Science in Christian Perspective
SPIRITUAL TRUTHS IN MATHEMATICS
Angeline J, Brandt
Prof. of Mathematics
From: JASA, 2, (June1950): 19-22.
One may well question the title of this paper for surely few people would think of finding God in a mathematics lesson. One expects the manner of presentation of mathematical material in a Christian institution to be the same as that in any university. It is agreed that the mathematical facts presented would necessarily be the same. However, I have found that there are certain analogies between these facts and spiritual truths and it is a delight to bring these to the minds of students and urge them to make some of their own comparisons. This does not mean that the mathematics lesson becomes a time of devotion nor does it mean that an endeavor is made to spiritualize everything. Just a passing remark is made and it seems that the mathematics involved is remembered longer because of the illustration given. A few examples will show how this is accomplished.
Nearly every person., whether engaged in scientific work or not,, will soma time in his life be confronted with postulational thinking. By postulational thinking, we mean simply deductive reasoning that is based on some defined torms, undefined terms and beginning axioms and postulates. In everyday life, certain decisions and judgments are made by postulational thinking when definite rules have boon set up governing the problem at hand. Euclidean geometry is the classic example of a geometry built upon postulates. But when a mathematician decides to build a new geometry or some other system of mathematics, he sets up his system of postulates and then is careful that no violation is made of this system. These postulates must be consistent. They need not be eternal verities since for each system they are only human assumptions. However, it is necessary that there be certain basic principles and definitions upon which to build, A mathematician, who has a sense of the vast consequences which arise from certain antecedents, can surely appreciate what it means to establish one's faith firmly on an eternal verity like John 1.1, "In the beginning was the Word, and the Word was with God and the Word was God. from certain antecedents, can surely appreciate what it means to establish one's faith firmly on an eternal verity like John lil, "In the beginning was the Word, and the Word was with God and the Word was God. If one believes this, other important truths will follows There is the "if-then" reasoning in postulational thinking. If by faith we accept the truth that "in the beginning God" we proceed upon a firm foundation and can build our thinking upon such a fact.
Usually people classify scientists as people who know and it is rarely felt that faith is an essential element for a scientist. President George Do Birkhoff.. past president of the American Association for the Advancement of Science, stated
some few years ago in his retiring address to that body that "whether it is the mathematician dealing with number, or the physicist with matter, the biologist with organism, the psychologist with mind, or the sociologist with social values, there Is behind one and all an inherent faith guiding the reasoned superstructure which they create upon intuitional concepts." He emphasizes faith as an "heuristically valuable, more general point of view, beyond reason, often in apparent contradiction, which the thinker regards as of supreme importance as he endeavors to give his conclusions the greatest possible scopo.1 If an outstanding mathematician recognizes the need of faith in scientific reasoning,. is it not plausible that we must accept
1 J, W, Lasley, Jr., "Mathematics and the Sciences," Mathematics, Our Great Heritage (New Yorks Harper and Brothers, 1948) p. 190.
certain facts by faith? "Through faith vie understand that the worlds have been framed by the word of God,, so that what is soon hath not boon made out of things which do appear." (Hebrews ll.3). Either we accept the Word of the Scriptures by faith or we have to reject it on the grounds that the principles derived from the facts in it are untenable. It would seem that a mathematician then might reasonably be the one who would recognize the need of faith rather than the one who would say, "If it cannot be demonstrated, I will not believe."
