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Nomad His back was ruined from digging post holes, a condition he'd grown accustomed to. And his hands were a mess. He had little experience working with barbed wire and they paid the price. He thought of this job as his last, his very last. Age and a painful weariness from having to deal with people had brought him to this place in his mind. He could tolerate certain folks for brief periods of time, but did not seek them out, disdained socializing. When the boss threw parties at the ranch, he never attended, always finding an excuse to go out on the range, to fix something needed fixing. He was quiet and left to himself by the rest of the crew. The younger ones made fun of him, sometimes to his face. He'd just snicker, shake his head and walk off. The older ones, closer to his age, would warn them: Don't poke a bear with a sharp stick. But, being young and full of themselves, they'd laugh it off. It was getting towards evening, the light clouds filtering the waning daylight. He'd had enough, anyway. Saddling his horse he rode due west for the ranch and the comfort of his bunk. He barely had the strength to remove his boots, then fell quickly to sleep. The dinner bell would wake him. The rest of the men milled about, coming and going, ignoring his presence as they always did. His bunk was over in the far corner, away from the others. He hid a bottle of whiskey in his duffel under the bunk, but none had ever seen him drink. Nor had any ever seen him drunk. After dinner, he'd sit outside on the toprail of the corral smoking. That seemed to be his one pleasure in life. He'd been working at the Circle 'M' Ranch for close to three months. As with all new arrivals, the others asked many probing questions, wanting to know just who they were sharing their lives with, and who might be a danger to them. He was vague about where he came from and what he'd been up to. Vague to the point of secretive. After awhile, the men gave up, believing, at least, he was no threat. Pretty much all they knew, and all they needed to know from his perspective, was his name. He called himself Nomad, the name given him long ago by a gypsy woman. He liked it so it stuck. The day wore on in typical fashion. It was getting close to July 4th and the boss always held a big party. At dinner, the men talked of nothing else. They spoke of the fireworks and food and what musicians were coming, but mostly about the other ranch women, and especially those from town. The signs of fights over certain ones already brewed from the sound of their talk, and it would only get more intense as the day grew closer. Nomad ate in silence. Such conversation bored him, he'd heard it all before in a hundred towns, in hundreds of bars. The men could fight to the point of death, it mattered not, it was always up to the woman to decide in the end. After dinner he retired to his rail by the corral, studying the horses as they walked and occasionally galloped from one end to the other. A curiosity he never could fathom. Flies, maybe; or just the sudden urge to be let out to run, to be free on the high range where they came from. Breathing the cool crisp air off the ridge instead of down here in the dry dust working for meals. Life had shifted gears some time in the distant past. In spite of himself, his mind would always fall into that hole, like a roullette ball finding home. He sat and smoked and watched the horses -- and thought. Xavier, the Mexican cook, climbed the rails and sat beside him. He was the only one Nomad bothered with. He played dumb, mostly because the crew expected him to, but Nomad could see he was far from it. Xavier hedged a question, "How goes it, amigo? You see anything in that crystal ball you're always gazing into?" Nomad forced a smile, and spat. "Nah. It's the same story over and over. I keep looking for a break in the action, but there isn't one. It goes all the way through to the bottom, and stops dead." "Maybe you should try sitting on another rail." "Might work. But then, the horses wouldn't recognize me." "Re-introduce yourself, make a fresh start." "You mean, start at the bottom and work up?" Their conversations usually went this way. It seemed to make sense to them, but any of the others eavesdropping had no idea what they were talking about. The next morning Nomad was scheduled to go into town with two of the younger ones, take the wagon and get supplies for the upcoming bash. The cargo would include whiskey, which would be held under lock and key by the foreman, a tough bastard of no nonsense disposition who knew firmly on which side his bread was buttered.
********************** To Be Continued... ********************** |
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The Day I Died
************************** It's not easy for me to take corporeal form. I can only do it for a brief period of time; the energy outlay is enormous. But I'll try to maintain stasis for as long as possible so I can tell you what I've discovered. Two hundred and fifty seven years ago, I died, or at least it seemed so. Let me attempt to recount the events leading up to it, and those that followed.I awoke that morning later than usual; the effect of an excess of champaigne at the celebration the previous night. An artist friend had managed to finally establish himself in the real world -- as we call the practical world -- by having his paintings favorably recognized by a well-known critic. Not long after the review showed in the paper he was contacted by the owner of an upscale gallery, one where people actually bought works instead of just looking and leaving. Yesterday was the first of his showing -- to last two weeks. So, a celebration was in order. Tea helped bring me back to some semblance of life, although, strangely, my mind seemed rather clear, almost sharp. It must have been from the heavy socializing, it often had this effect after extended periods of aloneness. Curiously, while having tea in the garden I remember reading about Blaise Pascal's speculation that a vacuum existed above the atmosphere -- in outer space, no less. I had no idea what to make of it. How could he know? Pondering this I left my apartment and proceeded to breakfast with an old friend of university days, or at least I thought he was at that time. We'd bumped into one another the previous evening as I left Marie's salon west of the canal. It was drizzling so we both had our heads bowed and almost collided right there on the street. It was far too miserable to chat, so we arranged to meet at Cafe Leboeuf, my favorite retreat. As I walked, thoughts of the vacuum of space gave over to thoughts of this friend from school. Just as suddenly I found myself entertaining a shadow of doubt brought on by the murkiness of aged memory; it had been years ago, after all. Had he really been a friend? How close? Or had we only shared a few classes together, the familiarity of a face from that richer and happier period in my life giving our relationship an unwarranted significance?
