In the twenty years since the Skylab workshop, micro-gravitational environmental design has progressed from an almost anti-terrestrial disregard for Earth-normalcy to a realization that some Earth norms can serve a useful coordinating function. We now see designs for Spacelab and Freedom that provide distinct "Earthy" floor, wall, and ceiling references and consistent cues for vertical orientation, without denying either the possibility of ceiling-mounted utilities or the necessity of foot restraints.
Exactly the opposite sort of progression is needed in artificial-gravity design. Virtually all concepts published to date have implied complete Earth-normalcy with regard to perceived gravity, stability, and orientation. A more appropriate approach calls for preserving those Earthly elements that serve a positive function while incorporating modifications that account for the peculiarities of rotating environments. This may require a reappraisal not only of artificial-gravity engineering studies, but also of architectural theory itself. According to Norberg-Schulz :
To be meaningful ... the inventions of man must have formal properties which are structurally similar to other aspects of reality, and ultimately to natural structures ... Natural and man-made space are structurally similar as regards directions and boundaries. In both, the distinction between up and down is valid, as well as the concepts of extension and closure. The boundaries of both kinds of space are moreover to be defined in terms of "floor", "wall", and "ceiling".
On the one hand, he testifies to the importance of reality and nature (whatever they may mean) in architectural expression. On the other hand, his characterizations of the directions and boundaries of natural and man-made space must be reevaluated - if not refuted - in extraterrestrial environments.
With regard to acceleration and trajectory deflection, artificial gravity can be made Earth-normal within any finite tolerance, provided that the radius of rotation is sufficiently large. However, to make the abnormalities imperceptible, "sufficiently large" may be ten kilometers or more. The alternative - more interesting theoretically, and the real focus of this research - is to adapt the architecture to the gravitational abnormalities associated with rotation at smaller radii.
In such an environment, falling objects follow involute trajectories and dropped objects deflect noticeably to the west, as if blown by a sort of "gravitational wind". East and west are gravitationally distinct in a manner akin to up and down. Therefore, there are not three, but at least five principal directions: up, down, east, west, and axial. The smaller the radius, the stronger the distinction between east and west. It is as inescapable as the distinction between up and down, and cannot be masked by architecture. Perhaps it follows that "eastwall" and "westwall" must be introduced as new elements in the grammar of architecture.
As a secondary effect, axial is decomposable into north and south through derivation from east, west, left, and right. But, if inside and outside observers are to agree on the location of the north pole and south pole - important for rendezvous and docking maneuvers - then the handedness of north-south relative to east-west is reversed in artificial gravity. In that inside-out, concave landscape, north is to the right of east, and south is to the left. (See figures 4.1 and 5.5.) While terminology may have a negligible effect on engineering, it is intricately tied to orientation, and this represents yet another adaptation required of people immigrating from a convex planetary surface.
North and south may also be distinguishable through cross-coupled rotations. If a torque is applied to an object about the up-down axis while the environment spins about the north-south axis, there is a cross-coupling effect about the east-west axis. In other words, turning to the left or right will cause a tendency to tip toward the north or south (about the east-west axis). The magnitude and direction of this effect depend on the object's particular inertia components, so it is a less consistent reference than the free-fall involute curve. Nevertheless, it should be consistent for rotations of the head - the most important object for gravitational orientation.
Unlike up and down, which are continuously distinct, east and west are intermittently distinct - only during relative motion within the rotating environment, in proportion to the relative velocity. While a person is stationary, he may forget that there is such a distinction - only to be rudely reminded of it when he rises out of his chair or turns to his side. Anything that keeps a person "passively" oriented relative to east and west would allow him to prepare himself for the consequences of his actions, aiding his coordination and adaptation to the rotating environment.
Hesselgren discusses the "transformation tendency", in which a perception in one modality may produce a mental image of a perception in another. One modality that he never discusses - that is taken for granted on Earth but cannot be in space - is vestibular perception. It may be possible, through experience in a properly designed environment, to acquire a transformation tendency to vestibular perception from visual, acoustic, haptic, or other perceptions. Not that we wish to induce motion sickness by the mere sight of some visual cue. Rather, we wish to provide visual or other reminders that motion relative to these cues will result in certain inescapable side effects, inherent in the artificial gravity. By doing so, we may be able to aid the inhabitants' orientation and adaptation to their rotating environment. Keeping with Hesselgren's system of meanings, these perceptual cues would act primarily as signals, triggering adaptive coordination in the inhabitants. From the designer's point of view, a consistent "vocabulary" of such signals would have to arise from convention. From the inhabitants' point of view, these conventions might to some extent be taught, but the unconscious transformation to a vestibular image would rely on association based on direct experience.
