Friday, 28 December 2012
Game Theory- The Rock-Paper-Scissors Algorithm
From the roll of a die and the shift of a pawn to the spin of a cue and the flip of a card, its principles come into action through the players, their strategies and their payoffs. A premise that entails the methodology, skill and technique behind even the most primitive forms of human leisure and makes something serious out of the business of games. One where equilibria are sought, risk and choice are evaluated and conflicting interests are observed in a manner of critique; a platform where competition and completeness are deduced and location, segregation and randomisation are considered. A formulation of not only the players but the games themselves in a means that quantifies the tricks and flicks to winning and the shortcomings to losing. Game theory is to games as calculus is to change, for games offer a wealth of profundity regarding the mechanics of human skill and strategy as well as the strategic basis to decision making; extending well into frontiers such as economics and evolutionary biology where the flux of mutation and competition play themselves out like a well choreographed game. Consider the prisoner's dilemma, where two suspects are apprehended on the suspicion of thievery, if a bargain is offered to each suspect with the promise of mitigated jail time in return for cooperation the end result will be unfold with defection by both parties due to the notion of strict dominance despite the seemingly logical outcome of cooperation by both parties. Furthermore, the classic battle of the sexes takes form in game theory whereby a man and woman desire boxing and ballet respectively however they simultaneously desire to be together. In order to go about such a game, one necessitates the utility of the Nash equilibrium in its mixed strategy form; an equilibrium in which there exists a set of strategies, one for the man and one for the woman such that no player has an incentive or advantage to change his or her strategy given what the other players are doing. Analogous to a law that no one would break despite the absence of law enforcement or capital punishment. A more familiar circumstance would be that of rock-paper-scissors, whereby Nash equilibrium may be reached via mixed strategy given the zero sum nature of the game. An overall nexus of balance and conformity driven towards the satisfaction of both parties and the achievement of a realistic and level headed outcome, comparable to an algorithm that plays the game over and over until scissors and paper fit hand in hand.
Thursday, 27 December 2012
Chaos- The Butterfly Effect
Sunday, 23 December 2012
Calculus- The Integral Differentiation
Its incalculable complexity reduces arithmetic to child's play while its unsurpassed applicability belittles algebra with the rest of its regularity. A mathematical scheme bent on the diversity of change, the correlation of the input with its output and the continuity of functions. Since its inception via Newton and Leibniz, it has emerged as a union between the celestial and the terrestrial; a language of fluxions and fluents and the manifestation of the laws of nature. Calculus is a dimorphic synthesis of integration and differentiation linked via its fundamental theorem. The former of the two, seeks the area between the curve of a function f(x) while the latter pursues the way a function behaves as its input differs such as the of instantaneous rate of change. While the regularity, uniformity and discreteness of institutions such as algebra remain most apparent, calculus intervenes through the annihilation of such regularity and uniformity,assuming the curliness of slopes and curves. Calculus remains the gateway to realising the spread of vector and tensor fields permeating and changing through space and time, the medium towards the fathoming of continuums beyond that of the discrete. For instance, in realising limits for functions f(x), we may realise their behavior near certain values and extrapolate them for understanding the behavior of particle frequencies near magnetic fields, dummy variables and their jump discontinuity or even the interference pattern of photons via double slits. The elliptical orbit of the celestial bodies, the logarithmic spiral of a chambered nautilus shell and Zeno's paradox; whereby an infinite number of halves may be crossed in a finite amount of time, all share this common denomination of change and fluctuation as quantified by calculus. Trigonometric functions included, as their differentiation reveals the rate of change of such variables relative to one another. But the applicability of calculus exceeds that of the two dimensional, path integrals give rise to higher dimensions of application such as integration above curves while volume integrals consider the everyday reality of three dimensional spatial freedom. It is a ever encompassing framework, played by certain simple rules yet fulfilled by a nature's laws and governing dynamics; a formulation of maxima and minima, of input and output and of limit and continuity.
