Saturday, March 24, 2012

Decoding the Universe: Patterns in the Ulam Spiral

The Ulam Spiral is one of the most intriguing of all mathematical images.  The spiral is a graphing of all real numbers in a clockwise direction, starting with the number one.  A peculiar pattern emerges when you look at it from a distance.  It turns out that the primes aren’t arranged randomly, as one might expect, but along diagonal clusters that resemble the design of folded circuitry, or a fractal of swastikas. 

This begs the question: is this diagram of prime numbers analogous to spiral-like dynamical systems in nature?  A colleague of mine came up with the idea of using a transform algorithm on the Ulam Spiral to depict a typical galaxy, which is apparently something that others have already done.  I took it even further and suggested that the Ulam Spiral might be a concrete dynamical system for the entire universe: one that serves as a blueprint for the scattering of matter after the Big Bang.  Perhaps the dispersion of primes in the Ulam Spiral represents how matter would have assembled if the force of gravity had never existed to bring matter into globular clusters.  Instead of the clusters being globular, they might have remained linear, like the primes on the Ulam Spiral. 

The origin of the swastika is of some importance to it.  The Rig Veda, an ancient Indian text full of cosmological hymns, is the earliest known source of the swastika.  Swastika literally means “mark of the sun” in Sanskrit, but Wikipedia says that “the Hindus represent (the Swastika) as the Universe in our own spiral galaxy in the fore finger of Vishnu.”  The Vedas were spiritual texts, but they introduced many mathematical concepts to the world, including the number pi.  If the progenitors of Vedic tradition had used the Ulam Spiral to spiritualize the swastika, I wouldn’t be surprised. 

It also begs a comparison to the game of chess and the I-Ching philosophy of causality.  Geometrically, the 8 hexagrams of the I Ching revolve around a five-sided pentagram.  The hexagrams make up the inner arm of the mandala, and they culminate in one of sixty-four possible outcomes on its outer arm.  The directional changes depicted on eight swastikas can represent the 64 possible paths of I-Ching causality. 

It may seem like the prime numbers are too arbitrary to be a legitimate model of causality in the universe; the only special property about them is that they can only be divided by the number one and themselves.  Even if there aren’t any mystical qualities about the Ulam Spiral, it’s still pretty interesting that an infinite amount of odd numbers can create such an orderly, virtual chess-board on something as chaotic as a spiral. 

Monday, March 19, 2012

Parabola

            As a young man I crept into the palaces of female minds with exceptional charm, perceptive aphorisms, witty retorts, dashing showmanship, and adventures in creativity.  My mind is seductive, no more than my body is, nor my unyielding chivalry.  The soul of a woman is a treasure chest of fantastical possibilities, and a unique imagination swarming with tangents that overlay a magnetic charm conjures the keys to unlock it.  Their secrets are tender and secure, safe inside the vaults of history, and when you have this magical key, the only way to unlock their hearts and hear them is simply to listen. 

I’m the type of man to attract the odd ones, the misfits, and even a lesbian or two.  The women who think I fit the mold of a typical suburban beefcake are quickly surprised and sadly intimidated.  Within these walls of cerebral matter and powerful masculinity there exists a fragile being, a being who has seen much of the world, and worlds beyond this one.  I like to think it’s my mysterious aura that draws women to me like bees to honey, but no, a handsome body is the only thing that makes a man mysterious.  It’s always the quiet handsome types who steal the heart of a woman in old Hollywood movies.  If I were an ugly man, most women would be unsettled by my need for privacy.  They would likely think me to be a creep with a dirty secret kept hidden away from the world, a secret such as being a killer, a rapist, or a drug dealing con artist. 

Now all that’s left are broken fragments, unwritten dialogues, bits and pieces of the women I knew from the past.  They’re all scattered about on a canvas that I haven’t completed painting yet.  Wheels and angles, angels within wheels.  Parabolas and soft-spoken words, inverted diagrams, atlases of hairless skin, cacophonies of screaming glass, words in the end that were left unspoken.  They’re scattered, moving about in a torrential storm of psychotic abnormalities, abnormalities that defined my lovers, abnormalities that made me love them.  I wish for this shifting atlas to be engraved on my tombstone when I am dead, though I know that no artisan could possibly draw it.  I feel old and beaten as the autumn draws near, as if my life had already passed me by.  Now I’m just waiting, waiting for those lost pieces of the cartographic puzzle to find their way to me, the colors that will allow me to complete my painting of the right woman, and wondering if she even exists.  Thus, with a whimper I feel the zenith of life’s parabola inching past me, and I can already smell the roses ‘neath the rocket-rimmed rainbow, waiting for me in bloom on the other side. 

