Profane /prəˈfeɪn/


Adjective – not relating to that which is sacred or religious; secular.

Synonyms: secular, lay, non-religious, non-church, temporal, worldly, earthly.

I am a practicing Sacred Geometry Artist, and have drawn over 1000 representations of this art form, having explored hundreds of philosophical, alchemical, magical, astrological concepts.

The world appears to be experiencing and witnessing a profound polarity in this year of 2017, and with trepidation and caution I feel the need to explore the darker extremes of geometry, in order to deepen my understanding of its function within our common shared constructs.

The ubiquity of geometry in our lives, experienced through architecture, computation, medicines, astronomy, biophysics, physiology, neurology, chemistry, art, science, movement, location, geography, social sciences, planning, finance, literature, design and construction leads me to assume that no part of our experience cannot be quantified in terms of geometry, and thus to explore the darker aspects of geometric expression is necessary to complete my artistic journey.


The sacred–profane dichotomy is an idea posited by French sociologist Émile Durkheim, who considered it to be the central characteristic of religion: “religion is a unified system of beliefs and practices relative to sacred things, that is to say, things set apart and forbidden.” In Durkheim’s theory, the sacred represented the interests of the group, especially unity, which were embodied in sacred group symbols, or totems. The profane, on the other hand, involved mundane individual concerns. Durkheim explicitly stated that the sacred/profane dichotomy was not equivalent to good/evil. The sacred could be good or evil, and the profane could be either as well.

This dichotomy has been denigrated, notefully that “many societies have no words that translate as sacred or profane and that ultimately, just like the distinction between natural and supernatural, it was very much a product of European religious thought rather than a universally applicable criterion.”



Donald Trump. If one was to enter his mind, navigating the complex patterns of his protective processes, what might be found? But perhaps the more interesting question might be, what would you do if you were able to influence his thinking?

This is an open question, of course, but I am going to play an artistic game here, during the journey of this essay, with the intention of sowing the Seed of Bodhichitta within his mind, by using the Fibonacci spiral as a map (or cross-hairs if one feels so inclined).

The following images and accompanying texts I consider to be the circles of history, power, intoxication, political deviousness and evil that surround this man, and thus ‘knowing one’s enemies’ becomes the tool of the adept.

Let us play.



Geometric abstraction is a form of abstract art based on the use of geometric forms often, though not always, placed in non-illusionistic space and combined into non-objective (non-representational) compositions. Although the genre was popularized by avant-garde artists in the early twentieth century, similar motifs have been used in art since ancient times.

The avant-garde geometricians (from the French ‘advance guard’) are artists whose works are experimental, radical or unorthodox with regard to culture and society, often characterised by non-traditional, innovative and initial unacceptability, often offering a critique of the relationship between producer and consumer.

Let us assume that money is a prime motivational key into his mind, and money/profit the tensor twixt producer and consumer.



Reductio ad Absurdum – A method of proof which proceeds by stating a proposition and then showing that it results in a contradiction, thus demonstrating the proposition to be false. In the words of G.H. Hardy, “Reductio ad absurdum, which Euclid loved so much, is one of a mathematician’s finest weapons. It is a far finer gambit than any chess gambit: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game”

Absurdism – Intentionally ridiculous or bizarre behaviour or characters, of the belief that human beings exist in a chaotic universe.

The absurd confuses, befuddles and disorientates through juxtapositions of dissimilarity. Not us though, we have our map…



“Error: Fix EXT4-fs is bad geometry (block count exceeds size of device). Since I was not able to find any other solution, I reformatted the EXT4 partition. This eliminated the bad geometry error. Wish I knew why”. UNIX & LINUX Forum

There comes a time when the rule book is tossed out of the window, when circumstances demand radical and potent action, and one surrenders to a path of the unexpected.

The format of the obstacles ahead can be defined as bad geometry, those impediments to one’s goal, and thus the partitions can be dismantled and reformatted, to one’s advantage.

This is dangerously compelling work.



Social geometry is a theoretical strategy of sociological explanation, invented by sociologist Donald Black, which uses a multi-dimensional model to explain variations in the behaviour of social life. In Black’s own use and application of the idea, social geometry is an instance of Pure Sociology.

In The Geometry of Genocide, Bradley Campbell argues that genocide is best understood not as deviant behaviour but as social control – a response to perceived deviant behaviour on the part of victims. Using Donald Black’s method of pure sociology, Campbell considers genocide in relation to three features of social life: diversity, inequality, and intimacy. According to this theory, genocidal conflicts begin with changes in diversity and inequality, such as when two previously separated ethnic groups come into contact, or when a subordinate ethnic group attempts to rise in status. Further, conflicts are more likely to result in genocide when they occur in a context of social distance and inequality and when aggressors and victims cannot be easily separated.

Campbell applies his approach to five cases: the killings of American Indians in 1850s California, Muslims in 2002 India and 1992 Bosnia, Tutsis in 1994 Rwanda, and Jews in 1940s Europe. These case studies, which focus in detail on particular incidents within each instance of genocide, demonstrate the theory’s ability to explain an array of factors, including why genocide occurs and who participates. Campbell’s theory uniquely connects the study of genocide to the larger study of conflict and social control. By situating genocide among these broader phenomena, The Geometry of Genocide provides a novel and compelling explanation of genocide, while furthering our understanding of why humans have conflicts and why they respond to conflict as they do.

These are unprecedented times, though history has lessons for the alert.



“This is an Official and Original Restyle Product!”

Our history of bondage is deeply aligned with our histories of the slave trade – that of the imperial exploitation and manipulations of servitude.

Slavery is a legal or economic system in which principles of property law are applied to humans allowing them to be classified as property, to be owned, bought and sold accordingly, and they cannot withdraw unilaterally from the agreement. A person may become a slave from the time of their capture, purchase or birth.

Vast diametric inequalities are the very tensors that facilitate the billionaires, they who turn a subtle blind eye to the multiple sources of exploitation along the supply chains.

Compassion and Empathy – In Business?



“Jean Cocteau – The Cubist stage curtain, with its brutal geometry; the loud volley of the four Underwood typewriters marking the return of Marie Chabelska as an American typist, creating concrete poetry with the typewriter keys – Hammering.”

Brutal – Savagely violent.

Brute force is used to solve geometric problems or complex algorithmic problems, and computers have the capacity and work tirelessly to achieve their set goals. Machines that do not tire, nor allow their concentration and focus to wander, and thus ‘number crunching’ leads inexorably to resolution.

They never give up. Neither will I.



The World’s Hardest Easy Geometry Problem

Using only elementary geometry, determine angle x. Provide a step-by-step proof.

You may use only elementary geometry, such as the fact that the angles of a triangle add up to 180 degrees and the basic congruent triangle rules (side-angle-side, etc.). You may not use trigonometry, such as sines and cosines, the law of sines, the law of cosines, etc.

This is the hardest problem I have ever seen that is, in a sense, easy. It really can be done using only elementary geometry. This is not a trick question.