Thursday, 13 December 2012
String Theory- A Primer
Moreover, because patterns of string vibration arise in pairs, varying by around half a unit of spin, it creates an internal supersymmetry (SUSY). SUSY allows one to merge bosons and fermions given that they return to their original states after 360 and 720 degree rotations respectively, if one can define such transformations as manifestations of a greater multidimensional geometry, each of the known particles can be related by heavier superpartners. The additional dimensions are for mathematical consistency and Kaluza was the first to realise that adding a fifth dimension to spacetime mirrored Maxwell's equations, the extra dimensions curled up like a cartesian plane passing via each point in space. But among the hallmarks of string theory included the ability to mimic spin-2 gravitons with closed strings, allowing the possilibity of describing gravity quantum mechanically but without invoking fields directly. The only free parameter in question is the tension of the string, which can be calibrated more precisely using the graviton to meet the strength of the strong force. As a result, the minimum energy of a string, the planck energy, can be multiplied many times over by the amount of wavelengths in each mode or oscillation to give a large resultant, such may be cancelled out by quantum fluctuations leading to a massless string. As for other particle properties, spin simply becomes the aspect of how a string vibrates, as these vibrations can extend over curled up dimensions it becomes relatively simply to imagine a fermion moving in a gyrating fashion in another dimension, thus gaining a 720 degree rotation in the 3D space to resume its original position. So if mass and spin can emerge from a multi-dimensional geometry, what about the other forces?
By the 80's, the 5 string theories which all paired their bosons and fermions differently were united by Witten into M-theory into a context of an 11 dimensional Calabi-Yau space-time (10+1). It incorporates one dimensional strings in conjuction with branes (membranes), allowing gravity and the non-gravitational forces to unite at a single energy. This wasn't previously possible, given that the gravitational coupling constant refused to match the quantum forces except until an energy density that exceeded the unification energy; in M-theory it matched neatly. But we are talking ridulous scales on the order of 10^-35m, around 10^-20 the diameter of a proton; at such tiny scales gravity competes with the other forces so we need to unite quantum field theory with general relativity. Such a stark incompatility between the two arises because of the Uncertainty principle; in general relativity, perfectly flat space arises in the absence of a significant mass (such as the quantum vacuum) and thus the value of the gravitational field should be exactly zero. However, the Uncertainty principle needs only a mean value of zero and so the value of the gravitational field can fluctuate in a random 'foam'; therefore we get infinities (or ultraviolet divergences). These infinites come about because in quantum field theory, you deal with points that act as sources of fields, but with one dimensional strings infinities never occur because the energy of a vibrating string is dependant on its frequency as well as the amplitude at which it oscillates (closed strings and loops rely on circumference) and more frenzied modes of vibration produce more energy than placid ones. Much like a Feynman diagram, which capture the history of a particle, a 'worldsheet' capture snippets of a bunch of strings and recording their history as a static network of connecting tubes in spacetime; when the loops interact, two loops may merge and split into a different figuration. Such allows gauge bosons to be expressed as aspects of vibrating strings rather than the conventional view of seperate fields for each charge and particles as point-like bundles of energy osillating in those fields.
Thursday, 15 November 2012
Infinity- The Sky's Not the Limit
Tuesday, 6 November 2012
Chinese Philosophy- A Slice of the Orient
Friday, 26 October 2012
Logic- The Reason Pathway
A wave of reason cast by a gale of coherence. The rationale of argumentation and the sheer thrust behind thought and endeavour, it remains the epitome of systems; the envy of all rational systems. It is the magic of logic in both its precursory and prevenient flavours that has expounded and conveyed a means beyond just another methodology. It deploys a pathway compelled towards coherence, sense and soundness; one laced with consistency and the strive for completeness. For we are in constant pursuit of both formal and informal schemes of reason that lack contradiction, promote logic truth, envisage theorems and propositions and make sense. The principles of induction, deduction and abduction remain the cornerstones, the mainstay of such a logic pathway. In the inductive sphere, logic is envisioned as the derivation of not only statements but propositions from certain examples, quite a dichotomy may be observed, for the deductive sphere constructs examples on the basis of propositions. Taking it a step further with the abductive sphere, where hypotheses are evaluated and composed, logic entails a miscellany of frontiers, namely the mathematical. In the mathematical sense, logic is a business of the contrasting faces of completeness and incompleteness; confined to the bounds of predicate or formal systems. There is no axiomatic construct capable of proving its own consistency and completeness in mathematics, thus such systems lack simultaneous completeness and consistency. But logic is beyond the arbitration founded in philosophical circles, much more than the symbolism employed by numbers and exponents; greater than the scope of formal systems. From rationalism to logicism, the superficial pursuit was to extrapolate reason beyond mere experience; yet the transcendent goal and ground of all being was to architect and harness a universality. A universality that underpinned a universal pathway, one that would separate the fallacious from the logically sound. Such a pursuit sounds rather presumptuous, to create or to envisage a system that detects those crooked and circular modes of reason and simultaneously be conducive to those that make sense. Analogous to a mechanism that executes sound instructions and rejects or even destroys ill-formed and irrational means of reasoning. But since the Aristotelian view of logic grounded on both major and minor premises that generate so called syllogisms, there is a rejection of the usual pathways by which logic is applied and attained; the premise that logic does not correspond to anything in the material and physical world. Wherever the cards fall in such a light, logic as a pathway, a methodology and a deduction will progress as a cosmopolitan exultation of reason, comparable to a colony of worker ants tunneling through the rough terrain...