In designing signals, it is usually best to incorporate multiple perceptions. For example: stop signs are both red and octagonal; no other traffic sign possesses either attribute. We may speculate on the use of color and form in artificial gravity to distinguish eastwall from westwall. Just as ceilings are usually lighter than floors in color, we may propose that eastwalls should be tinted with receding colors and westwalls with advancing colors. Hesselgren  and Thiis-Evensen  both note the receding character of cool colors tending toward blue and the advancing character of warm colors tending toward yellow. The forms of the eastwall and westwall may incorporate literal casts of the involute curve, or other symbolic shapes such as triangles for advancing (westwall) and circles for receding (eastwall). These forms may be merely chromatic, or they may be cast in bas-relief - convex for advancing and concave for receding.
Classical architecture is the premier example of a system of design rules for the proportion and placement of forms. Over the centuries, it has evolved a rich vocabulary - linguistic as well as formal - of pedestal, base, shaft, capital, architrave, frieze, cornice, triglyph, metope, fascia, and so on . The classical orders specify the proportion and placement of these forms in minute detail with mathematical precision, reflecting the order in the Renaissance conception of the universe. One can imagine the invention and evolution of a new set of design rules for artificial gravity, involving, for example, pilasters with involute profile, and friezes composed from advancing and receding colors and bas-relief shapes.
I offer this Classical analogy merely as an example, certainly not as a specific recommendation or conclusion. Prak is careful to distinguish between formal and symbolic aesthetics: the former deals with general rules of rhythm, proportion, balance, and consistency; the latter with heuristic aspects of style . What is important is that general rules of composition can be developed and applied to the architecture of artificial gravity - to impart, as Norberg-Schulz suggests, formal properties which are structurally similar to other aspects of the environment. The specific style in which this is done will evolve as a function of mission, population, and time.
Figures 5.1 and 5.2 represent simple experiments with architectural forms, conducted via computer-aided design techniques . Starting with an unadorned room and the elements of floor, wall, and ceiling, forms are added or modified to express the rotation of the room in space and the consequent distinction between east and west. The involute curves on the back wall trace the path of a particle dropped from ceiling height, assuming a floor radius of 250 meters - the approximate proposed radius of the Bernal Sphere. The frieze (just below the ceiling) is punctuated with recessed blue circles on the eastwall and raised yellow triangles on the westwall. The scene through the window would appear to rotate clockwise at about 1.9 rpm.
The formal approach suggested here is relevant only to the extent that it is adaptive to function in a rotating environment. Forms of one sort or another are unavoidable, whether they result from apathetic adherence to Earth norms or proactive design for a new environment. However, formalism for its own sake - the triumph of style over substance - serves no purpose; to the extent that it interferes with adaptation, it may even be detrimental.
Apart from the gravitational peculiarities, the very geometry of artificial-gravity environments precludes Earth-normal design. This is especially true of the large space colony concepts that make the strongest claims for Earth-normalcy - such as the Stanford Torus, the Bernal Sphere, and O'Neill's "islands". Artists' renditions of these environments are often taken from points of view that minimize or obscure the concave upward curvature of the landscape - for example, "aerial" perspectives looking north or south, parallel to the axis of rotation. In these, the viewer is disconnected from the ground, the path ahead is flat and straight, and the curvature is relegated to peripheral vision - somebody else's problem. Ground-level views looking east or west, in which the curvature confronts the viewer head-on, are rare. Many of those that have been attempted are obviously flawed. For example, several views of the Stanford Torus depict sight lines much longer and flatter than the radius of the torus would allow. At a radius of 895 meters, a 1-kilometer arc would subtend an angle of 64 degrees; yet several views seem to show kilometer vistas with little or no curvature.
A geometrically correct rendition of such a landscape is difficult to construct without the aid of a computer, simply because nothing like it has ever been seen. As an experiment in visualization, I developed a computer program for bending objects in a geometric modeler , and applied it to a model of a neighborhood in downtown Ann Arbor, Michigan. (The original "flat" model was developed by students in an architectural design studio, for other purposes.) Figures 5.3 and 5.4 show the results. Standing at street level and looking straight east, the aerial view of roofs a few blocks away gives an impression similar to looking down from the top of a hill. Yet the upward curvature of the ground indicates that we are in a valley, not on a ridge. Even while east and west become gravitationally distinct, up and down become visually indistinct and ambiguous - especially when looking directly across the diameter of rotation. This incongruous vista is like nothing on Earth. And, the flat computer-generated images give only a dim prediction of actual experience. A recurring theme in the writing of Norberg-Schulz is that humans dwell between the earth and sky - the sky above and the earth below. In one of O'Neill's cylindrical colonies, one is nearly as likely to see the ground above and the sky below, depending on one's position relative to the large windows. In fact, the best view of the heavens would be from a glass-walled observation deck in the sub-basement, protruding beneath the ground like a gondola beneath a blimp.
