Glossar-English:Syntactic Density

Sub-Item to: Image Syntax

Original: Syntaktische Dichte

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Goodman's syntactic characterization of images The concept of »syntactic density« goes back to Nelson Goodman's semiotic considerations when comparing image and language. While different linguistic signs – words, sentences, texts – usually differ very clearly from one another, two different images can – according to our everyday understanding – be infinitely similar, at least in principle, i.e., they can differ as little as desired from one another, without already becoming the same iconic sign. This syntactic peculiarity of images leads to a strong focus on the originals since each copy, no matter how similar it may be designed, ultimately results in a different image. The mathematical background of syntactic density The term ‘syntactic density’ denotes a property belonging to a sign system (not a single sign). As the name suggests, it refers to the peculiarities of the physical sign carriers or, more precisely, to the relations between sign carriers. Sign systems that are not syntactically dense are called syntactically disjoint. The expression ‘density’ is derived from the mathematical term »density«: In contrast to the integer numbers, the rational numbers are dense because for any two rational numbers a and b (where a is smaller than b: a < b ) there is always at least one further rational number c such that a is less than c that again is less than b (a < c < b). In other words, c is between a and b. For example, the arithmetic mean (a + b / 2 ) of a and b is always between a and b in this manner. That is not true for integers: when b = a + 1, there is no integer between a and b. Applied to the sign carriers of a sign system, this means that if there is density, there is a property of these sign carriers such that a “between” relation is defined on this property such that for any two unequal carriers for signs A and B of this sign system there is always another carrier for a sign C, which is not identical to those two, and which lies between the carriers for A and B in the syntactic property considered. In Goodman's own words ([Goodman 1968a]Goodman, Nelson (1968): Languages of Art. Hackett, Indianapolis. Notiz: 2. rev. Aufl. 1976 Nicht angezeigt: dt.: Sprachen der Kunst. Frankfurt/M.: Suhrkamp, 1998 ): "A scheme is syntactically dense if it provides for infinitely many characters so ordered that between each two there is a third." In the case of images, the locations of color boundaries or gradients and the dimensions of the colors (or gray tones) themselves form the range of properties of the sign carriers that lead to density: On an otherwise completely identical image carrier, a specific color spot distinguishable from its environment can be shifted a little bit compared to a given image carrier. No matter how small this displacement of that color patch is between those two images, A and B, there is still another image carrier on which the color patch is just between its relative positions in those image carriers of A and B (for instance, the geometric mean) and which is understood as the image carrier for an image C that differs from A and B. For, this small displacement can embody a semantic or pragmatic aspect that is decisive for the picture. It is important to look at the signs, and not just the sign carriers, since the dissimilarity of the sign carriers does not necessarily mean the signs themselves have to be different: A word printed in different fonts has unequal sign carriers – this is just what distinguishes the various fonts from each other. However, these different sign carriers are each used as the same word (sign). With regard to this sign, they form an equivalence class (⊳ Identity of pictorial signs). An example: traffic signs as traffic signs and as images Figure 1: Elements of two sign systems: above from the syntactically disjoint system of traffic signs; below from the syntactically dense system of images The sign marks in the upper row of Figure 1 are intended to belong to the syntactically disjoint sign system of international road signs. The first three sign carriers pictured in the bottom row can all be used as embodiments of the first sign above. As images – the sign system to be considered in the lower row – those three must be understood as sign carriers of very different signs. Effects on other concepts The data structure »raster graphics« or »bitmap«, which is often understood as images in computer science, provides a number of sign carriers that lead to a sign system that is not syntactically dense but rather disjoint. The mathematical concept of density is closely related to set-theoretic infinity classes on the one hand and logical decidability on the other. This connection plays a vital role in the question of identity criteria for image carriers. See also: Color as an image-syntactic category Digital image processing Identity criteria for image carriers Identity of pictorial signs Image and language Notation Original Replica, faksimile, and copie Sign, sign carrier, sign system Space and geometry Typography

Notes Literature [Goodman 1968a]Goodman, Nelson (1968): Languages of Art. Hackett, Indianapolis. Version 1: 2013 Responsible: Schirra, Jörg R.J. Editing: Birk, Elisabeth Contributions by: Joerg R.J. Schirra und Marcel Lemmes — (Note) Quote as: Schirra, Jörg R.J. (2013). Syntactic Density. (Ausg. 1). In: Schirra, J.R.J.; Halawa, M. & Liebsch, D. (Hg.), Glossar der Bildphilosophie. (2012-2026). [bildglossar.org/index.php?title=Glossar-English:Syntactic_Density].