Thursday, 11 October 2012
Relativity- Through Einstein's Eyes
Tuesday, 2 October 2012
Scientia- A Philosophy of Science
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Friday, 21 September 2012
Memes- The Mimic Machines
Friday, 7 September 2012
Bertrand Russell- Politics and Celestial Teapots
Wednesday, 29 August 2012
4D- The Fourth Dimension
We reside upon a reality of dimensions. From the very objects we maneuver and manipulate to the curvature of space and time we extrapolate, the realm of dimensions seems the definitive platform of existence. And while limited to a discrete degree of three of such dimensions we begin to reflect on the feasibility of the fourth as a platform of existence. An abstract and abstruse concept compounded with the axioms and the theorems, the vectors and the coordinates. A fourth dimension truly breaks physical bounds of space and time, pushes the envelope on our profundity regarding the topological, geometric or even metaphysical nature of the known universe. A fourth dimension may well and truly express itself in the discipline of mathematics as a series of vectors, augmenting the degree of spatial liberty in a manifold; in physics, this comes as a grand unification of space and time via the Minkowski continuum of special relativity. But the central premise remains a fourth poled realm of space, where the minimum prerequisites central to the definition of a point are four. Envision a one dimensional terrain, a single coordinate is the prerequisite for the definition of a point, a two dimensional terrain requiring two coordinates, our three dimensional world requiring three and the four dimensional requiring four. But in terms of spatial freedom, a one dimensional world would restrict motion to right and left movements; a two dimensional reality limiting movement to right-left, forward-backward motions; a three dimensional world allowing right-left, forward-backward, up-down and around motions. The spatial freedom of a four dimensional world seems best represented by a tesseract cube, a four dimensional analog of its proportion, allowing the freedom of a three dimensional reality in conjunction with 'inside' movements. And while the verbosity of spatial movements and coordinates aims to tackle the abstract nature of a four dimensional world, we are only beginning to cut the Gordian Knot of its perplexity and mystery. We are only beginning to unearth and unveil the range of ramifications such an array of dimensions poses, only beginning to fathom the sheer extents and heights such an order of spatial freedom may reach as both an abstract and a temporal reality. For we are not merely entities of three spasmodic dimensions, rather we are beings of a higher purpose...
Saturday, 25 August 2012
Freud- A Portrait
Tuesday, 21 August 2012
Tabula Rasa- Debunking the Blank Slate
Saturday, 18 August 2012
Hormones- Messengers of Fight and Flight
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adds further to their psychological worth, their capacity for priming the mind to a biological degree. But perhaps most revered and renowned remains their mantle as the pivots of the fight-or-flight response, a complex of secretion by glands such as the adrenal, notable for its epinephrine output. Such a response to acute stress, followed by the production of dopaminergic molecule subsequently enhancing vigor and suppressing pain, giving rise to the 'adrenaline rush'. Moreover, one may observe the dynamic processes of hormones as a direct facet of a cohesive functional unit, neuroendocrine units such as the hypothalamic-pituitary-adrenal axis or even the hypothalamus-pituitary-gonadal axis function in unison in maintaining homeostatic, enteric, immunologic and other regulatory processes. It remains conspicuous the sheer cohesion and interdependence that fulfills the molecular realm of hormones, their enthralling action and intriguing reception, further kindled by their capacity to evoke and to stimulate. And as we converge deeper than ever conceived, further than ever; from the oasis of the posterior pituitary to the extremities of a lymphatic gland we realise an internal labyrinth of not solely symphony and synchrony but action upon reaction. Down to their genesis and synthesis, hormones have an uncanny resemblance of enzymes during their initial composition and inhibition, their subsequent activation and reception. There is an added resemblance of specificity, in the case of enzymes; stereo-specificity to the substrate and target cells guided by functional receptors for their hormonal counterparts. Anything but unkempt.