Tuesday, March 13, 2012

Elven Star, Margaret Weis

I’ll start by saying that Pryan is another fascinating, otherworldly planet, unique in scope like Arianus in Dragon Wing and Aberrach in Fire Sea. The planet is turned inside out, meaning its surface is on the inside, subjected to constant daylight by four “stars” centered at the core. Naturally, this creates a planetary greenhouse effect, which causes the jungle-laden surface to sprout mega trees the size of continents.

Elven Star is also interesting for its diverse cast of species and characters. Elves, dwarves, humans, giants, dragons, and one kooky wizard bring balance to a story loaded with contrasting personalities. The thing that really enhances this book, at least for me, is the coupling of forbidden romance with raw, apocalyptic adventure. Not to mention the well-placed comic relief; there’s no shortage of wisecrack humor and dramatic hysterics. The unstable relationships between Alethea & Roland; the dragon and Zinfab; Roland and Rega; the dwarf and pretty much everyone; Zinfab and pretty much everyone; Haplo and pretty much everyone; is the chaos one might expect after centuries of racial instability yields to the sudden unification of a global alliance, much like in Lord of the Rings.

It has its moral perks and immoral downfalls as well, from the breaking of race barriers to betrayal and abandonment (Haplo, you dick!). Don’t let the first hundred pages of character development turn you off, or the fact that it’s far different from Dragon Wing. The action and drama come at you in full force for the remainder of the book. Once the giants invade the land it’s an unrelenting page turner. One of the most intense passages I've ever read was when the giants first rumbled onto the pages- when Paithan and Rega were trapped on that enormous mushroom.


Veins of the Frontier

Butterfly free, that’s never seen the Ocean, glides across the open Plains aflight, wing to wing, journeying afar to that Ultraworld of American promise, past abandoned Shawnee tents and through the homes of industrial inventors, across the largest of all the planet’s Deltas- the steamboat-fogged Mississippi- pas’t morn’ and elevating through noon, into the windswept grass of the Flatlands.  Out there beyond the Wheat Fields, newfound Settlements of the cattle boom lay lamenting in the foreground of its destin’d western Precipice; that golden Horizon on the sugar of spring, grinning wide ‘neath the brim of a Front that tumbles in convective Currents that rageth over the Land; rolling forth, dark and voluminous, ear-shattering claps of Thunder steadfast approaching, Hill upon Hill, the Sunlight fading as she soars, flapping above the Corn, animated as Treasure: God’s most illustrious Creation.  Hidden she lay in the delicate Soil, as the Storms shaketh the Land.  Tremendous hammers of doom, balls of Salt, expound from the vent of ionic transference that percolate through the obsidian Cloud, thermodynamic and supreme, furiously casting Hailstones upon the Earth below.  Estranged butterfly, so vulnerable and small, warily disengages from Gravity’s grip, continuing her Saga in the aftermath of the Storm, while Sunlight prevails, illuminating the Plains of promise with emblems of aqueous Resurrection that shineth like Pearls adorned ‘round the neck of a Goddess. 