That which appears simple can often be the most complex, and the enigmatic nature of actual solutions are deeply hidden within the matrix of existence. We can seed in the present however, unaware of how resolutions might arise, and this can be understood by reflecting upon the nature of karma (cause and effect) and through the viewing and analysis of synchronicity.

Everything is connected.



At the beginning of the 18th century, Gottfried Leibniz took a break from quarrelling with Isaac Newton over which of them had invented calculus to confront a more formidable adversary, Evil.  His landmark 1710 book Théodicée argued that, as creatures of an omnipotent and benevolent God, we live in the best of all possible worlds.  Earthquakes and wars, he said, are compatible with God’s benevolence because they may lead to beneficial consequences in ways we don’t understand.  Moreover, for us as individuals, having the freedom to make bad decisions challenges us to learn from our mistakes and improve our moral characters.

In 1844 another philosopher, Arthur Schopenhauer, came to the opposite conclusion that we live in the worst of all possible worlds.  By this he meant not just a world is full of calamity and suffering, but one that in many respects, both human and natural, functions so badly that if it were only a little worse it could not continue to exist at all.   An atheist, Schopenhauer felt no need to defend God’s benevolence, and could turn his full attention to the mechanics and indeed (though not a mathematician) the geometry of badness.  He argued that if the world’s continued existence depends on many continuous variables such as temperature, composition of the atmosphere, etc., each of which must be within a narrow range, then almost all possible worlds will be just barely possible, lying near the periphery of the possible region.  Here, in his own words, is his refutation of Leibniz’ optimism.

Mandelbrot’s eclectic research led to a great breakthrough summarized by a simple mathematical formula: z -> z^2 + c. This formula is now named after its inventor and is called the Mandelbrot set. It is significant to understand that this formula, and the Law of Wisdom which it represents, could not have been discovered without computers. It is no accident that his discovery, which many say is the greatest in twentieth century mathematics, occurred in the research laboratories of IBM.

Most have an innate fear of chaos, though it resides within the considerable 94% that is unknown, that which science describes as dark matter and dark energy. Chaos underlies and informs all that is, it is the engine that drives the universe, including you and I.

As the world tips ever deeper into its chaotic state in 2017, the appeal of order becomes increasingly beckoning, and thus we tend to offer up more of our individual need fulfilments to others, seeking government and authority to create the answers to our apparent problems, thus Donald Trump appeared as saviour to unhappy Americans.

Ordo ab Chao? Perhaps in the past yes, but the answers today reside in the chaos.



Talreja reported brittle and tough polymer matrix composites to show different cross-ply laminate stiffness reductions due to transverse cracks, despite very similar elastic properties. Studies of crack opening displacement (COD) in laminates may help in solution of this problem. Approximate analytical models based on the variational approach pioneered by Hashin were therefore applied in addition to FEM-calculations. Approximate models were concluded not to be reliable for future analyses of this problem. Experimental COD for brittle GF/EP laminates at low crack densities was fairly well predicted by FEM-calculations. None of the models were able to predict experimental data at high crack densities. Residual plastic strains are suggested as an explanation and may also be responsible for reported matrix-related differences in stiffness reduction.

Cracking is random, unpredictable and chaotic. It has a resonant beauty, called upon by artists and creatives, though feared by structuralists, architects and designers, as the integrity and capacity to function and perform can rapidly cease.

Stress fractures in the wings of aircraft, or the load bearing beams of bridges suffer from the constant push and pull of dynamic loading and ultimately lead to failure.

Seismic activity, in the tectonic plates of earth, or within the all structures of society can lead to catastrophic failures, and the watchful are aware, and also relaxed in their acceptance, for resistance is futile.

Change is inevitable. Impermanence is Truth.



Sonic Geometry (a.k.a. Andy Beyer) is one of the most creative and unique acts emerging from today’s conscious bass music movement. Born from the fusion of Colorado’s jamtronica and bass music scene, Sonic G combines ear-bending live glitch performance with passionate guitar playing and a deep atmosphere that echoes the pulse of the universe in a one-of-a-kind live electronic experience.

The crazy ones, the mad ones were often in history the visionaries, those who could see further, dive deeper into the vortices and mechanisms, unafraid or compelled to explore the madness of disorder, and discord, sometimes returning, surfacing with vital information that carried answers to problems that had hitherto been hidden.

Beautiful Crazy.



Crooked planes are polyhedra used to construct fundamental polyhedra for discrete groups of Lorentz isometries acting properly on Minkowski (2+1)-space. This diagram represents the intersections of crooked planes. Criteria for the disjointness of crooked planes are developed. These criteria are applied to derive sufficient conditions for affine deformations of a discrete subgroup of SO(2,1) to act properly on Minkowski space.

Crooked – bent or twisted out of shape or out of place. Dishonest, illegal.

A distortion in the process, of conversation perhaps, a redirection (misdirection perhaps) and powerful influencer, as the power of words to realign two previously unconnected attributes with one another.

Words. Comprised of 26 letters. 26 geometric shapes. 26 sigils. This is magic.

Crooked, anybody?



The Dark Geometry of Picasso’s Mistress from Every Angle – An exhibition of 18 paintings, 3 sculptures and 31 drawings and gouaches present the geometric structure of Cubism in the process of emerging. This nascent style was itself unusually concentrated at this stage: fraught with rigid herniated surfaces, complex feelings and a sorrowful prevailing darkness.

In addition, nearly all the artworks are portraits of, or were inspired by, the distinctive physiognomy and emotional climate of one woman: Fernande Olivier, Picasso’s mistress from 1905 to 1912 and perhaps the great love of his life. With her dark, almond-shaped eyes, charmingly peaked upper lip, slight double chin and intricate braided and piled topknot, Fernande was a crucial presence in Picasso’s art.

Are you afraid of the dark?

There appears to be a growing understanding of the need to acquaint and familiarise ourselves with what Carl Jung described as ‘Shadow’, those inner attributes of fear, envy, anger, dissatisfaction – in short negativities, and this essay is my attempt to address this growing conversation.

Light and Dark are an example of the extremes of polarity, and the wise seek Union (Yoga) of the Middle Way, and to complete this Spiritual Path it feels appropriate to cease denial of one’s negative attributes by highlighting them facilitating their resolution.

High Light.


Shadow Work.



An exhibition featuring 23 participants, all Latin Americans working in geometric abstraction between 1950 and today, who explore a kind of creolization of orthodox geometric style. They effectively reinvent geometry into a notion that is free from theory – a ‘dirty war’ according to Romberg. Like the controversial French philosopher George Bataille, who believed that ‘divine filth’ leads to pure ecstasy, Romberg believes it is possible to bring about an eroticism of geometry through dirt.

By twisting and reinventing classic shapes using contemporary cultural prisms, the organic pared-down works in the exhibition questioned the role of geometry in human experience.

Don’t get dirty!

