Points 1, 2, and 3 are illustrated in the animation that follows:

Point 1: Blue line at bottom of the blue rectangle that aligns with the inner spiral
Point 2: Blue line that divides the blue and white sections of the rectangle at the golden ratio point
Point 3: Blue line at the outer edge of the white rectangle that aligns with the outer spiral.

Thanks for the thoughtful discussion, Tim. I’ll add a few thoughts in response:

There’s one significant challenge in thinking of the “Designer” as merely a “process.” It’s easy to create a natural process that shifts a shoreline, because a random result from a random process is a viable result. Life, however, is very different by its very nature. It requires information that is expressed in a code, a language, and then systems to read the code and act on it. If you doubt this, take a look at the video I created at https://www.youtube.com/watch?v=AcGw21Wbcgk.

If you think that this “thing” (i.e., God) has to be far beyond our meager faculties, then how is it consistent to assume that it “may not have any self awareness of itself?” If it’s greater than us, then wouldn’t it be greater than us in every way, have all of our capabilities and then much more? Wouldn’t we be a reflection of it, created in its image, just as a painting or invention would be a reflection of the artist or inventor?

Whatever is ultimately behind creation does not have to be a conscious entity to produce things of beauty that also exhibit signs of intelligent handiwork. As the Golden Ratio and PHI show, since we all emerge out of the same creative matrix that has produced oceans and shorelines and nautilus shells and sunflowers, this mathematical property must have some universal significance on many levels because it appears everywhere from the microscopic to the galactic. This ratio, being fundamental as it is, will naturally generate expressions of itself everywhere in creation. This universal aspect makes us think “somebody or some “thing” must have “designed” this. But can a painting or an invention conceive of it’s creator – the artist or inventor who produced it? By the same token, self-conscious beings though we are, it may be too much to assume that we are capable of conceiving accurately the true nature of that which is behind all creation.

I have been making an effort in my old age to let G-d out of the box. I think such a thing exists, but the limits we place on our imaginings, the way we anthropomorphize creation simply cannot due justice to such a “thing”. For such a “thing” to exist that has the capabilities we attribute to it, such a “thing” has to be far beyond our meager faculties. So rather than some kind of genie, or Lord, or Father figure, or Grandmother, I think there is some eternal emergent process at work throughout the universe, (or multiverses). This process may or may not have any self awareness of itself. Maybe, as some believe, we are participating in some project of the universe developing self-awareness through us, along with our mathematics, our philosophies and our technology. I don’t know. But things like the Golden Ratio and PHI do seem to support interconnections between all things on multiple levels.

Any resource that explains all that turn?

“There is a peristent misconception about the character (and naming) of this curve. In fact, the curve drawn in the first two illustrations (by joining subsequent quarter arcs) cannot be named “spiral”. ”

A volute IS a spiral. Not a logarithmic spiral, correct, but it IS a spiral and therefore it’s not wrong to name it a spiral, as long as you don’t name it a logarithmic spiral.

And yes, some people think Fibonacci spiral (volute spiral) and golden spiral (logarithmic spiral) are the same. They’re not. Correct.

I had assumed a full turn of 360 degrees or 2Pi radians. Of course, one can create different spirals depending on your reference angle – whether it be full turn, half turn, third turn, quarter turn, fifth turn; or 1 radian or 2 radian, etc So there is a range of possibilities of making a match.

Thank you, Gary. That is very helpful.