A day passes, slowly the Land arises, to where aggregates of igneous Protrusion jut forth from the stormy Plains, as the Insect angles itself to scale the mighty Mountains of the continental Shield.   O Colorado, what magnificent Armor ye hold; what Watchtowers ye edify to keep guard on the Prairies of Nebraska that lay threaten'd by Tornadoes spinning o’er the yellow canvas of Kansas.  What powerful Rivers ye spawn, that spring forth from the high Crown of your Brim, cutting Pathways of Life through the Heartland below.  At the Crest of a monstrous Bulb of Granite there pours into a Valley some pristine Tributaries of melting Snow, one of which the Butterfly spotted from o’er the Divide.  It struck a course for it, upon which, enjoining another Stream, and Stream after Stream beyond that, it saw them inevitably converge after plunging down the sides of the verdant Valley, where collectively they gave Birth to the most accomplished River known to Man.  On this side of the Range the thin Air exposes Minerals and Landscapes that few on the other side- Man, Beast, or Bird- have ever beheld.  Here the courageous Specimen settles on a Spruce to rest for the night, as the setting Sun invites every terrestrial Traveler into this unknown world of extreme diversity.  Ah, the American West, paragon of Geology.  Here the nocturnal critters bear witness to the Sky as it travels thru’ the Zodiac’s Moondial.  Strange noises abound in the Wilderness, where slumbering in every Bush, Pine, and Fir, the dreaming Mythologies of every Species are churning, born from the primeval consciousness of Evolution’s marriage to God.  At the tail end of Hydra’s dimming chain there comes a shooting Star, a Meteor ablaze, creating a Pathway for the Holocaust of Dawn.   Rays from the Sun seep thru' the cracks of the yawning Mountain range. Our fluttering Friend’s wings glitter in the Dew, cast prismatic by the light’s bright Glare, so that upon awaking, it flitters its thin wings, showering the surrounding Timber with its early morning rise from sleep.  The sun breaks free of the Clouds, we have lift-off.  Full thrust ahead; the winged Beauty embarks on its course down the curvaceous River.  There the Rapids rage, the Driftwood drowns, the mast of a Ute canoe bobs its way down the deepest Vein of the New World. 

In time the Mountains give way to a barren Expanse of wasted Earth.  The great mold of the Desert reveals a broken surface of burnt Sandstone.   Each bend of the River offers distinct malformations of Rock, as if God’s practice as a Sculptor had been placated on a Plateau of Monuments.  A Furnace of acrobatic Goblins here, a Boulder balancing on top of a Pinnacle there; Arches, Columns, mega Mesas and bawdry Buttes that stick out o’ the Earth like fists punching thru’ the Ground.  Tributaries of the River carve jagged hollows through the ancient Canyonlands; Canyons with thin walls all about- concave Canyons, baked by the sizzling Heat, converging and diverging from one another in Mazes of Redrock that support daring Heights, all together painting Utah’s Labyrinth of Stone.  Down the Colorado it flies, miles upon miles, for days on End, the course of its journey ending at a Juncture of the grandest Canyon of all: Arizona’s signature Wonder, and one the natural Seven, revealing to our Friend the tales of all eras in its Geologic history, edged on its ragged Facade, as if the Earth had never healed from the River's deep cut wound.  Out of the Canyons and into the Desert, thru’ Saguaros silhouetted by dusty Sunsets, o’er the Ocotillo Outback of the Mojave, undulating thru’ the Skeleton Winds, dodging Tumbleweeds and the tongues of Iguanas, our fair-winged Friend follows the Sun west into Valleys of small round Rocks sheltered by Joshua Trees.  Then she veers right, fluttering away from the end of the World, straight into the prosperous Bosom that parts the Great Valley of California. 

The transformation from Death to Life, from Desert to temperate Soil, never was so evidently rapid.  The change is sudden and mysterious- such is the diversity of Nature’s plethora; these Biomes on the Surface of her spinning Sphere, a billion times the Butterfly’s own size, levitates the swift moving Critter with an expansive euphoria.  Next morning, oe’r steady Fault-lines that nudge each other near the Surface, a swarm of color on the Gorman Hills o’erlooking the fragrant San Joaquin, yields to an extensive Patchwork of ripe Farmland irrigated by the Delta of the golden West’s secluded Xanadu, where Gardens of the finest Fruits and Wildflowers bloom in abundance on the tumbling Hills.  Roses, Poppies, and Lupines are set ablaze on the Gorman Front, giving way to a fresh populace of Greens spread out on the Valley Floor, as if the very Fountain of Youth had opened before its Eyes.  Grapes, Cherries, and Oranges shine in competition, their Color possessed by exotic pastel: none so vibrant as the pink Orchards of Nectarine blossoms, or the white Almond clusters flanked by Fig Trees; their fallen Leaves looking like fallen Snow, fragmenting songs that come from Birds a’perched on their slender Shoulders.   Below them, sweet Indian Girls sing other songs; songs of their love for the young men who prowl the land on stalwart Stallions.  Blushing, the girls watch their mates, their swollen Cheeks scarlet like the Raspberries they’d picked; ones that hung on bushes to receive the charm of Sunrise. Now they settle into the girls’ baskets as sources of energy for the young Warriors, who, armed for glory, stand on lookout above the golden Wheat Fields at the foot of the Sierras: California’s mighty Crown. 

