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

CHAPTER XVI: ASCENSION

### 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.

### Arithmosophy

#### 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."

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