Feb 3, 2009 Fractals: The Intelligence of God’s Design – Is Creation a Series of Divine Algorithms?

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Fractals: The Intelligence of God’s Design – Is Creation a Series of Divine Algorithms?

by Gary Stearman

The illustrations accompanying this article are designs derived from a mathematical discipline that produces images called “fractals.” This word was coined by the French theorist Benoit Mandelbrot in 1975, and was used to describe the bizarre configurations that emerged from his unique mathematical analysis of the physical world. In that year, he revolutionized the way that science looks at a landscape. Two years later, he published the landmark Fractals: Form, Chance and Dimension.   What is a fractal? The Oxford American Dictionary calls it “… a curve or geometric figure, each part of which has the same character as the whole. Fractals are useful in modeling structures (such as eroded coastlines or snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth, fluid turbulence, and galaxy formation.” The word itself is derived from French, and the Latin fract, meaning “broken.” Observe that in the above definition, everything from crystals to galaxies can be described by fractal geometry. Large structures can be broken down into smaller and smaller ones, ad infinitum. Likewise, small structures can be expanded into larger ones … into infinity. The Encarta World English Dictionary says the following: “frac·tal n an irregular or fragmented geometric shape that can be repeatedly subdivided into parts, each of which is a smaller copy of the whole. Fractals are used in computer modeling of natural structures that do not have simple geometric shapes, for example, clouds, mountainous landscapes, and coastlines.” Plants, trees, land forms, mountains and clouds can now be modeled, using a few simple formulas. Mandelbrot’s ground-breaking discovery is that nature – from the very large to the very small – is formed of a myriad of repeating shapes. For the Christian observer, an intelligent pattern and plan emerge into plain sight. His imitators have inadvertently discovered that God chose to build the universe, using a system of repeating shapes. But for the secular scientific mind, the natural patterns have simply evolved according to the mathematical rules of fractals. At the heart of the debate: Did God create fractals, or do fractals create God? To the household of faith, the answer seems plain enough.   Doing Science   As we think of it today, the scientific method dates back to the 16th and 17th centuries. It involves observing a phenomenon, devising a hypothesis to explain that phenomenon and developing a test to prove or disprove the hypothesis. Early scientists proceeded on the basis that the visible creation could be attributed to God. Today, the scientific majority has doctrinally divorced itself from the concept of a Creator God. The rigorous discipline of the scientific method was once used to glorify God. In the 17th and 18th centuries, Isaac Newton visualized God as the one and only Master Creator whose existence was proven by the mathematical perfection of the universe. Now, the method has come to be called, “doing science.” It prides itself on being ahead of religious thought. Yet, from the Christian perspective, everything science discovers simply confirms biblical truth. This is especially true since the invention of computers, which have lately achieved the capacity to model reality so effectively that it is sometimes difficult to tell that you aren’t looking at the real thing. Using Mandelbrot’s formulas, clouds, mountains, water and every form of landscape can be duplicated by simply entering the appropriate formulas into video programs. Computer realism is daily becoming more spectacular. To believers, this scientific achievement reveals more the creative power of God than the mind of man. After all, the computer is only imitating that which is already real in nature … that which was created by God. Galileo, sometimes called “the father of modern science,” is held up as a scientific hero for discovering the moons of Jupiter, the rings of Saturn and the craters on the Moon. He upheld the heliocentric view of Copernicus that the Earth rotates around the Sun. However, Catholic authorities imprisoned him for making statements they called heresies. Galileo made them, based upon common observation. For example, he reported that our Moon has craters, Jupiter had its own moons, and Saturn had “ears,” his name for its rings, as seen through a primitive telescope. The priests objected, saying, among other things, that God’s creation is perfect, and that the Moon would not have blemishes like craters. After a series of epic battles with the Roman church, he was forced to recant his view that the earth rotates around the Sun. The closing years of his life were spent under house arrest. But time proved his theories to be correct. It wasn’t long before he came to be regarded