As before mentioned., a set of postulates must be consistent. One can not violate or disregard any of them when establishing a new mathematical system, If one does so, he may find it necessary, in the end, to discard a whole body of truth thought to be correct. A person may not be willing to accept one law or truth found in God's Word and may feel that as long as he accepts the majority of the Bible, all is well but he may rest assured that the discarding of part of the Word is the beginning of disaster. Is it any wonder that the solemn warning is given in the very last chapter of the Bible concerning "taking away from the words of the book of this prophecy?" (Rev. 22.19)
There is no branch of mathematics which needs fear a searching into its foundations, A scientific study of the foundations is welcomed from century to century. The bases of Euclidean geometry have been more firmly fixed through a thorough search into its foundations, Christianity, too, need fear no searching inquiry. Throughout the centuries. Christian scholars have investigated the basic truths of Christianity but all of this inquiry has only led us to know more assuredly that the truths of God's Word are eternal verities. Mathematics is a body of consistent thought which has maintained itself for generations and has withstood the attacks of logic and the tests of practical life. The certainty of mathematics is not absolute; it is relative. But as Professor Carmichael of the University of Illinois has suggested we have a moral certainty for the consistency and permanence of mathematical truth for "when thousands of -persons through thousands of years examine thousands of theorems proved by numerous methods and in numerous connections and there is always absolute unanimity in the compelling character of the demonstration and the consistency of the results, we have a ground of moral confidence so great that we can dispense with the proof of logical certainty and comfortably lay out our lives on the hypothesis of the permanence, consistency and accuracy of mathematical truth."2 Surely we can say that throughout the ages.. what Christ has to offer to mankind has worked. The claims which He made for Himself cannot be denied, Thousands of persons through thousands of years have found that He has been all that He claimed to be.
The Concept of Infinity
Ono cannot go far into the field of mathematics without some concept of infinity, nor is it long before a child fools the inadequacy of the numbers which he knows. Some years ago a six-year old nephew asked his mother what a Ph.D. in mathematics meant. She replied that it meant that one knew a great deal about numbers. He immediately inquired if he could ask me any question he wished about numbers upon my next visit. His question was "What is the biggest number in the world?" When I tried to explain to him that there there always larger numbers than any he could mention,, he did not seem to understand and only expressed disappointment in my lack of mathematical knowledge. God trios to give us some concept of infinity in His Word Y&on He says, "God telleth the number of the stars; He calleth them all by their names" (Psalm 14714), or again, "The very hairs of your head are all numbered" (Matthew 10130). As human beings we realize that the stars in the heavens and the hairs of
2Robort D. Carmichael, "The Larger Human Worth of Mathematics," Mathematics, Our Great Heritage (New York: Harper and Brothers, 1948) p. 285.
our head are impossible to count and as we begin to got some grasp of the bigness of
numbers, the greatness of our God is impressed upon us.
Or say to college students, "Take the numbers 1,2,3,4.,5, ... indefinitely. Now
secondly take, 2,4,6,3,10, ... indefinitely." Then ask, "Are there not just as many
numbers in the second class as in the first class, since to each number one can have
its double to correspond to it?" So there are as many numbers in the second class
as in the first class but the second class is only part of the first class, or in
other words-, the part is equal to the whole This gives one a helpless feeling
about the whole concept of infinity. One can take away from infinity (take away
the odd numbers in the first class) and still have infinity left.
So, how long will eternity be? Is there any way to express its endlessness? Perhaps the Lord wanted to bring to our attention the limitations of man's mind in regard to this matter when He says, "One day is with the Lord as a thousand years., and a thousand years as one day" (2 Peter 30). The best illustration of1the concept of infinity I can think of giving the student, and I find it is one he never forgets, is the last verse of the hymn, "Amazing Grace." The hymn writer puts it this ways
When we've been there ten thousand years, Bright shining as the sun, 7.7161ve no less days to sing His praise, Than when we first begun."
The student admits that it is inconceivable to take away ten thousand years from infinity and still have infinity left. To the human mind it is inconceivable, but in eternity our minds will not be bound by the finite. Only our own ignorance makes it impossible to conceive the idea. Does this not show how much greater our God is than any human being and are we not constrained to say with the Psalmist, 'What is man, that thou art mindful of him? and the son of man, that thou visitest him?" (Psalm 8:14). Surely the unending character of eternity forces one to face the issue squarely as to where he or she individually will spend this unending time.