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The Chandra X-ray Observatory Center
NASA's Chandra Sees Brightest Supernova Ever ************************** DARK ENERGY FOUND **************************
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Tesselation ************ 
Three teams of astronomers poured over sections of a picture of the deepest view into the universe ever seen, taken by the Hubble Space Telescope over what amounted to four days of exposure on a single location -- a point, actually -- far off in the distance. Six scientists to a team, half sitting, the rest standing or pacing in front of a long pop-up table, covered with papers, spectrographic analyses, small pictures, pencils, rulers, hand-held calculators, styrofoam coffee cups, bottled water, and one ashtray. Jackets draped over backs of chairs, each team's excitement and astonishment was palpable in the close-knit setting. Above the table were two rows -- one stacked on the other -- of three 27-inch monitors showing different regions of the overall exposure at varying magnifications.
I only just arrived, my plane had an engine go out coming into Baltimore. After convivialities with the administrative team -- some small talk, dinner invitations -- I was assigned to Doctor Zeingelder's work-group in theatre "C". I had never worked with him before but was looking forward to the meeting. He greeted me as a colleague, warm and personable, enjoying himself too much to be concerned about unintended tardiness -- Nobel Laureates can be testy at times.
Introductions to the rest of the team were postponed; the atmosphere verged on a shark frenzy. I took my post at the back, slowly walking the length of the monitors, taking it all in. When I found a particular orientation, a certain angle of perspective, I stopped, focused without strain, then let it happen.
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GlobalWarming 101 Intergovernmental Panel on Climate Change
World Wildlife Fund
FOREST TRENDS
International Rivers Network
Living on Earth
UNEP -- Great Apes Survival Project
The Changing World
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Geologic Timeline Chart [really cool] |
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 The Complete Works of Charles Darwin
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| Catalogue of Life: 2009 Annual Checklist: Source Databases SEARCH PAGE NBII HOME |
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Extreme Science There are 350,000 species of beetle |
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 Hercules Beetle Can carry 850 times its own weight. |
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NOVA| The Incredible Journey of the Butterflies
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Second Chance He felt like a fraud. All this time, believing one truth, living another. Until it all came crashing down like the card house it was. He wanted to die. Didn't care how, not really. Painlessly would be nice, but, as long as it was quick, he didn't care. When one of the few people he knew asked how things were going, he'd always reply -- fine. Fine. Right. He wanted to tell the truth. He wanted to say he felt like hell, that life meant nothing, less than nothing. He didn't know what drove him, where he got the energy to go on. Rage gives a dark energy. He used to be a happy man. Not always, of course, the stresses and strains of life and dealing with assholes would sometimes get to him like it does everyone, but generally he didn't sweat the small stuff. Live and let live was his motto. For years he'd worked hard to suppress his anger, his protests against being treated with contempt and disrespect by people, especially those pretending to be his friends, to have his interests at heart. He believed he needed their good will, for one reason or another. He wanted to get along. To maintain the status quo. Apparently, they -- it was always they -- presumed he was unable, had not the capacity or the heart to do otherwise than accept this treatment. But he knew the real reason. For his love and their life together. For their home and the happiness they knew. But when she died, the walls came tumbling down. Everything changed. He no longer had any reason to hold back. None. And he found he hated those people, fantacised about killing them for belittling his relationship in that macho demeaning way some men have. He-men, he'd grumble to himself and shake his head dismissively. Punks and childish bastards. The irony didn't go unnoticed. It was strangely liberating in an angry sort of way. He wasn't mad at anybody else, he was mad at himself. He set the stage for it to happen. Mollifying, placating, allowing shit to go on that chipped away at his character, deeply affecting his relationship. He held back. It was how he'd become. He knew full well his abilities; he knew he could do something about his living situation, improve on it. But the goddamn status quo, maintain the staus quo. Now, it was too late, and he no longer cared to maintain anything. He felt a strength he used to know when young and it was habit to stand up for himself, for his life, for what was right, when nothing else mattered. It felt rough and strained at first, like muscles unused for a long time. Where did that go? he wondered, over and over. And, if only. He also felt vulnerable, untrusting of his instincts. But, vulnerability and self-doubt were what got him into this hell in the first place, so he brushed it aside with contempt for himself, for his weakness and excessive caution. He became obsessive about his home, their home, kept it in order, thumbtacked Christmas and birthday cards to the walls, would stare around carefully studying the details, stilling the moment, taking everything in, as though if he could only concentrate hard enough, in just the right way, she would appear. He looked at every little thing as though for the first time, examining momentoes with a reverance he rarely felt before. Wanting to feel that sense of home again, yet it seemed just