1. Algebra and the Physics of Motion by James Nickel, B.A., B.Th., B.Miss., M.A. Copyright  2008 www.biblicalchristianworldview.net

2. Summary Algebra and Operational Science. Algebra and its Symbols. Biblical Christian Foundations. The Physics of Motion. Implications for Education. Copyright  2008 www.biblicalchristianworldview.net

3. Algebra and Language Algebra is a language. Algebra is the language of operational science. Operational science: the science that deals with explanation, description, and prediction of God’s orderly world. Copyright  2008 www.biblicalchristianworldview.net

4. Elementary Algebra Elementary algebra deals with simple functions such as y = f(x) = 5x, y = f(x) = 3x 2 + 6x, and the like. As purely mathematical expressions they are dull, devoid of interest; but they can be and are used to represent an enormous variety of motions. Copyright  2008 www.biblicalchristianworldview.net

5. Motions The motions of balls, projectiles, rockets, and spaceships. Motion of the Moon, which exhibits striking contrasts with motion on the Earth, provides a fascinating exposition. Copyright  2008 www.biblicalchristianworldview.net

6. Motions The motion of objects dropped into water is another readily understandable and interesting phenomenon. Further exploration of simple functions leads to the law of gravitation, and to remarkable calculations such as the mass of the Earth and the mass of the Sun. Copyright  2008 www.biblicalchristianworldview.net

7. Algebra and Symbols Mathematics would be a cumbersome system if it would not be for its concise use of symbols. Symbols are not only shorthand notations; they are pictures that point to deeper truths. Copyright  2008 www.biblicalchristianworldview.net

8. Algebra and Symbols Functions are not merely symbolic expressions; they represent laws of the universe, and they encompass the behavior of grains of sand and the most distant stars. Copyright  2008 www.biblicalchristianworldview.net

9. Symbols and Law A simple equation can represent (symbolize) the law that governs the motion of the planets. Copyright  2008 www.biblicalchristianworldview.net

10. Questions What governs the motion of the planets? Is law impersonal as naturalistic science would have us believe? Copyright  2008 www.biblicalchristianworldview.net

11. Analysis Early scientists all believed that the God of Scripture, being all-wise and all- powerful, created the universe. They also believed that this same God created man in His image (imago deo). Copyright  2008 www.biblicalchristianworldview.net

12. Analysis The ability to reason is an attribute of both God and man. Hence, man, with his reason, can investigate the universe with the full confidence of “finding out the reality of things,” things of which include laws that can be described using Algebra. Copyright  2008 www.biblicalchristianworldview.net

13. Reality of Things: What is it? This “reality of things” involves the interconnection of things, patterns, and uniformity. Without the belief in pattern and uniformity, no science is possible. Copyright  2008 www.biblicalchristianworldview.net

14. Open System The birth of modern science required a belief in the uniformity of natural causes with a proviso: The grand system of the universe was limited or open. God could act in this system and man, made in God’s image, could restructure and reorder it. Copyright  2008 www.biblicalchristianworldview.net

15. Cause-and-effect The universe is a cause-and-effect system which had a beginning; i.e., it is not eternal in nature. Copyright  2008 www.biblicalchristianworldview.net

16. Fruits The Scientific Revolution (16 th and 17 th centuries) exploded with fresh and vibrant revelations of this cause-and- effect system. All of the technology of the modern world has been a result of this mindset. Copyright  2008 www.biblicalchristianworldview.net

17. Newton and His Heirs Sir Isaac Newton (1642-1727), co- inventor of the calculus, a method of analysis that requires symbolic Algebra in order to work, was the leader of this revolution. So successful was the program initiated by Newton, that his heirs began to forget the foundations. Copyright  2008 www.biblicalchristianworldview.net

18. Mechanism “Cause-and-effect” began to be seen as a “machine-like” perfection. There came a worldview shift: from the universe governed by the infinite, person, and Triune God of Scripture to a universe governed by impersonal, mechanistic law. Copyright  2008 www.biblicalchristianworldview.net

19. Mechanistic Man Eventually, man became part of this process and began to be viewed, not as imago deo, but as a machine, as a merely the collocation of interacting atoms and chemical processes, and the firing of neurons. Copyright  2008 www.biblicalchristianworldview.net

20. Modern Modern Science Francis Schaeffer (1912-1984) calls the result “modern modern science.” We still have the uniformity of natural causes (Algebra is still operative). The system is no longer open, it is closed and deterministic. All law-like patterns, and man included, are the product of impersonal + time + chance. Copyright  2008 www.biblicalchristianworldview.net

