The Allure of Semmetry: Sex, God and Fractal Geometry = E8


Sometime between 1564 and 1642 Gailileo served us a dish of Copernican-istic support, along with a very bold revelation:  “Mathematics is the language with which God has written the universe.”  The Italian physicist/mathematician/astronomer and philosopher’s advice has generally been headed by the scientific community and at once turned the geocentric world upside down.  I will not speculate into his abilities at the aforementioned roles played, but I will inquire further into his later listed occupation and one this author feels to be quite neglected:  philosopher.  To be more exact, I will be donning the theorist cap upon my own head whilst examining the accuracy of his declarative statement.

To be very blunt: did God create geometry or did mankind construct the many formulas, shapes, and symbols now being tattooed into student’s minds.  Very blunt indeed, but the profoundness of such a question cannot be disputed.  It is essential that while undertaking exploration—one need be open-minded as well as quite deft.  To question the authority of Geometry is not the aim of this pen—for I am simply following up on Plato’s request of questioning the situation we find ourselves crudely lumped together in.

To begin the examination of geometry’s role in nature I will offer categories—or subjects into which I feel fall into our creator’s hands (presupposing said creator is not necessary however—as  I am attempting to seek evidence pointing away from man’s imagination, and falling into the category of natural).   After all, gravity was alive and operant before evolution found us holding apples in which we quickly released the incorrectly ancient knowledge—sucking down the apple with a new label: gravity.  The object bounces at Newton’s foot.  This holds true, connecting with several other legs to which we are looking to find a unification of everything or rather, explanation of all.  Mathematicians around our globe speed to decipher the unfortunately small fragmented clues we now have in hopes of finding that “magic bullet”, giving rise to the very legs supporting such a theory.  Gravity is one leg in our IKEA assembly.

James Clark Maxwell crafted another during the mid 19th century, titling his masterpiece discovery: magnetism—which in turn powers electromagnetism.  The swinging seventies brought our generation the weak nuclear force—governing and molding the will of radioactivity, and later still the electroweak theory.  Understanding the complex inter-workings of the above boasted forces do not concern us during the reading of this essay, which is to say, we need only think of their power in terms of providing steps toward “unification”.

Today we find zero shortage of those interested in finding the table top—or in more precise detail: the single granddaddy of all the theories we currently know (scientist have been tossing the term “singularity event” at us recently) Like the fully revealed moon above our night sky hails our constant reflection of gravity’s spherical pull—we must now peer into smaller corners of our world, revealing the scientists’ jackpot.  To explain each law, we talk in a singular language, to which of course we all must in order to truly unify.  The language is mathematics.  It’s visual manifestation, geometry.

Surely a creator—whether it be He or Big Bang must have been fluent in geometry.  Egyptian scholars knew of the triangle’s power which is still inscribed into the green of our cash money dollar bills today. Their torch was then romanced by the Greek’s and their search for beauty, while the Mayan’s beheaded gifts to war gods at the foot of their pyramidic climb toward the heavens.  And lo now—we find ourselves in Adonis’ sandals striving to understand our current situation.

The shapes that surround us all with mystery and allure—are they to have been the outcome of circumstance, luck, or as Mr. Gililie offers, the all perfect creator?  This query will serve perfectly as the central thesis of this paper’s topic.  To bring this thesis depth, I will dive into the before mentioned categories at once—before the enthusiastic wordiness of this author gets the better of him:

Symmetry

Like Genesis, we will begin our observations from the beginning: Adam and Eve.  Humanity relies on the attraction between the two.  Without it the two of us are never born.  What gives rise to this phenomenon, or what is this attraction and who put it there?

1487‘s Vitruvius Man via a personal hero of sorts, Leonardo DaVinci illustrates the importance of attraction in terms of symmetry.  The perfect man was to be—well, perfect, and from the beginning of his inception he would have been splitting cells bilaterally (one cell division, little by little) one at a time.  Only mutations and environmental effects molest said DNA, which results in our imperfection.  The fact remains however, that initially the design is intended or instructed to be an exact mirror image of the other side.  So in a very fundamental way, we are all made to begin life perfect—before random and chance join the game.  Does this give rise to the creator hypotheses?  Possibly, but we should be take a closer inspection of the attraction event itself, given this is the singularity event of mitosis.

Love, attraction, or simply lust—either way you call it, we can see geometry hard at work powering the enigmatic engine.    Dr. Randy Thornhill (very scholarly sounding name) residing in the University of Carolina’s Department of Biology writes in “Scent of Symmetry” of the key role geometry plays in our love lives—birthing our life in general.  The Doctor’s journal illustrates this in the following: non-directional deviation from perfect bilateral symmetry is essential in establishing attractiveness.  The lesser extent of deviation, the more likely the animal (yes animals and humans) is to have more partners thus holding higher potential to perpetuate life.  Lower deviation also accounted for increased genetic, physical health, and surprisingly mental health including cognitive skill and Intelligence Quotient. (Furlow et al. 1997; Shakleford and Larsen 1997)

The above experiments were conducted asking men and women what subjects they considered to be pleasant looking, assigning scores as in the time honored traditional one to ten scale.  Compiling the data brings us to a conclusion:  the master behind our progress designed us to be geometrically appealing, or at least to multiply, we have receptors of symmetry along with value assigned brain scores.  In fact this study confirms that scent scores follow the same upward curve as the symmetry of the animal owning it, but for brevity’s sake I will leave that smelly matter to another essay.

