Use of Visual Semiotics to Analyze Images

In 1969, a group of intellectuals (including Barthes, Benveniste, Greimas, Jakobson, Lévi-Strauss, and Sebeok) adopted semiotics as the general term for the study of systems of verbal and non-verbal signs (^{Nöth, 1995}). In practice, according to Peirce, semiotics was often limited to the theory of non-linguistic signs and signals. By contrast, according to Saussure, semiology referred to the study of textual elements used in the linguistic tradition (^{Sonesson, 2016, Lecture 1: 4}). Semiotics -which is used to describe materials that transmit a visual language, such as paintings or sculptures- has undergone a different theoretical and pragmatic process than that of verbal linguistics. That is, given the lack of a theory of grammar of visual language or a visual semiotics that allows for a preliminary level of description of a work of art (^{Greimas, 1994}), semiotics schools in Paris, Lund, Prague, and Quebec have proposed a variety of modes of analysis (^{Sonesson, 2016}).

The present study considers the tradition of the Quebec school, represented by ^{Fernande Saint-Martin (1990)}, which distinguishes, defines, and classifies the basic aspects of visual language with the aim of understanding the way in which elements of an artistic work are linked to each other and form an integral work of art, through their spatial relations. The aim of this paper is to elucidate and compare the visual response of six paintings of the pre-Columbian Maya ^{Dresden Codex (1983)}, called the Venus Table. This is done using a method that combines an understanding of the complexity of the calendrical-astronomical message of the paintings, the mathematical theory of communication, and the visual semiotics applied to the visual arts.

The article is organized in several sections. Firstly, a calendrical description of the Venus Table of the Dresden Codex is provided in order to present an interpretation of the pre-Columbian message. Secondly, visual semiotics for paintings according to Fernande Saint-Martin is discussed. Next, the plastic description of the codex and its Venus Table is provided. Subsequently, Saint-Martin's visual semiotic method is applied to six paintings of the Venus Table, and their entropy is evaluated (^{Saint-Martín, 1990}). Finally, the results are presented, followed by a discussion and final comments.

Use of Communication Theory to Measure the Content of a Message

In 1948, ^{Claude E. Shannon} first proposed a mathematical theory to define fundamental limits of communication processing in order to study quantification, storage, and communication of information. Subsequently, ^{Shannon and Weaver (1998)} expanded the scope of this theory to address how the amount of information from a source may be determined. They attempted to address this issue by defining Shannon´s entropy as a measurement of how much information a message produces. Classical entropy refers to the tendency of physical systems to become increasingly less organized. It is a criterion for deciding whether or not a given process between two states may occur and under what conditions. For example, we observe that heat flows from hot bodies to cold ones, but we never observe that this process occurs spontaneously in the opposite direction (^{García-Colín, 1972: 58}). Shannon´s entropy quantifies the uncertainty of information contained in a source and is calculated as indicated in equation 1 (^{Shannon and Weaver, 1998: 23}):

Although this appears complicated, let us suppose a simple example of the six paintings in the Venus Table of the Dresden Codex. There are six possible messages. The probability that the messages of the paintings are the same or different will depend on the proportion of the individual characteristics that are compared. If one calculates, in this case, the numerical value of H (in bits) of each Venus paintings, H would have its greatest value when the proportion of individual characteristics is unlikely to resemble the characteristics of the other paintings or messages. When it is very likely that no difference occurs among the messages, that is all Venus paintings are equal, the value of H will be smaller. The entropy value H allows us to compare different degrees of variety or singularity contained in an object.

History of the Dresden Codex

The Dresden Codex -or Codex Dresdensis- is a manuscript on a 3.5 m long foldout sheet of plant fiber paper of a species of Ficus, consisting of 39 pages that measure 20.4 cm high by 9.1 cm wide. Four pages are blank on one side and the rest are painted on both sides. It is possible that the codex formed part of the taxes that Hernan Cortes sent to Emperor Carlos V in 1519 (^{Coe, 1996: 90}). The book was first made known in Vienna, and Johann Christian Götze -chaplain to the king of Poland and director of the Royal Library of Dresden- purchased it in 1740 (^{Coe, 1996: 92}). In the early 1800s, Alexander Von Humboldt -upon learning about it from a book published shortly before- made the first reprint of pages 47-52. Between 1831 and 1848, the entire codex was copied by an Italian artist and reproduced by Lord Kingsborough (^{Thompson, 1988}).