21. Implications Man, as a person imago deo, is destroyed. It is no mere coincidence that the 20 th century revealed the destruction of man (through wars, genocides, and infanticides), to a quantitative degree unknown in the annals of human history. Copyright  2008 www.biblicalchristianworldview.net

22. Back to our Question What governs the motion of the planets? According to naturalistic science, impersonal law, written in the form of Algebra, governs this motion. Copyright  2008 www.biblicalchristianworldview.net

23. In Contrast According to Colossians 1:15-17, all things visible and invisible cohere (or find their harmonious unity or reference point) in Christ. According to Hebrews 1:3, God upholds all things by the word of His power. Copyright  2008 www.biblicalchristianworldview.net

24. Christ: The Mediator of Creation A mathematical equation that describes the motion of planets is really a description of the faithfulness of God in Christ holding all things together. Christ is not only the mediator of redemption; He is the mediator of creation. Copyright  2008 www.biblicalchristianworldview.net

25. The Vision of Mathematics Are we to see mathematics in the context of the mechanistic impersonal or in the context of a Living Person? Copyright  2008 www.biblicalchristianworldview.net

26. Implications Far from being neutral in its relationship to God, mathematics draws its very life and sustenance from Him who is the essence of life  transformation (individually and culturally). Copyright  2008 www.biblicalchristianworldview.net

27. Dynamic The truth that God is the foundation of all knowledge, including mathematical knowledge, gives the Christian student a dynamic to learning that the non-Christian student does not possess. The Biblical Christian sees that mathematics is a wondrous tool that can be used to describe the order that exists in a universe made by the infinite, person, and Triune God. Copyright  2008 www.biblicalchristianworldview.net

28. Pertinent Scriptures Psalm 111:2, “Great are the works of the LORD, studied by all who delight in them.” Psalm 19:1, “The heavens declare the glory of God, and the sky above proclaims his handiwork.” Copyright  2008 www.biblicalchristianworldview.net

29. Pertinent Scriptures II Corinthians 3:18, “And we all, with unveiled face, beholding the glory of the Lord, are being transformed into the same image from one degree of glory to another. For this comes from the Lord who is the Spirit.” Copyright  2008 www.biblicalchristianworldview.net

30. Pertinent Scriptures Genesis 1:28, “And God blessed them. And God said to them, ‘Be fruitful and multiply and fill the earth and subdue it and have dominion over the fish of the sea and over the birds of the heavens and over every living thing that moves on the earth.’” Copyright  2008 www.biblicalchristianworldview.net

31. Exposition When one studies what God has made, then one will encounter a revelation of God’s glory–the inescapable weight of the sheer Godness of God. God’s glory, properly comprehended, transforms the beholder into the same image from glory to glory. Copyright  2008 www.biblicalchristianworldview.net

32. Exposition Mathematics is also an effective tool whereby we can utilize what God has made to fulfill man’s royal calling–to take dominion and rule the creation. Copyright  2008 www.biblicalchristianworldview.net

33. Algebra in God’s World With this background, we can now understanding the place of Algebra in God’s scheme of things. Algebra allows you to solve a mathematical problem that describes some aspect of God’s creation, whether scientific (as in the motion of planets) or dominion-mandate related (as in optimizing profit and loss for a business). Copyright  2008 www.biblicalchristianworldview.net

34. Algebra as a Tool Algebra consists of a set of tools that helps you solve an equation involving an unknown entity. Copyright  2008 www.biblicalchristianworldview.net

35. Algebra and History The ancient Egyptians used it to help build the great pyramids. The ancient Greeks began to develop and systemize it. Embellished somewhat by the Arabs. Copyright  2008 www.biblicalchristianworldview.net

36. Algebra and History Came into full-flowering in Christian Europe where the doctrine of the Trinity, the Ultimate, Infinite, and Personal One and the Many, and the Incarnation undergirded the cultural ambiance or matrix. Modern science (starting with the physics of motion) is built upon its mathematical symbolism. Copyright  2008 www.biblicalchristianworldview.net

37. Common Impressions The impression most people have of mathematics, if it is a good one, is that it is practical in terms of paying bills, figuring a mortgage, paying taxes, balancing a checkbook, planning for retirement (although computer tools do most of this math for you anyway). Copyright  2008 www.biblicalchristianworldview.net

38. Common Impressions A goodly number of people (too many, in my opinion) have bad feelings about math. They say: “I hate math” or “I’ve never understood math” or “Math was (or is) my worst subject in school.” The reason for these negative responses is what I call the “missing pieces” in math education. Copyright  2008 www.biblicalchristianworldview.net

