Ternary codes in psychology,
culture, and art:
Information roots
Vladimir Petrov & Lidia Mazhul
State Institute for Art Studies
5 Kozitsky per., Moscow 103009, Russia
E-mail: [email protected]
Informational approach in cultural studies (see, e.g., Golitsyn & Petrov,
1995). Links between its branches. Some of such links, connecting
properties of human memory, information processing, threshold of
perception, and works of art.
‘Spatial’ Structures: Many-Sided Arguments in
Favor of Triplicity
• Universal procedures of the information processing 
regularities inherent in creativity and works of art. Two
preliminary notes:
• – The properties of objects (events), the information
received being stored using certain symbols in the
memory (the form much more advantageous than
keeping in the form of images, or “gestalts”);
• – The primary data are structured to provide maximal
effectiveness of the usage of the information. Symbols
grouped in certain clusters named “parameters.”
• Four partial models for the spatial aspect.
1). Efficiency of Ternary Encoding. Fixed ‘resource’ of W symbols. Symbols divided
into equal groups each consisting of x symbols (each group – a scale of a certain
parameter). Hence, the number of groups W/x, permitting to describe the number of
objects y = (x)W/x.
Maximum when x=e=2.718… The number of gradations – integer.
The ‘economic’ system: ternary or binary parameters (x=3 or x=2)
•
Figure 1. The number of different
objects (y) which can be
described by a set of parameters
possessing the given number of
gradations (x). In this example the
total number of gradations (W) is
24. Maximal value of the function
responds to x=e=2.718… The
preference for x=3 is clearly seen.
• 2) N-dimensional Vector Quantization. ‘Genuine
informational’ model: the ‘response’ of a system (e.g., a
man) characterized by n independent components of a
vector (‘degrees of freedom’), each component
possessing x gradations of equal probabilities. The
resource expenses proportional to the number of
gradations:
• r=ax
• (a being the constant). The total resource expense
restricted:
• R = a x n.
• The information contained in one degree of freedom:
I(m). The maximal total information I for the total
resource expense R:
• I = (ln xR) / a x.
• Maximum when x=e=2.718… – again ternary or binary
parameters.
• 3). Classification (Sukhotin, 1983): the task of economic
‘non-motivated classification,’ using arbitrary numbers of
gradations for different scales. Series of B objects to be
described by a set of parameters, each consisting of several
gradations. If β(x) parameters with x gradations (‘words’),
then the number of possible classes is
• y =  xβ(x) ,
•  designating multiplying over all x. The number of ‘words’
• W =  x β(x).
• The informational optimization – the economy of the total
number of ‘words’ needed to describe the given number of
objects:
• yB,
• W min.
• Solution of the system of equations: only parameters
possessing x=2 or x=3, i.e., binary or ternary parameters.
• 4). Intensity-Independent Color Encoding. The model
of visual perception of objects’ color properties in
changing illumination (and other properties).
• Supposing spectral photodetectors with bell-like
distribution of the response. How to determine the color
of the object perceived, e.g., whether the given apple is
red or green? To compare the signal from the object,
with the signal from the background (e.g., from the sun).
Ambiguous comparison because of two ‘decreasing
branches’ of the spectral dependence. Changing
background illumination. Hence, three types of
photodetectors needed to determine the color of the
object.
• Choice of the Nature in the process of the biological
evolution, e.g., three-parametric system (three types of
cones) realized in human photoreceptors.
Time and Order:
Thresholds for Rapid Perception
• Two universal situations when changing signal
from objects perceived:
• identification of the very fact of the change in the
signal;
• – fixation of certain regularities in the changing
signal.
• 5). The Value of the Relative Threshold. Identification
of the change: the necessity of the threshold deduced
theoretically (Golitsyn & Petrov, 1995). The value of the
threshold? its constancy(12-15%) for different stimuli?
Proceeding from the model of three parameters:
• fast speed as the main criterion for the first step of
memory; choice of the evolution: the simplest and the
most reliable way – three informational channels, with
binary signals (e.g., 0 or 1); result: operative memory
device, with the total amount of cells V=23=8 – capacity
of the first step of human memory (‘Magic Number 7 
2’);
• – the relative threshold of perception as a result of the
functioning of 8-cell memory device (e.g., when all 8
units occupied, to empty one  1/8 of the magnitude,
i.e., 12.5%). So, the threshold S1/V.