The pathological sensibility that we are taught as children, that drives and compels society.

Everyone eats a peck of dirt in their life.

Dirt is subjective to a large extent, and dirty is a provocative word, evoking repulsion, revulsion and abhorrence. The paradox is that all we eat grows, lives, depends and arises through dirt, and upon dirt we walk, and into dirt we return.

An open expansive mind can see dirt as what it is, the same nature as all that exists, known through our minds, dirty minds if it be.


Clarity: being able to see through the dirt, and recognise the perfection within.



Dead Lotus Couture’s identity is borne of an emotional world, comprising sinuous, sensual shapes that reveal a dark spiky elegance with a sophisticated touch. Volumes and devious geometry are combined to bring out your foxiest alter ego.

Each item is specifically designed to caress and accentuate your body shape at its best, transporting you to a parallel universe of imaginative and surreal beauty. Every creation holds in itself a precious little world built around a foundation of research, quality and innovation.

Emotions and sensuality are fundamental elements for Dead Lotus Couture as is merging the past with a sci-fi imaginary, and pushing the limit between fantasy and temporality.


The subversive use of the Sacred, the hijacking of Archetype, the misuse of the Holy, all grist to the mill of the artful commerce machine. Portraying Icons is the art of today, birthed by Andy Warhol and greedily consumed by the mass.

And I too, as a point of highlight, am of this world. Seeking.



“Waleed Kadous: This document will step you through the process of making your first Orca component. In particular, we will build an Orca component called “drunkrobot” that simulates a robot that takes a random walk. We’ll use the existing Orca component “position2dmon” to watch the robot as it moves around.”

The illustrated geometry here is of a drunken spider, whose web-weaving abilities are somewhat denigrated through LSD25.

Many of the giants of the technological world, most notably Steve Jobs (Founder of Apple) celebrated the fact that his visionary foresight and genius was amplified by the use of LSD25.

The World Wide Web

“Oh, what a tangled web we weave, when first we practice to deceive”



“Up on the tower, I battled the vertigo enough to make it back down to land. Safe on stable ground, I tell J my experience. I am giddy! It’s my first experience of vertigo in memory, but my body knows this feeling so well. I tell J, maybe vertigo is equivalent to what Sappho feels in Fragment 31, when the speaker looks at her lover talking to another and all her senses break down in the gaze. Vertigo too is about triangles, I tell J. My body has felt this metaphor deeply—the sickness of vertigo is like the sickness of desire. Sappho’s poetry is not only about jealousy, which we already knew, it’s about vertigo. My feeling at a great height can teach me something about love. I begin to talk about vertigo as a way to talk about erotic triangulation. I begin to believe erotic triangulation is just like motion sickness.”

Eroticism – a quality that causes sexual feelings, as well as a philosophical contemplation concerning the aesthetics of sexual desire, sensuality and romantic love, somewhat dependent upon culture and time.

Dare I follow the lines of desire, travel the pathway of ecstasy, of that forbidden history? For now the pornographer’s eye seeks an avaricious taste, of those souls whose witness degrades their imaginations, participating in the destruction of love.

And be thee gone destroyer of youth.

Oh tenderness, be mine. Complicit in the touch of grace, where fingers meet, and eyes glance to tell.

Soft Geometry.


“In The Brothers Karamazov, nineteenth century Russian novelist Fyodor Dostoyevsky parallels the problem of evil with the discovery of non-Euclidean geometry.  Despite the naturalness with which evil and mathematics go together, Dostoyevsky’s discussion of mathematics is still surprising.  His point isn’t that mathematics causes human suffering, as true as that might be.  He’s showing us, rather, one of the reasons the problem of evil is the most powerful objection to the existence of God; namely, it forces us to lay aside our preconceived notions of what’s reasonable, something we’re loath to do.  But the problem of evil isn’t an intellectual problem – or at least not primarily intellectual.  Rather, it’s in part a problem stemming from mistaken loyalties.  So too, the problem of geometry.

One of the novel’s characters, Ivan Karamazov, is an astute intellectual who in many ways represents modernism (a version of rationalism), where reason claims our ultimate devotion. In a crucial conversation with his younger brother, Alyosha, Ivan divulges his beliefs about God. He begins with geometry, of all things. Ivan believes that reason constrains God to create the cosmos according to ordinary, Euclidean geometry (Euclidean geometry is the geometry that Euclid presents in his famous book the Elements, the geometry most of us learned in school). But, Ivan says, there were and are even now geometers and philosophers, even some of the most outstanding among them, who doubt that the whole universe, or, even more broadly, the whole of being, was created purely in accordance with Euclidean geometry.

The problem, according to Ivan, is that the real world may not be Euclidean, but non-Euclidean.  That is, physical space doesn’t answer to all the “truths” of ordinary Euclidean geometry.  In real life, for example, parallel lines can meet!  (Einstein’s general theory of relativity later seemed to confirm this possibility.)”

Evil – Profoundly immoral and wicked, and … rational?

Euclid suggested that the laws of nature are but the mathematical thoughts of God. And to these laws of nature we must all surrender.

The literal meaning of Swastika (Sanskrit) is “One that is self-existent”, or “self-existing”, in other words; “Unborn and directly originating from eternity since time eternal”.

The chiral attribute of the swastika reflects both the perpetual story of the ‘Evil Twin’, both as understood in the classical mythological tales, and also in the ‘Evil Twin’ as current description of a combination of nanotechnology and a unique twisting property of light that could lead to new methods for ensuring the purity and safety of pharmaceuticals.

Evil can be good?

Shall we go there?

Ordinary matter — the type comprising the earth, our bodies, and much of the visible universe — is made up of three kinds of particles: protons, neutrons, and electrons. Protons and neutrons are the heavy bits that make up the centre (nucleus) of an atom, while the much lighter electrons form a cloud around it. A proton and an electron have equal but opposite charge, so when there are the same number of protons and electrons in an atom, it’s neutral and stable.

Each of these particles, though, has a sort of “evil twin” — its antiparticle. For instance, a proton’s antiparticle, simply enough, is called an anti-proton, and an electron’s antiparticle is called a positron. A positron weighs the same as an electron, but it has the same charge as a proton. Since opposite charges attract, electrons are drawn to positrons the same way they are to protons. If a particle ever meets its antiparticle, though, something happens — they completely destroy each other. Scientists call this annihilation, and even though it sounds frightening, you’d have a hard time collecting enough antimatter for it to be dangerous — virtually the only time we see antimatter is when it is made in the lab.

This annihilation can be useful, though. When two particles annihilate each other, they don’t just vanish without a trace. Their charges cancel out, but the energy that they contained has to go somewhere. This has a lot to do with the most famous equation in modern physics: E=M×c2

From the tension between good and evil arises a known energy.

A Union. Yoga.