as a hero in the quest for the scientific method. In a way, his conflicts with the religious authorities of the 17th century set the tone of the disagreement that persists to this day. Scientific authority still sees itself as ascending over theology, which it views as a stubborn and ignorant throwback to the superstitions of the past. Science now shapes the contours of society. It proudly expresses itself through supercomputers crunching massive quantities of data through speeding streams of electrons. With increasing rapidity, complex formulas become everyday reality. Boeing uses them to build airplanes; General Motors uses them to build cars. From the computer screen to the runway or test track is a symphony of keystrokes and robotic syncopation. In short, science creates, and never hesitates to celebrate its new role. Increasingly, as it has reduced nature to the intricacies of mathematical formulas, it has come to view itself as the creator. It has gone beyond the physics of the past, but in a way, it still worships them. The sacred geometry of Pythagoras, who lived five hundred years before Christ, has become the virtual reality of the computer screen. The Greeks believed that geometric forms held the mystical answers to creation, but their mathematics was not sufficiently developed to see how true their suppositions really were. The basic ideas of the ancient philosophers would have to rest through the centuries, until the development of modern mathematics, and then a while longer, for the invention of the computer. Today, tiny microprocessors can perform in seconds what would have taken a lifetime for a mathematician with pen and paper. Little could the ancients have known how right they really were. Their conjectured unknowable and untouchable god was, in fact, the very knowable Judeo-Christian God of Creation. And His methods actually express themselves as geometry. But it is a geometry that the Greeks could scarcely have imagined.   The Fractal World   It is based not only upon calculation, but million-fold reiterations performed at lightning speeds. The mathematical models of science enter daily life in make-believe worlds seemingly without end. Everything from “A” to “Z” – from astronomy to zoology, and all stops in between – is digitized, stored and studied with the thought of improvement. Science now looks at disease, poverty, pollution and starvation as shortcomings to be perfected. It foresees a man-made utopia. That, of course, is the dominant thought of twenty-first century culture. Computers have not only advanced science; they have become the dominant medium for public entertainment. The imaginary has become so realistic that an entire world of secular faith has been established. Movies become video games and alternate realities, in which one’s entire identity can be submerged in a fictional electronic world. This generation is accustomed to viewing life as a synthesis of digits, displayed on a video screen as imaginary worlds that surpass daily life. An entire generation has grown to adulthood in the 26 years since 1982, when a film called Tron first came to major movie theaters. It was a ground-breaking effort at making a realistic computer-generated motion picture. In the story, its major character (a real human being) becomes digitized. He is converted to an electron stream, enabling him to enter a computer world where he battles an evil force scheming to take over all the world’s computers and become their electronic leader. His artificial world bore little resemblance to our everyday physical world. It was a bizarre place of simple geometry … an artist’s conception of microchips given life. It seemed that almost overnight, this blockbuster movie gave birth to the idea of a computer-generated reality. Tron was the first film of its kind. The significance of this film is its convincing attempt to propose the reality of an electronic world. In rapid succession and increasing believability, other filmmakers quickly brought their digitized worlds to the silver screen. Films like Star Trek, Star Wars, The Matrix and a host of computerized Disney productions have since enthralled the child in all of us. As a society, the last generation has grown up believing in ideas that begin as written scripts, which are reduced to programmed visualizations real enough to ignite the imagination, and stimulate belief in the idealized worlds that whirl before our eyes. As mentioned earlier, these worlds are only feeble imitations of the one that God has already created. But importantly, computer programmers have learned techniques, which now give us remarkable insight into God’s creation. In effect, they have “reverse engineered” the earth’s existing panoramas to produce the pictures that are so persuasive to the human eye.   