The manuscript was revealed in its entire splendor with the chromolithographic reproduction of Förstemann in 1880 (^{Toscano, 1984}; ^{Spinden, 1975: 152}). In 1892, the second edition by Förstemann (^{Thompson, 1988}) was printed, with the same images but with the page order corrected. In 1930, a black and white copy of the Förstemann edition was published by Villacorta and Villacorta (^{Thompson, 1988}). In 1932, the first foldout reproduction by Gates of the Maya Society was published (^{Thompson, 1988: 45}). ^{Bricker and Bricker (2011)} offer an exhaustive explanation of the history as well as the structure and current interpretation of the Dresdensis. Below we present pages 24 and 46 to 50 of this codex as they appear in color in the facsimile of the first Förstemann edition from 1880, ordered according to the 1892 edition.²

Calendrical Message of the Venus Tables of Dresden Codex

We selected the Dresden Codex for analysis because its drawings are an inestimable source for studying the pictorial art of one of the pre-Columbian cultures of Mexico (^{Toscano, 1984: 136}). ^{Toscano (1984: 124, 125)} mentions that the figures are vigorously trim, without shadows or dark colors; they have a polychrome liveliness given the absence of medium tones and presence of primary colors; they show dazzlingly beautiful colors given the absence of dull colors or shade; they express an ingenious perspective given their planographic nature and displaced profiles; and the figures reveal disproportion and a lack of reality. All of this contributes to the delicate freshness of the enigmatic glyphs.³

Within the Dresden Codex, we selected pages 24 and 46 to 50 of the Venus Table, given that according to ^{Aveni (1979: 275)} the Maya Venus cycle combines “long term precision with short term faults as a true ephemeris”, that is, it portrays important happenings that occurred on a single date but in different years that generally coincide with certain domestic religious ceremonies. Furthermore, the morning star (Venus) was adored and attended to because it represented natural forces that were understood to affect earthy activities. The appearance of gods in the Venus cycle predicted the rainy season -and thus the most propitious time to plant- as well as the quantity of the resulting harvest. The content of the Dresden Codex undoubtedly belongs to the calendrical system and the computation of time; consequently, its significance is not only plastic but also mythological and calendrical-astronomical (^{Toscano, 1984: 136}).

No pre-Columbian culture has provoked such interest, posed so many enigmas in deciphering its writing, or been so little understood regarding its obsession and precision for counting time as the Maya culture (^{Coe, 1996}; ^{Freidel, Schele and Parker, 2001}; ^{León-Portilla, 1994}; ^{Martin and Grube, 2002}; ^{Pallán, 2011}; ^{Proskouriakoff, 2007}; ^{Rice, 2007}, ^{Schmidt, De la Garza and Nalda, 1999}; ^{Stuart, 2011}; ^{Taladoire and Courau, 2005}).

All civilizations have been interested in counting time (^{Aveni, 1991: 13}). Measuring time involves a social encounter (^{Van de Ven and Poole, 2005: 1391}), that responds to a need to carry out certain activities such as harvests, religious rites, or hunting; through this encounter, objectives shared by the group are harmonized. Time is measured; that is, changes that affect us through arbitrary norms or rules are determined by convention, given that without common measurements of time it would be impossible for social groups to function (^{Savater, 2003}).

The Dresden Codex is the most studied codex of the three pre-Columbian Maya codices existing in Europe (^{Sotelo, 2012}). It contains calendrical, astronomic, and esoteric information in the form of calendars and prophetic passages (^{Kettunen and Helmke, 2011: 46}). ^{Thompson (1988)} grouped the contents of the codex into three categories: calendars and calculations of 354 days, including indications for adoration as well as prophecies (which occupy the majority of the book); an astronomic-astrological section (the eclipse tables and Venus Table); and prophecies for the year and the k’atun (19.7 years of 365 days each).

Figures 1 and 2 show the Venus Table, which contain three paintings per page and illustrate the general structure of the almanac of the planet Venus (^{Bricker and Bricker, 2011}). According to ^{Aveni (1979}; ¹⁹⁹¹⁾, ^{Bricker and Bricker (2011)}, ^{Fuls (2002)}, ^{Milbrath (1999)}, ^{Thompson (1988)}, and ^{Wells (1991)}, Tables 1 and 2 show the organization of the calendrical message of the Venus Table. It communicates mathematical operations using the Maya dot-bar numerical notation⁴ and describes the functioning of the sacred 260-day calendar, the names of the days, the glyph for the cardinal directions, as well as representations of the moon, Venus, and other planets.