Thursday, 9 August 2012
Molecular Biology- Symphony in the Gene
A haven of order and complexity, playing to the symphonic rhythm of nature. The synchrony of cell and molecule in a cascade of biological marvel that ever confounds, gripping the secrecy of life. Standing as an endeavour rather than a mere attempt at expounding the interplay of genes and biochemical catalysis; it remains ever universal in both its form and direction. From the pithiness of its central dogma to its implications for modern genomics, molecular biology has fulfilled the embodiment of a grander scope of life. One readily laced with intricacy and elaborateness yet doused with the elegance of lucidity and intrigue. And while genes remain the powerhouse blueprints for powerhouse macromolecules, it is their stupendous odyssey from a humble polymer of nucleotides, to a polypeptide chain of amino acids and beyond that broadens the biological horizons of the cell and accounts for its elusive processes. From the copycat phase of replication that gives rise to twins from a parental strand of DNA; to the methodic phase of transcription that takes the stuff of genes to the stuff of RNA; to the interpretation of a residue by residue sequence by means of translation. Molecular biology seems the starting point at the terminating point of biochemistry, ever pushing the envelope of understanding further than ever. In addition, the dynamics of gene expression remain deeply encapsulated in the cellular preference for one gene over the other; hinting a biological symphony devoid of sound and note yet superfluous in authority and governance. Ruminating even further, we realise the exactitude at the heart of the gene, the initiating prelude of the promoter's bond to RNA polymerase, its elongation as DNA is copied into RNA and the finishing touches indicated by the omission of introns ans the expression of exons. Rather superfluous in terms of jargon, yet the most efficient and industrious of biological contraptions on the planet. A contraption bent on more than merely a central dogma, rather myriad indications and implications for cutting-edge science. For when a neoplastic mutation results in a malignant growth of cellular entities, the interplay between oncogenes and tumor suppressor genes grounds a molecular basis to understanding the pathophysiology of disease and disorder. Telomeres and telomerases included, their roles catalyzing such molecular mayhem and unrest. Molecular biology is at the coalface of disseminating the nature and causes of such mutations, but apart from cancer or oncologic phenomena, an ever emerging movement to dissecting the induced mutations caused by mutagens and the flaws the polymerases of replication spontaneously evoke. A realm of utility, viability and feasibility is deeply and intimately woven throughout the fabric of molecular biology, not solely for its groundbreaking and paradigm-shifting efforts in the genetic world but also for the spirit of discovery and lucidity it kindles and arouses...
Monday, 30 July 2012
Richard Feynman- The Quantum Mechanic
Saturday, 21 July 2012
Paranormal- Beyond the Bounds of Reality
Lurking figures of ectoplasm, reigning over the night; haunting and spooking in a manner of delight. The conveyance of thought seamlessly from mind to mind, telepathically converging on the psychic experience. The bending of cutlery and utensils via the power of will, telekinesis and its mystical fields of force. While such phenomena sound rather familiar to the exoteric mind, their incidence and documentation as figments of the paranormal remain far-fetched. Phenomena that breaks the ever known boundary of 'reality', is dismissed by skeptics and postulated by rigorous individuals of the scientific fraternity. And while paranormal happenings grip the mind with ever increasing anticipation and awe, a great challenge to the empirical basis to the scientific method is readily indicated. Paranormal events ranging from the magic of telepathy and clairvoyance to the mystic near-death and apparitional experiences exhibit such a challenge to conventional wisdom in a manner that enforces the spirit of inquiry. Latter-day parapsychology has yielded the finer rudiments of such happenings; from the extrasensory perception indicated by sensory deprivation to the telekinetic phenomenon as indicated by the manipulation of random number generation; the movement for an applicable and practical evidence-base seems to transcend the parameters of scientific methodology. But it remains the extrapolation of the scientific means of inquiry, to revamp its tenets and to redefine the nature of reality that is at the nucleus of such an intellectual saga. Above all, parapsychological research seems to unveil a coexisting reality alongside reality, indeed the term 'paranormal' serves an inconvenience, given some parapsychological experiences remain inherently ordinary. Such a controversial stance may be substantiated with the notion of the poodle that knows when its owner arrives home or the telepathy that is evident among callers of a phone conversation; the realm of ubiquity is unparalleled. The paranormal may remain a conception, an abstraction per se; the parapsychological movement for its objectivity and a sensation of consensus regarding not solely its plausibility but also rationality is paramount. For if such phenomena prove difficult to adapt into our current system of the universe, the implicit fallacy that such phenomena are fictitious is readily indicated. So in turn, the realm of the paranormal is indicative of the great challenges to scientific methodology and a primer to the incorporeal, the immaterial, the universal...
