Transcript Philosophical Principles of Mathematics

Algebra and the Physics of
Motion
by
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1011 Nickel,
James
B.A., B.Th., B.Miss., M.A.
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Summary
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Algebra and Operational Science.
Algebra and its Symbols.
Biblical Christian Foundations.
The Physics of Motion.
Implications for Education.
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Algebra and Language
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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.
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Elementary Algebra
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Elementary algebra deals with simple
functions such as y = f(x) = 5x, y = f(x) =
3x2 + 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.
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Motions
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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.
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Motions
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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.
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Algebra and Symbols
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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.
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Algebra and Symbols
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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.
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Symbols and Law
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A simple equation can represent
(symbolize) the law that governs the
motion of the planets.
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Questions
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What governs the motion of the planets?
Is law impersonal as naturalistic science
would have us believe?
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Analysis
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Early scientists all believed that the God
of Scripture, being all-wise and allpowerful, created the universe.
They also believed that this same God
created man in His image (imago deo).
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Analysis
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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.
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Reality of Things: What is it?
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This “reality of things” involves the
interconnection of things, patterns, and
uniformity.
Without the belief in pattern and
uniformity, no science is possible.
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Open System
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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.
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Cause-and-effect
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The universe is a cause-and-effect
system which had a beginning; i.e., it is
not eternal in nature.
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Fruits
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The Scientific Revolution (16th and 17th
centuries) exploded with fresh and
vibrant revelations of this cause-andeffect system.
All of the technology of the modern
world has been a result of this mindset.
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Newton and His Heirs
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Sir Isaac Newton (1642-1727), coinventor 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.
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Mechanism
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“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.
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Mechanistic Man
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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.
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Modern Modern Science
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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.
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Implications
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Man, as a person imago deo, is
destroyed.
It is no mere coincidence that the 20th
century revealed the destruction of man
(through wars, genocides, and
infanticides), to a quantitative degree
unknown in the annals of human history.
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Back to our Question
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What governs the motion of the planets?
According to naturalistic science,
impersonal law, written in the form of
Algebra, governs this motion.
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In Contrast
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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.
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Christ: The Mediator of Creation
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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.
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The Vision of Mathematics
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Are we to see mathematics in the context
of the mechanistic impersonal or in the
context of a Living Person?
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Implications
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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).
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Dynamic
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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.
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Pertinent Scriptures
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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.”
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Pertinent Scriptures
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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.”
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Pertinent Scriptures
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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.’”
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Exposition
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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.
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Exposition
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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.
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Algebra in God’s World
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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).
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Algebra as a Tool
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Algebra consists of a set of tools that
helps you solve an equation involving an
unknown entity.
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Algebra and History
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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.
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Algebra and History
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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.
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Common Impressions
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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).
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Common Impressions
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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.
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Quadratic Equations: Remember?
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Quadratic equations, of the form ax2 + bx
+ c = 0 where a  0, can be solved by
using this formula:
b  b  4ac
x
2a
2
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Algebra, Motion, and Quadratics
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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.
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Algebra, Motion, and Quadratics
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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, 16th to 17th century army
generals were interested in this type of
analysis.
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Algebra, Motion, and Quadratics
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Astronomers like Johannes Kepler
(1571-1630) used these “second degree”
equations to mark the regulatory patterns
of the motions of the heavenly bodies.
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Algebra, Motion, and Quadratics
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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.
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Algebra, Motion, and Quadratics
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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.
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Algebra, Motion, and Quadratics
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In our jet age, scientists are able to trace
the shock wave of a sonic boom using
quadratic equations that describe
hyperbolas.
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Pedagogical Implications
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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).
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Pedagogical Implications
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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.
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Critical Puzzle Piece
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That critical piece, a piece missing for
every public or government school, is the
revelation of the God of Scripture.
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Biblical Christian Pedagogy
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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 lawword, the creation covenant, instigated and
sustained by the God of Scripture (see
Jeremiah 31:35-37).
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Biblical Christian Pedagogy
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Since all of God’s covenants are Christocentric, 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).
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Biblical Christian Pedagogy
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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.
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Steps to Christ
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Step 1: Abstract equation.
Step 2: History and the physics of
motion.
Step 3: Christ, in whom all things are
sustained.
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Biblical Christian Education
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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.
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Biblical Christian Education
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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!
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Summary
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Algebra and Operational Science.
Algebra and its Symbols.
Biblical Christian Foundations.
The Physics of Motion.
Implications for Education.
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Copyright  2008
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