The first page (24) serves as a user´s guide to the Venus Table; this guide principally consists of approximate multiples of the length of the table of 2920 days (584 days x 5 periods), as well as dates of initial series corresponding to the starting point in the table. The dot-bar numbers in the lower left corner in five positions (columns B and C, lines 18-24, Table 1) represent the number of days that passed from the moment of the final creation period⁵ to the events of Venus mentioned in the table. The 1,366,560 days since the mythic period are termed “long count” (LC), mentioned in column B (Table 1). In column C, of Table 1, the other LC number, 1,364,360, begins 2200 days before the first; the number 2200 appears in the lower part of column A (lines 21, 22, and 24, Table 1) with a “ring” around the zero; the ring date closely approximates the appearance of Venus as the morning star (5 x 584 = 2910 days) and is approximately the difference between the two long count numbers.

The LC number (1,366,560) is divisible without a remainder by 260 (days of the sacred calendar, Tzolk’in), 365 (days of the civil calendar, Haab), 584 (days of the synodic⁶ period of Venus), 2920 (days during which Venus appears on the horizon or ortho⁷), and 37,960 (length of the Venus table). The LC number probably was invented for the simple reason that it was commensurable with a multitude of cycles of Maya time.

The remaining pages (46-50) address the Venus ritual through a long series of important dates of the 260-day calendar (Tzolk’in dates) related to the planet, and -in the final four right-hand columns on Tables 1 and 2- drawings of the Maya ruler god, the personification of the planet Venus, and the victims of the rays of the planet Venus (from above to below). The five paintings are equivalent to five cycles of Venus or 8 Earth years.

In the first four left-hand columns (A-D) on Tables 1 and 2, in line 26, four numbers are shown (read from left to right) in dot-bar notation: 236, 90, 250, and 8, which added together sum 584 -the closest whole number to the average synodic cycle of Venus. The number 8 (column D, line 26, Table 1 and 2) is the most significant number of the Venus cycle, representing the period when Venus disappeared behind the sun; the other 3 numbers (236, 90, and 250) also denote the days that Venus appears or disappears behind the sun.

The longest section of the paintings consists of the first 13 lines in the upper left, in columns A-D Tables 1 and 2. Each line contains four symbols representing the start of the four seasons of Venus. Each symbol designates a day in the 260-day calendar. Each symbol consists of two components: a number from 1 to 13, and a glyph representing the name of a day in a 20-day cycle. Given that 13 and 20 have no common factors, each day in a 260-day cycle may be individually designated in this manner. Thus, for example, on page 46, line 8, column A, Table 1, the start of the appearance of Venus for 260 days as the evening star designates the day Kib with the number 7; the disappearance of Venus for 90 days designates 6 Kimi (column B); the period of the morning star designates 9 Kib (column C); and the disappearance of Venus 8 days designates 4 Kan (column D). With respect to our calendar, a comparable statement would be that Venus disappears “Wednesday, the fourth”.

All lines of the Venus table are read consecutively from one page to the next. Line 1, columns A-D, of the five pages (46-50), Tables 1 and 2, represents five consecutive journeys through the 584-day cycle; line 2 represents the next five, and so forth. The length of the entire table is therefore 5 x 13 x 584 = 37,960 days, an interval that has the special property of being divisible, with no remainder, by the 584-day period of Venus, the sacred 260-day period, and the 365-day so-called civil year.

The numbers on the left of lines 14, 20, and 25, Tables 1 and 2, provide alternate positions of the civic year (365 days) that are equal to positions in the Tzolk’in calendar (or wheel), as seen in lines 1-13 of the appropriate column. Thus, the complete entry of the calendar wheel on page 46, column C, line 14, Table 1, would be 4 Yaxkin, 14 Zac, 19 Zec, 7 Xul.

The glyphs to the left on lines 16 and 24 of Tables 1 and 2, indicate the directions (North, West, South, East) repeated in variable order. Evidently, the successive appearances of Venus were associated with different quadrants of the horizon. The glyphs to the left on line 17 are associated with the order of “gods”; these series of glyphs that appears in numerical order (#1, #2, #3…#20). The glyphs to the left on lines 18 and 23 of the tables were identified by Förstemann (^{Thompson, 1988}) as Venus glyphs. They are frequently associated with a sign, which is interpreted to mean “red”.

On each page, the numbers to the left of line 19 of each Venus Table represent the accumulated totals obtained upon adding the number of line 26 of the same column to the number of line 19 of the previous column. Thus, on page 46, columns A-D, line 19 of Table 1 the numbers are 236, 326, 576, and 584. If 90 days are added to 236 from line 26, column A, the result is 326. This process continues throughout the 5 pages; therefore, the final accumulated quantity on page 50 is 5 x 584 = 2920.

