Architecture Symmetry Quotes

The Roman genius, and perhaps the Roman flaw was an obsession with order. One sees it in their architecture, their literature, their laws—this fierce denial of darkness, unreason, chaos. Easy to see why the Romans, usually so tolerant of foreign religions, persecuted the Christians mercilessly—how absurd to think a common criminal had risen from the dead, how appalling that his followers celebrated him by drinking his blood. The illogic of it frightened them and they did everything they could to crush it. In fact, I think the reason they took such drastic steps was because they were not only frightened but also terribly attracted to it. Pragmatists are often strangely superstitious. For all their logic, who lived in more abject terror of the supernatural than the Romans? The Greeks were different. They had a passion for order and symmetry, much like the Romans, but they knew how foolish it was to deny the unseen world, the old gods. Emotion, darkness, barbarism.

[Donald] Keene observed [in a book entitled The Pleasures of Japanese Literature, 1988] that the Japanese sense of beauty has long sharply differed from its Western counterpart: it has been dominated by a love of irregularity rather than symmetry, the impermanent rather than the eternal and the simple rather than the ornate. The reason owes nothing to climate or genetics, added Keene, but is the result of the actions of writers, painters and theorists, who had actively shaped the sense of beauty of their nation. Contrary to the Romantic belief that we each settle naturally on a fitting idea of beauty, it seems that our visual and emotional faculties in fact need constant external guidance to help them decide what they should take note of and appreciate. 'Culture' is the word we have assigned to the force that assists us in identifying which of our many sensations we should focus on and apportion value to.

It is a pretty structure, isn’t it? It makes you think of something solid, stable, well linked. In fact it happens in chemistry as in architecture that ‘beautiful’ edifices, that is symmetrical and simple, are also the most sturdy: in short, the same thing happens with molecules as with the cupolas of cathedrals of the arches of bridges. And it is also possible that the explanation is neither remote nor metaphysical: to say ‘beautiful’ is to say ‘desirable’, and ever since man has built he has wanted to build at the smallest expense and in the most durable fashion, and the aesthetic enjoyment he experiences when contemplating his work comes afterward. Certainly, it has not always been this way: there have been centuries in which ‘beauty’ was identified with adornment, the superimposed, the frills; but it is probable that they were deviant epochs and that the true beauty, in which every century recognises itself, is found in upright stones, ships’ hulls, the blade of an axe, the wing of a plane.

Petrie found nothing that disproved the pyramidologist's assumption that the Great Pyramid had been built according to a master plan. Indeed, he describes the Pyramid's architecture as being filled with extraordinary mathematical harmonies and concordances: those same strange symmetries that had so haunted the pyramidologist. Petrie not only noted, for example, that the proportions of the reconstructed pyramid approximated to pi - which others have since elaborated to include those twin delights of Renaissance and pyramidological mathematicians, the Golden Section and the Fibonacci Series ...

the architecture of our brains was born from the same trial and error, the same energy principles, the same pure mathematics that happen in flowers and jellyfish and Higgs particles. Viewed in this way, our human aesthetic is necessarily the aesthetic of nature. Viewed in this way, it is nonsensical to ask why we find nature beautiful. Beauty and symmetry and minimum principles are not qualities we ascribe to the cosmos and then marvel at in their perfection. They are simply what is, just like the particular arrangement of atoms that make up our minds. We are not observers on the outside looking in. We are on the inside too.

A Puritan twist in our nature makes us think that anything good for us must be twice as good if it's hard to swallow. Learning Greek and Latin used to play the role of character builder, since they were considered to be as exhausting and unrewarding as digging a trench in the morning and filling it up in the afternoon. It was what made a man, or a woman -- or more likely a robot -- of you. Now math serves that purpose in many schools: your task is to try to follow rules that make sense, perhaps, to some higher beings; and in the end to accept your failure with humbled pride. As you limp off with your aching mind and bruised soul, you know that nothing in later life will ever be as difficult. What a perverse fate for one of our kind's greatest triumphs! Think how absurd it would be were music treated this way (for math and music are both excursions into sensuous structure): suffer through playing your scales, and when you're an adult you'll never have to listen to music again. And this is mathematics we're talking about, the language in which, Galileo said, the Book of the World is written. This is mathematics, which reaches down into our deepest intuitions and outward toward the nature of the universe -- mathematics, which explains the atoms as well as the stars in their courses, and lets us see into the ways that rivers and arteries branch. For mathematics itself is the study of connections: how things ideally must and, in fact, do sort together -- beyond, around, and within us. It doesn't just help us to balance our checkbooks; it leads us to see the balances hidden in the tumble of events, and the shapes of those quiet symmetries behind the random clatter of things. At the same time, we come to savor it, like music, wholly for itself. Applied or pure, mathematics gives whoever enjoys it a matchless self-confidence, along with a sense of partaking in truths that follow neither from persuasion nor faith but stand foursquare on their own. This is why it appeals to what we will come back to again and again: our **architectural instinct** -- as deep in us as any of our urges.