6). Detection of Periodicity. Regularities in changing signal; the
most universal task: fixation of the repetition of signals. The main
“personages” – the probabilities of events. In search for regularities
within the ‘world of events’: statistical links capable of generating
positive emotions. ‘Hedonic subject’ in the typical situation:
‘Lattice’ of events which are regular (e.g., the sequence of dawns
possessing 24-hour periodicity). ‘Secondary lattice’ (e.g., Sundays –
7-day periodicity). Events important for the personality. The
probability to meet the given secondary event in a certain position
pk (e.g., pk= .2, if a person plays roulette every day, one day
winning a large sum, then after four ‘waste’ days, again winning).
When it is possible to realize the periodicity, accompanied by
positive emotion?
•
Figure 2. Lattice of primary periodical events and secondary ones (black circles).
• Regularity – when the probability of accidental
occurrence of the secondary event at this knot is
negligible, i.e., less than the relative threshold of
perception. To meet the event n times in ‘due’ positions
• p(n) = (pk)n  S,
• S being the relative threshold of perception. S  .15, and
the value n integer. The most widespread situation: pk=
.5, hence n3. The first discovery of the regularity as the
most striking for the person, resulting in positive emotion.
The moment depends on pk: to be the indicator of a
periodicity, pkS  .39. Devices in poetry and prose.
• The most typical situation: pk= .5 – for the first repetition
of the secondary event, i.e., when n=2, because of
unknown a-priori probability of the event considered.
Further, when n=3  the sequence is perceived as
evidently quite regular: p(n)=.125<S. Hence, again the
preference for three events ‘dictated’ by the perception.
From Psychological Regularities –
to Artistic and Cultural Ones
• Three-gradation scales, three-parametrical
systems, and three-event situations preferable.
The triplicity – should it be met in all situations?
– Of course, no! Because of the “content” of
objects perceived. E.g., sad events: negative
emotion, the triplicity is disadvantageous.
• The sphere of art: the disinterested perception
playing an important role. Colors used by painting.
The regularity deduced in the framework of the
information approach: in each national culture, a set
of three ‘main colors’ (the so-called ‘national color
triad’) should dominate the system of painting.
Spectral characteristics (determined by the
character of the sunlight): French and Italian
painting – yellow, orange, and dark blue colors, in
Spain – white, red, and black, in Russia – white, red,
and green. Empirical investigation: paintings of the
15th-20th centuries: French, Italian, Spanish, and
Russian school (311, 109, 106, and 296 works, in
total 167 painters). In each work– its ‘main color
elements’ identified by experts.
Table 1. Percentage of paintings with the following ‘main colors’ and ‘due’ national color triads
Country
Red
Orange
Yellow
Green
Blue
Dark
blue
Violet
White
Black
France
37
51
55
30
19
25
33
29
20
Italy
46
42
63
17
39
23
22
21
26
Spain
55
5
58
4
14
19
25
55
59
Russia
50
14
47
40
11
35
34
44
24
National
triads
42*
25
52*
29
* – 95%-level of statistical significance
• The preference for triads. Significant difference between
usage of each ‘triadic color’ in different cultures: though
French and Italian paintings are almost identical, they both
differ from Spanish and Russian painting; the last ones differ
from each other and French-Italian school. Views on French
and Spanish cultures as ‘rigid’ ones, Italian and Russian
cultures as ‘soft,’ influenced by foreign cultures.
• Other numerous evidences of the preferred triplicity:
three main personages in fairy tales and prosaic works,
ternary structures in religion, language, politics, and
other fields.
• The realm of the phenomenon considered: due to rather
universal (non-specific) character, it is capable of
penetrating many other spheres, based on unconscious
processes:
• – the three-dimensional semantic space inherent in most
perceptual processes (fixed in psychological
experiments using ‘semantic differential techniques’);
• – the three-dimensionality of our perceptual space: we
wish to receive positive emotions when perceiving
various objects and/or events; hence, it is desirable to
plunge them into the three-dimensional space.
• Synergism of ‘spatial’ and ‘temporal’ motives
“pushing” us to such worldview.
• Our positive emotions caused by the processes
of identification of links in the world of objects
and events, are tightly connected with our very
survival. The triplicity – observed both in
everyday life and works of art – as one of our
means in unconscious search for regularities.