art sale

art sale
Originally uploaded by chillrock.

cone

cone
Originally uploaded by chillrock.

Sizes and Shapes of Visual Objects

1) It has been pointed out by philosophers since at least George Berkeley's time (if not from the time of Heraclitis or before) that the size and shape of objects, in terms, of their visual appearance, changes relative to our apparent position to them. We tend to overlook this most of the time. For example, a friend of mine has a square table (top) in a dining area just off the kitchen. But the table only looks square from two directions -- straight over its center or straight under its center. From any other angle, the table will look trapezoidal or rhomboidal or some such. From straight on edge, it even just looks like a straight line. If one took a photograph of the table from different angles and then outlined or cut out the table top as shown in the photograph, only those cutouts from photos taken straight over or straight under the table would be square (or, as with the table, would appear square from directly in front or directly behind it). Moreover, the size of the square depends on how far away from it one gets and whether or not one uses a telescope or magnifying lens to look at it. Hence, in the sense of appearance, there is no correct or single shape or size of the table; it is all relative from how and where we are looking.

Nevertheless, of course, we normally talk about the table's being a square table with sides of a specific, particular length. When we shop for a table cloth, we look for a square one of a particular size. If we measure the sides and corner angles of the table, we find the sides to be a certain length and the angles to be 90 degrees. We think that the table has one particular shape and size and that its appearances otherwise are to be accounted for by perspective, geometry, the physics and geometry of light, etc. The way we describe and measure the table involves preferred angles (straight over or under the center is the preferred viewing angle apparent shape we ascribe to the table) and preferred ways to measure length of sides and size of angles -- by putting a tape measure and protractor against the sides or corners of the table close up in certain ways. This is much easier, apparently, than using some optical instrument from just any distance and angle and then looking for a table cloth that gave the same dimensions and shape from the same angle and distance in order to know what would fit the table close up from on top. But we perhaps could find appropriate table cloths that way. And, of course, we make the assumption, justified by experience generally, that if we find a table cloth that matches the size and shape of the table from one angle and distance, it will also match from any other angle and distance. There is a commonality or an invariant aspect to the fact that however the table appears differerent from different angles and distances, so does the "proper" cloth. As the appearance of the one changes, so does the appearance of the other1. Hence we tend to speak, not of many tables or many relatively different sizes or shapes of tables, but of "the" table with a single, particular size and shape.

It seems to me from Professor Bondi's and from other explanations I have read of relativity that we do something similar to this when talking about time, that time within an inertial system, or that time from some fixed point in space-time is somehow the "preferred" or conventionally accepted vantage point. We speak of, say, 6 minutes in Alfred's time being equivalent to, or taking up, 9 minutes in Brian's time as though we are some universal observer plotting out both sets of times and the relationship between them. Similarly we speak of 6 minutes of Charles' time registering as 4 minutes in Alfred's time as though, again we are some universal observer that can make sense of lengths of time within a given perspective, in the same way we can describe how (what looks like) a square (from 'straight on') will look from different angles. I will come back to this, but it seems to me that there is a parallel between our normal thinking about shapes in space that is not dissimilar about how we should think about events in time in regard to relativity -- including that generally an unrealized conventional, essentially "absoute" or "ideal" "observation platform" is used to conceive of and describe spatial shapes and temporal events, and to account for the relative differences when viewed from other perspectives or "platforms".

i read this at:
http://www.garlikov.com/teaching/time

tree

tree
Originally uploaded by chillrock.