BIBLICAL INTEGRATION IN MATHEMATICS: WHY AND HOW?
James Sellers
Assistant Professor of Mathematics
Cedarville College
One of the biggest issues in Christian higher education
today is the issue of Biblical integration or integration of
Scripture and faith. As a faculty member of Cedarville
College, I am faced with the challenge to integrate in the
classroom everyday. I must admit that Biblical integration in
mathematics is not necessarily as easy as it is in other
academic areas. In his book The Pattern of God's Truth, Frank
Gaebelein refers to mathematics as "the hardest subject to
integrate."1 However, I firmly believe that it is possible to
integrate in mathematics even if the opportunities are not
obvious.
My goal in this paper is laid out in the title. I will
answer the following two questions pertaining to integration:
1. Why integrate Scripture and faith in mathematics courses?
2. How can I integrate in mathematics?
One answer to the first question is that integration is
tied closely to the first objective of my teaching
institution, Cedarville College: "To undergird the student in
the fundamentals of the Christian faith, and to stimulate him
to evaluate knowledge in the light of Scriptural truth." This
objective of the college, as well as the others, guides me in
the education process; it drives me to integration.
But this is not the only reason to integrate. I believe
that there is a need for integration driven by the influence
of nonbiblical philosophies and worldviews prevalent in our
society today. What are some of these nonbiblical mindsets
that are infiltrating our lives? I will mention a few. Note
that this list is not meant to be exhaustive. My goal is
simply to highlight some of the worldviews that exist today.
In the late nineteenth century the theory of naturalism
emerged, whose most basic tenet is that nature is in control,
and that nature determines who or what survives. Man is
reduced to a mere animal, and human responsibility is reduced
to virtually nothing since man is a victim of nature. This
mindset opened the door for theories such as the theory of
evolution proposed by Charles Darwin. Naturalism clearly
denies the existence and power of God, as well as the ethical
and moral codes found in His Word, since man is at the mercy
of nature.
The theory of pragmatism then appeared during the
twentieth century as an attempt to "redeem" man from natural
determinism. This, too, clashes with Scriptural beliefs in
many ways. First, under pragmatism, man creates truth. Put
another way, truth is a product of man's action. Man, not
nature, determines, leading to a concept of free will.
However, we are also led to a view of relativism or relative
truth. We hear statements like "if it works, then it is truth
to him." Clearly, this contradicts the concept of absolute
truth or biblical truth. The concept of morality becomes
relative, dependent upon each individual.
But how can any of this apply to mathematics? After
all, isn't mathematics "above" all of this or separate from
it? Isn't it possible for mathematics to be viewed by theists
and nontheists alike without disagreements? The answer, which
is surprising to many, is no. The worldview of the
mathematician still influences his work and the view of his
work.
Let me give an example. How does a mathematician view
his latest result? When he proves a theorem, is he creating
this result or discovering it? There have been many letters
published in mathematics journals in the last few years
concerning this. Most humanists seem to believe that they are
creating new identities which did not exist before they
"created" them. Most theists, on the other hand, view their
work as discoveries of already existent, but previously
unseen, mathematical truths. Most theistic mathematicians
hold this view of "discovery" because of their view of God as
Creator. The humanist has no God and becomes creator himself.
Note now how the worldview affects one's attitude toward
mathematical work, as well as the giving of credit where
credit is due.
A second example along these lines is important. In his
recent book entitled Chance and Chaos,2 noted mathematician
David Ruelle compiles several short essays dealing with a
range of topics. One of the common themes throughout the book
involves the issues of chance and chaos and how they should be
viewed mathematically. Ruelle shares his thoughts on areas
such as classical determinism, historical evolutions, quantum
theory, intelligence, and even a mathematical view of the true
meaning of sex.
One of the elements of the book that I found most
fascinating was Ruelle's constant mentioning of the theory of
evolution. Indeed, the book is mathematical in nature, but
deals with the subject of evolution quite often. It is easy
to see how this topic fits in with the title of the book. It
is clear from statements such as the following that Ruelle's
worldview permeates the text and strongly guides his writing:
"The structure of living organisms has
changed a lot through evolution, by
the process of mutation and
selection, but the genetic code is so
basic that it has remained
essentially the same from bacterium
to humans. Presumably, in the first
hesitant steps of life, there was an
evolution of the genetic code. When
at a certain point an efficient
system was evolved, it killed off the
competition and survived alone."
"With the advent of sex, then, the
evolution of life can proceed much
faster. Mutations are still
occurring, of course, but a more
intelligent innovative process is now
also at work--the reshuffling of
genetic messages. And after the
reshuffling, selection operates, of
course, to keep the fit and the
lucky."
