The citation for the dissertation is:

Zausner, T. (1993). Transformation of Personality and Emergence of Self in Titian’s “Presentation of the Virgin to the Temple.
Ann Arbor: UMI Dissertation Services. ©Tobi Zausner

Excerpt on properties of numbers and dynamical geometry of aesthetics from

The Stairs

Eliade remarks that ascension is often seen as a climbing of stairs, and cites the ceremonial staircase in the Orphic and in the Mithraic initiations. He says that stair symbolism is culturally universal and part of the archaic content of the human mind. According to Jung, stairs symbolize the process of psychic transformation in which the contents of the unconscious are brought into conscious awareness.

My research suggests that in the humanist symbolism of the painting, Mary's ascension is emphasized by the upper bank of five stairs and by the number of stairs in the staircase. (Fig. 11)

Schneider discovered that the angle of the upper five stairs is different from the angle of the lower eight stairs. He believes Titian did this deliberately because the lower stairs are formed of shorter stone rectangles, while the upper stairs are formed of slightly longer ones. (Fig. 11, 34)

Unlike the lower bank of eight stairs, which forms a triangle with angles of 36, 54 and 90 degrees, Schneider has found that the upper bank of five stairs has angles of 38, 52, and 90 degrees, which forms the triangle found in the heptad, or seven pointed star. In humanism, the heptad was revered and associated with the spiritual realm. As part of its symbolism, it was called a virgin and ascribed to Athena.

Coincidentally, the angles of 38, 52, and 90 degrees also form a triangle associated with the Great Pyramid of Cheops. It was known in the Renaissance that the pyramid was a tomb and place of final resurrection and ascension, but I have not been able to find that the angle of the Pyramid of Cheops had been calculated by that time.

It is possible that the symbolism of the lower 36, 54, 90 degree triangle signifies cyclical recurrence, while the upper 38, 52, 90 degree triangle symbolizes an ascent to a more evolved level. I hypothesize the triangles relate to the intrinsic meaning of Titian's painting, where repeated struggles of the personality result in the emergence of a new self.

Mathematical Proportions

In the legend of the Presentation, there are fifteen steps to the temple, after the "fifteen psalms of degrees," but in Titian's painting, Mary is ascending thirteen steps to the portal of the temple. (Fig. 11)

Hope believes Titian changed the number of stairs because of visual considerations, while Reau sees the number change as a lack of religiosity in art. However, Rosand and Funck-Hellet both note that the two flights of stairs exhibit the ratio of the Golden Mean. Five is the same the percentage of eight, as eight is of thirteen, and the proportion between the numbers is the Golden Mean. This proportion, also represented by the Greek letter "phi," has a numerical value of approximately 1.618.

The groups of eight and five stairs also exhibit the Golden Mean in the triangles formed by each flight of stairs. (Fig. 34) The lower triangle refers to the pentagram/pentagon and the Golden Mean proportions inherent in that structure. Schneider finds that the ratio of the upper triangle's sides are 1 for the upright, the square root of phi for the base, and phi for the hypotenuse.

Not only do the flights of eight and five exhibit the Golden Mean, but there is an additional set of three stairs from the portal into the temple, which produces the Fibonacci Series. (Fig. 11)

The Fibonacci Series, in which each number is the sum of its predecessors begins: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, and continues ad infinitum. It was named after the great medieval mathematician Leonardo Bigollo Fibonacci da Pisa, who applied its information to forms in nature.

The Fibonacci Series, also called the logorhythmic spiral, is an order of growth throughout the physical world. Examples can be found in sea shells, in cacti, in the proportion of human bone lengths, in the pattern of hurricanes, and in the spirals of galaxies.

Funck-Hellet calls the upper bank of three stairs a symbol for the Trinity. It is curious that he does not associate them with the lower stairs in the Fibonacci Series because he shows that Titian was aware this mathematical relationship. Funck-Hellet finds the Fibonacci Series indicated by the hands of the little girl leaning on the bottom flight of eight stairs. (Fig. 11)

Funck-Hellet points out that by having her hands on the fourth and fifth steps, the child divides the staircase into a group of five and three, and by her two hand positions also indicates the number two, all numbers in the Fibonacci Series. In addition, I believe that the child's hands on the fourth and fifth steps show the Golden Mean, because each of her hands marks a point where the stairs are divided into a group of five and a group of three.

I hypothesize that in presenting these numerical relationships, Titian was painting the mathematics of humanism. Pico says everything flows from a primal source through a "secret doctrine of numbers." Those viewing the painting who knew the Fibonacci Series, realized that after the flight of three steps visible (Fig. 11) came hidden flights of two, then one, and then one as the source.

The Golden Mean and the Fibonacci Series, which represent the generation of the many from the one, and the return of the many to the one recalls the Renaissance concept of emanatio, raptio and remeatio. Mary's ascent of a flight of stairs organized according to the Fibonacci Series would infer a climb from multiplicity to unity and can be seen psychologically as a path to integration.

According to Lawlor the Golden Mean and the Fibonacci Series lead "back toward a sense of Oneness through a succession of proportional relationships." Lawlor notes that "Phi," associated with the divine being and with the self, is a part of the symbolism of Jesus and of Osiris.

Critchlow calls the Golden Mean a tool for self-awareness, and Edinger believes that the "image of the Golden Mean can be understood psychologically as a symbolic expression of the ego's relation to the self."

Cross-culturally, the Golden Mean is part of the culture of Egypt, Greece, Rome, India and Islam. A book on the Golden Mean by Pacioli was published in Venice in 1509.


It is possible that the number symbolism in the painting is an example of arithmosophy, the philosophy of mathematics, central to humanism. According to Cassirer:

While in scientific thinking number appears as the great instrument of explanation, in mythical thinking it appears as a vehicle of religious signification ... For whatever partakes of number in any way, whatever reveals in itself the form and power of a definite number, no longer leads a mere irrelevant existence for the mythical-religious consciousness but has precisely thereby gained an entirely new significance.

The division of Arithmosophy that deals in visual order is called Symbolic Geometry. For Pico, numbers and patterns were part of a universal teleology, where "nature never acts by chance but only for the sake of some resulting good." Pythagoras calls number, the universal ordering principle and "the wisest thing."

In the Renaissance, it was thought that repeating patterns found in nature aligned the painting with the harmonics of the universe. The work was then expected to produce a beneficial reverberation in the viewer, who along with the artist, and the work of art, was a participant in a universal order.

In analytical psychology, Von Franz believes that there is an order in the universe, and that "orderedness affects us as meaning."

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Created: 1/18/97 Updated: 3/20/97