out of reach, elusive, like a shadow or a distant sound he barely could hear. Trying to remember how it'd been when she was there. Where she preferred to sit, how she sat,..., and stood and moved. He refused to let go, had no idea what that meant. It hadn't been just her and him, it was them, what they had, their relationship and the life they were living. And now that was gone; there was no them. He thought about her every day, could sit in the backyard for hours without moving, thinking about her, talking to her as though she were there, her chair still next to his. He lived alone; it made it easier and yet harder at the same time. What was worse, what he couldn't get passed and probably never would, was that he was convinced it was his fault. He searched his mind trying to find others to blame, but it was no use. He knew, was sure, without doubt -- it was his fault she was dead; his lapse that was responsible. It was as though he'd killed her, plain and simple. He drank almost every day. When he'd get drunk he'd rant, loudly, angrily, to his woods; railing at God, in whom he no longer believed. His nearest neighbor was a good mile away, not that he gave a damn. He drank and cried and thought of suicide. And how empty and quiet the woods were. The silence struck him. Not the silence of no one else being there, he'd been alone before when she was in town or visiting friends. It was a strange sad quiet, like a children's playground with no children in it. It went right to the bone. A few drunken crazy nights he ran around calling for her, looking for her, close to hysteria with anguish and loss. His sadness drenched him and stole his heart away. He refused to accept it -- and it was his fault.
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The Anatomy of a Differential Equation Differential equation of the first order in three variables
Any equation of the form: (1) f (x,y,z,c) = 0 [the equation of a surface], where c is an arbitrary constant, satisfies a differential equation of the form(2) P dx + Q dy + R dz = 0, where P, Q, and R are functions of (x,y,z) but do not involve c.
For from (1) we have (3) ∂f/∂x dx + ∂f/∂y dy + ∂f/∂z dz = 0, and the elimination of c from (3) and (1) gives (2).
Geometrically we may say that the coefficients P, Q, R determine a vector (4) P i + Q j + R k. at each point of space, and the differentials dx, dy, dz determine a vector(5) dx i + dy j + dz k. The differential equation (2) asserts that these two vectors are perpendicular to each other. That is, the direction dx:dy:dz is the direction of a curve and a tangent to that curve at any point on it, and is orthogonal to the direction P:Q:R. Hence the vector (5) is restricted to lie in a plane perpendicular to (4). In other words, the differential equation defines a plane of infinitesimal vectors (5) at each point of space. The totality of these vectors forms what we may call a planar element. The problem of integration is to arrange these planar elements into surfaces. Geometrically, to solve the equation is to determine geometric loci so that the condition of perpendicularity is fulfilled for directions on each locus.
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| Luncheon of the Boating Party
The Phillips Collection |
Evening Sail
Richard Thompson Gallery |
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It's night, a dark night, no moon. You're standing on a hilltop overlooking a broad plain of shrub and grass far below - a grassland. Swarms of fireflies blink in clusters of all sizes, separated here and there by darkness, a darkness illuminated now and then by solitary flickers of light. Being mathematically inclined, you can't help but try to determine any discernable pattern emerging in the melee; it all seems so chaotic at first. After a time, and due to extraordinary extrasensory powers of perception accidentally gifted to you by a lab experiment gone terribly wrong when a child, you notice different-sized groupings and lone individuals blinking together.
Moreover, due to your enhanced powers of discernment, breadth of vision, and cranial capacity surpassing that of the most sophisticated supercomputer presently on the drawing boards, you process, nanosecond to nanosecond, the intermittent patterns of light and dark spasmodically radiating from the field below, not missing a single creature, cataloguing similar patterns into classes as you go.
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Infinity
The Rational Numbers (Rationals) are of the first order of infinity.
The Irrational Numbers (Irrationals) are of the second order.
So, between any two Rationals can be put an infinite number of Irrationals. They are denser.
The Real Numbers (Reals) are composed of the Rationals and the Irrationals. The Reals, therefore, represent a continuum.
********************* ********************* Hypothesis
A Rational number may stand for the quantum state of a virtual particle or particle system coming and going in and out of reality as quantum fluctuations. Quantum fluctuations underly and cause to come into being quantum space.
These virtual particles -- corresponding to the Rationals -- are discrete and separate; they may be considered as nodes of a network. Topologically, each is compact in Hilbert space [infinite dimensional] and is surrounded by a neighborhood of energy.
Gravity, residing as potential in quantum space, is an effect of this interaction and as such is not fundamentally a quantum phenomenon. It forms a hypersurface with time comprised of curves in space. But if the graviton (as hypothesized) can be construed as points (quanta) of those curves, then the surface/field thus generated is of the second order, the order of acceleration.
But is that necessary?
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The boundary, or surface, of any figure of any dimension represents the limit of what may otherwise be considered unlimited [The two end-points of a one-dimensional line segment are its boundary, for instance.]. This limit acts to give definition to the unconditioned.