Consider a sequence of trials, where each trial has only two possible outcomes (designated failure and success). The probability of success is assumed to be the same for each trial. In such a sequence of trials, the geometric distribution is useful to model the number of failures before the first success. The distribution gives the probability that there are zero failures before the first success, one failure before the first success, two failures before the first success, and so on.

For example, a couple plan to have children, and will continue until the first girl. What is the probability that there are zero boys before the first girl, one boy before the first girl, two boys before the first girl, and so on?

“Failure is not an option”

Failure is essential and inevitable. It comprises the polarity of all non-failures, all successes, all achievements and is largely ignored as the necessity.

Failure creates beauty, failure creates movement, failure is the nature of impermanence.

We celebrate failure.

The failure of death is life.



Abstract: In the physical model of particle formation by the catastrophic failure of a brittle solid, it is postulated that cracks sequentially form the surfaces of the fragments and that the resulting particles may be characterized by faces, edges and points. Using this simple model and several apodictic observations, three equations are derived that relate the number of points on a particle to the number of edges and faces on that particle surface.

It was found that the number of points on the surface of a particle is always even, there are 50% more edges than points and the number of faces is 2 plus half the number of points. Unusual or forbidden shapes were found that are both rare and tend to disappear on further size reduction, and, moreover, are characterized by pairs of multiply connected points. Moreover, because a fragment is one of a very large number of particles, it will have traces (faces) of other particles on its surface, and its shape will be complex. Finally, using a point counting system, a particle characterization system for angular particles is proposed.

A fracture can be the result of high force impact. An impact that creates the powerful effect of fracture.

In today’s world I might ask the question, who or what is making a great impact? And follow that question with another, will that impact create a fracture?

Perhaps the most dynamic impact upon the collective psyche of the world recently is the presidency of Donald Trump, and the fractures within the systems of balance and containment are visceral. No intelligent person has not taken consideration of this catalyst of profound psychological fracturing, also manifesting in the divisional fracturing potential of cultures and societies around the world.

Think, Egg.



If you’ve never played Geometry Wars, the concept is simple: You pilot a claw-shaped ship at the centre of the screen, and your goal is to survive as long as possible, racking up as many points as you can. You do that by shooting other ships that appear on the playfield. Their destruction leaves behind objects called geoms; collecting them increases the value of a point multiplier, which helps run up your score.

Its style is very evocative of the vector-based games of the 1980s, especially Tempest: Bright neon-coloured abstract objects on heavily contrasting grids, with a pulsing electronic dance music soundtrack as backdrop.

Frantic – distraught with fear, anxiety, or other emotions.

This not simply a computer game, but a metaphor for all war. Full stop.

After all, what is a Meta for?



“Frozen Geometry emerged from years of sketching new textures on guitar, which were layered and looped into immersive capsules of harmony and drift. The original intention was to use them as melodic foundations for future compositions but then he “became aware of them existing on their own.”

Offering the first full-length offering from legendary ambient act ‘Casino Versus Japan’ in over half a decade. An intriguing opus of hypnotic beauty and peripheral consciousness.”

Music to my ears… As music hath charms to soothe a savage beast.

Let us melt his heart, ease his soul, hypnotise him, and charm him into being peace incarnate.

It can be.



“The Furious is a level by Knobbelboy, the creator of Dark Rainbow Rebirth and Crying Souls. It takes the name from the song used. The level, with its 53k objects, boasts highly detailed effects and lots of animation. The level focuses on memorisation and crucial timing during the double/triple speed parts. The level is also well known for its 2.1 fan made boost rings. It’s considered a medium demon.”

The modern city is the loci of system energetics, in terms of finance, power, communication, population, transport and movement. Subsequently these nodes act as crucibles of catalyst.

This seething web of energy – in the airspace, underground, upon the ground and of the hi-rise is a frenetic dynamic of forces that cross pollinate and feed the collective city psyche.

Amidst the furious cacophony exists the potential of seeding, equalised with the chaotic flow that carries subtle messages of wisdom, love and compassion, and serves as an antidote to the collective angst.

Geometry is the diagrammatic of delivery.



“I have to say that I truly hate geometry. I made it through TT geometry with my oldest left brained child. She totally understood everything except the proofs but we somehow managed to finish it. Fast forward to today. Middle dd, right brainer, is doing TT geometry and hates it. Somehow I thought geometry would suit her right brain (she hated algebra 1). What was I thinking? Today I suggested that she watch the teaching dvd’s. Maybe listening to it and watching practice problems would help cement the material in her brain. She adamantly refuses. She tells me she hates math and really doesn’t care about the proofs and she will just skip them. Math has always been an issue between the two of us.”

Not. My. Words.

Hatred is something that I can hate. Or is that a contradiction? I suppose I can say that I hate cancer, but even that seems to open a paradox within my mind, for it serves to deny what exists, and as the function of hatred appears to be that which destroys inner peace it might be that it serves no ultimate purpose.

The world might be a different place without hate.

Imagine that challenge.



Wikipedia mentioned the limitation of Gödel’s theorems. According to it, Euclidean geometry doesn’t satisfy the hypotheses of Gödel’s incompleteness theorems, that is, it cannot define natural numbers. Why is that? Isn’t the number of points, lines, or polygons natural number? I thought it would be easy to define natural numbers in Euclidean geometry. Gödel’s two incompleteness theorems are among the most important results in modern logic, and have deep implications for various issues.

Logic (originally meaning “the word” or “what is spoken” but coming to mean “thought” or “reason”), is generally held to consist of the systematic study of the form of arguments. A valid argument is one where there is a specific relation of logical support between the assumptions of the argument and its conclusion. 

An incomplete argument offers an opening for resolution, an opportunity to allow development of communication, for philosophy serves no purpose other than to describe reality.

And reality is a work in progress, it is a continuing conversation with the changing circumstances of experience, which necessarily aligns with an evolutionary trajectory of universal dimensions.

The universe is both complete and yet incomplete, it is all that is, but also is not what it shall be, and this incomplete logic is a reflection of the continuation of hope.

Logic has neither to be proved, nor proved.



The Theory of Inconsistency has a long lineage, stretching back to Herakleitos, Hegel and Marx. In the late twentieth-century, it was placed on a rigorous footing with the discovery of paraconsistent logic and inconsistent mathematics. Paraconsistent logics, many of which are now known, are “inconsistency tolerant”, that is, they lack the rule of Boolean logic that a contradiction implies every proposition. When this constricting rule was seen to be arbitrary, inconsistent mathematical structures were free to be described. This book continues the development of inconsistent mathematics by taking up inconsistent geometry, hitherto largely undeveloped.

It has two main goals. First, various geometrical structures are shown to deliver models for paraconsistent logics. Second, the “impossible pictures” of Reutersvaard, Escher, the Penroses and others are addressed. The idea is to derive inconsistent mathematical descriptions of the content of impossible pictures, so as to explain rigorously how they can be impossible and yet classifiable into several basic types. The book will be of interest to logicians, mathematicians, philosophers, psychologists, cognitive scientists, and artists interested in impossible images. It contains a gallery of previously-unseen coloured images, which illustrates the possibilities available in representing impossible geometrical shapes. Chris Mortensen is Emeritus Professor of Philosophy at the University of Adelaide. He is the author of Inconsistent Mathematics (Kluwer 1995), and many articles in the Theory of Inconsistency.

