Filling in the Blanks

Eugene Gendlin claims that he wants "to think with more than conceptual structures, forms, distinctions, with more than cut and presented things" (WCS 29).1 He wants situations in their concreteness to be something we can think with, not just analyze conceptually. He wants to show that "conceptual patterns are doubtful and always exceeded, but the excess seems unable to think itself. It seems to become patterns when we try to think it. This has been the problem of twentieth century philosophy" (WCS 29). As a result he has "long been concerned with what is not formed although always in some form" (TAD 1). In this essay I would like to explore some of the issues surrounding the relation of the unformed and the formed. Gendlin says that "we get beyond the forms by thinking precisely in them" (TAD 1). The two emphasized words have to be considered separately as well as together. In many essays Gendlin's main concern is with the "precisely": can something that is not fully formed and definite still direct us as we carry forward language and action? My discussion begins with that issue; I suggest ways that Gendlin's proposal connects with and differs from some current ideas in epistemology and the philosophy of language. Then my discussion moves to the "in": what sense can we make of the formed being unformed? Finally I suggest that Gendlin's program runs into some difficulties in this connection

An illusion induced by an illusion -perceptual filling-in of coloured negative afterimages

Visual filling-in relates to a perceptual phenomenon in which a stimulus pattern apparently undergoes dynamic changes assuming an attribute such as colour, texture, or brightness from the surround. This perceptual completion effect has up to now been shown only for real images. Here, we present filling-in in negative afterimages, a phenomenon not yet reported. Using coloured disk-ring patterns for stimuli, we demonstrate that afterimage filling-in arises independently, and is not simply a replica of filling-in observed in real images. Such filling-in does not occur when the afterimage is elicited dichoptically, suggesting its emergence within the monocular visual pathway. In this way, our findings indicate that filling-in under certain conditions may derive from an active neural mechanism located at low levels of the visual pathway

Dehn filling in relatively hyperbolic groups

We introduce a number of new tools for the study of relatively hyperbolic groups. First, given a relatively hyperbolic group G, we construct a nice combinatorial Gromov hyperbolic model space acted on properly by G, which reflects the relative hyperbolicity of G in many natural ways. Second, we construct two useful bicombings on this space. The first of these, "preferred paths", is combinatorial in nature and allows us to define the second, a relatively hyperbolic version of a construction of Mineyev. As an application, we prove a group-theoretic analog of the Gromov-Thurston 2\pi Theorem in the context of relatively hyperbolic groups.Comment: 83 pages. v2: An improved version of preferred paths is given, in which preferred triangles no longer need feet. v3: Fixed several small errors pointed out by the referee, and repaired several broken figures. v4: corrected definition 2.38. This is very close to the published versio

“Filling in”, thought experiments and intuitions

Recently Timothy Williamson (2007) has argued that characterizations of the standard (i.e. intuition-based) philosophical practice of philosophical analysis are misguided because of the erroneous manner in which this practice has been understood. In doing so he implies that experimental critiques of the reliability of intuition are based on this misunderstanding of philosophical methodology and so have little or no bearing on actual philosophical practice or results. His main point is that the orthodox understanding of philosophical methodology is incorrect in that it treats philosophical thought experiments in such a way that they can be “filled in” in various ways that undermines their use as counter-examples and that intuition plays no substantial role in philosophical practice when we properly understand that methodology as a result of the possibility of such filling in. In this paper Williamson’s claim that philosophical thought experiments cases can be legitimately filled in this way will be challenged and it will be shown that the experimental critique of the intuition-based methods involved a serious issue

