ecently, a woman asked what I thought of Michael Moore’s upcoming visit to Utah Valley State College. (Even now, months after Moore’s visit to Utah Valley, the fact that he was even invited remains a contentious local issue. Prominent donors and local businesses are threatening to boycott the college.) I expressed to her my support for the invite to Moore, keeping the lid on my simmering sentiments. Her thoughtful response was; “Well, I don’t like his music.”

Stumped, I sought clarification. Upon finding that she considered him a bad musician, I explained that Moore was a producer of documentaries, not music. Unfazed, she persisted; “Well, I’ve heard his music, and I don’t care for it.”

I admitted to being unfamiliar with Moore’s music (later satisfying my suspicions), but I insisted that he was not coming to Utah Valley as a musician. The invite was because of his recent documentary.

She wasn’t trying to pull the wool over my eyes. She really believed Moore was a musician. She knew from the disparaging talk of the locals that Moore was “bad”; she heard the general character assassinations but caught no specific offenses. Assuming that he was coming to perform, she drew a natural conclusion about his music. I suspect that she inadvertently generated a memory, or an erroneous mental link, to give a sense of legitimacy and personal independence to her view.

To her credit, she eventually yielded to my insistence that Moore was a film director. I failed to thank her for providing such a fascinating example of the fallout from certitude.

How is it that people fall into the trap of thinking that their religious or political views cannot possibly be wrong, to the point of supporting them with illusions? Some obvious suggestions come to mind.

Without reminders, some of us just don’t know when to get off the bus. We can’t help it. We are not to be ridiculed or castigated. It is a natural endowment and/or a product of our formal and informal education. Of course in our defense, virtually all of us qualify as dolts, given a narrow enough and high enough standard for comparison.

Some of us have intellectual tools enough to catch on, but the blinds are kept shut. Our eyes have adjusted to the shadows, and too much additional light causes discomfort.

Some of us are caught up in chasing and embracing illusions. We fail to realize, or we forget, that illusions can be comforting and delightfully distracting, but they make a dangerous foundation for our future.

Some of us, in a misguided defense of our image, concentrate on bolstering our previous conclusions. This is my preferred method for self-induced blindness, and I have noticed other people with at least one foot in that door.

A Short Trip

Actually, for most people, intellectual failure is more complex than what these inane explanations suggest. Consider this hypothetical experiment.

Let us imagine a visit to the Bonneville Salt Flats in Utah, which is renowned for its smooth surface. Every winter, the snow and water dissolves the salt and acts as a big Zamboni, leveling the surface bumps and nicks. Let us assume that last winter’s Zamboni did an exceptional job over a large region on the salt flats, leaving no detectable nicks or bumps, rises or dips.

We go to the northwest area of this region and with a fine-point felt-tip pen we mark the surface with a small red dot. We position our imaginary, hi-tech, touring vehicle facing south and directly over the red mark on the salt surface. Climbing into our vehicle, a small hovercraft, we start our simple journey. We head exactly south for ten miles, then exactly east for ten miles, then exactly north for ten miles. (Aren’t the salt flats lovely this time of year?) Finally, we turn left and travel west exactly ten miles, then stop.

Assume we have navigated meticulously and that our vehicle is capable of very sharp turns, perfect right angles to be exact. At the end of our simple trip, where will out hovercraft be? If you have had just enough geometry to guess that our path outlines a square, you might agree with some other intelligent people that our craft is directly over the red mark on the salt flats, or at least pretty close.

In truth, at the end of this perfectly executed journey, we will have overshot the red mark by more than 100 feet. A look at the longitudinal lines on a world globe will suggest one reason why we ended up so far off. The longitudinal line segments running through Utah don’t appear parallel. They are closer to each other at the north ends.

To resurrect an old accusation thrown at me by calculus students after a difficult test, some might cry, “You tricked us!” Indeed, I did, and I may just lose sleep over it; however, I am tempted to say that you tricked yourself.

You know the story of Columbus. You know the world is not flat. You’ve noticed longitudinal lines before. If you were tricked, it was because your focus was too small scale, leaving you with a flat-earth perspective. My intent was to show how easily we are fooled.

History provides a host of examples of more profound and enduring trickery than my salt flats example. Some stubborn, false beliefs have persisted virtually unchallenged through generations. Religion has provided its share of such beliefs; but surprisingly, the history of mathematics and science provides some of the most stunning examples.

Lost Opportunity

Around 300 BC, Euclid wrote a book on geometry, The Elements. It has been one of the most influential books in history. Euclidean Geometry helped us anticipate the nature of our surroundings; it helped us figure out the shape and size of the earth, it provided a classic example of logic and its usefulness.

Euclid gives a short list of postulates (axioms) upon which he develops Euclidean Geometry. However, through the years, the fifth (parallel line) postulate vexed some mathematicians. It was like the religious person’s axiom, “God Exists.” Some people believe that God must be taken on faith, as an axiom, while others believe that God can be proven, as a theorem. So it was with mathematicians and the fifth postulate.

The vexed mathematicians failed to prove the fifth postulate. In a strange twist of fate, one involved attempt at a proof by contradiction produced a logically sound system of geometry that did not coincide with Euclidean Geometry. The attempted proof appeared to be a total failure to most mathematicians of the day, and Non-Euclidean Geometry was cast off. Hundreds of years later, it was discovered that the once ridiculed system of Hyperbolic Geometry does in fact model aspects of our universe that Euclidean Geometry cannot.

Columbus, by mistaking the New World for the East Indies, helped dismiss the flat-earth myth. Einstein’s General Theory of Relativity helped place into question the Euclidean Universe concept.

The twists and turns continue. The General Theory of Relativity describes the cosmos, on a large scale, very accurately. Then, there is Quantum Physics with its set of axioms that accurately represent the cosmos, but only on a micro level. What unnerved the scientific world was that these two paradigms were incompatible. Super String Theory may be the next step in the quest for a unifying theory and in refining our ever-changing understanding of the cosmos.

The complexities of life are overwhelming. We each do our best to piece together a consistent model because we crave the security that knowledge brings. There are a few core axioms to which we cling. They influence us significantly. Besides our own observations and judgment, we are forced to rely upon the testimony and rational of a host of predecessors and contemporaries. We find that it is easy to be fooled, and we learn to distrust the evidence placed before us that contradicts our hard-won worldview. We naturally tend toward the habit of one-directional skepticism, testing all new theories against our own axioms. Thus, like a cherished pet, our certitude is fed and reinforced. Neither mathematicians, scientists, freethinking apostates, nor religious disciples are immune to the virus of one-directional skepticism.

In Summary

There are hazards to unyielding certitude. We may be partially or utterly mistaken. A few naive, ill-founded axioms can lead to unfathomable inhumanity. Even if our system of axioms is perfectly consistent in our narrow domain, there may be a bigger domain or a different domain for another group of people, for which another set of axioms seems to work.

Some people dismiss the scientist because of her/his godless agenda. Some people damn the free thinker who rejects their personal moral axioms. Some people over-simplify Islamic or Christian fundamentalism, claiming that fundamentalists see every difference as evil and a heavy-handed crusade as the only fix. Many people thrust their gods and heroes up as paragons of wisdom, while sheltering them from the sacred tempest of critical analysis.

Bertrand Russell (whose music, in my eyes, rivals Michael Moore’s) suggested that, “The biggest cause of trouble in the world today is that the stupid people are so sure about things and the intelligent people are so full of doubt.” Standing on the shoulders of Russell, and other philosophical giants, suggests another thought. The greatest source of trouble in the world today is intelligent people who ignore their own naivety and who fail to understand and give due credit to followers of a different moral geometry.