Inconsistent – not staying the same throughout.

Seeking consistency has great similarity to the expectation that things will not change, inasmuch as neither are ultimately possible. The illusion of permanence brings succour to the unstable, though the wise recognise transience.

As a result of the primacy of inconsistency, balance is ever shifting, necessitating both subtle and profound adaptation.

At the heart of the pure, consistency resides, and it is this within this thread of space-time where the magician travels, along a super string of golden thread – generous, luminous and numinous.



“Sheet intrusions (inclined sheets and dykes) in the deeply eroded volcanoes of Geitafell and Dyrfjöll, eastern Iceland, were studied at the surface to identify the location, depth, and size of their magmatic source(s). For this purpose, the measured orientations of inclined sheets were projected in three dimensions to produce models of sheet swarm geometries.”

Intrusive – causing disruption or annoyance through being unwelcome or uninvited.

Intrusion is considered by many to be on the increase, labelled the surveillance society, where the monitoring and electronic governing of our communications becomes the ubiquitous currency of big data interpretations, manipulations and misunderstandings.

Seismic Changes.

Intrusion fails, as intrusion skews.

Though the magician wears invisibility’s cloak.



“I can’t get rid of unwanted and invisible geometry at origin in block. I’ve an issue with some dwg files we’re working with, where there is a block somewhere in the file that has some hidden geometry in it near the origin, while the model itself is at the project’s coordinate location. Is there any way to exclude anything that isn’t visible from all blocks, or alternatively ‘unmask’ the bits that are hidden so I don’t have to explode everything?”

Masking, cloaking and invisibility the language of magic. At times empowered distraction, often illusory, but at its heart is reversing the maxim – rendering the invisible, visible.

The geometries that form the substance of the connective tissues of Karma’s filaments, have been called ‘Indra’s Web’ the invisible non-substance that interconnects all, with all.

Fractal and holographic by modern description, aether by ancient seer.

I see invisible geometry in night sky, I feel invisible geometries hold me as I walk and sit, I breathe invisible geometries and I think of invisible geometries – for I connect dots, systematically, habitually.

Patterns unseen, but known.



Background: Multiple factors impact subcutaneous insulin injection pain. Injection devices [e.g., syringe or pen needle (PN)] affect pain due to needle length, diameter, needle polishing and lubrication, and needle tip geometry.

Methods: We evaluated a modified 5-bevel PN tip in 32 G × 4 mm 31 G × 5 mm and 8 mm PNs vs the equivalent marketed 3-bevel PNs in laboratory penetration force testing, as well as in insulin-taking subjects for overall acceptability, comparative pain, and preference. The clinical tests were done in three ways: paired insertions with the subjects blinded to PN tip geometry, after brief at-home use of 5-bevel PNs, and again with subjects informed about each needle’s tip geometry in paired insertions.

Precision Incision – at the tip of a needle.

Pain – a signal of necessity, alerting through heightened awareness, serving to take evasive or considerate action.

Mindfulness and Alertness – the 2 components of meditation.



In mathematics, point-free geometry is a geometry whose primitive ontological notion is region rather than point. Two axiomatic systems are set out below, one grounded in mereology, the other in mereotopology and known as connection theory. A point can mark a space or objects.

Point-free geometry was first formulated in Whitehead (1919, 1920), not as a theory of geometry or of spacetime, but of “events” and of an “extension relation” between events. Whitehead’s purposes were as much philosophical as scientific and mathematical.

Whitehead did not set out his theories in a manner that would satisfy present-day canons of formality. The two formal first order theories described in this entry were devised by others in order to clarify and refine Whitehead’s theories. The domain for both theories consists of “regions.” All unquantified variables in this entry should be taken as tacitly universally quantified; hence all axioms should be taken as universal closures. No axiom requires more than three quantified variables; hence a translation of first order theories into relation algebra is possible. Each set of axioms has but four existential quantifiers.

What is the point?

The circle has no point, and neither does the sphere.

“Life without geometry is pointless”



Abstract: This experiment looks at porphyrins and the molecules which coordinate to their metal centres in terms of ligands and the Lewis acid-base model. The poisonous nature of some small molecules is investigated by molecular modelling (using both the MacSpartan and CAChe programs). The first stage involves molecular modelling of the HOMO and LUMO orbitals on the ligands. The second stage investigates the energetics of the porphyrin-ligand complexes by calculating energies of optimized models.

Hendoku Iyaku – Making Medicine from Poison Through the skill of the medicine maker, the venom is distilled as a medicine. Drops of venom are gathered within the crystal amethyst chalice, inset with cut emeralds and golden droplets. Upon blending with the tabellarius liquid in 36 cycles, with fire, water, earth and air, an alchemy occurs, whereupon the poison is diluted to become a medicinal remedy. Nagarjuna, he of the Snake People (Nagas), proponent and expounder of the Prajñāpāramitā Sūtras teaches the mantra of the Perfection of Wisdom is like a great physician who can change poison into medicine. Tayata Om Gate Gate Paragate Parasamgate Bodhi Soha.



Correcting poor initial geometry – One of the most common problems faced by users of any data processing program is incorrect information about the experimental geometry in the input. This will often cause outright failures in indexing, but sometimes more subtle effects are possible, such as mis-indexing. In such cases, it may be possible to index and refine a lattice that on the face of it looks reasonable but is actually shifted so that ,  or  (or some combination of these) are off by some integer value (often +/- 1).

DIALS uses the information written to the image headers to form its initial model for the experiment geometry. That is, we trust that the beamline has been set up correctly and the files produced at the beamline are a good description of the experiment that was performed. Using the dxtbx library within cctbx means we even recognise specific beamlines in many cases, and interpret the files according to custom format readers that are appropriate for those beamlines.

Graphical representation – an object of misuse and confusion, as in the process of statistical analysis the variables and scale can be used to create a story that is the opposite of truth.

And in this age of post-truth, and revisionist history, perspective and alignment is being distorted, and one potential destination is, The Death of History.



Something abstract existing in thought or as an idea but not having a physical or concrete existence. Visual geometry containing the non-explicit description of sexual organs or activity. Arising in the mind it intends to stimulate erotic rather than aesthetic or emotional feelings.

Geometric Porn App was rejected by Apple Inc. Feb 1, 2012 05:47 PM.

I have sat in circle in men’s groups, where the fellowship offers the safe exploratory space to share from the heart, about matters of manhood, parenting and a range of masculine conversations, from A to Z.

Amongst the 20 to 30 age group, the problem that was uppermost in the men’s mind was that of pornography – it was THE most addictive issue in their lives. Not drugs, not drink, not cigarettes, but pornography.

