironically, as mathematical knowledge has increased over the years, so has uncertainty.  For many centuries, it was widely believed that Euclidean geometry was the most certain of all the sciences.  However, by the late nineteenth century, it was discovered that one could create different geometries that were just as valid as Euclidean geometry — in fact, it was possible to create an infinite number of valid geometries.  Instead of converging on a single, true geometry, mathematicians have seemingly gone into all different directions.  So what prevents mathematics from falling into complete nihilism, in which every method is valid and there are no standards?  This is an issue we will address in a subsequent posting.

Science, Authority, and Knowledge

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Harvard psychologist Steven Pinker argues in a recent essay praising the virtues of science:  “Most of the traditional causes of belief—faith, revelation, dogma, authority, charisma, conventional wisdom, the invigorating glow of subjective certainty—are generators of error and should be dismissed as sources of knowledge.”

This is the sort of sweeping statement that one is apt to make when making an abstract case for the scientific method without examining too closely how scientists actually acquire knowledge in the real world.  The fact of the matter is that no one — including the most brilliant of scientists — can acquire knowledge without relying on social processes that include hierarchical authority and “conventional wisdom.”

How does a psychologist such as Steven Pinker know about the Big Bang theory of the universe?  Did he purchase a telescope, conduct his own observations, track the movement of the galaxies, and come to the conclusion that the universe began with a big bang?  No, like the rest of us, he was taught the Big Bang theory in school.  He had neither the time nor expertise to critically evaluate whether or not his teachers might have been wrong.  He had to accept their authority because there was no good alternative.  “Faith” might be too strong a word, but there is a certain degree of trust that when specialists in physics write textbooks and give lectures, they are providing the truth, as best as they are able to.  In an earlier time, Pinker would have been taught not the Big Bang theory but the Steady State theory of the universe — and he would have accepted that, without trying to verify it himself through empirical observation, because that was the conventional wisdom.

How does Pinker know that the theory of evolution is true?  Did he study living organisms and fossils for years and years, matching each empirical observation with the claims of Darwin, Stephen Jay Gould, and others?  No, he accepted what his teachers taught him, for the same reasons he accepted the Big Bang theory.  Like everyone else, he trusts the specialists that are doing their jobs, and when these specialists have a strong consensus that something is true, he accepts this.

What happens when there are outstanding disagreements among scientists, whether involving string theory, multiple universes, the “punctuated equilibrium” theory of evolution, or other issues?  Does Steven Pinker get right to work on these issues, making his own observations, and testing multiple hypotheses?  No, like the rest of us, he either pleads ignorance, accepts the findings of the most recent article he’s read on the subject, or tries to gauge the majority opinion of scientists on that issue and adopts that opinion as his own.

Now, I’m not trying to discredit science here.  I fully accept the Big Bang theory and the theory of evolution, and I have a low opinion of various attempts at “creationist” theory.  But I didn’t arrive at these conclusions by disregarding authority, but by embracing authorities that seemed to me to be genuinely interested in studying the real world, willing to share their methodologies and observations, accept criticisms, and change their minds when necessary.

We are born into this world as ignorant as the lowest animal, we gradually absorb knowledge from our parents, teachers, peers, and our culture, and we may — if we are very, very lucky — make one or two truly original contributions to knowledge ourselves.  Even the most hardheaded skeptic, the bravest dissenter, the most diligent and persistent questioner, cannot do without some reliance on authority and conventional wisdom.