You say it is not necessary to enter the affective realm when discussing Platonic realities, and then, in the same breath, you say you find discussing Platonic realities [oddly] soothing. Soothing, oddly or not, to me, is an affective experience. If you do not agree, then to what faculty or realm of consciousness do you attribute "soothing?"You are entering the affective realm again. I don't think that is necessary, but you may find it productive - I find discussing Platonic realities oddly soothing as opposed to metaphysical discourse.
It is also true that metaphysical discourse is not always soothing; for the most part, it is mostly anything but. From my experience, that is its 'purpose.'
I am not disputing the perfection of the circle as it exists, as you say, always inside one's head; what I am saying is that this perfection "of the head" is intellectually circular, bringing one always back to the original "point" of departure. That regardless of the journey one takes into the depths of the realms of the maths and sciences, which include the soft sciences of art, music and psychology, that one is always brought back to the beginning of the thought, which is also the ending of the thought. In the bible, in the Book of Revelation, this is called the Alpha Omega point of consciousness.My point was in the very well understood Platonic sense, the circle is the set of all points in a plane that are equidistant from a given point. This distance, which is called the radius of the circle, entirely defines the circle. All circles differ only in their radii, ignoring the location of the circle, since it really is always in one's head. Without loss of generality, the study of the circle is usually done with letting the radius r=1. From this, all of the Trigonometry functions spring. Since we are always letting r=1, the units do not matter.
The ratio of 2C/r (=2C since r=1) where C is the circumference or "distance around" this unit circle is given the name π. It turns out that π cannot be expressed as a repeating decimal, so therefore is an irrational number. Another way of saying this is that π cannot be expressed as the ratio of two whole numbers, although 22/7 is somewhat close.
The irrational unit-less quantity π is also the area of the unit circle.
This may be only true if space itself is Euclidean. If not, then the actual physical area of a circle might be different from π and may not be irrational after all! Just a guess...
From my experience, one's initial arrival to the silent invisibility of the Alpha Omega point is indeed, most unsettling. This is the fear and trembling experience; where and when there is no visible form appearing for interpretation, it is no wonder that a man is afraid and trembles. Should he return again and again, however, in faith that he won't be destroyed or be annihilated if he cannot attach himself to form, then the fear and trembling passes and he passes into the "peace that passes all understanding."
Of course, no one "has" to "go" to their Alpha Omega point. However, this refusal to "go" does not change the fact that it exists for one's discovery. :-)