Fractal Computer Creation   To do this, computers are programmed, using what are called “algorithms” to turn patterns of numbers into pictures. An algorithm is simply a written pattern, procedure or routine for solving problems in mathematics. To create fractals, these algorithms are repeated hundreds, thousands or millions of times. The result of one logic loop feeds back into the next, and so on, until the desired end is reached. There is not a human being alive who could write fast enough over a long period of time to perform the required number of operations. In short, algorithms are instructions that can be followed by a computer. Their translation into visual realization had to await the invention of the high-speed computer. As computers of ever-higher speed repeat these algorithms over and over again (in operations numbering perhaps in the millions), they weave a recognizable picture. More than that, they are so convincing that human beings respond to them in an emotional manner. They have the air of reality.   They become spheres, loops, branches, mounds, peaks, swirls and every possible combination of the shapes that greet us as we go about our daily business on planet Earth. The illustrations that accompany this article demonstrate the range of fractal visualization. They might be vegetable, like the real-world fractal in a stalk of broccoli, a fern or a branching tree. They might be animal, insect-like or a variety of marine life. They might be mineral, like rocks and mountains. In fact, they have revolutionized the motion picture industry, creating the impressive visual landscapes that back up the action/adventure melodramas that blaze across the movie screens of the world. They are the vistas of science fiction; the fiery demise of a burning space platform, or the “middle earth” of Lord of the Rings, with its castles, walking trees, smoldering mountains and seething pools of lava. Repeated fractals can make everything from mountains to a convincing head of hair. But the main point that should not be forgotten is this: The incredible reality of these screen-worlds is possible only because they successfully mimic God’s creation. From the human perspective, they are quite complex; but when compared with the actual creation, they are ridiculously simple. Nevertheless, on a limited scale, they reveal the way our world is assembled.   God’s Computer Program   The more one thinks about the creative process, the more one is convinced that this world was created by programming a series of algorithms. God gave instructions that acted not only to create matter out of nothing, but to shape it into the familiar forms and systems observed in our daily lives. He even built it to reproduce itself! But where man’s algorithms create only a flickering screen shot, His create reality:   “In the beginning was the Word, and the Word was with God, and the Word was God. “The same was in the beginning with God. “All things were made by him; and without him was not any thing made that was made. “In him was life; and the life was the light of men. “And the light shineth in darkness; and the darkness comprehended it not” (John 1:1-5). Here, we have one of the most familiar Scriptures in the Bible. It speaks matter-of-factly about the act of the original creation. In plain language, it asserts that out of nothing, our world — our universe — was created. Given our experience with computerized imagery, this is not at all difficult to believe. If we can write instructions that create a picture, why can’t God do the same to create a universe? The raw material of creation was light; the instruction for its assembly was the “Word.” May we be bold enough to say that this Word was in fact, an algorithm, or sets of algorithms that were reiterated into forms, overlaid upon a substrate of time/space. As we have often observed, this explanation is not new. The righteous sages of ancient Israel not only identified the Word, they explained it in terms common to their system of learning and teaching. Referring to the 19th century rabbi considered the father of Hasidic Judaism (Israel ben Eliezer, called Baal Shem Tov), Michael Munk writes: “The Baal Shem Tov explained that the ‘word’ of God to which the verse [Genesis 1:6] refers is His utterance, ‘Let there be a firmament.’With these words, the heaven came into existence at that primeval instant — but what prevents the heaven from aging, decaying, crumbling? Why shouldn’t the heaven grow stale like yesterday’s loaf of bread or crumble like the last century’s highways? Why are some parts of the universe eternal, while others last for only a brief season? “The Psalmist answered these questions when he said: Forever, Hashem [Lord] Your word stands firm in heaven. The word of God that brought the heaven into being remains within them. The heaven continues to exist because not an instant goes by without God continuing to say, in effect ‘Let there be a firmament’– otherwise they would return to the status that prevailed before God’s will was uttered. So it is with every aspect of Creation. God’s original Ten Utterances are repeated constantly in the sense that the Divine will of the original six days