This is an age old question - one that has been asked over the millennia by the greatest of minds. Anaxagoras was the first Greek to be associated with the problem - which was even mentioned by Aristophanes in his play 'The Birds.' Many say it is an impossibility - others say it is simply a metaphor for accomplishing the impossible.
In one of the articles in the latest Rosicrucian Digest Alchemy - "The Philosopher's Stone" by Frater Dennis Hauck - the "Squaring of the Circle" is fully explained in 'alchemical terms' along with a Michael Maier symbol - below is a partial explanation extracted from the article - which can be found online here: https://5482ff13812fff93b4b0-f30566d4c910ec79e48ff03c503d3718.ssl.cf5.rackcdn.com/04_hauck.pdf
"A third cipher for the Philosopher’s Stone first appeared in the early Renaissance. It depicts the Squaring of the Circle, which is a formula for the creation of the Stone. The recipe for it was first revealed in the Rosicrucian text
Rosarium (1550):
Make a circle out of a man and woman. Derive from it a square, and from the square a triangle. Make a circle and you will have the Philosopher’s Stone.
This symbol is actually another depiction of the Sacred Marriage in alchemy." 
The symbol is further discussed in another article - same Digest - "Michael Maier's Atalanta Fugiens" by Frater Peter Bindon - link below:
https://5482ff13812fff93b4b0-f30566d4c910ec79e48ff03c503d3718.ssl.cf5.rackcdn.com/08_bindon2.pdf
Replies
Dear Soror Kathy,
Perhaps this subject has come to my attention - although you created this Forum subject in 2013 - because it came to me in meditation that I needed to resolve this paradox more fully.
It does say in the Kybalion that all paradoxes will be resolved...likely because within the Cosmic there are no paradoxes because all is One. Paradoxes are only existent when our sensory experience is limited by our physical sense organs and the laws of physics and time that govern the vibrations of density in which we live.
Do we not "square the circle" as we leave the atrium and enter the Rosucrucian Temple in a symbolic manner as we walk in?
Nature creates in curved lines in organic life, but in linear motifs in inorganic life, such as crystals. Humans can build linear or organic constructs. Linear and right angle constructs tend to arise in technological cultures with stone and steel, while organic, curvilinear constructs tend to arise in cultures that build with organic elements and live in a harmonious way with nature, using boughs, palms, and grasses, and sometimes stones.
Of course, there will always be some exceptions to this model linear/curvilinear model. Perhaps these "exceptions" may be the connecting points between seeming paradoxes?
Game trails and human paths in the woods tend toward curves. Suburban streets and homes tend to be linear, squared, rectangular.
Squaring the circle, and circling the square, by rounding the corners/right angles may be one in the same and as we do this symbolically, mentally, emotionally, and spiritually - smoothing our "rough edges" - honing our ability to metamorphise our concepts to embrace "this and that" rather than "this or that"; holistic rather than dualistic"; Oneness rather than separation may be the key to resolving the seeming paradoxes?
Just a few thoughts that have arisen in contemplation upon this subject, yet there are always more nuances to discover on these subjects. And so it goes as we tackle the Work of the Akchemy of Self/self.
Peace
😊
Unfortunately there is mo edit feature on the forum replies. Thus, "rakes" should be "takes", and "in" should be "on", and so on...
...and mo should be no...
Hi Soror Kathy,
I recall reading that article on the Music of the Spheres, but it was awhile back and reading it again will be a good refresher.
Frater Bob's comments were illuminating. Ir seems the only way to square the circle in this realm of density is to destroy the square, much as a sculptor takes a block of marble and removes the corners to create a statue. Or, a lapidary artist takes a small, right angled chunk of stone - diamond lapidary saws can only cut stone in straight cuts. The rest of the shaping must be done by grinding in a sphering machine that rakes off all the corners and angles until a perfect sphere is obtained. Perhaps, there is a hint here that the "grinding" is a metaphore for the mystical work that must be done to hone the consciousness.
Creating a square from a circle would also result in destroying the original structure.
Perhaps, squaring the circle is a metaphor for creating the New Person? There's a lot that arises when contemplating mystical axioms, symbols, and phrases 🤔
Thus, we cannot square the circle, or circle the square without destroying the original shape. We simply have to di what the ancients did by putting the circle within the square, or visa versa, to symbolize the impossible task, but perhaps, convey the mystical concept of "this and that", or a type of Cosmic wholeness that cannot be replicated in our current state of density.
Just a few more thoughts in this conundrum. 😊
Hi Soror Gail,
It seems this question keeps coming up - and if you look at the comments below - you will see at least one Frater makes the statement that squaring the circle in our physical world is not possible - but in the realms of the mystical it is possible. While pondering this 'problem' think maybe it is a mathematical equation which will give the answer - since the 'Universe is vibratory in nature and can be expressed numerically.'
There is a great article in THE PYTHAGOREANS Rosicrucian Digest - links below - which gives some insight into the Universe being vibratory in Nature and therefore can be expressed numerically. The article is entitled 'The Music of the Spheres' by Frater X and originally published in the Rosicrucian Forum, February 1951.
From the article:
"...To Pythagoras, number was “the key to
the universe.” If we learn the number and
proportion of all reality, we know the secret of
the universe."
Rosicrucian Digest - The Pythagoreans | The Rosicrucian Order, AMORC
The Music of the Spheres (rackcdn.com) (article)
ok - this question came up again today - so time to resurface this thread???
So again - this question was asked.
And again!
Hi Sr. Kathy,
Thanks for your very intriguing question. As a new group member, I am enjoying a lot reading the replies.
Peace profound
Hi - Frater Elsyd - happy to see you are enjoying the replies on this thread. Possibly you have another point-of-view?
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