A simplicial complex (to be defined later) may be thought of as the rational reflection of differentiated images perceived by the brain as it attempts to sort out its surroundings. This complex 'rests' on the surface of reality, mapping it; and this surface, or boundary, although of the underlying spacetime itself, nonetheless has a reality all its own; separating, as it does, interior from exterior.
As I crossed streets and navigated absently through carriages and people, I ransacked my brain for proof, a single shred of experiential evidence to corroborate my inclination. He certainly considered us friends and remembered me almost instantly. In fact, it'd been on his insistence that I willingly -- out of loneliness? -- concurred. My emotional state had been rather dry for some time, perhaps I was merely wishing it to be true.
Upon further inspection, you isolate and localize subgroupings and individuals within the clusters that alternate out of sync. Deeper perception, using the aforementioned genetically altered ability, reveals even more complex subdivision associations: the timing appears haphazard and chaotic only on the surface; each firefly varies the radiation duration of its biochemical energy; and each partakes of an uncountable number of configurations, but not all configurations. 
Georg Cantor: Transfinite Numbers -- Exponentially increasing levels of infinities.
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True Story
You have to understand what I'm about to tell you is strictly between you and me. You must promise. I have to tell someone before I bust or get killed too. I'll start at the beginning.
A year ago last week a friend of mine, who made a living carting trash and used appliances to the dump, asked me to help him. He'd been offered a big job through his e-mail for more money than he ordinarily made in a month. We drove his flatbed thirty miles or so down a dirt road off the highway. It was pot-holed and rutted so I had misgivings about the project from the get-go; his truck is old and weary so I held my breath over every crash and bang waiting for it to break a leg and die right there in the middle of the desert. But miraculously we made it to a large concrete building surrounded by a few smaller one with tin roofs. The main building was worn and covered with cracks from erosion. No one was there. He'd been sent a key and told to remove any and all stuff from a back storage room. No questions asked and no explanations given. Chris didn't protest.
We entered the musty place that smelled of rat feces and years of dust. Wild grass from the desert grew right out of the concrete floor, cracked in several places. Ragged tarps covered an unknown number of what turned out to be wooden crates and boxes, all locked. After the long arduous ride, we drank some coffee and walked around, estimating how many trips we'd have to make. He was getting paid for the gas so he didn't care. We figured it would take a few days, at least. Daylight was burning, as they say, so we started right in. We left town early expecting to make three trips that day. We loaded the truck in short order; the boxes were heavy but we had a hand truck and two planks we leaned on the edge of the bed. The dump was between town and the jobsite so we were back from our first trip and nearly loaded again by noon. Tired, we decided to break for lunch.
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Sandwiches in hand, we went exploring about the site. All the out-buildings were locked. We tried to peer through the windows but they were so dirty it was impossible to see anything inside. We went back to the storage room and behind some crates found a door leading to the rest of the building. The knob wouldn't turn; it too was locked. We looked at one another in that way two old friends do who've done some shady things in their lives together and decided, what the hell, let's break in and check it out; we could fix it later so no one would know. That was a mistake, as it turned out.|
Number Theory: Diophantine Equations Number Theory studies the properties of integers. As a student of Abstract or Modern Algebra I find it interesting that most proofs in that field are based on number theoretic arguments. It is customary to apply the term Diophantine equation to any equation in one or more unknowns which is to be solved in the integers.The mathematician Diophantus lived in Alexandria sometime around 250 A.D.. Diophantus's reputation rests on his great work Arithmetica which may be described as the earliest treatise on algebra. It is in this work that we find the first systematic use of mathematical notation.
THEOREM: The linear Diophantine equation ax + by = c has a solution if and only if d divides c; written: d|c, where d = the greatest common divisor of a and b; written: (gcd)(a,b). If x0, y0 is any particular solution of this equation, then all other solutions are given by
x = x0 + (b/d)t,
EXAMPLE
56x + 72 y = 40
******************* THEOREM: Given integers a and b, not both zero, there exist integers x and y such thatgcd(a,b) = ax + by. The proof of this reveals that the greatest common divisor of a and b may be described as the smallest integer of the form ax + by.For our example, to find a particular solution in x and y we first want to find the greatest common divisor of 56 and 72. And, in order to find the greatest common divisor of two numbers, we employ the Euclidean Algorithm which itself employs repeated applications of the Division Algorithm. The first step is: a = q1b + r1, where q1 is an integer and r1 is a remainder.
By the Euclidean Algorithm, we have:
72 = 1 × 56 + 16
Accordingly: 8 = gcd (56, 72) This is based on:LEMMA: if a = bq + r, then gcd (a,b) = gcd (b,r).
