From Trees to Galaxies: The Potts Model on a Random Surface

The matrix model of random surfaces with c = inf. has recently been solved and found to be identical to a random surface coupled to a q-states Potts model with q = inf. The mean field-like solution exhibits a novel type of tree structure. The natural question is, down to which--if any--finite values of c and q does this behavior persist? In this work we develop, for the Potts model, an expansion in the fluctuations about the q = inf. mean field solution. In the lowest--cubic--non-trivial order in this expansion the corrections to mean field theory can be given a nice interpretation in terms of structures (trees and ``galaxies'') of spin clusters. When q drops below a finite q_c, the galaxies overwhelm the trees at all temperatures, thus suppressing mean field behavior. Thereafter the phase diagram resembles that of the Ising model, q=2.Comment: 25 pp. (voodoo PostScript replaced by original LaTeX), NBI-HE-94-2

Embodied induction: Learning external representations

The problem of inductive learning is hard, and--despite much work--no solution is in sight, from neural networks or other AI techniques. I suggest that inductive reasoning may be grounded in sensorimotor capacity. If an artificial system to generalize in ways that we find intelligent it should be appropriately embodied. This is illustrated with a network- controlled animat that learns n-parity by representing intermediate states with its own motion. Unlike other general learning devices, such as disembodied networks, it learns from very few examples and generalizes correctly to previously unseen cases

Matrix Models on Large Graphs

We consider the spherical limit of multi-matrix models on regular target graphs, for instance single or multiple Potts models, or lattices of arbitrary dimension. We show, to all orders in the low temperature expansion, that when the degree of the target graph $\Delta\to\infty$, the free energy becomes independent of the target graph, up to simple transformations of the matter coupling constant. Furthermore, this universal free energy contains contributions only from those surfaces which are made up of ``baby universes'' glued together into trees, all non-universal and non-tree contributions being suppressed by inverse powers of $\Delta$. Each order of the free energy is put into a simple, algebraic form.Comment: 19pp. (uses harvmac and epsf), PUPT-139

Motor processes in mental rotation

Much indirect evidence supports the hypothesis that transformations of mental images are at least in part guided by motor processes, even in the case of images of abstract objects rather than of body parts. For example, rotation may be guided by processes that also prime one to see results of a specific motor action. We directly test the hypothesis by means of a dual-task paradigm in which subjects perform the Cooper-Shepard mental rotation task while executing an unseen motor rotation in a given direction and at a previously learned speed. Four results support the inference that mental rotation relies on motor processes. First, motor rotation that is compatible with mental rotation results in faster times and fewer errors in the imagery task than when the two rotations are incompatible. Second, the angle through which subjects rotate their mental images, and the angle through which they rotate a joystick handle are correlated, but only if the directions of the two rotations are compatible. Third, motor rotation modifies the classical inverted V-shaped mental rotation response time function, favoring the direction of the motor rotation; indeed, in some cases motor rotation even shifts the location of the minimum of this curve in the direction of the motor rotation. Fourth, the preceding effect is sensitive not only to the direction of the motor rotation, but also to the motor speed. A change in the speed of motor rotation can correspondingly slow down or speed up the mental rotation

Self-motion and the perception of stationary objects

One of the ways we perceive shape is through seeing motion. Visual motion may be actively generated (for example, in locomotion), or passively observed. In the study of how we perceive 3D structure from motion (SfM), the non-moving, passive observer in an environment of moving rigid objects has been used as a substitute for an active observer moving in an environment of stationary objects; the 'rigidity hypothesis' has played a central role in computational and experimental studies of SfM. Here we demonstrate that this substitution is not fully adequate, because active observers perceive 3D structure differently from passive observers, despite experiencing the same visual stimulus: active observers' perception of 3D structure depends on extra-visual self-motion information. Moreover, the visual system, making use of the self-motion information treats objects that are stationary (in an allocentric, earth-fixed reference frame) differently from objects that are merely rigid. These results show that action plays a central role in depth perception, and argue for a revision of the rigidity hypothesis to incorporate the special case of stationary objects

Depth Affects Where We Look

SummaryUnderstanding how we spontaneously scan the visual world through eye movements is crucial for characterizing both the strategies and inputs of vision [1–27]. Despite the importance of the third or depth dimension for perception and action, little is known about how the specifically three-dimensional aspects of scenes affect looking behavior. Here we show that three-dimensional surface orientation has a surprisingly large effect on spontaneous exploration, and we demonstrate that a simple rule predicts eye movements given surface orientation in three dimensions: saccades tend to follow surface depth gradients. The rule proves to be quite robust: it generalizes across depth cues, holds in the presence or absence of a task, and applies to more complex three-dimensional objects. These results not only lead to a more accurate understanding of visuo-motor strategies, but also suggest a possible new oculomotor technique for studying three-dimensional vision from a variety of depth cues in subjects—such as animals or human infants—that cannot explicitly report their perceptions

The Shifting Discourse on Third Places: Ideological Implications

Within the social sciences, literature on third places attempts to assist in the construction of a social concept of “place”. This notion of a place is an idealization of the bridging space with home and family on one side, and work with the rule-based impersonality of life in mass society, on the other. Like the idea of work-life balance—as seen through the vocabulary of placemaking—third places provide people with a place in which there is a balance between the emotive attachments of home and family and the challenge striving for merit and reward in the marketplace. To date, third places have been treated as a unified construct. This paper makes the case that both the discourse and design models used to make sense of third places are significantly different. After reviewing and placing third-place literature in its historical context, we distinguish communitarian, commercial and digital third places. These three types of places—in both their physical and virtual forms—are important parts of the private, public and not-for-profit sectors. Subsequently employing a cui bono approach or who benefits framework, we highlight the ways in which ideological points of view imbedded in the varying versions of third places have implications for practice and theory

New critical phenomena in 2d quantum gravity

We study $q=10$ and $q=200$ state Potts models on dynamical triangulated lattices and demonstrate that these models exhibit continuous phase transitions, contrary to the first order transition present on regular lattices. For $q=10$ the transition seems to be of 2nd order, while it seems to be of 3rd order for $q=200$. For $q=200$ the phase transition also induces a transition between typical fractal structures of the piecewise linear surfaces corresponding to the triangulations. The typical surface changes from having a tree-like structure to a fractal structure characterizing pure gravity when the temperature drops below the critical temperature. An investigation of the alignment of spin clusters shows that they are strongly correlated to the underlying fractal structure of the triangulated surfaces.Comment: 22 pages, uuencoded compressed ps-file. Use csh file.uu to get ps-fil