Squaring the circle jung

The phrase arrives in Jung already weighted with two thousand years of impossibility. Greek geometers had tried and failed to construct a square with the same area as a given circle using only compass and straightedge; the problem was proven transcendentally insoluble in 1882. Jung inherits this failure as a psychological fact. The impossibility is not a defect to be corrected but the very point — the tension between two incommensurable forms is what makes the symbol alive.

The circle, in Jung's symbolic vocabulary, is the oldest image of wholeness: boundless, centerless, without beginning or end. The square — or its arithmetic cousin, the quaternity — is the minimum structure by which a circle can be "naturally and clearly defined" (CW 16, §406), the four cardinal points that give psychic space its bearings. Thinking, feeling, sensation, intuition: four functions, two opposed pairs, the crossed threads through which consciousness takes its orientation. The circle is the Self as totality; the square is the Self as differentiated structure. Neither alone is sufficient.

The alchemist tried to express with his Rebis and his squaring of the circle, and what the modern man also tries to express when he draws patterns of circles and quaternities, is wholeness — a wholeness that resolves all opposition and puts an end to conflict, or at least draws its sting.

The alchemists worked this problem for seventeen centuries without knowing they were working on the psyche. Their quadratura circuli — the squaring of the circle — named the opus itself: the attempt to unite the volatile and the fixed, spirit and matter, the infinite and the bounded. Jung's contribution was to recognize that the compulsion driving that labor was not chemical curiosity but an archetypal pressure from within the psyche, the same pressure that produces mandala drawings in patients who have never heard of alchemy.

Edinger, reading the alchemical poem Ripley Scrowle in his Mysterium Lectures, gives the clearest geometric formula: the individuation process moves from an original circle (unconscious wholeness, the uroboric state before ego-formation) through a square (the differentiation of the four functions, the ego's hard-won orientation in the world) and then back to a circle — but now a conscious one, the wholeness that has passed through discrimination and returned. The sequence is not regression but spiral:

Original circle, square, final circle. The first circle would represent the condition of initial unconscious unity that we start with when we're born. Then, in the course of ego development, the gradual and conscious discrimination of the four functions turns the initial circle of unconscious wholeness into a square. Harmonizing and unifying can only be achieved by a further circling of the square.

The irrational number pi haunts this geometry. The relationship between a circle's diameter and its circumference cannot be expressed as a finite ratio — it is transcendent, inexhaustible, never fully resolved. Edinger reads this as the image of the coniunctio itself: the curved and the straight belong to different orders of reality, can be approximated but never perfectly reconciled. The individuation process is not a problem that gets solved; it is a tension that gets inhabited.

What makes the symbol clinically significant is that it appears spontaneously. Jung waited thirteen years before publishing his findings on mandalas precisely to rule out suggestion — he needed to be certain that patients were producing these images from inner necessity, not from his own theoretical enthusiasm. The circle-with-center, the circle-within-a-square, the fourfold division: these arise in dreams, in active imagination, in the drawings of people who have never encountered the alchemical tradition. Jung took this spontaneous recurrence as evidence that the squaring of the circle names something structural in the psyche, not a cultural borrowing.

The symbol also carries a specific therapeutic function. It appears, Jung observed, not as the announcement of achieved wholeness but as compensation for its absence — in states of "chaotic confusion and lack of orientation" (CW 16, §536), the psyche produces images of order it has not yet attained. The mandala drawn in crisis is not a portrait of the Self but a yantra, an instrument for bringing order into being. The squaring of the circle is less a destination than a practice: the repeated attempt to hold the incommensurable together long enough for something new to emerge from the tension.

  • mandala — the circle-with-center as spontaneous symbol of psychic wholeness
  • quaternity — the fourfold structure underlying the square in Jung's symbolic geometry
  • individuation — the process the squaring of the circle images and enacts
  • Edward Edinger — portrait of the analyst who gave the circle-square-circle sequence its clearest clinical formulation

Sources Cited

  • Jung, C.G., 1954, Collected Works Volume 16: The Practice of Psychotherapy
  • Edinger, Edward F., 1995, The Mysterium Lectures: A Journey Through C.G. Jung's Mysterium Coniunctionis