"Possession of higher functions was
of course beneficial, and encouraged
by natural evolution."
My goal here is not to single out David Ruelle,
but to cite a recent example of mathematical discussion
that is strongly influenced by the author's worldview.
As we strive to equip young men and women of Christ to
go into the world, we need to help them understand the
differences between theistic and nontheistic worldviews. As
one of the objectives of my college states, they need to
"evaluate knowledge in the light of Scriptural truth" at
this stage of their lives. We need to integrate so that our
students can be witnesses for Christ in such a way that
others will find them intellectually or logically valid.
With this somewhat general answer to the
first question raised at the beginning of this paper, I wish
to move to the second. How can I integrate in mathematics?
To answer this "how" question I want to discuss three
threads which can be developed in mathematics curricula with
integration in mind.
The first thread comes in the area of logic.
As a faculty member of Cedarville College, I
strive "to enable the student to develop sound
critical and analytic reasoning," which is the
fourth objective of the college. A logic class is
the perfect setting for this. In our mathematical
logic course, students are shown the basic
constructs of both propositional and predicate
calculus as well as the basic methods of proving
mathematical theorems. While discussing some of
the basic logical forms, passages of Scripture can
be used to provide examples. Students can then
begin to see the logical arguments used by the
biblical authors in proving points. Several
biblical authors employ numerous techniques of
logical proof in their arguments and students can
understand these constructions through a logic
course.
Examples of logical constructions in the
Word abound. For example, instances of universal
and existential quantification of predicates
appear frequently. These are statements like "for
all have sinned . . ." (Romans 3:23) and "there is
no one who does good" (Psalm 14:1). Constructions
involving conditionals, or "if / then" statements,
are also numerous. Paul's discourse concerning
Christ's resurrection in 1 Corinthians 15:12-19
contains at least six conditional statements, such
as "if Christ has not been raised, your faith is
worthless" (1 Corinthians 15:17). John includes a
conditional and its inverse, which are two
nonequivalent statement forms, when he says, "He
who has the Son has the life; he who does not have
the Son of God does not have the life." (1 John
5:12). By combining these two statements, John
develops a biconditional, or "if and only if"
statement: one has eternal life if and only if
one has the Son. This, of course, is one of the
cornerstones of the Christian faith.
Also, let me mention a proof strategy used by
Christ himself which is frequently used in
mathematics -- that is, proof by contradiction. In
this type of proof, the negation of the desired
result is assumed, proven to be absurd, and then the
desired result follows. In Mark 3:22-26, the
scribes believe Christ is casting out demons by
Beelzebul. To prove them wrong, Christ (implicitly)
assumes this, then goes on to argue that such action
is absurd. As Christ says, "And if Satan has risen
up against himself and is divided, he cannot stand,
but he is finished!" (Mark 3:26). This then implies
that Christ was not casting out demons through
Satan's power, but some other source, implicitly
God's power. This is a classic example of proof by
contradiction.
Note that I am not advocating that we look at
Scripture only from a logical framework. There are
many biblical truths that cannot be explained
"logically" but must be accepted by faith. (Take,
for example, the concept of the Triune God, three in
one.) However, as I mentioned in my remarks above,
I believe we need to be equipping our students with
an ability to produce valid logical arguments as
they go out into a highly intelligent, sophisticated
world. A. W. Tozer once wrote:
"There is, unfortunately, a feeling in
some quarters today that there is
something innately wrong about learning,
and that to be spiritual one must also be
stupid. This tacit philosophy has given
us in the last half century a new cult
within the confines of orthodoxy; I call
it the Cult of Ignorance. It equates
learning with unbelief and spirituality
with ignorance, and, according to it,
never the twain shall meet."3
If a believer's logic is poor or invalid when
witnessing, then the unbeliever is less likely to be
receptive. We must be able to serve as apologists
when needed. Frank Gaebelein writes, "Our task is
not only to outlive and outserve those who do not
stand for God's truth; it is also by God's grace to
outthink them."4
The second thread concerns the practical
application of mathematics to the physical world.
One of the largest uses of mathematics is that of
modeling the physical world around us, the world of
our Creator. We can model the orbits of the
planets, the flow of blood through an artery, the
trajectory of a ball thrown in the air, and
countless other phenomena. But as we do so, the
Christian mathematician has an excellent opportunity
to simultaneously honor the Creator and exhibit the
limitations of the creature.
First, modeling of many phenomena, like
atmospheric conditions and weather patterns, ignores
many variables. Because of the complexity of the
creation, we are forced to simplify our models to a
great degree in order to get a handle on them. In
this we see how little man understands compared to
the knowledge of God. We can merely approximate the
true phenomena; in most cases we cannot achieve
exact models.
