| It appears that our mind probably has to make the rigid body assumption an assumption about the world in order to be able to organize the contours of objects into a set of objects. To get some feel for what we are talking about, look at the pictures shown below which were designed to thwart out ability to quickly organize the world into a set of objects. | |||||
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Try to organize the mass of connecting lines shown above into a single partition of objects. I created this picture from a basic rectangular wire frame that outlines a rectangular solid. Unless you use certain types of computer graphics programs you rarely encounter this type of schematic information. When we view a rectangular solid we see only a subset of the edges of object. What you should have experienced, if you are at all like me, is that you could organize these wire frames in a variety of different ways...but, you probably weren't able to fix on a single coherent partition of the lines into a set of "objects". Even though the shape of this object is not changing; it is difficult to come to a fixed organization of the object. The next picture is more of the same, but I made it larger and a little more complex. If you have a large enough screen, then expand your browser window so you can view the entire picture. Now, try and focus on the center and note the ways in which your mind organizes the lines. |
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| If this didn't challenge your mind enough, then try the next picture which is more of the same, but lots more and and now all in a jumble. The lack of regularity in the composition will probably make it harder for you to structure this picture. | |||||
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| And, if this hasn't sated your visual appetite, then sink into this next one which is constructed solely from a simple triangle. You should be able to see many ways in which to organize this picture, some of which are triangles, others squares and other rectangles. | |||||
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Now that you've experienced some of the difficulties your mind has with both photographs of the natural world and with these artificially created pictures, we are now ready to ask why the mind doesn't run into these kind of difficulties all of the time. Well, we don't really know the full answer to this question. But, one intriguing line of research that addresses this issue also fits in with our emphasis on comparing the logical possibilities with those that actually seem to be considered by the mind. The discussion here is based on work done by David Waltz in the early 70's on the question of how one might go from two dimensional information about lines and the way they are connected to an organization of these lines and their connections into a set of objects. One way to try to get your mind around this problem is to focus your eyes on some messy area in your current environment. My desk is always available to fill this bill. Notice that the objects overlap each other and only parts of their surfaces are visible. Now think of simply drawing a line on a sheet of paper for each object edge that you can see. These lines will intersect and form vertices. This set of lines and the vertices that they created were what Waltz took as the input to his computer program. The output was to be an organization of these lines and vertices into a set of objects....what I referred to above as a partition of this vertex information into a set of objects. The next page will briefly present the work of Waltz on this partition problem. |
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| © Charles F. Schmidt | ||