Sept. 2, 2007 — -- School begins again, and we read more about the intrusion of pseudoscience into school science curricula in this country, particularly into the study of biology and evolution.
The motive, despite the claims of proponents of intelligent design and other bogus "disciplines," has been religious. Although some of the creation scientists' arguments presented have a probabilistic flavor, the mathematics curriculum has seemed somewhat resistant to this trend. Recently a number of readers have sent me course descriptions from various schools that suggest otherwise, however.
The issue is complicated (perhaps too complicated for a column), but I'll also briefly discuss the relevance of evolution to a more defensible, but still flawed argument relating religion and mathematics.
Consider first a Baptist school in Texas whose description of a geometry course begins:
Students will examine the nature of God as they progress in their understanding of mathematics. Students will understand the absolute consistency of mathematical principles and know that God was the inventor of that consistency. They will see God's nature revealed in the order and precision they review foundational concepts while being able to demonstrate geometric thinking and spatial reasoning. The study of the basics of geometry through making and testing conjectures regarding mathematical and real-world patterns will allow the students to understand the absolute consistency of God as seen in the geometric principles he created.
I wonder if the school teaches that non-Euclidean geometry is the work of the devil or at least of non-Christians.
The Web site's account goes on like this for a while and then is followed by similar descriptions for algebra and pre-calculus. The blurb for the calculus course states:
Students will examine the nature of God as they progress in their understanding of mathematics. Students will understand the absolute consistency of mathematical principles and know that God was the inventor of that consistency. Mathematical study will result in a greater appreciation of God and His works in creation. The students will understand the basic ideas of both differential and integral calculus and its importance and historical applications. The students will recognize that God created our minds to be able to see that the universe can be calculated by mental methods.
Intermediate Algebra: Using Variables to Manage the Total Possibility of Numbers and Solve Practical Problems
Its New Age calculus sequence is described thus:
Calculus 1: Derivatives as the Mathematics of Transcending, Used to Handle Changing Quantities
Calculus 2: Integrals as the Mathematics of Unification, Used to Handle Wholeness
Calculus 3: Unified Management of Change in All Possible Directions
Calculus 4: Locating Silence within Dynamism
Of course, there are more sophisticated ideas that are vaguely similar, and there have been first-rate scientists who have taken mathematics to be some sort of divine manifestation. One of the most well-known such arguments is due to physicist Eugene Wigner. In his famous 1960 paper, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences," he maintained that ability of mathematics to describe and predict the physical world is no accident, but rather is evidence of a deep and mysterious harmony.
But is the usefulness of mathematics really so mysterious? There is a quite compelling alternative explanation why mathematics is so useful. We count, we measure, we employ basic logic, and these activities are stimulated by ubiquitous aspects of the physical world. The size of a collection (of stones, grapes, animals), for example, is associated with the size of a number and keeping track of it leads to counting. Putting collections together is associated with adding numbers, and so on.