Or think for a moment concerning space. Just where-does space end, or does it have an end? Why do we stop at three dimensions? With two variables one expresses the equation of a straight line in a plane, with three variables one expresses the equation of a plane in three dimensions, But now write an equation with four variables What kind of a figure does one got? Have dimensions given out? Architects and physicists talk of four dimensions. "In architectural ornamentation. Claude Bragdon has shown the beauty in tracerios that depend on four-dimensional order."3 Physicists have tried to create a four-dimensional space-time world. But if four dimensions, why not have more? Where is to be the stopping place in this speculation concerning dimension? Many a religious skeptic will say that he does not believe that there is a possibility of a world beyond, but this saw person will probably admit the probability of a dimension beyond the third or fourth. Does this not show us the bounds of human Impotence? Where is place for boasting then?
In the study of algebra, one learns that in the addition of two unlike signed numbers, that the positive addend has to be larger than the negative addend if the sum is to be a positive number. The negative number may well speak of the downward pull of sin in one's life. It takes the positive grace of God to send him in a positive direction,, The hymn writer caught the idea when he wrote,. "Grace that is greater than all our sin."
3 James Byrnie Shaw, "Mathematics - The Subtle Fine Art of Mathematics, Our Great Heritage (New Yorks Harper and Brother, 1948) p.42.
The Functional Concept ,
Relations in the world ate infinite in number. Mathematics is sometimes defined as the science of relations. Word problems in algebra require that a mathematical law be formulated which expresses the relationship between variables, For example, if a train travels at a uniform rate of speed, the distance traveled depends upon the time. The functional concept., or the idea of one quantity depending upon another, runs throughout the whole of mathematics, The human race is dependent upon a Being higher than itself, and it is only as the individual is rightly related to God and to His Son Jesus Christ, and he finds complete satisfaction in life# As the change in value of one variable affects the result so a change in ones relationship to the Lord Jesus Christ affects one's whole sense of life values.
Or think of the solution of a linear differential equation when the equation is not solvable until an integrating factor is introduced. As soon as this factor is introduced, the equation becomes exact or falls into some type which is readily solvable. Christ is the integrating factor in the individual's life. When He is introduced, and life's interests are integrated about Him, the problems in life resolve themselves into solutions.
Variables and Constants
In mathematics, we desire to find some unifying element, or unchanging law, about which other domains of truth may be systematically organized. In invariant theory, we are interested in certain combinations which have an unalterable value under certain transformations, "The laws of nature are expressions of invariant "4 relations under the changes occurring in nature or brought about by directive agency. Most of us are interested in the "constants" of life. In the realm of one's earthly life, there are many variables; everything is changing but in the midst of it all,, there is the unchanging Christ, who is the "same yesterday, today, and forever" (Hebrews l3t8). Happy is that one who finds that under the transformations of life, Christ remains constant, and is the unchanging one.
In analytic geometry, if the center of a conic section does not lie at the origin of the coordinate system, the axes are translated so that the equation of the curve is simplified. There are many advantages in having the center of the curve coincide with the center of the coordinate system. Here is an opportunity to speak of the translation in the spiritual realm of which the apostle Paul wrote in Colossians l.l3. "Who hath delivered us from the power of darkness, and hath translated us into the kingdom of His dear Son," for does not translation into the kingdom of His dear Son mean, among other things, a changing of the center of one's life and interests?
Other analogies could be given, such as the logical order of-the system of truth in the mathematical realm, the contribution of one law to another, and the definite pattern of the whole,, all of which is revealed in the world about us, but perhaps enough has been said to show that it is Rr conviction that mathematics should mean more than just mathematics to the Christian students And surely the challenge is ours as Christian teachers to make our subject contribute something to the spiritual life of the students entrusted to us.
4 Robert D, Carmichael, "The Larger Human Worth of Mathematics," Mathematics Our Great Heritage (Now York: Harper and Brothers, 1948) p. 277.