Hyperbolic Dehn filling in dimension four

We introduce and study some deformations of complete finite-volume hyperbolic four-manifolds that may be interpreted as four-dimensional analogues of Thurston's hyperbolic Dehn filling. We construct in particular an analytic path of complete, finite-volume cone four-manifolds $M_t$ that interpolates between two hyperbolic four-manifolds $M_0$ and $M_1$ with the same volume $\frac {8}3\pi^2$. The deformation looks like the familiar hyperbolic Dehn filling paths that occur in dimension three, where the cone angle of a core simple closed geodesic varies monotonically from $0$ to $2\pi$. Here, the singularity of $M_t$ is an immersed geodesic surface whose cone angles also vary monotonically from $0$ to $2\pi$. When a cone angle tends to $0$ a small core surface (a torus or Klein bottle) is drilled producing a new cusp. We show that various instances of hyperbolic Dehn fillings may arise, including one case where a degeneration occurs when the cone angles tend to $2\pi$, like in the famous figure-eight knot complement example. The construction makes an essential use of a family of four-dimensional deforming hyperbolic polytopes recently discovered by Kerckhoff and Storm.Comment: 60 pages, 23 figures. Final versio

Filling in the retinal image

The optics of the eye form an image on a surface at the back of the eyeball called the retina. The retina contains the photoreceptors that sample the image and convert it into a neural signal. The spacing of the photoreceptors in the retina is not uniform and varies with retinal locus. The central retinal field, called the macula, is densely packed with photoreceptors. The packing density falls off rapidly as a function of retinal eccentricity with respect to the macular region and there are regions in which there are no photoreceptors at all. The retinal regions without photoreceptors are called blind spots or scotomas. The neural transformations which convert retinal image signals into percepts fills in the gaps and regularizes the inhomogeneities of the retinal photoreceptor sampling mosaic. The filling-in mechamism plays an important role in understanding visual performance. The filling-in mechanism is not well understood. A systematic collaborative research program at the Ames Research Center and SRI in Menlo Park, California, was designed to explore this mechanism. It was shown that the perceived fields which are in fact different from the image on the retina due to filling-in, control some aspects of performance and not others. Researchers have linked these mechanisms to putative mechanisms of color coding and color constancy

Predictive coding: A Possible Explanation of Filling-in at the blind spot

Filling-in at the blind-spot is a perceptual phenomenon in which the visual system fills the informational void, which arises due to the absence of retinal input corresponding to the optic disc, with surrounding visual attributes. Though there are enough evidence to conclude that some kind of neural computation is involved in filling-in at the blind spot especially in the early visual cortex, the knowledge of the actual computational mechanism is far from complete. We have investigated the bar experiments and the associated filling-in phenomenon in the light of the hierarchical predictive coding framework, where the blind-spot was represented by the absence of early feed-forward connection. We recorded the responses of predictive estimator neurons at the blind-spot region in the V1 area of our three level (LGN-V1-V2) model network. These responses are in agreement with the results of earlier physiological studies and using the generative model we also showed that these response profiles indeed represent the filling-in completion. These demonstrate that predictive coding framework could account for the filling-in phenomena observed in several psychophysical and physiological experiments involving bar stimuli. These results suggest that the filling-in could naturally arise from the computational principle of hierarchical predictive coding (HPC) of natural images.Comment: 23 pages, 9 figure

Precise Control of Band Filling in NaxCoO2

Electronic properties of the sodium cobaltate NaxCoO2 are systematically studied through a precise control of band filling. Resistivity, magnetic susceptibility and specific heat measurements are carried out on a series of high-quality polycrystalline samples prepared at 200 C with Na content in a wide range of 0.35 =< x =< 0.70. It is found that dramatic changes in electronic properties take place at a critical Na concentration x* that lies between 0.58 and 0.59, which separates a Pauli paramagnetic and a Curie-Weiss metals. It is suggested that at x* the Fermi level touches the bottom of the a1g band at the gamma point, leading to a crucial change in the density of states across x* and the emergence of a small electron pocket around the gamma point for x > x*.Comment: 4 pages, 5 figures, submitted to J. Phys. Soc. Jp

Men in Nursing: Filling in the Ranks

Fred Calixtro sees a marketing problem. Paul Higgins ‘06 says it’s an underpromoted career. David Silva ‘04 thinks the name is a turn-off. All three agree that nursing needs more men