As far as the eye could see, one could perceive nothing but the abattoirs, the city wall, and the fronts of a few factories, resembling barracks or monasteries; everywhere about stood hovels, rubbish, ancient walls blackened like cerecloths, new white walls like winding-sheets; everywhere parallel rows of trees, buildings erected on a line, flat constructions, long, cold rows, and the melancholy sadness of right angles. Not an unevenness of the ground, not a caprice in the architecture, not a fold. The ensemble was glacial, regular, hideous. Nothing oppresses the heart like symmetry. It is because symmetry is ennui, and ennui is at the very foundation of grief. Despair yawns. Something more terrible than a hell where one suffers may be imagined, and that is a hell where one is bored. If such a hell existed, that bit of the Boulevard de l'Hopital might have formed the entrance to it.

The moral here is that nature and nurture should not be opposed. Pure learning, in the absence of any innate constraints, simply does not exist. Any learning algorithm contains, in one way or another, a set of assumptions about the domain to be learned. Rather than trying to learn everything from scratch, it is much more effective to rely on prior assumptions that clearly delineate the basic laws of the domain that must be explored, and integrate these laws into the very architecture of the system. The more innate assumptions there are, the faster learning is (provided, of course, that these assumptions are correct!). This is universally true. It would be wrong, for example, to think that the AlphaGo Zero software, which trained itself in Go by playing against itself, started from nothing: its initial representation included, among other things, knowledge of the topography and symmetries of the game, which divided the search space by a factor of eight. Our brain too is molded with assumptions of all kinds. Shortly, we will see that, at birth, babies' brains are already organized and knowledgeable. They know, implicitly, that the world is made of things that move only when pushed, without ever interpenetrating each other (solid objects)—and also that it contains much stranger entities that speak and move by themselves (people). No need to learn these laws: since they are true everywhere humans live, our genome hardwires them into the brain, thus constraining and speeding up learning. Babies do not have to learn everything about the world: their brains are full of innate constraints, and only the specific parameters that vary unpredictably (such as face shape, eye color, tone of voice, and individual tastes of the people around them) remain to be acquired.

Hitherto I have used the words imperfect and perfect merely to distinguish between work grossly unskilful, and work executed with average precision and science; and I have been pleading that any degree of unskilfulness should be admitted, so only that the labourer’s mind had room for expression. But, accurately speaking, no good work whatever can be perfect, and the demand for perfection is always a sign of a misunderstanding of the ends of art. This for two reasons, both based on everlasting laws. The first, that no great man ever stops working till he has reached his point of failure: that is to say, his mind is always far in advance of his powers of execution, and the latter will now and then give way in trying to follow it;... And therefore, if we are to have great men working at all, or less men doing their best, the work will be imperfect, however beautiful. Of human work none but what is bad can be perfect, in its own bad way. The second reason is, that imperfection is in some sort essential to all that we know of life. It is the sign of life in a mortal body, that is to say, of a state of progress and change. Nothing that lives is, or can be, rigidly perfect; part of it is decaying, part nascent. The foxglove blossom—a third part bud, a third part past, a third part in full bloom—is a type of the life of this world. And in all things that live there are certain irregularities and deficiencies which are not only signs of life, but sources of beauty. No human face is exactly the same in its lines on each side, no leaf perfect in its lobes, no branch in its symmetry. All admit irregularity as they imply change; and to banish imperfection is to destroy expression, to check exertion, to paralyze vitality. All things are literally better, lovelier, and more beloved for the imperfections which have been divinely appointed, that the law of human life may be Effort, and the law of human judgment, Mercy. Accept this then for a universal law, that neither architecture nor any other noble work of man can be good unless it be imperfect; and let us be prepared for the otherwise strange fact, which we shall discern clearly as we approach the period of the Renaissance, that the first cause of the fall of the arts of Europe was a relentless requirement of perfection, incapable alike either of being silenced by veneration for greatness, or softened into forgiveness of simplicity.

Hitherto I have used the words imperfect and perfect merely to distinguish between work grossly unskilful, and work executed with average precision and science; and I have been pleading that any degree of unskilfulness should be admitted, so only that the labourer’s mind had room for expression. But, accurately speaking, no good work whatever can be perfect, and the demand for perfection is always a sign of a misunderstanding of the ends of art. This for two reasons, both based on everlasting laws. The first, that no great man ever stops working till he has reached his point of failure: that is to say, his mind is always far in advance of his powers of execution, and the latter will now and then give way in trying to follow it;... And therefore, if we are to have great men working at all, or less men doing their best, the work will be imperfect, however beautiful. Of human work none but what is bad can be perfect, in its own bad way. The second reason is, that imperfection is in some sort essential to all that we know of life. It is the sign of life in a mortal body, that is to say, of a state of progress and change. Nothing that lives is, or can be, rigidly perfect; part of it is decaying, part nascent. The foxglove blossom—a third part bud, a third part past, a third part in full bloom—is a type of the life of this world. And in all things that live there are certain irregularities and deficiencies which are not only signs of life, but sources of beauty. No human face is exactly the same in its lines on each side, no leaf perfect in its lobes, no branch in its symmetry. All admit irregularity as they imply change; and to banish imperfection is to destroy expression, to check exertion, to paralyze vitality. All things are literally better, lovelier, and more beloved for the imperfections which have been divinely appointed, that the law of human life may be Effort, and the law of human judgment, Mercy. Accept this then for a universal law, that neither architecture nor any other noble work of man can be good unless it be imperfect; and let us be prepared for the otherwise strange fact, which we shall discern clearly as we approach the period of the Renaissance, that the first cause of the fall of the arts of Europe was a relentless requirement of perfection, incapable alike either of being silenced by veneration for greatness, or softened into forgiveness of simplicity.