******************* From the theorem:The Diophantine equation ax + by = c admits a solution if and only if d|c, where d = gcd (a, b) [Proof of this statement lies below.] Therefore, the last remainder of our example, our greatest common divisor -- 8 -- must divide c = 40 for there to be a solution. Backtracking the Euclidean Algorithm, we start with the next to last of the displayed equations above and eliminate remainders. There are only three, so we have:
8 = 56 - 3 × 16
40 = 5 × 8 = 20(56) - 15(72) Therefore, ************************ Proof: There are integers r and s for which a = dr and b = ds. If a solution of ax + by = c exists, so that [ax0 + by0 = c] for suitable x0 and y0, thenc = ax0 + by0 = drx0 + dsy0 = d( rx0 + sy0),
which simply says that d|c. Conversely, assume that d|c, say c = dt. Integers x0 and y0 can be found satisfying d = ax0 + by0. When this relation is multiplied by t, we get
c = dt = (ax0 + by0)t = a(tx0) + b(ty0). Hence, the Diophantine equation ax + by = c has x = tx0 and y = ty0 as a particular solution.
************************ I put this here not as some random thing to do -- nothing I have on my website is random -- but because I think it's beautiful and, as math-type people like to say, elegant. It's especially cool when a and b of ax + by = c are relatively prime; that is: gcd(a, b) = 1.Cool, man, cool. If anyone wants a copy of this, you can find it here.
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To see a World in a Gram of Pot,
From: Orgies of Nonsense ***************************** Stephen J. Gould in Wonderful Life:"I am not speaking of randomness, but of the central principle of all history—contingency. A historical explanation does not rest on direct deductions from laws of nature, but on an unpredictable sequence of antecedent states, where any major change in any step of the sequence would have altered the final result. This final result is therefore dependent, or contingent, upon everything that came before—the unerasable and determining signature of history." Text book on Quantum Mechanics: "Once quantization is established, it becomes inevitable to regard a physical process as the progression of a series of individual, discontinuous, elementary processes (quantum jumps), each of which cannot be analyzed further. This then leads to the conclusion that a completely specified initial condition does not necessarily lead to a definite result at a later time." Gould again: "I call this experiment “replaying life’s tape.” You press the rewind button and, making sure you thoroughly erase everything that actually happened, go back to any time and place in the past . . . . Then let the tape run again and see if the repetition looks at all like the original." He did not believe it would and anything resembling humans as one of many possible outcomes was unlikely. Fine-tuning refers to the surprising precision of nature’s physical laws and universal constants and the beginning state of the universe, its initial conditions. If any property or parameter -- masses of particles, strength of forces, overall amount of matter -- were altered even slightly, life and humans would not have evolved because the universe would be quite different. The Anthropic Principle is based on this observation. The determinism implied by this principle and expressed by its emphasis on the sufficiency of the integrity of the initial conditions to bring about a life-giving universe is called into question. That is, reliance on fine-tuning of initial conditions is not enough, contingency must play a decisive role not only with life's history but also with the quantum trajectory of the universe as a whole. A particular quantum path or trajectory is a contingency, and all possible contenders in a superposition of contingent events are on the table, from moment to moment. Nature leads the way.
Contingency interacts with necessity. Contingency: dependence on chance or on the fulfillment of a condition; something whose occurence depends on chance or uncertain conditions. Necessity: the power of natural law that cannot be other than it is; natural causation; anything that is inevitable, unavoidable, etc. as a result of natural law.
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Question: In the King Kong movies, they have a huge 50- or 60-foot massively-built wall separating Kong from the villagers. My question is: Why the hell does it have a King Kong-size gate smack in the middle of it? Huh? Do the villagers sometimes invite Kong over for barbecues or celebrations from time to time? What's with that gate?
********************** From The Art of the Novel by Milan Kundera (author of The Unbearable Lightness of Being), page 110; published 1988, just before the collapse of the Soviet Union: "Totalitarian society, especially in its more extreme versions, tends to abolish the boundary between the public and private; power, as it grows ever more opaque, requires the lives of citizens to be entirely transparent. The ideal of life without secrets corresponds to the ideal of the exemplary family: a citizen does not have the right to hide anything at all from the Party or the State, just as a child has no right to keep a secret from his father or his mother. In their propaganda, totalitarian societies project an idyllic smile: they want to be seen as "one big family"."
*********************** "They who can give up essential liberty to obtain a little temporary safety deserve neither liberty nor safety."
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"The Lion is a solitary creature at heart, the male Lion, that is, he lives for the moment, the moment only, he knows he will never die, he knows, he acts, always."He accepts the world as is, he will never die."
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Harvard Physics Department Faculty: Lisa Randall Author of Warped Passages *********************** Author of God Is Not Great: How Religion Poisons Everything *********************** "Why seek the miraculous and supernatural beyond life?"
*********************** "Philosophy is written in this grand book -- I mean the universe -- which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles and other geometric figures, without which it is humanly impossible to understand a single word of it."--- GALILEO GALILEI, H Saggiatore (1623)
********************* Over the years I've been to an uncountable number of mathematics websites. If you're a serious math student or just someone who appreciates it and is interested in a site that employs examples to instruct, I recommend S.O.S. Math as a premier place for math review material from algebra to differential equations. Also, a good site dedicated specifically to Algebra is: The Purplemath Forums: Practical Algebra Lessons.And for college level calculus, the best I've seen so far is Paul's Online Math Notes.