Friday, 13 July 2012
Linguistics- From Conjunctions to Chomsky
Tuesday, 10 July 2012
Immanuel Kant- Messenger of the Enlightenment
Saturday, 7 July 2012
Islamic Philosophy- Crucible of Faith and Thought
Tuesday, 3 July 2012
Optics-Physics at the Speed of Light
A luminary ray of mystique and romance. One that persists to confound and to astound, to gleam and shower all with its radiant luminosity. This familiar phenomena, bequeathed by nature and synthesised by that of man continues on a persistent basis to stagger and bewilder, not as a direct result of its refractory or reflective dynamics but rather its indispensable mantle. Light is ever ubiquitous and elementary yet the optic principles that deploy the image of a dynamic and versatile phenomenon prove paradigm-shifting. The inception of modern physics has foreseen myriad indications for optics; from the classical canons of refraction and reflection to the quantum constancy of photons to the boundless utility of lasers and optical fibre. Optics seeks the laws and axioms that drive and facilitate light; the 'bending' of a straw in a glass is a simple happening, but the mathematically sound, physically oriented and thermally dynamic explanation proposed by optics unveils a mechanism of infinite complexity and diversity. The laws of nature seem to articulate in synchrony, playing unanimously to a symphony; light remains the culmination of such a symphony, the crux of illumination and the subject of inquiry for optics. Understanding light was confined to the parameters of Newtonian particle theory until the advent of relativity and the elucidation of photons entered the scientific repertoire. It is the successive stances of optics that has redefined the approach to light and illumination, while bound by the universal laws of physics. Light is nothing short of dynamic and sprawling, it is our reduction of its form and function that has bequeathed the spectrum of electro-magnetism and forged new frontiers as to its velocity and insurmountable versatility. A preeminent instance of this versatility would be the oculi, commonly recognised as the eyes, centered on the concept of diffraction via a lens of biological tissue that warps light into a curvature prior to its conversion to nervous impulses. While the eyes may remain an inherently biological conception of light, the physics at the heart of the optic moment is both paramount and uncompromising. The advent of the lens as a sprawling optic application has reinforced the prospect of utility. Lenses, whether concave or convex, focus parallels of light rays upon a focal point in a fashion of diffraction. It remains synergy of light and the laws of physics that has surmounted gaps in understanding such dynamic phenomena and deployed a methodical means of first-hand investigation. And above all descriptors of physics and dynamics is an aesthetic pleasure that enriches the conception of light, divisible into its inherent spectrum of shades and hues; an elegant and alluring entity, abundant in beauty and charm. For all of natures laws lay hid in night, until optics was and all was light!
Saturday, 30 June 2012
Engineering- A Tour de Force
The very exultation of our practical genius. Furnishing the world over with wonder and synergy, synthesising things never before conceived and extrapolating the profundity of our imagination. A discipline doused liberally with the know-how and time-honoured innovation decreed by its forefathers and perpetuated by a spirit that yearns to push the envelope of design and technology further than ever. Making the systems and the contraptions at the core of modern life more robust, more efficient and more awesome while simultaneously embarking on a revolutionary tour de force to conquer the pragmatic nature of being. Engineering is a modality that has undeniably fostered a boundless realm of utility; the definitive fusion of principles and practice into an evident measure of equilibrium. One may reflect on the universality of engineering by observing the meticulous functions of an engine; pistons primed in linear motion, compelled towards combustion,driving stroke upon stroke; the kinetics of a chemical reaction, giving rise to novel substances and solutions; the aviation of an plane, maintaining velocity and opposing drag or even the irreducible complexity of a circuit, harboring resistance and conductivity. Engineering has transfigured both the tangibility of the material world and the intangibility of the imagination, extrapolating its depth and profundity. The synergetic integration of technological advance with that of the status quo is at the heart of the engineering spirit, the intellectual challenge of solving perplexing technical problems by means of an interdisciplinary approach is at its coalface. For it remains not solely the goal of making mechanisms more efficient and more robust but also more intimate and alluring in their simplicity that forms the tapestry of such an indispensable art.
Thursday, 21 June 2012
Ethics- At the Edge of Morality
Saturday, 16 June 2012
Nanotechnology- Size Does Matter
Saturday, 9 June 2012
Cortex- Fifty Shades of Grey Matter
Tuesday, 5 June 2012
Evolution- A Theory in Crisis
Friday, 25 May 2012
Gandhi- Pilgrim of Peace
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