Michael Benedikt

To take hold of space: isovists and isovist fields

The environment is defined as a collection of visible real surfaces in space. An isovist is the set of all points visible from a given vantage point in space and with respect to an environment. The shape and size of an isovist is liable to change with position. Numerical measures are proposed that quantify some salient size and shape features. These measures in turn create a set of scalar isovist fields. Sets of isovists and isovist fields form an alternative description of environments. The method seems relevant to behavioral and perceptual studies in architecture, especially in the areas of view control, privacy, ‘defensibility’, and in dynamic complexity and spaciousness judgements. Isovists and isovist fields also shed light on the meaning of prevalent architectural notions about space. In the latter role it is hoped that an information-field theory such as the one presented can help provide fruitful common ground for designers and researchers.

Computational Models of Space: Isovists and Isovist Fields

Abstract A new computational model for space representation, called the isovist, is defined. Given a point x in a space P, the isovist at x, Vz, is the subset of P visible from x. Procedures for computing Vx for polygonal spaces are presented. Next, isovist fields are defined by associating a scalar measure of Vx at each point x in P. The architectural and computational significance of these fields is discussed. Finally, an analysis of computing small, sufficient sets of points is given. A set of points is sufficient if the union of the isovists of the points in the set is the entire space P. Sufficient sets are related to the endpoints of branches of the skeleton in the case of polygonal spaces.

Complexity, value, and the psychological postulates of economics

Abstract Does the contemporary built environment—the ensemble of our humanly created surroundings—make us happy? This question prompts a consideration of the psychological dimensions of economic value, and of Tibor Scitovskys revisions of standard economic theory. With Scitovsky as a starting point, a model of value based on modern complexity theory and a Maslow‐like rendition of human needs can account for some of the more important exceptions to the law of diminished marginal utility, including those that may undermine the built environment in a market economy.

On mapping the world in a mirror

Small, very convex mirrors create images of effectively the whole visual world around themselves. Aspects of the geometry of such images are explored by employing optical ray-tracing techniques in mapping information in the optic array onto a plane. Some applications are suggested for representing and simulating the whole visual field.

Another Word on "God and the Twenty-First Century"

here’s the story of a young atheist arguing with his Orthodox Jewish father about the existence of God. It’s late Friday afternoon. After an hour or so, the father looks at his watch and concedes, “Well, my son, God might ormight not exist, but it’s time for evening prayers.” Mitzvot are what matter. And what are mitzvot—what are commandments? Ways of bringing goodness to life through actions, through deeds. Said Rabbi Shimeon: “Not learningbutdoing is thechief thing.”SaidJesus: “Noteveryonewhosays to me ‘Lord! Lord!’ shall enter the Kingdom of Heaven, but he who does the will of God” (Matthew 7:21). SaidMuhammad: “If you derive pleasure from the good you do, and are grieved by the evil you commit, you are a true believer.” These are the words of three champions of monotheism. Their pragmatism is bracing. Butwhat should followers of these theist traditions think of the good practiced by nonbelievers—people who would say it’s quite unnecessary, and even counterproductive, to bring “God” into ordinary morality, who would offer that morality can and should be understood from an entirely scientific, evolutionary, and historical point of view thus: the capacity for empathy, fairness, and altruism is wired into human beings and even other higher mammals from birth, thanks to millions of generations of reproduction-with-variation under the constraints of natural selection. Similarly, the laws of civility—from the Eightfold Way and the Ten Commandments to the Magna Carta, theGenevaConvention, and theUnitedNationsDeclaration ofHumanRights— are the culturally transmitted legacy of thousands of years of human social evolution overlaid upon older, natural reproductive-selective processes. Whereas laws of civility may once have needed the rhetorical force of God-talk to establish themselves, today they can be embraced rationally in the service of peace and prosperity. In short, the nonbeliever holds that arriving at the enlightened understanding that good actions are good-for-us, that better ones are good-for-us-all, and the best are goodfor-all-living-things requiresneitherGodnor religion.God(in their view) is actually “God,” a useful fiction at best, a mental catalyst, rather like the square root of minus one: put into the equation only to be taken out later. This dismissal of God and “his” goodness—in favor of evolution and its goodness— leavesmodern, science-educated theists (and deists) unsatisfied. They believe that centuries of religious architecture, literature, and music ought not be treated only aesthetically and/or anthropologically, bracketed from real life, and considered to be aboutwhatwasoncepicturesquelybelieved—but rather as capable, still, of transporting the self andtransformingtheworld for thegood.Theybelieve, likewise, that ceremonies calmly