A question arose to me the other day in contemplating the meaning of perception: at what angle, or angles, do we perceive two equal line segments in golden ratio with each other? How far away would we be when we perceive this phenomenon? Is it possible that we can perceive this ratio from equality at perspective at all? And, how is it that we should decide where to begin and where to end a discussion on the topic? Is it possible that there are multiple places at which we could perceive the transformation of Golden Ratio from equal ratio?
Obviously, taking 3D space perception into account would totally transform the question and make it much more complicated. That is why we shall begin discussing this in terms of only perception with one eye in a situation where one’s eye is perpendicular to the plane of the two equally lengthed line segments being perceived.
In mathematical and geometrical terms, we begin by bisecting a line segment, let’s call the total line segment AC, and when we bisect it, it because AB; BC.
Even the subjective experience is based on objective relations. For instance, when I perceive the two equal line segments, what is it that allows my eye to see the angle? Certainly I am looking at something. But what? Am I looking into the tiniest derivative of space for each part of the line segment, and thus an infinite number of arc lengths? Am I looking at each entire line segment separately? Am I looking at both line segments together? It would be clear that with one eye, all I am perceiving is within the angle measure. How, though, may I know what this angle measure is without first comprehending the meaning of angle measures through an expression which give meaning to the word “angle.”
An angle gets described in terms of a radius and arc length or the sine of other lengths available to describe it. Which arc length, then, am I perceiving that relates to an angle? How can I determine which angle it is if I am given no grounds by which I can begin to measure the angle? What expression could be determined other than an assumption of angle ratio? It seems that in our perception of Euclidian space, the rules governing the system break down in some ways, or are less clear and determinable. I believe however, that there may be three ways of looking at this that were outlined in the above set of questioning regarding the “subject” matter. Each of these ways may in deed be valid. It may be that there are multiple ways of regarding the phenomenon, thus producing different phenomena. How does one phenomenon transform into three phenomena anyway? Obviously, we would love to be able to come to an understanding of the ultimate unity of the phenomena, and this happens through the constant factor present in each of the diagrams, and could be discussed mathematically if necessary.
In the first way suggested, the line segments take on the clarity of perspective. That is the point at the origin, point A.