My philosophical investigations have revealed to me the concept of contraction, or contracted representation of information. These can be understood in comparision with abstraction and protraction which are themselves distinct. Today I mean to clarify what I mean by "contraction" and "protraction", and the distinction between them.
I will do this by examining various representations of an action vector. In the image below, an action pathway is represented by interlocking grey and white fields. The perimeter of the interior grey field is the fractal, or "recursively self-similar" action. I mean action in the sense of that transitory state of being which would arise from moving an infinitely precise laser along the boundary between the two colored fields.
Observe the action pathway in its entirety:
The image above shows an abstract view of the fractal action in its entirety. This represents the entire field of possible actions. Sensing the intricacies of detail in the action pathway, we select a small internal portion of the whole:
We next isolate this portion of the whole and show it by itself below:
This image is a selection, a portion of the unity above. If we examine this very same image file more carefully, by expanding its width and height by a factor of 13, we notice a distinct lack of resolution:
This close examination reveals to us that the small image we have considered previously is not at all clear, it is actually a rather careful optical illusion of clarity which purports to represent the action described above, but in truth is no more than a grid of colored boxes which reveal no more detail when subjected to closer examination. This is the nature of our present medium, which is the Graphics Image Format (GIF) file type. The GIF images do not store in memory any further information about this particular mathematical action, except that necessary to present the above likeness. However, in the original program, a great deal of memory is expended in storing the data represented in each particular vantage point.
The program used to create the original abstract image, however, is not limited to this contraction or compression of data. Using the very same selection in the fractal viewer, we are able to protract, or magnify the selection:
This is a protracted, or amplified portrayal of the same selection. It is not derived in any way from the pixelated selection above, but is a protracted representation of the same part of the original fractal action. The selection above had been contracted to a GIF image format, which explicitly and necessarily results in loss of data. This data loss is clearly shown when we expand the width and height as above.
The contraction of data in this manner is necessary, given the nature of its own manifold of representation, which is an electronic portrayal of the original fractal vector. Because of the finite resolution of computer displays, all visual representations are contractions necessarily--computer displays can represent at maximum 72 dpi, or "dots per inch" of data. The GIF algorithm is useful precisely because, through contraction, it dispenses with all data except that needed to portay a recognizeable likeness of an original, more protracted signification. This reduces the size of the "memory footprint" of each image, allowing faster data delivery over the Internet. Given the infinite complexity of the fractal vector, the size of the image file could scale infinitely, far outstripping the physical limitations of the computer hardware.
The fractal browser is not limited to the size constraints imposed by the Internet, and can allocate a large sum of memory to recording data about the fractal action pathway. This means that the representation of the fractal signifies a much greater resolution of information. The information present in this high-fidelity portrayal is "contracted" into the GIF format. Conversely, the information present in each small portion of the GIF format is "protracted" or magnified in the fractal viewer.
The process detailed above continues further "down" into the fractal. We can isolate another selection from our last vantage point:
Which we show here:
This GIF image, upon closer examination, is itself a contraction of the original action vector:
The pixelation shown in this close examination of the GIF is a contraction of the following, protracted signification:
We can see clearly here the relationship between contraction and protraction. It is important to note that computers can not protract an image, thereby increasing the resolution of that image and the amount of clarity or data which is stored in the image. This is shown frequently in popular films, but has no basis in reality. Compression is final for computers. Once they discard data, it is lost.
The human mind, however, does not suffer from this limitation. It freely contracts and protracts on a regular basis. Language is no less a contraction of meaning than the above images were contractions of an action pathway. However, the mind can "reconstitute" language, protracting it in order to derive the original meaning of its author, with varying degrees of success.
Another way to think about contraction and protraction is as a projection screen. If you were to project the image of a circle upon a flat, curved, and textured surface, you would get three different visual representations or contractions of the original, protracted form. Similarly, if you print a circle with varying qualities of equipment and material, ranging from dot matrix on green paper to color laserjet on glossy card stock, you get varying contractions of the original action. An action may be contracted multiple times, each time reducing the clarity or somehow distorting the original until it is no longer recognizeable by the mind.
In my own research, I have concluded that logic is a discrete and mechanized contraction of reason. Logical processes can not generate hypotheses as rational processes can. They are not able to resolve their own paradoxes or even prove all of their own axioms. They are severely limited in this regard. This is not to say that they do not have their uses. They may easily be automated, for example.
I suspect also that the mind is a manifold of action which admits certain contractions of truth, and that the nature of the mind admits of alterations which increase its resolution or expressive capacity, its ability to accurately reflect truth. This might be tied to our apparent ability to protract meaning from a contracted manifold.
I hope that my illustrations above help convey the meaning of my use of "contraction" and "protraction' as I continue my investigations. I will likely return to this entry several times in the future as an example of my meaning.
Please feel free to republish this document in its entirety, so long as proper attribution is given to its author. All fractal images were created with Tierazon and Photoshop CS2.
Enquiries on Contraction and Protraction in Philosophy