39. Quadratic Equations: Remember? Quadratic equations, of the form ax 2 + bx + c = 0 where a  0, can be solved by using this formula: Copyright  2008 www.biblicalchristianworldview.net

40. Algebra, Motion, and Quadratics Quadratic equations came into the forefront of scientific thinking as a result of the study of motion (e.g., free fall, projectile motion, the motion of planets). If you consider an object’s motion in terms of time and distance, then these second degree equations describe the situation perfectly. Copyright  2008 www.biblicalchristianworldview.net

41. Algebra, Motion, and Quadratics Not only do they describe the situation, they enable the scientist to make predictions (e.g., the maximum height of a projectile, the time a projectile hits the ground, the distance a projectile travels before it hits the ground). Needless to say, 16 th to 17 th century army generals were interested in this type of analysis. Copyright  2008 www.biblicalchristianworldview.net

42. Algebra, Motion, and Quadratics Astronomers like Johannes Kepler (1571-1630) used these “second degree” equations to mark the regulatory patterns of the motions of the heavenly bodies. Copyright  2008 www.biblicalchristianworldview.net

43. Algebra, Motion, and Quadratics He was able to take an ancient Greek geometrical idea (the conic sections: the circle, the ellipse, the parabola, and the hyperbola) and use a combination of algebra and geometry (called coordinate geometry) to trace out the paths of the planets using quadratic equations that describe ellipses. Copyright  2008 www.biblicalchristianworldview.net

44. Algebra, Motion, and Quadratics Galileo Galilei (1564-1642) and Isaac Newton (1642-1727) were able to trace the paths of projectiles or objects in “free fall” using quadratic equations that describe parabolas. Copyright  2008 www.biblicalchristianworldview.net

45. Algebra, Motion, and Quadratics In our jet age, scientists are able to trace the shock wave of a sonic boom using quadratic equations that describe hyperbolas. Copyright  2008 www.biblicalchristianworldview.net

46. Pedagogical Implications Hence, the study of quadratic equations must be understood in the context of the “missing pieces” of history and science (particularly, the physics of motion). Copyright  2008 www.biblicalchristianworldview.net

47. Pedagogical Implications Very few math teachers do this (the reason why is because of the way these teachers are being prepared to teach the subject and their significant deficiency of scientific history and knowledge). Now, even if all math educators were taught to teach these equations in the context of history and science, there would still be missing the most important piece in the puzzle. Copyright  2008 www.biblicalchristianworldview.net

48. Critical Puzzle Piece That critical piece, a piece missing for every public or government school, is the revelation of the God of Scripture. Copyright  2008 www.biblicalchristianworldview.net

49. Biblical Christian Pedagogy We have given an equation that is replete with a wide variety of symbols. This abstract mathematical construct reflects a real or concrete physical situation; i.e., the physics of motion. The physics of motion is governed by the law- word, the creation covenant, instigated and sustained by the God of Scripture (see Jeremiah 31:35-37). Copyright  2008 www.biblicalchristianworldview.net

50. Biblical Christian Pedagogy Since all of God’s covenants are Christo- centric, then the motion of objects (whether terrestrial or celestial) are part of the “all things visible and invisible” that “cohere or hold together” in Christ (Colossians 1:15-17). Copyright  2008 www.biblicalchristianworldview.net

51. Biblical Christian Pedagogy Therefore, when a student learns quadratic equations in the context of biblical revelation, then that student is two steps away from a glorious and transforming revelation of the person of Christ. Copyright  2008 www.biblicalchristianworldview.net

52. Steps to Christ Step 1: Abstract equation. Step 2: History and the physics of motion. Step 3: Christ, in whom all things are sustained. Copyright  2008 www.biblicalchristianworldview.net

53. Biblical Christian Education Exposing the student to the realities of a Christ-controlled creation is what biblical Christian education is all about. Since Christ is the source and sustenance of creation and since Christ is the foundation and the treasure of all wisdom and understanding (John 1:1-3; Colossians 2:3), then we dare not teach any subject, even quadratic equations, without a reverential submission to Him. Copyright  2008 www.biblicalchristianworldview.net

54. Biblical Christian Education If the Biblical revelation of Christ is removed from the acquisition of any type of knowledge, then all we will know is surface or pseudo-knowledge. It is the revelation of Christ that brings true meaning, perspective, and purpose to every subject under study, including Algebra! Copyright  2008 www.biblicalchristianworldview.net

55. Summary Algebra and Operational Science. Algebra and its Symbols. Biblical Christian Foundations. The Physics of Motion. Implications for Education. Copyright  2008 www.biblicalchristianworldview.net