Nor’ward our winged Friend continues, thru’ the Pines and Evergreens of the forested Northwest; right on up the jagged Oregon Coast, sprayed by the crashing of Waves that foment beaten Beaches resided by Bugs, tossed Seaweed smelling of Rot, shadowed by isolated Monoliths out on the Oceanic Plain that reach for the Sky like arms above a Sea of Faces.  It’s the Ocean! It’s the Ocean!, thinks the Butterfly, with the carefree joy of a newborn Child.  Rivers brimming with Rainfall drain into the Pacific Basin.  Flying inland and up the Colombia, it finds saturated Logs on the River Route drifting with the Salmon, shadowed from above by volcanic Giants of the snowy Cascades: the range a Tiara above the rest, superior in beauty with its Alpine splendor.  Up the corridor of the Puget Sound a most profound serenity embalms the Creature; where the bluest Lakes, the greenest Islands, and the lightest bands of Sky interspersed with the Olympic facades become illuminated by an Atmosphere devoid of Clouds, Sunny and succulent with Summer’s return, suggesting a Painting with such a Fauvist Enhancement that few in the East could ever imagine. 

Now her bearings reverse Course; she begins her retreat Eastward, back into the fabled Regions of migration spiced with financial opportunity and apprehension about the Wild.  Looming above the Precipice of the Eastern Horizon is the paramount Palace of the Western Sensorium, standing like a Nugget in the Heart of Montana.  Soaring pas’t Glaciers that glean off the Rocky Front, and Mountain Goats that scurry about the Ridge-tops, the Butterfly watches iced Rivers as they drain into deep turquoise Lakes below; Lakes that glow like Manta Rays weaving rivulets through the abyss of the Ocean.  Bees pollinate Bellflowers, buzzing their way over tinkling Waterfalls that slowly Cascade off the mossy Terraces, finding tranquility where such Remoteness is abundant.  ‘Round the bend of another Mountain, a most peculiar Volcano emerges from the Scenery.  It steams with sulfuric thermochemistry, fumes reactions which color the Pools of hydrothermal Homes across the whole spectrum of the Rainbow.  Lakes of sapphire here, Rivers of golden-green Magma there: Geysers erupting from the Surface, reaching for the Sun as Buffalo graze on the smoky Hills nearby.  The Crater seems to mock all who look upon it, showing them how foolish they'd been to think that Nature’s capacity for diversity had run out, and that all the wonders of Creation had already been observed.  No, there were more, and the more there were, the more inexplicable they became. 

Finally, the open Plains return; on the left, great Thunderheads pound their Drums o’er the Hail-struck and beaten Bighorns.  On the right come the Grasslands of Wyoming, teeming with Antelope, Prairie Dogs, and Cherokee Children who splash in Brooks bordered by communities of Grass gracefully waving their threads to the Sky.  Lastly come the Hollowed-out Black Hills; their minerals excavated by the greedy Hands of Foreigners who are skilled in the art of Machinery.  There on a Hill, against the Backdrop of the howling Badlands, dimly Lit by the Sun, gazes a Warrior named Crazy Horse, his eyes scanning the Frontier of his Homeland: the Dakotas, the last defense of a dying Race.  Our weary Butterfly lands on his outstretched Finger, relaying to him her adventure thru’ the Land of Western wonders.  The Native Man, her old Friend, no more made of Stone than the Mountains around Him, nods in consent, remembering which are the things worth dying for honor. 

 

Wednesday, March 7, 2012

The Creation of the American Republic, Gordon S. Wood

Heavy stuff, Gordon. You must be a professor or something. But really, to get a sense of the ideological evolution of American politics before the Constitution was written, this might not be the best place to start. It's written for elitist post-graduates; you know, the kind of book that purposefully tries to confuse undergraduate perfectionists and drive them crazy, so they'll follow up the readings with an agonizing amount of research, score poorer on papers, and be more miserable in general. It doesn't explain things the way a formal textbook would, as it assumes you already have a strong foundation on post-Revolutionary knowledge. However, if you're experienced in history or difficult literature, this might be one of the amazing books you'll ever read. Wood has a superior prose, the best of any historian I've read. Even if his topics tend to go on and on, all 500 some-odd pages flow with the elegant consistency of a gifted writer.


Software

My body is the motherboard, With circuits that calculate The answer to every imbalance. My eyes are the monitor With rods and cones intercep...