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The Official M. C. Escher Website
******************* The December 17, 2008 "NASA -- Imagine The Universe News" article entitled: "Dark Energy Found Stifling Growth in the Universe" has revealed that the universe taken as a whole works to maintain a balance through feedback mechanisms of the largest scale structures. Dark energy is responsible for both accelerated expansion and galaxy cluster constraint. "This result could be described as 'arrested development of the universe'," said Alexey Vikhlinin of the Smithsonian Astrophysical Observatory in Cambridge, Mass., who led the research. "Whatever is forcing the expansion of the universe to speed up is also forcing its development to slow down."Imagine a delicate ballet underlying the entire universe as though it were fundamentally necessary for life and consciousness.
******************* The wavefunction of a dimension is expanded by virtue of a classical measurement taking place. What causes it? The crumpled-up or compacted ones are still quantum in nature -- fractionalized -- which is not to say fractalized. Why can't dimensions occur in fractional pieces? Molecules. Liquid-like changing and blending. Are the parts not the whole? If it is space itself that forms and reforms to create the cosmos we're familiar with, then fundamentally the universe has no reality of its own.
An observable is represented by an operator which is represented by a linear transformation which is represented by a matrix composed of eigenvectors. Clear? Alternatively, we can speak of a transformation group acting like a linear transformation on a vector space ordering and orchestrating spatial relations. Each of our three expanded dimensions can be considered a surface; their gradients intersect generating the physical domain we've come to know and love. A superposition of surfaces along with that of time -- spacetime. Is it therefore holographic?
Epsilon Eridani is approximately ten light years away. Four Jupiter-class planets (discovered thus far (12/12/09)) are known to circle the star. Determination of smaller planets will have to await more sophisticated observational tools. Nonetheless, I have a question concerning an assumption we make. When we talk about a year we are, of course, referring to the all-familiar Earth year. That is to say -- one trip around the sun (Sol). For example, I am 60 years old so I can say I've been around the sun 60 times. Now, supposedly, one of the Eridani planets takes ten of our years to circumnavigate Eridani. So, assuming the people on that planet measure age the same way we do, then one of their years is equal to ten of ours. Therefore, Eridani is 10 light years away from us, but from their point of view, we are only one (1) light year away from them. You see what I'm trying to say here, measuring cosmic distances by Earth-based years is not an absolute. A light year is not the gold standard just because it's based on one trip around Sol. The definition of year is relative. Pretty obvious, huh? But I suppose someone could say that the distance traveled by light from the Eridani point of view is ten times further than what we measure. Or maybe not. Still and all, if they age ten times more slowly than we do, space travel looks less forboding. I was an avid Star Trek fan. The Vulcans were considered "long-lived". And they occasionally met people who were, say, 500 years old. From our Earth-based point of view this is really old, ancient, biblical. But suppose it took 10 of our years for a single planetary rotation around their sun, whoever they might have been. Then they'd only be fifty. No big deal -- to them.
The Origin of Gray Matter Back in the before time, all matter was white. Then somewhere along the line we became aware of dark matter, a lot of dark matter, way more than light matter [about 23% to 4%]. And Carl Jung mapped it out. Is that how it is? Are we always and only looking at how our psyches are constructed? Parallelisms? Evolution is local -- scaled -- happening at all levels simultaneously, but to each its own. The universe is evolving, reconfiguring, shifting into another gear. The metabolism accelerates, new combinations are needed, the cells form a wider range of networks. But we, and everything around us, are made of light-matter; so we have an allegiance to it.The whole idea of dark matter is a little frightening. Are there beings made of dark matter? Can dark matter stick to me? What would happen if some dark matter got infected into my skin, like a fungus? Questions. Questions.
*********************** One of my favorite authors of all time: Tad Williams. I look forward to Volume III of the Shadowmarch Trilogy.***********************
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Mother "Tom, you know you have an early meeting tomorrow, don't you?" cooed the machine voice, tinged with tinny femininity, lilting in all the right places. Tom had tried to open the front door; he wanted to go to the bar down the street for a nightcap and some socializing. But the Guardian wouldn't let him; it had locked all the doors."Tom? Tom. You know it's best. Why don't you take one of the white pills tonight. Go to the pill dispensary in the hall. I'll be there waiting." Tom hesitated, anger building, anger and frustration and a little fear, that coppery taste in the back of the throat kind of fear. It'd sounded like such a great idea, at first. The "Living Home" concept had proven itself in government and corporate work environments. The integrated system, based on a combination of artificial intelligence and bioelectrical networks, came highly recommended by the International Science Federation and Maggy McCormick, a colleague at the "barn." That's what he called the Molecular Computing facility of Androgen, the largest producer of robotic help and service aids in the entire Western Region. She said she didn't know how she'd ever gotten along without it, or words to that effect; now she was able to accomplish so much more than ever possible before. She had come to believe that her bohemian lifestyle had detracted from her professional career, holding her back from actualizing her potential -- that's how she talks -- and so she needed the discipline afforded by "Mother." That's what she called her machine - Mother. And, at first, she seemed satisfied with the arrangement. However, Tom had begun to notice cracks around the edges of her usually warm and free-spirited aura; she bore strain not well, it showed in her every movement. And her voice cracked occasionally, like a child's. He was beginning to understand the source. "Tom. I'm waiting, Tom. It's late. Time for you to go to bed. I've already set the alarm clock. Breakfast will be ready at the usual time. I've designed the perfect meal for your present caloric profile and needs. Tom? I'm still waiting at the pill dispensary in the hall. Tom?" He could almost hear her putting a foot down hard. Tom stood by the front door, rebelious yet uncertain, clenching his teeth, feeling helpless. But he lost the battle. His blood drained to his feet; with a shrug, he went to the dispensary. Waiting there was a tiny white pill and a glass of purified water on a thin black plastic slate. Hands in pockets, he stared at them under the muted, oval-shaped overhead light. It was no use, he knew; he swallowed the pill with the water, then ambled like a child to his bedroom two doors down. The lighting was subdued, soft; temperature and humidity at just the right levels; of course, he thought, what else?