Windows continue to be a matter of disagreement. In addition to concerns about structural integrity, environmental control (including radiation shielding), and cost, rotation introduces the issue of dizziness. Payne  and others have suggested that, "to avoid disorientation", windows should not be provided in rotating environments. But depriving the inhabitants of an outside view would do nothing to alleviate the vestibular effects of rotation. On the contrary, it may promote the mismatch between visual and vestibular perception that leads to motion sickness . Windows might provide an obvious, natural aid to orientation, in addition to the abstract, formalist cues discussed previously.
Figure 5.5 illustrates the apparent rotation of the star field. A celestial view to the north or south would rotate about the center of the window. (The parallax would be negligible.) To the south, the stars would rotate clockwise, while to the north, counterclockwise. To the east, the stars would move downward in the field of view, while to the west, upward. Looking up, the stars would move west-to-east, while looking down, east-to-west. Of course, as on Earth at night, the exterior view may be obscured by interior reflections.
Views are preferable, but direct sunlight is more problematic. Sunlight may be stroboscopic, or may "orbit" the room over the rotational period of the station, depending on the alignment of the rotation axis in space as well as on the placement of windows and mirrors. Unattenuated direct sunlight with virtually no diffuse light from sky or ground produces harsh contrasts, and ocular acclimation may be particularly difficult if the sun beam changes rapidly. Large colony concepts such as O'Neill's cylinders, the Bernal Sphere, and the Stanford Torus show particular attention to the problem of admitting steady sunlight, but most smaller concepts are silent on the matter.
The emergence of east and west as gravitationally distinct directions, the concave landscape, the inversion of earth and sky, and the rotating celestial scene combine to present a profoundly abnormal environment that artificial-gravity design studies have yet to come to terms with.
Perhaps it is human nature for colonists to long for the old world while settling the new. Several centuries ago, many Europeans emigrated to America not because they wanted to be Americans, but to escape political, economic, or religious oppression at home. Many tried to maintain their old ways of life, and starved in a land where indigenous people had prospered for thousands of years. Similarly, space colonization has been presented as an escape from over-crowding, resource depletion, and nuclear war. The architecture of artificial gravity has been conceived as an idealization of Earth, rather than a departure from it. Prak's views, on the relationship between architectural aesthetics and prevailing social conditions, seem relevant: "A person who knows that the road to a certain highly desirable goal is blocked, turns to wish-fulfillment in dreams. Analogously, the architecture of a society divided against itself becomes a dreamland, an image of the state desired" .
However, the persistence of Earth-normal concepts in space colony design need not be cast in such a negative light. The architecture derives from a global technological civilization that transcends national and cultural boundaries. It is the only architecture that most of us have ever known, and it is difficult for us to conceive of anything else. Perhaps our perspective can be widened by stepping back, returning to basics, and looking at nonconforming cultures - for example, the Zulu culture as described by Allport and Pettigrew :
Zulu culture is probably the most spherical or circular of all Bantu cultures, possibly the most spherical of all native African cultures ... The word "zulu" means heavens or firmament, and the aesthetic ideal of round rather than angular styles affects native art, architecture, and speech ... It is commonly said in Natal that Zulus fresh from reserves cannot plow a straight furrow and are unable to lay out a rectangular flower bed ... While it is possible to say "round" in Zulu, there is no word for "square". There is a word for "circle" but not for "rectangle". To speak of window, of square, or of rectangle at all, a Zulu is forced to borrow these terms from Afrikaans or from English - provided he is able to do so.
Allport and Pettigrew found that, compared to urban children, rural Zulu children were less susceptible to the "trapezoidal illusion", probably because their perceptions were not encumbered by the expectation of a rectangle. "In this particular case, therefore, one might say that the primitive children see things 'as they are' more often than do the children of civilization" . A spatial conception based on circles and spheres, rather than rectangles, may be particularly well suited to a rotating environment.
We can only guess as to the sort of culture that might one day be native to artificial gravity. In planning the first such environment, we may not be able completely to escape our terrestrial preconceptions, but we must make the effort. At small radii, artificial gravity is as different from natural gravity as weightlessness, and deserves the same attention to detail. Proper environmental design can improve habitability by reducing the need for off-axis motion and by providing visual cues for orientation to the distorted gravity environment. At the other extreme, O'Neill's descriptions of space colonies such as "Island Three" (four miles in diameter) invite much speculation: