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tags:holesmereologyislands
NOTE
Further readings on Holes
Do boundaries deserve a place of their own in the inventory of spatial articles? If so, how are they related to the entities they are boundaries of? If no, how do we do justice to the ordinary concept of a surface?
Spatial Entities
Connectedness is a topological relation. If it cannot be defined in mereological terms, it must be assumed on independent grounds.
Locke (identity)
We are never finding, nor conceiving of it possible, that two things of the same kind should exist in the same place at the same time, we rightly conclude that whatever exist any where at any time, excludes all of the same kind is there itself alone.
A shadow is not part of the wall the onto which it is cast, yet one could argue that everything connected to the shadow is connected to the wall Survey of Shadows
Adjectivalist - translates “there is a hole in the donut” to “the donut is perforated” Substantivalist - reduce holes to regions of space
geon - normalized cylinder, geometrical ion. Only three geons can theoretically describe 1.4 billion distinct object shapes.
Cave and Kosslyn have shown, first, that the recognition of an object depends crucially on proper spatial relations among the parts: when the parts of scrambled or otherwise scattered naming times and error rates increased.
Connection Structures
Cantor set - a set of points lying on a single line segment that has a number of unintuitive properties. Discovered by Henry John Stephen Smith in 1874, but mentioned by Georg Cantor in 1883.
Remove the middle third of a self-connected bar. Remove the middle of each of the remaining bars. Repeat over and over, creating a scattered object with no self-connected proper parts.
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Cantor set has zero measure.
Boundaries
boundaries seem needed in order to account for certain basic intuitions — to just do justice to the ordinary concept of a surface for instance.
Boundaries have a particular relation to space: they are located in space, yet they do not take up any space (just as temporal boundaries do not take up any time.)
Boundaries belong to the palette of basic ontological tools that we use to describe the spatiotemporal world.
Boundaries demarcate two entities, or two parts of the same entity are said to be in contact with one another. How can this contact be explained?
Our primary concern is with the ordinary conception of middle-size reality. But this does not mean that we are interested in taking a stand on the issue of whether middle-sized objects have true boundaries, if that is understood on the assumption that physical (microscopic) reality is all the reality that there is. We can assume that it is an obvious fact that ordinary physical objects (i.e. objects interpreted physically as aggregates of molecules) are not strictly speaking dense and do not have boundaries of any kind (at least, not boundaries of the smooth, continuous sort countenanced by our unreflected view of the world.) If the solid bodies of common sense are replaced by intricate systems of subatomic particles, speaking of a body’s continuous boundary is like speaking of the “flat top” of a fakir’s bed of nails.
Boundaries are merely imaginary entities enveloping smudgy bunches of hadrons and leptons, and their exact shape and properties involve the same degree of arbitrariness as those of any mathematical graph smoothed out of scattered and inexact data.
JJ Gibson “There’s a physical structure on the scale of millimicrons at one extreme and on the scale of light years at the other. But surely the appropriate scale for animals is the intermediate one of millimeters and kilometers, and that is appropriate because the world and the animal are then compatible.”
Boundaries of time. In the scientific spirit, a body’s being at rest amounts to the fact that the vector sum of the motions of the trillions of restless atoms of which the body is composed, averaged over time, equals zero.
The averaging of over time makes it impossible to pinpoint, even in principle, an instant at which this condition ceases to obtain. Thus it might be claimed that no real meaning can be attached to the assertion that the body’s beginning to move is an instantaneous event.
What color is the demarcation between a black spot and a white background?
HH Price
“Surface” it is true, is a substantive in grammar, but it is not the name of a particular existent but of an attribute.
Two objects, albeit disconnected, are vanishingly close to one another.
Clouds, dunes, hinterlands, let along the figures of impressionist painting all seem to elude the notion of a bounded object.
There is no line which sharply divides the matter composing Mount Everest from the matter outside of it. Everest’s boundaries are fuzzy. Some molecules are inside Everest and some molecules are outside. But some have indefinite status, there is no objective, determinate fact of the matter whether they are inside or outside. - Michael Tye
Alternatively, fuzziness of boundaries is merely a semantic fact:
The reason why it’s vague where the outback begins is not that there’s this thing, the outback, with imprecise borders; rather there are many things, with different borders, and nobody has been fool enough to try to enforce one of them as the official referent of the word “outback” - David Lewis
Empty Spaces
rel: Holes Survey of Shadows
Location is a relation to a spatial entity and its region. But location is also, a relation linking directly one spatial entity to another. The stone is located in the whole because it is located wholly in the region of the hole.
Taking holes seriously makes it possible to disclose conceptual distinctions that would be left in the dark if one focused only on paradigmatic cases such as spatial regions or material objects.
Convex hull: The be in a hole is to be region-located within the boundary of the hole. But what exactly is the boundary of a hole? Part of the boundary is supplied by the material object whose surface the hole is located; the inner surface of the containing part bounds the hole from the outside. They state the boundary is determined by the convex hull of the relevant containing part. It corresponds to the minimal surface determined by the rim of the hole- to the boundary of the ideal perfect filler of the hole.
Maps
Some entities themselves are spatial representations. The account they sketch can be extended to pictures (photographs perhaps) but will deal with maps constituting a simpler case.
NOTE
I have never thought of a photograph as a Map. But I love this view of Photography
Maps display no shortenings, or perspective effects: a photograph contains additional information about the POV of the camera.
Maps are as detached as possible.
The map and what it represents can be conceived of as spatial surfaces; and although this constitutes a an important methodological simplification.