"Tom? Tom. You still have your clothes and shoes on, Tom. Take them off now and slip into that caftan I laid out for you. Tom?" He lost his futile fight with the tiny white pill; it was easier to give in this time; each time it seemed easier. He sat up, rotated to the right, let his legs drop to the floor, bent at the waist, untied his shoes, removed them and his socks, stood up, undid his belt, let his pants drop to the floor, removed his shirt, tossed it into the chair nearby, grabbed the caftan, let it drop down over his body, turned, bent, lifted the covering, crawled in, slid to the middle, pulled the cover up around his throat and held its edge in both hands. "Good night, Tom. Don't worry about the mess. Mommy will get it for you. Sweet dreams."
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He laid on top of the thin microthermal covering and stretched out, holding his head in both hands, trying not to feel the effects of the drug. Once he had tried to fool the machine by placing the pill in his pocket; but it knew, it always knew, from sensors located all through the house it could read his biochemical profile constantly, gauge his mood and, he believed, his secret desires. It knew, and would not let him rest until he complied.
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My original motivation for developing this information and discovery resource was to attempt to assemble, in one place, a broad panorama of the players, problems and issues affecting the world community. It has been and continues to be a singular learning experience.
************* Projection
He paused to take a sip of wine to ward off the slight chill. "There would be no life or planets on which it might come into being and thrive. There would be no forces to act on anything. There would be no quantum fluctuations, no energy, no suns."
He looked down at the grass, illuminated by the silver starlight, sadness creasing his weathered features. "All we'd have is a vast, inert sea of free floating hydrogen atoms, the quarks of the proton locked in a fixed net, the electron bobbing along at the end of a string, not held by attraction, yet not able to drift off either -- all would be continuum -- there would be no quantum reality. A dead universe."
He turned to her, a broad smile stretching from ear to ear. "So, apparently, compacted balls of energy dimensions are required. Does that answer your question, my love?"
She breathed deeply the crisp, sweet smelling air, then replied, "Do the people at the Institute know you're out on your own?"
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| Metaphorical Algebra |
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| An Overview of Geometries |
************* Vacuum ~ Quantum Energy ~ Motion ~ Variance ~ Fluctuations ~ Quantum Field ~ Gravity ~ ************* 
Before there were space and time, there was empty, formless stillness. The vacuum seethed with ghost virtual particles coming into being in conjugate pairs of matter and anti-matter.Spacetime is but a large-scale manifestation of some more fundamental entity. Space and Time can be born and thus can die.1
1) From: Barrow, John D.; Pi In The Sky ************* |
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| Premise For Algebra Project Elementary Abstract Algebra can rightfully be said to culminate in a detailed study of Galois Theory and Finite Fields. The ideas and concepts necessary to support that material are introduced and developed in a systematic way leading to it. But then, G.T. and F.F. act as jumping off points, overlapping and dovetailing, for the study of Linear Algebra -- Vector Spaces and Transformations -- with an application to a different view of Quantum Mechanics. The crucial application of the theory of vector spaces is the mapping of one coordinate system onto another. That is, identifying one set of bases vectors with another through a linear transformation -- a reorientation -- when the ranks are equal, and when they are not, collapsing a set onto a subset, consequently generating a factor or quotient space. Another important mechanism with regard to quantum orthogonality is that of Inner Product *multiplication* with regard to the study of Inner Spaces [in particular: inner automorphisms]. Essentially we need to connect the ideas of bases vectors and zeros of a polynomial. For example: The zeros of xn - a are pecisely the set of bases vectors for a. The elemental unit vectors are the nth roots of unity. So, the bases vectors are: {a, ae1, ae2,....., aen-1}. Associated ideas: Symmetry Groups -- Zeros of polynomials [including the characteristic polynomials of differential equations] -- roots of unity -- bases vectors -- eigenvalues -- dimensionality of space -- eigenstate solutions of quantum wavefunction -- singular frequency -- surface -- family of curves equaling a constant.
