When I studied physics during the short time I spent at a university forty years ago, I learned a potent problem solving technique requiring the solver draw a circle around the problem. The circle drawing is an indicating endeavor, and as may be seen comparing the results of the exercise given to a group of students, the circle though shaped differently by every one in the class is still a circle. In other words, the circle is a concept independent of content.
Another key point is that, the drawing of a circle is independent of the talent of the solver. A solver of any level of intuitive capacity and capability may draw a circle.
The purpose of the circle is to provide a boundary at which to measure any variance in the problem. The task of the solver is to identify the function of the form, that is, to measure boundary transactions in an attempt to formalize the problem circled, in terms of function, it's interaction to the environment of the Form. It is to be understood, that the environment of the Form, is an undefined encompassing larger Form.
This is scientific endeavor.
What tends to escape monitoring is, what is happening to the solver? Will the problem-solving influence the development of the solver?
The answer is YES, the action of resolving a form always has an effect on a larger Form , in this case, the form incorporating the solver.
Another facet to this study is: The positioning of any concept such as an encompassing circle is purely arbitrary. The circle is related to line which curves uniformly in such a way that one end bends around to touch the other end. As a concept, it has no dimension, and content is undefined, This circle therefore can be conceived as a point and also as a line. As a boundary it has no real limit, and as a separating device, it essentially bisects an infinity where both sides form an identity.
Another point worth making in this introductory discussion is, without dimension, the form of a circle is a timeless concept.
A problem I have with mathematical discussions is: where is the observer ? What determines the apparent extensions?
ReplyDeleteTherefore, in order to create a proper foundation for any extensions whether in space or in imagination, a place for a willful observer must be allowed.
For example, given a formless void, determine a point. The point has no dimension. Therefore it exists only as a determined indication of a willful intelligence.
If you wish to follow the discussion it required an act of will on your part.