A generation whose introduction to the world of sex, and instruction thereof, is pornography.



The unique geometric philosophy utilised in the Punk® technology range can be applied to rotating systems as a means of transmitting torque whilst accommodating angular misalignment. In torque coupling applications, the use of matched pairs allows both angular and parallel misalignment to be accommodated. This philosophy allows a number of new functions to be achieved.

The geometry comprises a system of two or three nested rings with cooperating male and female spherical surfaces with a common centre point. Within the system, each adjacent pair of spherical surfaces is connected by a pair of cylindrical keys received into a pair of cylindrical keyways and/or by pairs of axles received into a pair of bores. These constrain relative rotational motion between the rings to a single plane. The axles/keys connecting the two spherical interfaces (in the three ring system) are placed on planes that are normal to each other.

No future: Nihilism. Dada is art that is anti-art. Punk is music that is anti-music. Existentialism is a philosophy that is anti-philosophy.

Sex. Pistol. And we don’t care.

I do.



A new frontier has emerged at the interface between probability, geometry, and analysis, with a central target to produce a coherent theory of the geometry of random structures. The principal question is the following: within a given structure, what is the interplay between randomness and geometry? More precisely, does the geometry appear to be random at every scale (i.e. fractal), or do fluctuations “average out” at sufficiently large scales? Can the global geometry be described by taking a suitable scaling limit that allows for concrete computations?

Spectacular progress has been made over the last ten years in this domain. The goal of the programme is to gather experts from probability, geometry, analysis and other connected areas, in order to study aspects of this question in some paradigmatic situations. Topics of particular relevance include the Gaussian Free Field, random planar maps and Liouville quantum gravity, in connection with conformally invariant scaling limits; spin glass models and branching random walks; percolation and random graphs; and random walks on graphs and groups in the case where the geometry is determined by some algebraic ambient structure.

Random – proceeding, made, or occurring without definite aim, reason, or pattern.

We are in 2017 where deliberate has ceased to function and random is encoding the mechanisms of doubt, confusion, misunderstanding, birthing sequences of chaotic unknown and unpredictability.

Gamblers can throw the dice, not even certain if the numbers of 1 to 6 will land, as moment by moment uncertainty becomes more certain.

Wanna bet on that?



Omul Negru – Edition 666 Do you like ghost stories? Want some new nightmares?

The invocation of Omul Negru at Galeria Nicodim in Bucharest, and then again with its resurrection at Nicodim Gallery in Los Angeles was an alignment of anthropology, ritual magic and sacrilegious geometry set inside curatorial red rooms. The corresponding codex is at once a grimoire and a folklore as much as it is an exhibition catalogue and an anthology of evil. It will define a new kind of pornography and should not be treated lightly as it possesses the most evil representations of humankind’s darkest nadir.

Representations and essays that encourage a challenge – And why is that?

Arguably an image of a man who has been nailed through his hands and feet is far more profoundly shocking, and thus it is the cultural interpretation where the supposed objectivity arises in all imagery.



Geometry Terms Are Easier to Remember With Art

Geometry terms in middle school geometry and elementary geometry are easy to remember when geometry lesson plans include art projects. Geometry activities which include art are helpful as a vehicle for memory and make teaching geometry more effective and fun for everyone.

Scary Scalenes

When my students had difficulty remembering the different kinds of triangles, I began searching for a way to help. So I created the Scary Scalene geometry project in order to reinforce this type of triangle. It is the perfect activity to do for Halloween.

Scared – the condition or sensation of sudden fear, which causes a change in metabolic and organ functions and ultimately a change in behaviour.

Fear can be used as a triggering mechanism, a response activator, by which control can be exerted.

A powerful tool that is biologically embedded, thus difficult to bypass.

Fear can generate results, through manipulation.



Threshold: Black Magic and Shattered Geometry exposes to the modern Satanist the problems our reality holds, and more importantly, it gives him the tools necessary to shatter it, and create a New World Order. The Ego must be tricked into defeating itself. Its abstractions must be torn apart piece by piece, its processes broken down and made visible to the individual, so that a special instant occurs in that individual similar to an Out of Body Experience – With the exception that is it Out Of Mind. In this instant, a sudden flash of the awakened Self can see the actions of the Ego consciously and understands its own involvement in its perception.

Black Magic, one of the greatest taboos, but also the name of one of the most popular brands of chocolate in the world, (so sweet at heart) though perhaps not surprisingly manufactured by Nestlé.

Guaranteed to evoke a response at the mere mention of the phrase, this concept has been explored by artists as a means of generating interest, and its relationship to geometry is aligned with the use of sigilistic ritual.

Shock. Tactix.



This paper will experiment with a notion of literary character in Moby-Dick not as the development of a psychological interiority or human personhood, but rather as a singular, yet trans-individual encounter of forces. It will thus attempt to understand both human and nonhuman bodies as processes of morphogenesis that happen concurrently with other emergent and transformative material processes. To do so, I will explore Melville’s affinities with contemporary developments in non-Euclidean geometry and more recent thinking regarding complex and turbulent systems. Protagonists: Melville, Riemann, Olson, Deleuze, Serres, Spinoza, Ishmael, whales. Antagonists: vortices, Ixion, Descartes, Ahab, Moby Dick. As Melville writes regarding Ishmael’s cetology, “the classification of the constituents of a chaos, nothing less is here essayed.”

Subversion – Subversion refers to an attempt to transform the established social order and its structures of power, authority, and hierarchy.

This is why I choose to be an artist. I wish to transform this world, to leave it in a somewhat more beautified state than when I arrived.

All art is subversive, and geometric art is directly so.



Sophie Taeuber Arp // Dada Puppets & Surreal Geometry // Libellés // Dada, Geometry, Mask, Print, Puppet Theater, Sophie Taeuber Arp //

Surrealism sought to release the creative potential of the unconscious mind, and resolve the previously contradictory conditions of dream and reality, for example by the irrational juxtaposition of images.

Incongruity creates a dynamic whereby the stupid can become the profound, and ridicule obtains the merit of value. Playful and serious, the non-approach gains historical accuracy, once reflected upon the present.

And thus the fool speaks into the ear of the King, and the King listens.



Terrorism in its purest form is self-help by organized civilians who covertly inflict mass violence on other civilians. Pure sociology explains terrorism with its social geometry—its multidimensional location and direction in social space. Here I build on the work of Senechal de la Roche (1996) and propose the following geometrical model: Pure terrorism arises inter-collectively and upwardly across long distances in multidimensional space. Yet because social distance historically corresponded to physical distance, terrorism often lacked the physical geometry necessary for its occurrence: physical closeness to civilians socially distant enough to attract terrorism. New technology has made physical distance increasingly irrelevant, however, and terrorism has proliferated. But technology also shrinks the social universe and sows the seeds of terrorism’s destruction.

Is nothing Sacred?

Whilst exploring and researching this essay, I found more and more profane references to geometry, exceeding the sacred.