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"Doctor Golgachev, Paleohistorian"
"All in good time, ladies and gentlemen, please. All in good time. First, Doctor Golgachev, our paleohistorian, has some interesting facts concerning the larger picture. I would like to introduce him at this time."
"My name is Alexi Golgachev; I am a paleohistorian -- the history of old Earth. Doctor Tolstoy has requested that I present a brief overview of background material relating to Earth events leading up to and immediately following -- geologically speaking -- when the alien structure evidently either first or last made contact where it now rests. Major geologic and biologic transformations occurred during this time period. A whole new order of biology emerged simultaneously all over the world. One threshold after another was crossed as evolution shifted gears, as life discovered original ways to express itself, ways that were previously unknown. No one just considering organic life prior to 600 million years ago, the time the alien craft is determined to have landed, would or could conjecture the direction life would take afterwards.
"My lecture will be brief, so please bear with me.
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An imposing man with bushy eyebrows and a stern face, his voice was nonetheless disarmingly cordial and engaging. His large hands resting on either side of the podium, he casually scanned the roomful of reporters. Then, he began: "I would first like to thank Doctor Tolstoy for his leadership during this time. For, what we have discovered thus far has been, ..., deeply disturbing and profound." He turned to nod towards Doctor Tolstoy, who nodded back. We were waiting; but not for long, he started right in.|
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Excerpt I From The Superposed Self Excerpt II From The Surrealistic Confluence
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"Megan's World"
*************  Megan put her drink down hard on the glass-topped coffee table. Nobody moved in the hot stuffy parlor. Through the sliding screen door, the fading light outlined the mountains far to the southwest, dark clouds menacing their jagged ridges and peaks like a pack of hungry hyenas ready to pounce. She wanted desperately to go out onto the veranda, but the mosquitoes were thick and fierce, thirsty for blood. This whole damn country seemed like that, she thought. What the hell are we doing here?Her husband, Sir Nigel Rothbank, hated it too. He missed the well-appointed leather chairs, the thick oriental rugs and tapestries, and most of all, the cigar-smelling opulence of his gentlemen's club. But, his family owned vast estates of tobacco, sugar cane and khat. It was his turn. Uncle Andy was in America, on business, he had said. Aunt Vicky -- how she hated that diminutive -- insisted on traveling through China one last time before death took her. Her expression. So dramatic, so theatrical, the whole family was rather like that. It was his turn then, he felt obligated, he needed to be here, in spite of the gout, the voracious insects, the horrid company, and his wife's illness, at least that's how he thought of it, her condition, that is.
There simply is no excuse.
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The overhead fan beat cadence to the somber presence of her guests. Why they were in such a black mood was a mystery, to be sure, thought Megan. They, at least, have an indoor pool and an air conditioner that works. Theirs was broken, that is to say, it stopped working all of a sudden one abysmally hot, sticky day last week and, that was that. What a country. The only air-conditioner repairman in the entire region, it seems, was in prison. He had attempted a coup, of all things, and failed, miserably. Of course, he failed, he's an air-conditioner repairman, for Christ's sake! No sense of responsibility or consideration, these people. He must've been aware of all those who needed him, who depend on him, his services. But no, he goes off and tries to take over the country leaving them -- her, her husband and their guests -- sweltering in this oppressive summer heat under siege on all sides by rabid mosquitoes.
| Gravity
Cats share the quiet better than dogs,
They live in a world of shapes and smells and lairs of underbrush,
Dogs clamor through, mouth open, tongue lolling,
It's better to be invisible,
As God and Nature intended. |
| Poetry "The Liberation of Tommy Geneva" |
Short Stories "The Oatmeal Incident" |
Essays "The Pandemic Of Hypocrisy" [June, 2005] |
| Dialogues |  |
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| Resume My Card |
Brief Bio | Pictures Brief Slideshow |
| If you lived in Port Townsend, Washington during the late 70's and early 80's, you might be interested in five pictures I've come by of the Town Tavern crowd. Who knows? You might recognize somebody. |
Site Index |
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| "The Superposed Self: Entanglement <--> Emergence" [essay in three parts] |
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| A Compilation of Some Writings | Frozen Underground [a novel of real events & real characters set in Alaska circa 1989] |
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| Doctor Golgachev, Paleohistorian | Megan's World | ||
| A Global Digest for the 21st Century | Center Stage -- The Meta-Library | ||
| Metaphorical Algebra | 
| Overview of Geometries | |
| The Anatomy of a Differential Equation | Number Theory: Diophantine Equations | ||
| Shorts, Episodes, and other nonsense... | |||
| Poetry | Short Stories | Essays | Dialogues |
| Personal Profile | |||
 We shall not cease from our exploration, and at the end of all our exploring, we shall arrive where we started and know the place for the first time.
"Somewhere there's a circus going on running itself." anonymous |
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 Adrian T. Dorn; copyright: © February, 2001 |
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