Almost all instances of organism reproduction rely on the beauty of bilateral symmetry.  Yes, just about every species on Earth have two sides attempting to mirror the other.  A question immediately forms in my mind: shouldn’t we have examples of tri, quad, and quint symmetry?  There seem to be an infinite more ways to construct an asymmetrical life-form than the two sided.  This very notion and knowledge of reality share the unifying power of the number: two.  As far back as fossil records go (500 million years), we see confirmation.  Two eyes, two arms, two legs, two wings etc.  This may be the key to unlocking our creator question.  A purpose may just be hidden behind this nature, which unfortunately escapes me at present time—but no doubt, there must be something here.  In fact everywhere we look, we find symmetry in the dual form; time translation symmetry, rotational symmetry, and without the dependency of this phenomenon we could not make estimates of the laws governing the nature around us.  Even the famous golden rule relies on this.  Still another example: to every electron we find its positron.  The electric and magnetic fields explained by Mr. Maxwell, abide as well—to join the electromagnetic power.  Under high power magnification we get closer to that desired explanation of everything, held in the grips of fractal geometry.  Let me clarify.

Fractal Geometry

Jedi destruction of the Death Star (regretfully, I can never resist the Star Wars analogy–though Star Wars and math!–Jesus Christ dear reader, thank you for sticking with me) showed us the awesome wonder of fractals in real time.  That is, the actual Death Star was created, or—computed for accuracy’s sake, by fractal geometry.  Simply stated, fractals begin with one very specific shape and by adding a duplication of this very shape repeatedly we see a new larger picture take place before our eyes.  Fractals merge the seemingly opposing subjects of art and mathematics, creating a masterpiece.

As a child I would stick my tongue into the frigid air to grab one of these tiny frozen, delicate and beautiful creations, which would then quickly melt.  The snowflake was my bounty.  The snowflake is one example of fractals culled straight from nature Herself.  In name, the Koch Snowflake is an excellent example.  An equilateral triangle begins this process.  Out of this singular triangle more are added, one third the original size, to which we may repeat infinitely.  The Koch Snowflake is born out of sheer geometric will power.  This is not of course the only example as the Sierpinski triangle serves as a perfect template as well.  Taking the midpoints of all three sides of an equilateral triangle we add another similar triangle at infinite amount, forming a new shape—something akin to the Legend of Zelda symbol naturally.

Next time we find ourselves around leaves we would be wise to take notice of this process.  Each part of the leaf will be the smaller similarity of the whole.  No human gave this process a beginning so we must surmise nature’s drawing of blueprints.  Weather resulting from creation or competition, fractal’s importance need not be ignored.  Continuing to plunge further into the microscope, I will offer we have not heard the last of fractal’s prowess.   Perhaps the world around us in which we observe is nothing but a reproduction of one original shape:

E8 String Theory

            It is bad character for an author to write on subjects not fully grasped by him, so I must apologize in advance for this upcoming offense.  I do however take comfort upon realizing I am not the only one falling quite short, as the information is infinite in regards to the complexities of the E8 String theory.  I will do my best to properly convey what limited events of this I understand.

Our modern culture’s race to the moon finds scientists colliding miniscule particles into each other at light speed.  The resulting tiny blood splatter show them what happens when very small worlds collide, sending atom and sub atomic particles alike, one respectively racing away from the other.  Here observers note the effects in hopes of grabbing that Holy Grail of math/science/philosophy: the Theory of Everything.

The E-8 String theory goes something like this:  Fundamental particles are not very fundamental at all, at least in the smallest and most primal forms.  They are in fact different expressions of one thing: a string.  This string vibrates allowing the particle to be expressed as different things.  An example:  one type of vibration expresses an electron, another a proton.  Again we find symmetry hard at work, the universal Ying to another’s Yang.   Behind the world of the subatomic particles electrons, quarks, Basons, and formions, we look to one singular shape giving rise to them all.  The circle.  Because of the previously mentioned rotational symmetry, the circle is thought to be powering every single particle of our universe, including us.  What a debt we may owe to the circle.

To better illustrate this:

Largest to smallest:  Macroscopic matter

Molecular

Atomic level of protons, neutrons, and electrons

Subatomic level electrons

Subatomic level II quarks

String level

Tiny very complex circle

Now is when I must plead ignorance or lack of intelligence to explain the other portions surrounding this theory, involving up to eleven dimensions.  Dimensions are of little importance to this topic as we are concerned only with the geometry designed perfect circle beginning us all.  Looking back at my research I clearly have failed as so many before, to find the answer to our initial question: who made geometry?  We have uncovered many new ideas and a new appreciation for the beauty of geometry and its key role in creating the world, and one can not dispute the importance of the circle will factor into the eventual Theory of Everything.  One thing I can’t help thinking:  if one shape is designing the matter around us, everything must be tightly connected together in unity—that is to say, everything in the universe has something very special in common.  Unification’s proof is probably lurking around the corner waiting for one smarter than I to explain, but I am betting the house fractal geometrics is heavily involved in the universal caper. Until that time, I must humbly thank you for your valuable time.  My aim is that we both have stumbled onto a few ideas to insert into Google’s mighty search engine.  If that evil dog, laziness, prevails—we can always donate our cells to science.

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