On the right of pages 46-50, columns E-H, lines 4-12, 16-20, and 23-26 of Tables 1 and 2 is a set of images that represent the celestial occurrences that accompany the appearance of Venus as a morning star or ortho after inferior conjunction,⁸ which is the reappearance of Venus after it has been blocked from human sight by the sun. Glyphic symbols are interspersed among the images and time intervals. The celestial events are presented in groups of three images on each page.

In the upper image on page 46 (Figure 1) is an old toothless god, seated on a throne, offering sacrifices to the deity Venus in honor of its appearance. The second image is an aggressive personifier of Venus, with an atlatl (dart thrower) raised for action. The third image represent the victims, and there on the following appear: deity K (of fertility?) during K’an days; the jaguar (warrior) during Lamat days; the god of maize during Eb days; the frog deity (rain) during Kib days; and the god 1055 (water?) during Ahau days. In the image halfway in the middle of page 46, lines 15-20 of Table 1 is deity L. A manifestation of the god Venus is shown with an atlatl (dart thrower) in its left hand and a shield in the other (Figure 1). Deity L throws the dart that represents the dazzling rays of Venus when the planet is made visible on the horizon. The lower image on the same page contains a sacrificial victim, God K, with a lance through his intestines.

Description of Visual Semiotics by Fernande Saint-Martin

Characteristics of Perception

Visual Description of the Dresden Codex and the Venus Table

Each page of the Codex Dresdensis has a red-painted border, except page 74, which has a black border; many pages retain only traces of this border. Most pages are divided horizontally into three sections; others have only two. In general, the sections are divided by red lines, which are absent in some arithmetical tables, perhaps due to wear.

Application of Saint-Martin's Visual Semiotic Method

Below, we describe the method used to analyze the Venus Table according to Saint-Martin´s visual semiotics approach. We describe the 11 steps that we followed with the aim that other studies may use the same approach to analyze other pictorial works.

Results and Discussion

This study determined the amount of information contained in the Venus Table on pages 24 and 46 to 50 of the Dresden Codex in order to compare levels of variation of information among paintings, which is not possible with aesthetic descriptions. The significant aspect of the value of entropy H is that when a message or a painting can be distinguished from others of the same type, the proportion of individual characteristics with respect to semiotic variables and coloremes regions is unlikely to resemble the proportion of characteristics of the other paintings. And when a message is very likely to show no differences among semiotic variables -in this case that all Venus pages- are equal the value of H would be very small, or almost zero.

In the visual description, we mentioned that pages 46 to 50 had a surprising level of homogeneity. Nevertheless, the entropy value obtained allowed for determining variations among pages or paints. Page 50 has the highest entropy value (51.86 bits) and page 24 the lowest (47.30 bits). Page 24 contains only calendric numeric notation; it does not include any image of Venus, the regent, or the victim, as do the other five pages. None of the Venus pages have an entropy value of zero, meaning that the message of the paintings is not easily predictable for the 15 semiotic characteristics (Table 6).

Two semiotic characteristics have an entropy value of zero bits (a3 and e2). This means that the message transmitted by these characteristics is very predictable. That is, in the Venus Table none of the pictorial messages contain vibrant colors or luminosity, neither symmetry or orientation of the plane. With respect to the characteristic “solid color” (a1), or the appearance of intensity of a color, there is little variability among the Venus pages: entropy ranges from 4.00 bits on page 47 to 4.28 bits on page 49. All the pages have completely defined colors for some of the chromatic poles mentioned. With respect to the characteristic “light color” (a2), or intensity of a light color, page 24 has the highest entropy value (4.38 bits), while values range from 3.49 bits to 3.89 bits for the other pages. As mentioned, page 24 does not include any image and the background is white, and therefore is clearer than the rest of the tables.

For the characteristic “fine granulation” (b1), referring to the surface on which a pigment is applied, the entire Venus Table has a fairly fine-grained texture. Entropy ranges from 4.08 bits on page 24 to 4.43 bits on page 49. The characteristic “worn material” (b2) determined the level of deterioration or fraying of the pages. Pages 48 and 49 are the least deteriorated, with entropy of 1.10 bits. The most deteriorated are 46 and 24, with entropy of 2.74 bits and 2.73 bits, respectively. Regarding texture, all the Venus pages show “brushstrokes” (b3), or the manner in which pigments were physically dispersed. Entropy ranges from 4.16 bits on pages 46 and 47 to 4.31 bits on page 49.