The first mile was torture. I passed beneath the massive stone arch at the entrance to the school, pulled off the road and threw up. I felt better and ran down the long palm-lined drive to the Old Quad. Lost somewhere in the thicket to my left was the mausoleum containing the remains of the family by whom the university had been founded. Directly ahead of me loomed a cluster of stone buildings, the Old Quad. I stumbled up the steps and beneath an archway into a dusty courtyard which, with its clumps of spindly bushes and cacti, resembled the garden of a desert monastery. All around me the turrets and dingy stone walls radiated an ominous silence, as if behind each window there stood a soldier with a musket waiting to repel any invader. I looked up at the glittering facade of the chapel across which there was a mosaic depicting a blond Jesus and four angels representing Hope, Faith, Charity, and, for architectural rather than scriptural symmetry, Love. In its gloomy magnificence, the Old Quad never failed to remind me of the presidential palace of a banana republic. Passing out of the quad I cut in front of the engineering school and headed for a back road that led up to the foothills. There was a radar installation at the summit of one of the hills called by the students the Dish. It sat among herds of cattle and the ruins of stables. It, too, was a ruin, shut down for many years, but when the wind whistled through it, the radar produced a strange trilling that could well be music from another planet. The radar was silent as I slowed to a stop at the top of the Dish and caught my breath from the upward climb. I was soaked with sweat, and my headache was gone, replaced by giddy disorientation. It was a clear, hot morning. Looking north and west I saw the white buildings, bridges and spires of the city of San Francisco beneath a crayoned blue sky. The city from this aspect appeared guileless and serene. Yet, when I walked in its streets what I noticed most was how the light seldom fell directly, but from angles, darkening the corners of things. You would look up at the eaves of a house expecting to see a gargoyle rather than the intricate but innocent woodwork. The city had this shadowy presence as if it was a living thing with secrets and memories. Its temperament was too much like my own for me to feel safe or comfortable there. I looked briefly to the south where San Jose sprawled beneath a polluted sky, ugly and raw but without secrets or deceit. Then I stretched and began the slow descent back into town.

Even the simplest of cottages often picked up the decorative elements of the more formal styles as is evident in this Italianate cottage. Almost square, the one-story frame cottage at 543 Coombs duplicates the symmetry of the larger Italianates. Note also its low-pitched roof and projecting eaves supported by elaborate pierced and scrolled brackets. The molded window hoods supported by brackets top tall, narrow sash windows. The front porch could grace a much larger house with its molded cornice, columns, brackets, pierced arches, and turned balusters. In 1908, auctioneer J.T. Gamble lived

Aside from the old architecture, narrow winding roads, and driving on the left, I wondered why England looked so different from America; then I realized that the trees and fields, the buildings and barns, the small villages and narrow winding roads all fit together seamlessly, blended by time into a harmony. No one thing intruded on the other. Each fit the scene as though a natural process had ordained symmetry. Nothing jarred the eye; all was quiet beauty and neatness. There was no litter, nothing offensive to the senses. Every snug cottage had its garden, each shop a quaint window; there were no ugly signs. Even the lettering above the shop doors looked wonderfully ancient and elegant.

Yet over the last fifty years or so, asymmetry has crept into our homes and buildings. Architectural critic Kate Wagner traces this shift to the suburban building boom of the blingy 1980s. While the energy crisis of the seventies kept home sizes modest, the Reagan years brought large incentives for the construction industry and a culture of conspicuous consumption that turned houses into status symbols. These luxury homes, dubbed “McMansions,” swelled to include all kinds of new features: exercise rooms, home theaters, three-car garages, and grand oversize entryways. Eager to please, developers sacrificed symmetry for scale, producing massive homes that often felt surprisingly awkward. They sometimes looped architects out of the equation entirely, using a modular approach that allowed prospective homeowners to customize their design based on a kit of options. These options included architectural details like arches, moldings, and bay windows, which were then applied haphazardly to the surface rather than integrated into the structure.

to speak of “polarization” is to assume symmetry. No fact emerges more clearly from our analysis of how four million political stories were linked, tweeted, and shared over a three-year period than that there is no symmetry in the architecture and dynamics of communications within the right-wing media ecosystem and outside of it.

architecture, as Goethe said, is frozen music; and symmetry is rhythm standing still.