did you see what you get if you spin a square really fast?
Just an interesting thought, as squaring the circle is one thing, circling the square is another. Both might be symbolic representations and actually be referring to the same thing in a way. You never know with everything we know being backwards
What is interesting though, is that the usual reference point of a square is one of its corners (where height and length is measured from), where as the usual reference point of a circle is its center (where its radius, diameter and even its area is indirectly measured from). By "squaring the circle" in the context of looking at drawn shapes, you are moving the reference point from the center to the corner of the square, and vice versa if you "circle" the square.
The one reference point is a view "inside the box", the other reference point is a view "outside the box". The one looks round and the other not. The one has a biased view (seeing corners as extremes that stick out like pointy things) and other has a uniform view (perfectly round, no extremes).
If we think of frequencies, they are usually represented by round uniform shapes. If everything is a frequency or vibration of some kind, then everything is much more like a circle than it is like a square (think of those amplitude waves when any machine measures sound frequency).
So to me, squaring the circle has a meaning that might not be expected. Suspicions include everything from the "measuring" of things to the "control" of things. If you can measure and control something, you transcend it, just like the center of the circle (being inside the box, measuring the box from the inside) is no longer the reference point, but you go outside it, and measure it from outside. You are no longer subject to the perspective from inside the circle only, you can now measure it from other reference points (like the corner of a square around it).
Take the 2D shapes into 3D. The circle keeps its uniform-like properties as a sphere, and the square becomes a cube, doubling its corners from the square's 4 to the cube's 8. Taking that another dimension up would double it to 16 corners, but the sphere remains uniform. It just becomes denser with information, but its biases aren't amplified or multiplied (like the corners of the square or cube).
Interesting analogy when thinking of the spiritual path and how what we do in this density / or life experience is amplified in higher densities or planes of existence.
But moving along - if we combine the ideas of having an "outer" reference point and having an "inner" reference point, it sounds like building a bridge between two worlds. Perhaps space-time and time-space? The one (i.e. circle) measures things differently, more like a clock, going around, rotating, cycling. The other (i.e. square) measures it like we're more used to. Straight linear lines of measure between this point and that point until we draw a square around the circle.
But we can't measure circles using squares and we can't measure squares using circles. We keep ending up with extra bits left over (e.g. the corners of a square when we have a circle inside a square and check the vice versa when circling a square, how the circle only touches the corners and bends around the square's straight lines). So how do you build a bridge between the two archetypes? How do you combine them and have them be "as one shape" and sharing the same properties?
I suspect it has something to do with frequency, just like when you spin the square really fast, it looks like you are seeing a circle.
Motion makes them the same. Motion is the common factor. They can "move" the same even though they are very different. The motion can create (or rather, unlock?) the bridge between the two worlds.
But the motion is a specific kind of motion. It is a geometrically calculated one. It is deliberate. It is aligning the circle and square to use the same reference point for the motion. So if we spin the square around its center, the borders between its own properties (e.g. its extremeties) and that of the circle's properties (e.g. its uniformity) begins fading. In fact, we can now do things we could not do before as either the circle or the square.
We can have motion like a helix (extremities moving in a uniform pattern). Which could be harnessed e.g. penetrating something else like using this helix-like movement as a drill's movement to penetrate into solid rock. So the circle and square properties could be combined to provide new properties that neither could accomplish alone.
Very interesting yes? Hope I did not confuse anyone with my train of thought.