I am of the minority, it seems.



The Good the Bad and the Ugly: The Geometry of Aesthetic Norms in Plato.

Plato often enthusiastically compares the normative images of the good, the true and the beautiful. Frequently this rough equating does more to conflate the meanings of the three conceptual frameworks than to mutually illuminate them. In this paper I will try to show that at certain select places within the dialogues, Plato defies this sloppy practice and instead presents very clear and elaborate analogies as to the precise set of relations that hold among his various aesthetic concepts. I will try to show that an understanding of this aesthetic system enables us to appreciate the full scope of Plato’s aesthetic normative system. I will further try to establish that this understanding can help us to make clearer possible mediation between certain dualities in both Plato’s causal model and his ethical-political system.

Beautiful geometry sings a pure song of resonance, whereas ugly geometry grunts of abrasive imbalance.

The story of aesthetics is a leading star of evolution, and the cessation of the ugly appears to be one of nature’s imperatives to the extent that repulsion and rejection of the ugly creates a natural aversive reaction.

Apparently this geometric logo of created a reaction of epileptic fitting when watched in video form.

A puzzling reaction to ugly geometry.



Geometric Correction for Uneven Quadric Projection Surfaces Using Recursive Subdivision of Bézier Patches


This paper presents a scheme for geometric correction of projected content for planar and quadratic projection surfaces. The scheme does not require the projection surface to be perfectly quadratic or planar and is therefore suitable for uneven low-cost commercial and home projection surfaces. An approach based on the recursive subdivision of second-order Bézier patches is proposed for the estimation of projection distortion owing to surface imperfections. Unlike existing schemes, the proposed scheme is completely automatic, requires no prior knowledge of the projection surface, and uses a single uncalibrated camera without requiring any physical markers on the projection surface. Furthermore, the scheme is scalable for geometric calibration of multi-projector setups. The efficacy of the proposed scheme is demonstrated using simulations and via practical experiments on various surfaces. A relative distortion error metric is also introduced that provides a quantitative measure of the suppression of geometric distortions, which occurs as the result of an imperfect projection surface.

Keywords: Bézier surface, recursive subdivision; geometric correction, projection surface, quadratic surface.

Topography, the mapping of the uneven, as 2 dimensional representations of 3 dimensions, and therefore capable of representing distribution throughout the entire plane.

Uneven has many disadvantages, though the natural tendency is so formed. But in this set form, a levelling out, or entropic attractor holds the destiny until resultant climactic erupts?



This book considers the so-called Unlikely Intersections, a topic that embraces well-known issues, such as Lang’s and Manin-Mumford’s, concerning torsion points in sub-varieties of tori or abelian varieties. More generally, the book considers algebraic subgroups that meet a given sub-variety in a set of unlikely dimension. The book is an expansion of the Hermann Weyl Lectures delivered by Umberto Zannier at the Institute for Advanced Study in Princeton in May 2010.

Where the unexpected occurs, at unlikely intersections.

Moments in the space-time continuum where the impossible happens.

2017 – Donald Trump as President, this to me is the opening stage of ultimate closure. For as the sequence of unlikeliness begins is exponential surge, we will be awakened to the necessity of realisation that the impossible is happening.

And once the impossible begins to happen with growing intensity and frequency, the realisation that all is a dream will become inescapable.

Buddha = Awakened One.



A gömböc or gomboc (Hungarian: [ˈɡømbøts]) is a convex three-dimensional homogeneous body which, when resting on a flat surface, has just one stable and one unstable point of equilibrium. Its existence was conjectured by Russian mathematician Vladimir Arnold in 1995 and proven in 2006 by Hungarian scientists Gábor Domokos and Péter Várkonyi. The gömböc shape is not unique; it has countless varieties, most of which are very close to a sphere and all have very strict shape tolerance (about 0.1 mm per 100 mm).

The most famous solution has a sharpened top. Its shape helped to explain the body structure of some tortoises in relation to their ability to return to equilibrium position after being placed upside down. Copies of gömböc have been donated to institutions and museums, and the biggest one was presented at the World Expo 2010 in Shanghai, China.

A Gomboc is a self-righting object, and in the context of this particular essay I suggest this geometric construct as the attractor of evolution’s destiny. For whatever the short term, blinkered view of humankind upon the face of Gaia, the mechanisms of geological and cosmic time scales appear to be self-righting and balancing, in the Great Picture.

Taken in isolation, this moment we dwell upon offers very little guidance of our ultimate goal, so as we sit in complacent patience, the succour of Nature’s nipple gives a maternal assurance that all is well in the world, though humankind seems destined for a self-righting apocalypse of some sort.

The universe has a long term strategy that we can only extrapolate from the past.



Tracking eye movements when solving geometry problems with handwriting devices

John J. H. Lin, Sunny S. J. Lin


The present study investigated the following issues: (1) whether differences are evident in the eye movement measures of successful and unsuccessful problem-solvers; (2) what is the relationship between perceived difficulty and eye movement measures; and (3) whether eye movements in various AOIs differ when solving problems. Sixty-three 11th grade students solved five geometry problems about the properties of similar triangles. A digital drawing tablet and sensitive pressure pen were used to record the responses. The results indicated that unsuccessful solvers tended to have more fixation counts, run counts, and longer dwell time on the problem area, whereas successful solvers focused more on the calculation area. In addition, fixation counts, dwell time, and run counts in the diagram area were positively correlated with the perceived difficulty, suggesting that understanding similar triangles may require translation or mental rotation. We argue that three eye movement measures (i.e., fixation counts, dwell time, and run counts) are appropriate for use in examining problem solving given that they differentiate successful from unsuccessful solvers and correlate with perceived difficulty. Furthermore, the eye-tracking technique provides objective measures of students’ cognitive load for instructional designers.

The basis of my own geometric art is predicated upon the communication of light with the retina, as a stimulus for emotional reaction, birthing a bio-chemical release.

Design, and geometry in particular, communicates far more than is commonly realised, and the mechanisms are extremely subtle, and the unsuccessful designs are immediately obvious to both trained and untrained eyes.

Our instinctive visual programming and subsequent interpretations are magnificent guidance systems, steering us along safe and correctly aligned paths, those that nurture our growth and security.



Archimedes’ many machines proved the value of science in war and peace even at that early date. Yet he did much more important and far-reaching work in pure mathematics. He and the other Alexandrian geometers were every bit as devoted to abstract thought as their predecessors. In fact, from the Golden Age through the Age of Plato and right into the Hellenistic Age, they were all absorbed in a set of fascinating abstract questions.

These were the three famous puzzles-constructions that had to he performed using only straightedge and string. One was called ‘squaring the circle”: how could you construct a square with the same area as a circle? Another was “trisecting an angle”:

How could you divide air angle into three equal parts? Another was doubling the cube”: how could you construct a cube whose volume would be double that of another cube?

