A student of mine was recently making up some lab work, and the lab was a simple analysis of the variables that affected the motion of a pendulum bob as it oscillated back and forth. In this inquiry-based lab, the student was to gather data on how the pendulum bob mass, the amplitude of oscillation, and the length of the pendulum affected the amount of time it took the pendulum to oscillate. They were to use these data to come to conclusions about how an oscillating pendulum behaved.
As usual many students come to this lab work with a certain pre-conceived notion (what I like to call “intellectual baggage”) of how they think the pendulum is supposed to behave – most think that all three variables (mass, amplitude, and length) will affect the pendulum period (time for a complete oscillation) pretty much equally. Imagine their surprise when they end up discovering, assuming they are true to the process and not “tweaking” the data, that the mass and amplitude have relatively little or no effect on the pendulum motion – a fact that might also surprise the reader of this article!
In fact, when the student making up the lab got to that point in the work, he asked me a question I’ve heard numerous times before in such inquiry-based lab work: “Mr. Lowry, this seems weird – is that what I should be getting for an answer?”
When I get that question I like to answer, summoning up as much a sagely wisdom-filled voice as I can muster, “What you think the answer should be is irrelevant. What is relevant is what the data tell you.”
This anecdote of mine is particularly illustrative, I think, concerning an issue that is at the heart of pretty much all science as well as much philosophy, especially regarding philosophical discussions regarding the nature of reality, existence of God, etc. It focuses in upon a key assumption that, in my opinion, is a fatal flaw in much reasoning concerning these (and other) topics: too many people assume that, usually based upon some kind of belief system, the universe should function or behave as we would have it and – even worse – appeals to this sort of reasoning should, without the need for any other analysis or argumentation, settle whatever matter there is in question. The idea that the universe is somehow limited in the same manner as our own thinking is downright laughable to me as a scientist, teacher, skeptic, and armchair philosopher.
Allow me to illustrate the point more clearly with a classic philosophical argument regarding the existence of God. This ontological argument, an a priori argument which is made through reason alone with no appeal to direct interaction with the world around us, was first made by the great rationalist philosopher Rene Descartes. It involved an appeal to well-understood (for the time) geometrical principles and a strictly logical analysis to argue that God – as Descartes envisioned this being – did indeed exist.
The crux of Descartes’ ontological argument goes like this: If one defines a triangle as the geometrical structure outlined by straight line segments which are bounded by three non-collinear points, then the sum of all the internal angles of this triangle will always add up to 180 degrees, with no exceptions. This analysis is a strict, logical deduction based upon the assumptions that Descartes made in his definition of a triangle followed by an application of well-understood (or so it was thought) geometrical principles.
Descartes then used an almost identical form of argumentation, along with replacing the definition of a triangle with an appropriate definition of God, to make an analogous argument for the existence of God. To quote Descartes’ formal argument directly from his Meditations on First Philosophy, he states:
-
Whatever I clearly and distinctly perceive to be contained in the idea of something is true of that thing.
-
I clearly and distinctly perceive that necessary existence is contained in the idea of God.
-
Therefore, God exists.
Based upon arguments such as these, for many a year, it was assumed by many people that the perfection of basic & fundamental geometrical principles of the universe served as a strong argument for God’s existence, since the logical form of the argument regarding triangles is analogous to this argument for the existence of God. And note that because this argument was based solely upon the reasoning powers (and underlying beliefs) of the arguer, it necessarily assumed that our human reasoning alone is sufficient to address such questions without appeal to anything beyond that reasoning – such as actually examining the world around us.
Of course, as any serious student of mathematics knows, there is a fundamental and fatal flaw in Descartes’ reasoning: it assumes that the understanding of the world within the context of Euclidean (or flat) geometry is sufficient to describe the universe. And this assumption is incorrect, because it was shown in the 19th century that a different kind of geometry existed called non-Euclidean (or curved) geometry, and non-Euclidean geometry challenged some very, very basic notions which are so fundamental that most of us just naturally assume them to be true, just as Descartes did.
For example, how many of us have heard – and subsequently believe it because it “just makes sense” – that the shortest distance between two points is a straight line? In Euclidean or flat space, this is true, but in non-Euclidean or curved space it isn’t – in curved space the shortest distance between two points is a curved path called a geodesic. And remember Descartes’ ontological argument starting with triangles? Well, there’s a twist there as well: it ends up his argument is sound when dealing with Euclidean space, but not in non-Euclidean space where the internal angles of a triangle can add up to either more or less than 180 degrees depending upon the specific curvature of that space. Needless to say, this presents a problem for Descartes’ arguments and their subsequent conclusions because in light of this evidence one must begin to question the premises of the ontological argument.
And before the reader provides an anticipated criticism, it should be noted that non-Euclidean geometry is not simply relegated to the realm of ideas (like Descartes’ ontological argument) – non-Euclidean geometry in fact exists in reality. That’s because it is the geometry that is used to describe the mathematics of Einstein’s theory of general relativity, one of the most thoroughly and successfully tested physical theories in science. General relativity describes the world of strong gravitational fields quite accurately, and we have technology (such as GPS receivers) that is based upon the physics and non-Euclidean geometry of general relativity. When you use the GPS in your car or on your iPhone, you can see the clear-cut reality of non-Euclidean geometry in action.
But look what just happened: in the course of a few paragraphs I put paid to the notion that we can use our preconceived notions (or beliefs) of the world to draw solid conclusions upon certain subjects. If we fall into the trap of assuming, without actually examining the universe around us and performing the proper tests of our preconceptions, that the world caters to our beliefs, then we will – more often than not – end up deceiving ourselves. And this is why the modern scientific method and skeptical outlook, of which doubt of our own assumptions is a key ingredient, is critical to gaining a truer and more accurate view of the universe.
As I tell my students, we have one of two choices when viewing the world around us: we can take the conceited view that it should behave as we would expect and wish it to do so (and subsequently wallow in our own ignorance); or we can learn to put our assumptions on the back burner, carefully and systematically examine those assumptions, and deal with the universe on its own terms in the manner of how it actually works.
The choice is ours to make.
Matt Lowry is a high school & college physics professor with a strong interest in promoting science education, skepticism and critical thinking among his students and the population in general. Towards these ends, he works with the JREF on their educational advisory board, and he also works with a number of grassroots skeptical, pro-science groups. In what little spare time he has, he blogs on these and related subjects at The Skeptical Teacher.