With respect to the characteristic “nearness” (c1), or the perception of proximity among elements in the visual field, all the Venus Table show tension in the size of the formants, and proportionality among the neighboring blocks. Therefore, entropy varies little, ranging from 4.14 bits on page 24 to 4.55 bits on page 48. In relation to the characteristic “horizontal division of the plane” (c2), or the optical effect of position in the plane, the entropy value varies little, ranging from 4.14 bits on page 24 to 4.55 bits on page 48. That is, the formants are visually perceived to be placed horizontally within the plane.

The characteristic “lack of depth” (d1), or the orientation of the formants in three spatial dimensions, along with characteristics a3 and e2, are the most homogenous. The position of the formants lacks depth, and entropy values range from 4.46 bits to 4.70 bits. The characteristic “proportions of positions” (d2), or relative position of groups of coloremes in the visual field, indicates that the observer upon perceiving the space detects outlines and creates the illusory effect of position in the plane. The Venus Table reveals proportion of positions; page 46 shows a lesser effect than that of page 48, with entropy values of 3.41 bits and 4.65 bits, respectively.

The characteristic “vertical axis of location” (e1), or the orientation of the formants in three spatial dimensions, addresses the relationships between near and far regions within the visual field. The elements of each Venus page appear to be oriented according to a vertical axis, as demonstrated by entropy values ranging from 4.19 bits for page 24 to 4.71 bits for page 48. For the characteristic “movement effect” (e3), or the perception of forces that produce movement, page 24 has no images and therefore shows no movement and has entropy of zero, while on pages 46 to 49, the images of Venus and the victim show movement, with entropy values ranging from 2.32 bits to 2.77 bits. On page 50, all three images show movement, and entropy is 3.20 bits.

The characteristic “closed form” (f1), or the perceptual characteristic between two neighboring regions in the visual field, indicates the transition from one visual zone to another with diffuse outlines. The Venus Table have undefined borders due to the forms of the glyphs. The lowest entropy value is 4.19 bits on page 24, and the highest 4.66 bits for page 48. Finally, the characteristic “outlines” (f2), or the borders which mark the division among visual zones, indicates distinct lines separating one visual zone from another. The Venus Table has borders around the images of the regent, Venus, and the victim, as well as borders around each page. Page 50 has the clearest borders -throughout the page- with an entropy value of 4.11 bits. Page 24 has the lowest entropy value -2.25 bits-, while pages 48 and 49 both have entropy value of 3.98 bits.

Final Comments

In the prologue of Miguel León Portilla´s book (^{León Portilla, 1994: 13}), and in an introductory note of Anthony Aveni´s book (^{Aveni, 1991: 154}), Eric Thompson warns us that it is difficult for someone from twentieth-century western culture to fully comprehend the mystic and emotional nature of Maya philosophy of time. Our cultural education impedes us to appreciate the value of the Maya belief system because Mesoamerican thought was dominated by the principle of cosmic existence, which tends to be incompatible with our Cartesian thought.

The Venus Table of the Dresden Codex is not only a painting on a foldout canvas; it communicates a calendrical message that has taken 500 years to decipher. The Maya described their calendrical knowledge with mathematical operations using positional numeric notation to explain the functioning of the sacred 260-day calendar in a cycle of 8 terrestrial years. This knowledge is represented by glyphs that include the names of the days, the cardinal directions, and personifications of Venus.

The astronomical-astrological knowledge that the Mayan painters wished to transmit through pictorial images of the almanacs and prophecies were representations of their thoughts, which were expressed in the Maya Ch´olan language. So, the visual semiotic message decoded from their paintings may not only be interpreted by a Maya priest but rather by any trained person of the 21^st century.

This decoding system allows for understanding the function of the Venus Table, which was to connect the ritual celebration of a significant celestial position in the cycle of Venus with civic, religious, and agricultural aspects of daily life. This required precise comprehension of the synchrony of planetary movements with the heavenly cycles. The Maya ideology regarding time, which was based on their knowledge of planetary synchronization, formed part of their worldview.

Shannon´s entropy is a value of reference that allows us to recognize the structure of the message in a cultural object such as a painting and determine its levels of uniqueness. That is, the information contained in paintings in which visual and perception characteristics can be codified, and then conveyed through by a channel and decode in a message, can be compared, reproduced exactly or approximately in another point knowing the entropy value. Furthermore, Saint-Martin´s visual semiotics method of analysis allows for correlating ocular fixation with objective and perceptual characteristics to contrast objects, regardless of who evaluates the object.

By applying visual semiotic analysis, as presented in this study, as well as to determine the entropy of an artistic work, as the paintings of the Venus Table of a pre-Columbian manuscript, it is possible to explain the practical functioning of knowledge that underlies a system of meaning, such as that contained in a pictorial work of art, and to offer data that allows us to compare old and modern paintings.