seeing god in creation through mathematics by james nickel, b.a., b.th., b.miss., m.a. copyright ...

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Seeing God in Creation Through Mathematics

by

James Nickel,

B.A., B.Th., B.Miss., M.A.

Copyright 2008www.biblicalchristianworldview.net

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Thesis

• The infinite, personal, and Triune God revealed in Scripture is the foundation for understanding and doing mathematics.


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Language• Sir Oliver Graham Sutton (1903-1977), “The

universe, both as a whole and in its microstructure, suggests that in neither aspect can it be treated merely as an enlarged or diminished version of the world which we know through our senses. The ultimate secrets of nature are written in a language which we cannot yet read. Mathematics provides a commentary on the text, sometimes a close translation, but in words we can read because they are our own.”


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Intelligence

• Heinrich Hertz (1857-1894), “One cannot escape the feeling that these mathematical formulas have an independent exis tence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally put into them.”


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Reality

• Godfrey H. Hardy (1877-1947), “I believe that mathematical reality lies outside of us, and that our function is to discover or observe it, and that the theorems which we prove and which we describe grandiloquently as our ‘creations’ are simply notes of our observations.”


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Truth • Philip E. B. Jourdain (1879-1919), “Some

philosophers have reached the startling conclusion that Truth is made by men, and that Mathematics is created by mathematicians, and that Columbus created America; but common sense, it is refreshing to think, is at any rate above being flattered by philosophical persuasion that it really occupies a place sometimes reserved for an even more sacred Being.”


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Proximate and Ultimate

• Proximate: close to (what we experience and observe).

• Ultimate: far away (God, the transcendent One).


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Logos

• Genesis 1:1, “In the beginning God created the heavens and the earth.”

• John 1:1-3, “In the beginning was the Word, and the Word was with God, and the Word was God. He was in the beginning with God. All things were made through him, and without him was not any thing made that was made.”


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Logos • Colossians 1:15-17, “He [Christ] is the

image of the invisible God, the firstborn of all creation. For by him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities—all things were created through him and for him. And he is before all things, and in him all things hold together.”


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Church History

• Athanasius (ca. 293-373) stood contra mundum (against the world) of Arian heresy (that purported Christ as not being fully God).

• In this context, he recognized the significance of a fully rational and wise God creating a fully rational and good (interconnected and interacting) creation.


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Against the Heathen • After citing John 1:1, Athanasius described the

universe as a divine hymn: “For just as though some musician, having tuned a lyre, and by his art adjusted the high notes to the low, and the intermediate notes to the rest, were to produce a single tune as the result, so also the Wisdom of God, handling the Universe as a lyre, and adjusting things in the air to things on the earth, and things in the heaven to things in the air, and combining parts into wholes and moving them all by His beck and will, produces well and fittingly, as the result, the unity of the universe and of its order …”


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Against the Heathen

• “He produces as the result a marvelous and truly divine harmony.”


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What is Mathematics? • “The spirit of genuine mathematics, i.e., its

methods, concepts, and structure–in contrast with mindless calculations–constitutes one of the finest expressions of the human spirit. The great areas of mathematics–algebra, number theory, combinatorics, real and complex analysis, topology, geometry, trigonometry, etc.–have arisen from man’s experience of the world that the infinite, personal, Triune, and Sovereign God has created and currently sustains.”


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What is Mathematics? • “These branches of mathematics,

constructively developed by man made in the image of God [imago deo], enable man to systematize the order and coherence (the unity in diversity … the proximate one and the many) of creation mediated to us by the Creator and upholder of all things–the logos and wisdom of God revealed in the person of the Lord Jesus Christ.”


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What is Mathematics?

• “This systematization not only gives man a tool whereby he can take effective dominion over the creation under God in Christ, but also gives man the experience and enjoyment of a rich intellectual beauty that borders the sublime in its infinitely complex, yet structured mosaic.”


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Mathematics: Two Complementary Contexts

• Practical, as a tool of dominion (personal, business, scientific).

• Beauty (seen via the study of its symmetry and structure); mathematics unveils fresh and exciting vistas into the nature of truth, beauty, and goodness.


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The Mystery of the Comprehensible

• Albert Einstein (1879-1955), “At this point an enigma presents itself which in all ages has agitated enquiring minds. How can it be that mathematics, being after all, a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? ... The eternal mystery of the world is its comprehensibility.”


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• John Von Neumann (1903-1957), “The relationship of mathematics to the natural sciences is quite peculiar, but this is the most vitally characteristic fact about mathematics.”


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• Nicholas Bourbaki (pseudonym for a group of 20th century French mathematicians), “Mathematics appears thus as a storehouse of abstract forms ... and it so happens–without our knowing why–that certain aspects of empirical reality fit themselves into these forms, as if through a kind of preadaptation.”


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• Eugene Wigner (1902-1995), “The enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious. There is no rational explanation for it.”


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The Confidence of the Comprehensible

• The fact that there is a correlation between the subject (man) and the object (creation) is no mystery for the Biblical Christian.


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• The infinite, personal, Triune, and sovereign God revealed in Scripture made the universe.

• This same God made man to live in the universe.


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• This same God gave man the Bible, verbalized, propositional, and truth revelation, to reveal to man what he needs to know.

• In the Bible, God gives comprehension to correlate our knowledge.


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• The reason why the Biblical Christian has no problem with the “mystery of the comprehensible” is because the all-wise God, being the ultimate in reason, made both things, the world outside of man and the world inside of man, the subject and the object … He is the creator of both.


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• Since the Biblical God is the creator of the physical universe that reflects mathematical properties and the human mind that can think in mathematical terms, the fact that the world is comprehensible is what we would expect!


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The One and the Many

• The Triune nature of God (One and the Many) forms the foundation for understanding the proximate “one and the many”–and mathematics is adept at unveiling this “unity in diversity.”


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Universals and Particulars

• Scientific law (a unity derived from a variety of observations).

• Scientific law reduces particulars into a universal.

• Scientific law is often written in mathematical form.


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Number: Unity in Diversity

• Number is unity (i.e., the concept of “oneness,” “twoness, “threeness,” etc.)

• Note: Numerals are symbols of number.

• This unity is revealed through diversity (one coin, two coins, three coins, four hens, five dogs, etc.).


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Number: Unity in Diversity

• Without a philosophy that confidently justifies the connection between unity to diversity, number is in limbo.

• That the world is comprehensible (in terms of mathematics) is a mystery only for those who reject God’s word is that starting point for knowing anything.


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Unifying Elements

• Why are there so many unifying elements in mathematics (functions, vectors, etc.), interlacing what initially appears to be completely diverse ideas invented independently by different people at different times in different parts of the world?


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Trigonometry

• Trigonometry was developed by mathematicians of Alexandria, Egypt (ca. 200 BC) and starts with ratios of the sides of a right triangle.


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Trigonometric Functions

• y = sin(x)

• In the 16th century, mathematicians developed analytical or coordinate geometry.

• The graph of this function is periodic or wave-like in nature.


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Trigonometric Functions


5

4.5

4

3.5

3

2.5

2

1.5

1

0.5

-0.5

-1

-1.5

-2

-2.5

-3

-3.5

-4

-4.5

-6 -5 -4 -3 -2 -1 1 2 3 4 5 6

f x = sin x

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Fourier Series

• The sum of trigonometric functions.

• In the 18th century, Joseph Fourier (1768-1830) uncovered this series in his study of heat.

• From right triangle ratios to the dynamics of heat!


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Stunning Connections

• Music (sound waves)–oscilloscope.

• Electromagnetic spectrum.

• Meandering rivers.

• Tides: ingoing and outgoing.

• Branch of a tree swinging in the breeze.


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• The swell of the ocean when the sea is smooth.

• Rotation of galaxies.

• Alternating current: ebb and flow.

• Radio waves (AM & FM).


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• Spring and bob motion, studied by Robert Hooke (1635-1705).

• John Harrison (1693-1776) used the theory developed by Hooke to invent the first practical marine chronometer.

• This clock enabled man to “conquer” the longitude.


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Super Law

• Isaac Newton (1642-1727) connected motion celestial with motion terrestrial with one law, described mathematically as the inverse-square law:


1 22

GmmF

D

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Inverse Square Law

• Law of Universal Gravitation.

• Electricity: Coulomb’s law.

• Intensity of light and sound waves at a distance.

• What unity in diversity!


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Golden Ratio

= extreme/mean ratio.

• Divide a line segment into two sections, one larger than the other.


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Golden Ratio

• If we set , then x = !

1.618


x

xx 1

1

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Stunning Unity in Diversity

• Infinite nested radical.


1 1 1 1

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• Infinite continued fraction.


11

11 1

1 11

1

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• Fibonacci Sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 134, …

• Related to how large populations grow often reflected in God’s created order.


n 1

nn

Flim

F

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Simultaneous Inventions

• Why are there so many simultaneously produced identical mathematical “inventions”?

• Calculus (Newton & Leibniz), Non‑Euclidean Geometry (Gauss, Lobachevsky & Bolyai), and vector analysis (Hamilton and Grassman).


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Simultaneous Inventions

• It is like a group of artists who independently all find themselves painting the same gigantic picture; and some are painting the same parts at the same time!

• God, in His providence, orchestrates these historical unities in diversities.


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Language, Logos, and Unity

• Johannes Kepler (1571-1630), “The chief aim of all investigations of the external world should be to discover the rational order and harmony which has been imposed on it by God and which He revealed to us in the language of mathematics.”


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• Stanley L. Jaki (1924-), science historian, notes that in Kepler we find the “heroic groping of a great man of science with facts, with ideas, with perspectives, and not least with the need to arrive at a law which enabled the prediction of planetary positions with the greatest possible accuracy.”


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• Kepler saw harmony in the universe, a harmony derived from his commitment to God the Creator, not the sovereignty of number (as the ancient Pythagorean’s posited).


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• Harmony is only possible if one can discern patterns (unity) in observations (scientific and mathematical).

• Einstein, regarding Kepler’s approach as a basic principle of scientific work, comments, “Knowledge cannot spring from experience alone but only from the comparison of the inventions of the intellect with observed fact.”


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• Mathematics is a language.

• By learning this language you will be able to better sense the “language fabric” that sustains the universe (the logos of God in Christ).


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• Vern Poythress (1946-), “The created world, as result of God’s speech, bears within it from top to bottom a kind of quasilinguistic character ... through God’s act of creation, things in the world themselves become wordless voices to the praise of God.”


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• Larry Zimmerman, “It is possible, that mathematics is an entity which always exists in the mind of God, and which is for us the universal expression of His creative and sustaining word or power.... So we would expect the deepest scientific probes into the micro‑ or macro‑cosmos to reveal a language fabric in which are woven the forces and relationships governing the tangible creation.”


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• “This language fabric should itself be suggestive of an intellectual antecedent, an orderly, powerful, infinitude of thought, a ‘terra incognita of pure reasoning’ which ‘casts a chill on human glory.’”


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• Richard Feynman (1918-1988), “To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature.”


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• Larry Zimmerman, “Without the knowledge of the patterns of God’s speech in the creation, we are powerless to replenish the earth and will instead be subdued by it .... the lyric of the ‘music of the spheres’ is mathematics, a knowledge of which unveils not only vistas of beauty and power unsuspected before but also an order, symmetry and infinitude which stuns and awes the beholder.”


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Thesis

• The infinite, personal, and Triune God revealed in Scripture is the foundation for understanding and doing mathematics.


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Implications

• Resolves the mystery of comprehensibility.

• Justifies the “unity in diversity” that we see all around us.

• Frames mathematics where its picture of wonder, beauty, and power directs the observer to worship, in transcendent awe, the infinite, personal, and Triune Creator and Sustainer of all things!


seeing god in creation through mathematics by james nickel, b.a., b.th., b.miss., m.a. copyright ...

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