Most mathematical methods are indeed
approximative. Does this make the mathematics
useless? Certainly not. We can approximate desired
values with as much accuracy as is deemed necessary
and then minimize the error. (This is done, for
example, when using 3.14 as an approximation of the
number p, whose decimal representation does not
terminate.) However, we must admit that there is
often some error in the process. George Polya once
wrote:
"Although almost invariably in science we must begin
with what is only an approximation to the truth, we
need not rest content with it. A crude
approximation can be made to lead to a less crude
approximation; a good approximation to a better one.
That the notion of successive approximation is a key
to more exact knowledge makes it a worthwhile
study."5
Let me also point out that much of mathematics
also appears quite "exact." Clearly, for example, 2
+ 3 = 5. No approximation is necessary here! But
now the question should be asked: Is this absolute
truth? The answer is no, for this fact is based on
a set of axioms, or postulates -- the Peano
Postulates. All mathematics is based on a set of
axioms, whether it be Peano's for arithmetic or
Euclid's for Euclidean geometry. However, if the
axioms are changed, then the "mathematical truths"
based on the axioms can also change.
For example, in a nondecimal system, 2 + 3 may
not be 5. In a base 4 system, the value of 2 + 3 is
11 (to be read "one one", not "eleven"), since, in
decimal numbers, we have
1*4^1 + 1*4^0 = 1 + 4 = 5 = 2 + 3.
So 2 + 3 = 5 is certainly not absolute. Our
students need to see this distinction between
absolute truth and truth based on axioms. Although
mathematics is one of the purest of sciences, it is
based on an axiom system or belief system and,
therefore, does not generate absolute truths.
The third thread that I will mention involves
areas such as calculus and differential equations.
Typically, the material in these courses does not
lend itself to integration. The integration
normally discussed in a calculus class is not the
kind of integration that I am concerned with in this
paper. However, there are some ways that
integrative discussions with students can be
achieved.
For example, topics such as radioactive decay
and carbon dating arise within the calculus course.
In most textbooks, examples and homework problems
involving the age of the earth or the universe
appear. These can be used as springboards for
discussions involving origins. Assumptions made in
such problems can be discussed, and the issues of
worldview and its effect on one's perception of a
problem can be analyzed. I have found these
interactions quite lively, especially as students
with differing scientific worldviews and backgrounds
interact.
Similar mathematical problems have arisen
when the historicity of events in the Old Testament
are challenged, usually by skeptics. A classic
example of this is the account of the Red Sea
crossing in Exodus 14. While striving to invalidate
Scripture, some have argued that it was impossible
for the whole nation of Israel to have crossed the
Red Sea in one day (or one night, as some interpret
the passage). Another such critique of Scripture
involves the growth rate of the nation of Israel
while in Egypt. It seems absurd to some that Israel
could have grown so large in such a short amount of
time.
These sorts of "rate" questions can be
studied using differential equations. Using
reasonable assumptions, the problems can be studied
and the plausibility of such historical events in
the Bible can be documented. However, I must state
one strong caveat. Plausibility does not imply
proof. We must not replace God's Word and its
truthfulness with plausibility and probability. The
fact that some event is plausible, or even highly
probable, does not imply that a scientific proof has
been achieved. This is especially true in the area
of origins. I believe students need to realize this
and should discuss this in the classroom.
Ultimately, we should go back to the Bible and rely
on it in any matter.
As I close, let me comment on some general
aspects of a Christian professor's life which I
believe should be apparent, especially if one wishes
to integrate. I believe that integration can take
place outside of the classroom, away from the
chalkboard. The courtesy with which I treat
students, the justice shown in the grading process,
the compassion and "listening ear" evidenced in the
office, the conversations held at the gymnasium
during a basketball game, and the prayers offered
for students, family, and friends all should appear
in the life and work of an integrating faculty
member. Moreover, not all integration needs to be
canned or planned. Questions that surface and
discussion that occurs in the class should be guided
through a pathway lined with integrative truths.
I end this paper with a comment from a former student which
sums up this insight:
"You never had to force in the occasional bit of 'Biblical
integration,' because your faith permeated everything you did."
Notes
1Gaebelein, Frank, The Pattern of God's Truth: Problems of Integration in
Christian Education, Moody Press, Chicago, 1968.
2 Ruelle, David, Chance and Chaos, Princeton University Press, Princeton,
N.J., 1991.
3Gaebelein, Frank.
4Gaebelein, Frank.
5Polya, George, Mathematical Methods in Science, The Mathematical
Association of America, Washington, 1977.