About the origin of the cube puzzle, a curious story was told. It seems that a great plague ravaged Athens in 430 B.C., and the 142

citizens appealed to the oracle at Delos for help. The oracle replied that the plague would be stayed if the Athenians would double in size the altar of Apollo without changing its shape. The altar was a cube.

Historians do not think this tale is true. Rather, they believe, it was made up later to hide the fact that the “three geometric puzzles” were really useless problems. But working on what may seem useless has frequently been the task of mathematicians, and such tasks, pursued with care, patience, and persistence, have led to most useful results. A whole book could be written about useful results from useless problems.

In the case of the three geometric puzzles, they were not only useless but quite impossible with only those tools. These constructions simply cannot be made with string and straightedge alone. But more than two thousand years elapsed before that was definitely proved.

“Working on what may seem useless” – Art in general, and geometric art in particular?

The alchemist geometers that play with useless constructs have revealed/created the very basis of politics, society, finance and Western philosophy. No mean feat for players.



The Geometry of Violence

“Earlier theories of violence focus on the characteristics of individuals or collectives (for an overview, see, e.g., Smith and Zahn, 1999). However, a shortcoming of individualistic theories (such as those attributing violence to learning or frustration) is that no individuals are violent in all their conflicts. And a shortcoming of collectivistic theories (such as those attributing violence to cultural traditions or social inequality) is that no collectives are violent in all their conflicts. Individualistic theories are thus badly near sighted, unable to see beyond the individual to each conflict where violence actually occurs, and collectivistic theories are badly farsighted, unable to see within the collective to each conflict where violence actually occurs. In other words, individualistic theories over individualize violence (as if individuals alone explain violence), while collectivistic theories over collective violence (as if collectives such associates or communities alone explain violence).

Because both ignore the conflict structures that generate violence – the violent structures – both under-structuralise the explanation of violence. They therefore fail to predict and explain precisely when and how violence takes place – who is violent in a particular way, toward whom, and on what occasion. Pure sociology focuses on the social geometry of each conflict that might arise, including the various social distances between the parties, their social elevation, and the social direction of the grievance. It specifies how particular conflict structures attract particular forms and quantities of violence.”

A rough and somewhat violent explanation huh?

Violence is defined by the World Health Organization as “the intentional use of physical force or power, threatened or actual, against oneself, another person, or against a group or community, which either results in or has a high likelihood of resulting in injury, death, psychological harm.”

There are platitudes a’plenty regarding violence, but I understand this. Violence, if motivated by angry intention create the causes for suffering.

Anger serves no beneficial purpose. Period.



A wobble base pair is a pairing between two nucleotides in RNA molecules that does not follow Watson-Crick base pair rules. The four main wobble base pairs are guanine-uracil (G-U), hypoxanthine-uracil (I-U), hypoxanthine-adenine (I-A), and hypoxanthine-cytosine (I-C). In order to maintain consistency of nucleic acid nomenclature, “I” is used for hypoxanthine because hypoxanthine is the nucleobase of inosine; nomenclature otherwise follows the names of nucleobases and their corresponding nucleosides (e.g., “G” for both guanine and guanosine). The thermodynamic stability of a wobble base pair is comparable to that of a Watson-Crick base pair. Wobble base pairs are fundamental in RNA secondary structure and are critical for the proper translation of the genetic code.

Brief History – In the genetic code, there are 43 = 64 possible codons (tri-nucleotide sequences). For translation, each of these codons requires a tRNA molecule with a complementary anticodon. If each tRNA molecule paired with its complementary mRNA codon using canonical Watson-Crick base pairing, then 64 types (species) of tRNA molecule would be required. In the standard genetic code, three of these 64 mRNA codons (UAA, UAG and UGA) are stop codons. These terminate translation by binding to release factors rather than tRNA molecules, so canonical pairing would require 61 species of tRNA. Since most organisms have fewer than 45 species of tRNA, some tRNA species must pair with more than one codon. In 1966, Francis Crick proposed the Wobble Hypothesis to account for this. He postulated that the 5′ base on the anticodon, which binds to the 3′ base on the mRNA, was not as spatially confined as the other two bases, and could, thus, have non-standard base pairing. Crick creatively named it for the small amount of play that occurs at this third codon position. Movement (“wobble”) of the base in the 5′ anticodon position is necessary for small conformational adjustments that affect the overall pairing geometry of anticodons of tRNA.

I have to question myself, as to how and why my journey through the languages of profane geometry has led to an understanding of the very basis of life on Earth as held within RNA.

Is it because the basis of life is Geometry, revealed on this occasion by an analysis of the profane, as a measured balanced to the sacred.

Sacred + Profane = Yoga



Google “G” logo is wonky

From Toby Keller, UI Director at Bletchley Park

“Overall I’m a fan of Google’s new logotype. But does it bug anyone else that the diagonal separating yellow and green on the “G” logo version is just, almost the same angle as the terminal of the G but not quite?”

Google even inexplicably emphasizes this in their design case study by animating the grid lines used to construct the G, making it plainly clear that the two lines just don’t quite match up:

Any ideas why they wouldn’t chop the counter at the same diagonal? They had to have known about and discussed this…

G for God.

G for Google.

G for Geometry.


Geometry is never wrong – Jessica Helfand

The ‘exact beauty’ of De Stijl could provide cyberspace with a new set of design co-ordinates.

In his collected essays, Architecture and Disjunction, Bernard Tschumi argues that frames as architectural elements derive their meaning through juxtaposition. ‘They establish memory,’ he writes, ‘of the preceding frame, of the course of events.’ The idea that a structural element can serve a graphically direct yet intensely personal need is a compelling notion, and recalls the ambitions of earlier twentieth-century visionaries, particularly the De Stijl group, an informal confederation of artists, architects and designers working in the Netherlands between 1917 and 1931, who sought to embrace social order and spiritual harmony through simple, formal means. Strangely, though, white the lessons of Modernism in general, and De Stijl in particular, have found their way into contemporary design education and practice, the formal principles upon which this thinking was based remain virtually absent in the design of new media.

In 1915 and 1916, M. H. J. Schoenmaekers, the theosophist, published The New Image of the World and Principles of Plastic Mathematics, in which he suggested that reality might best be expressed as a series of opposing forces – a formal polarity of horizontal and vertical axes and a juxtaposition of primary colours. Schoenmaekers posited a new image of the world, expressed with ‘a controllable precision, a conscious penetration of reality and exact beauty.’ Not only is his statement refreshingly straightforward, read literally, it also provides an inspirational way of deconstructing the complex role that design plays in our increasingly digital culture. Most important, perhaps, to the designer lamenting the intractable restrictions of today’s technological climate, the formal language of De Stijl – and its celebration of the purity of the x/y axis – is inspiration indeed.

Co-ordinates in cyberspace – is all we will be in the future.

That is all.



Co-ordinates in cyberspace – is all we will be in the future.

That is all.

Then it will be time again for Sacred Geometry to serve as the Map.



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