Dimensionality Quotes
The oxide superconductors, particularly those recently discovered that are based on La2CuO4, have a set of peculiarities that suggest a common, unique mechanism: they tend in every case to occur near a metal-insulator transition into an odd-electron insulator with peculiar magnetic properties. This insulating phase is proposed to be the long-sought "resonating-valence-bond" state or "quantum spin liquid" hypothesized in 1973. This insulating magnetic phase is favored by low spin, low dimensionality, and magnetic frustration. The preexisting magnetic singlet pairs of the insulating state become charged superconducting pairs when the insulator is doped sufficiently strongly.
Philip Warren Anderson
The idea of having an ambient space-time of some specific dimension seems to play less of a role of string theory than in conventional physics, and certainly less than the kind of role that I would myself feel comfortable with. It is particularly difficult to assess the functional freedom that is involved in a physical theory unless one has a clear idea of its actual space-time dimensionality.
Roger Penrose
At the most abstract level, the relation between urbanism and microelectronics is scalar (fractal). The coming computers are closer to miniature cities than to artificial brains, dominated by traffic problems (congestion), migration / communications, zoning issues (mixed use), the engineering potential of new materials, questions of dimensionality (3D solutions to density constraints), entropy or heat / waste dissipation (recycling / reversible computation), and disease control.
Nick Land
Most studies employing three-dimensional objects as stimuli have used simultaneous presentation whereas most studies employing two-dimensional objects have used comparison of a single visual stimulus with a memory presentation. We suspect that it is this procedural difference rather than the difference in dimensionality that is the principal determiner of rate of mental rotation.
Roger Shepard
The true function of phantasy is to give the imagination a ground for limitless expansion, and to satisfy aesthetically the sincere and burning curiosity and sense of awe which a sensitive minority of mankind feel toward the alluring and provocative abysses of unplumbed space and unguessed entity which press in upon the known world from unknown infinities and in unknown relationships of time, space, matter, force, dimensionality, and consciousness.
H. P. Lovecraft
O Thou Whom I shall always call, everywhere and in all Dimensions, my Priest, Philosopher, and Friend - some yet more spacious Space, some more dimensionable Dimensionality, from the vantage-ground of which we shall look down together upon the revealed insides of Solid things, and where thine own intestines, and those of thy kindred Spheres, will lie exposed to the view of the poor wandering exile from Flatland, to whom so much has already been vouchsafed.
Edwin Abbott Abbott
Hence I am absolutely destitute of converts, and, for aught that I can see, the millennial Revelation has been made to me for nothing. Prometheus up in Spaceland was bound for bringing down fire for mortals, but I - poor Flatland Prometheus - lie here in prison for bringing down nothing to my countrymen. Yet I exist in the hope that these memoirs, in some manner, I know not how, may find their way to the minds of humanity in Some Dimension, and may stir up a race of rebels who shall refuse to be confined to limited Dimensionality.
Edwin Abbott Abbott