remains in force. Otherwise, everything would revert to the nothingness of before Creation. “Just as the ‘word of God’gave being to the heaven, it is His word that gives being to everything. Let us try to understand further what is meant by God’s ‘word.’And how do the specific, limited utterances of Creation account for the infinite number of species and objects in the universe?” For thousands of years, the Jews have taught that God began His work of creation by creating the twenty-two letters of the Hebrew alphabet. They offer this figurative statement to assert that God used them to create the universe. Munk continues, “The twenty-two sacred letters are profound, primal spiritual forces. They are, in effect the raw material of Creation. When God combined them into words, phrases, and commands, they brought about Creation, translating His will into reality, as it were.”   The rabbinic observation quoted above is a perfect description of computer programming, long before modern computers were invented, or even thought about! “The Word of His Power”   The rabbinic idea that God supports the Creation on a continuing basis is well supported in the New Testament. The epistle to the Hebrews goes out of its way to assert this fact to its Jewish readers:   “God, who at sundry times and in divers manners spake in time past unto the fathers by the prophets, “Hath in these last days spoken unto us by his Son, whom he hath appointed heir of all things, by whom also he made the worlds; “Who being the brightness of his glory, and the express image of his person, and upholding all things by the word of his power, when he had by himself purged our sins, sat down on the right hand of the Majesty on high” (Heb. 1:1-3). Here, we find a statement that reflects the beliefs of Israel’s sages. The writer begins the epistle with the statement that the Son of God continuously proclaims the existence of our reality. His word is power; it has substance and reality. It states the instructions of actuality. According to Jewish sources, this idea dates back to Abraham and those who preceded him. The letters of the Hebrew alphabet represent “cosmic spiritual forces,” that God can use as tools to create what we call “reality.” In Revelation, we see still another example of the word of power. It is a metaphor that would be puzzling, but for the fact that we have some understanding of the actual effectiveness of His Word. When the risen Christ appeared to John, His glory was practically indescribable:   “And in the midst of the seven candlesticks one like unto the Son of man, clothed with a garment down to the foot, and girt about the paps with a golden girdle. “His head and his hairs were white like wool, as white as snow; and his eyes were as a flame of fire; “And his feet like unto fine brass, as if they burned in a furnace; and his voice as the sound of many waters. “And he had in his right hand seven stars: and out of his mouth went a sharp twoedged sword: and his countenance was as the sun shineth in his strength” (Rev. 1:13-16). Here, in a display of transcendent light, Christ is pictured with a sword — the Word — emerging from His mouth. It would be difficult to paint a picture that properly represents this image. But we can understand it as a metaphor for His “word” of creation. That which He speaks is so palpable, so substantial, that it is seen by John as having shape and form. We think of it as having the power to create. He speaks, and His words become form. How is this different from what computer scientists now call an “algorithm?” Even as we ask this question, we recognize that the best man-made computer is but a dim bulb next to God’s absolute light. But it was, in fact, light of a different order that He crafted into the universe that we understand only in an incomplete way. The opening words of John’s Gospel make it clear that it was “light” that shines into empty darkness that became our world. The “Word” and “Light” are metaphors for our Lord the Creator:   “This then is the message which we have heard of him, and declare unto you, that God is light, and in him is no darkness at all” (I John 1:5). These words are so simple that the average six-year-old can understand them. But they transcend even the comprehension of the most brilliant physicist. They are not simply metaphoric; they are what we call shape, form and reality.   “Let there be light”   The Bible opens in a bold declaration of this fact. God injects light into a dark, formless void. As He does this, detailed form congeals into what we call reality.   “In the beginning God created the heaven and the earth. “And the earth was without form, and void; and darkness was upon the face of the deep. And the Spirit of God moved upon the face of the waters. “And God said, Let there be light: and there was light. “And God saw the light, that it was good: and God divided the light from the darkness. “And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day” (Gen. 1:1-5). In a strange sense, when God caused His light to shine into the darkness of the pre-Creation void, He performed an action that science attempts to duplicate. In a miniscule imitation of His act, we recall His creative light every time we turn on a computer. To the believer, its illuminated screen is a humble reminder of God’s grandeur. Our scientists, working to discover the secrets of His creation, stare at their screens, wishing for greater accuracy and more definition. Even now, they are working to bring forth the first truly three-dimensional presentations. Not so long ago, their screens were grainy black-and-white. Then came color, and higher resolution followed by digital high-definition, which will inevitably lead the way toward 3-D, then high-definition 3-D. Will that satisfy the research engineers? Certainly not. They’ll still be working to achieve the first holographic, stand-alone images, in higher and higher resolution presentations. It is certain that they won’t be satisfied until they have fully modeled an actual creation that can be felt as well as seen. And what will they use to achieve this? Of course, they will use more highly defined algorithms, never being fully satisfied until they have duplicated nature, itself. They want to create life. One thing is certain. The multiple strategies of theoretical mathematics are really systems for decoding God’s algorithms of creation. They are aimed at unlocking the mysteries of absolute creation. But another thing is equally certain. They will never achieve their goal.   A Divine Interview   To these celestial interlopers, the Lord would speak clearly. As a superior to inferiors, He would “interview” them, and they would be without answers. Once, he asked Job a series of questions that might be very similar to the ones he would put to the scientists. Essentially, he asked Job to comment upon five aspects of the physical creation:   “Then the LORD answered Job out of the whirlwind, and said, “Who is this that darkeneth counsel by words without knowledge? “Gird up now thy loins like a man; for I will demand of thee, and answer thou me. “Where wast thou when I laid the foundations of the earth? declare, if thou hast understanding. “Who hath laid the measures thereof, if thou knowest? or who hath stretched the line upon it? “Whereupon are the foundations thereof fastened? or who laid the corner stone thereof; “When the morning stars sang together, and all the sons of God shouted for joy?” (Job 38:1-7). First, the Lord asks Job to present himself as a reliable witness concerning the earth’s “foundations.” The Hebrew word here, is yasad, meaning “to establish.” He asks, “Where were you when I established the earth?” Of course, Job could not possibly answer this question, having no idea where he was at that time. Question one sets the scene for the four that follow. The second question: The Lord inquires of Job about the “measures” of the earth. These would be the earth’s measurements or dimensions, from the Hebrew word memad. This is the common word for the act of measurement to determine size. The Lord is really asking Job if he knows how the earth’s dimension were ascertained. Of course, he couldn’t have the slightest idea. The third question: The Lord asks “who?” In other words, who actually stretched out a measuring line (from the Hebrew qav) over the earth? This is a strange question, but it suggests that perhaps the angels in some way participated in the earth’s foundation, even as they are seen in Scripture, when they measure the Temple. In any case, whether it was the Lord acting alone, or with a host of angels, Job could not possibly know the answer. The fourth question: In the King James version, the Lord asks in what way earth’s “foundations” are “fastened.” In the Hebrew, He is asking, “Upon what are its bases sunk?” A base, being a translation from the Hebrew ehden is a pedestal, pillar or socket. This would somehow be “sunk” (tava) or imbedded in something substantial. Job could not so much as guess as to what kind of pedestal is imbedded into another substance. Neither can we. Do these have to do with layers within the earth? Are they a reference to gravity? Finally, the fifth question: He asks Job who hurled down the earth’s cornerstone? Would this be its core, its mantle or perhaps some reference to the Solar system in general? Again, human beings cannot answer any of these questions. All of which brings us back to computer-aided design and the world of fractals. Science has discovered that regular geometric figures hold the secret, both to the world and to its myriad of organic life forms. Mountains and coastlines are subdivisions of triangles; trees correspond to forked lines of smaller and smaller proportion; spirals and circles model the endless variation of curves … from snail shells to river beds to solar systems to galaxies. When the Lord spoke, His utterances were what we now understand to be algorithms. To realize this is not to understand it, but to be awed by it