M. Leyton: the inferred histories on the shape

Leyton’s New Formalism is a theory widely used in other fields of science. Leyton himself describes the use of his geometry in the processes of discovering structures of paintings and the creation of architecture (described in the publication The Structure of Paintings, 2006). In his opinion, works of art are a storehouse of information. Leyton also believes that the emotions expressed through images or architectural shapes are in fact the memory, which is easy to reconstruct based on certain laws. He says that these laws that concern keeping/storing memory allow for the systematic and rigorous mapping not only of the compositional structure, but also emotional structure.

M. Titman, Zoom Geometry

New Formalism introduces a new approach to geometry. In the New Formalism, a shape is the means of reconstructing history, is the way by which past actions are restored. The shape is equivalent to the memory storage; it is no longer only a form.

Leyton believes that memory is stored in asymmetries and erased in symmetries. He developed a ‘principle of asymmetry,’ which says that any asymmetry must return to the symmetry if it goes back in time. This allows reconstructing the history of shapes. The form is the result of history; in other words, form is memory.

M. Leyton: the inferred histories on the shape

Referring to the architecture in cyberspace, Leyton says that it itself is a living structure, asymmetric, which allows us to rediscover and restore the history of the process by which it was produced - bending, cutting, twisting, breaking, etc.; in other words, it is a magazine of memory about itself.

[Architecture] is no longer dull and aloof, like the conventional building. It is alive with time, and, because it is filled with memory it is alive with mind. [2]

Leyton, like Titman, pays special attention to the problem of time and movement in cyberspace. Both also introduce new ways of looking at the cyberspatial dimensionality. A fundamental change from geometry in cybermetry lies in redefining dimension.
 
3.2. An alternative understanding of dimension - a cyberspatial dimension

The process of creating cybermetry is based on redefining certain geometrical values. The basic change, and the base for the creation of the new language, is redefinition of the concept of ‘point,’ replacing it with the concept of ‘event.’ This brings the need to change the concept of line, which is no longer just a set of points, but a collection of events, thus losing continuity. Similarly, we can look for redefinition of the plane, solid, and in the end, the space itself. To conclude: electronic virtual space consists of events, and the movement is a condition of its existence.

We will also need to redefine the concept of dimension for the purposes of cyberspace. Since the notion of distance or scale does not exist, we lack the tools of description to establish location and determine the 'size' of an object or event. Dimension in the mathematical sense cannot function in an environment where there is no reference point (it can only function in the local systems, in which encoding is unified, and every user knows its predefined rules), so the notion of dimension in cyberspace should be considered to be based on completely other values of 'measuring.'

These values may not be quantitative, but they must be considered in terms of quality. This means that the dimension of cyberspace is a characteristic (property), not a number.
 
3.2.1 Metadata

Dimensions in cyberspace are often interpreted as properties of the data - metadata.
Metadata is information helping to identify data in cyberspace. It is basically data about data. Most metadata consist of information about the author, date, and time of creation of the file (or information), size of a document, date of last change, format, etc. This information identifies the uniqueness of the document and its location in cyberspace. It can be defined as dimensions of the document / information / event in cyberspace.

To determine the location, shape, transformation of an object in physical space, we use geometry; to determine the location, shape, transformation of the object in cyberspace, we use metadata. Metadata is therefore one of the key factors that shapes cybermetries. The object is information, and its dimension is information about itself and its properties.

Understanding of metadata as the characteristic features of the document / object / event / in cyberspace can be extended to a description of properties such as color, the frequency of sound, etc. All of unified qualitative systems can be metadata, thus dimensions of cyberspace.
 
3.2.2. Semantic Dimensions. Semantic Spaces

Alan Wexelblat’s concept of Semantic Spaces and Semantic Dimensions relates to the idea of metadata.

Wexelblat says that through the combination of properties such as the document’s language, lines of code, date of modification, and author with the concept of dimension, we create n - dimensional information space in which objects are identified and classified according to the characteristics of these dimensions, as he calls them: semantic dimension.

The semantic dimension is a way to combine elements of different values. Semantic dimensions are mechanisms to help solve the problems of positioning and composition. They create ways to organize the elements according to their importance.

Semantic space is n - dimensional space where each dimension is a semantic dimension and n is the number of properties that express forms of objects in space (including the values not found). According to this concept, cyberspace is a multi-dimensional information space.

The goal of semantic dimension is to give a representative meaning for the arrangement and position of abstract information. As a result, we are creating the logic of the position in accordance with the structure of objects.

Wexelblat describes two basic types of semantic dimension that exist in cyberspace: the Absolute Dimensions, i.e. those that can be described based on examination of a particular isolated object (such as author and the size of the object), and the Relative Dimensions, which refer to the relationship of object with other objects and users. In the group of Relative Dimensions, furthermore, we can distinguish five types: Linear Dimensions, which correspond to those dimensions which can be described in the form of conventional lines (i.e., values correspond to real numbers); Ray Dimensions, similar to linear but connected at one end to a fact or feature; Quantum Dimensions; Nominal Dimensions; Ordinal Dimensions; and Functional Dimensions.

Because the dimensions carry information, both editing and changing the position of the object influences its dimensionality. Editing is done by movement of the object:

Movement – in semantic space we change the meaning by moving them along one or other dimension. [It is] Editing by moving. [3]
 
3.3. Cybermetries without geometry

A cybermetric system is used to describe the creation of electronic and virtual worlds. Cyberspace, as a visualized world of ideas, uses symbols - images. It also produces its own language of symbols, which evolves adapting to the environment.

Does cyberspace seek to abandon the figurative language of symbols? As it is the product of abstract intellect and it relies on abstract ideas, what is the role of figurativeness in cyberspace? To be able to communicate, must cyber architecture be linked to forms of ‘spatial’ forms or must it be based on the spatial geometric system?”

Cybermetries are associated with a new understanding of the properties of geometric objects and are the result of thinking about cyberspace as a space environment. Defining new properties, dimensions, may lead to conclusions which in effect starts to change perception of space itself.

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[1] ‘Geo’ – ‘Earth’ is not adequate for Cyberspace environment, as we are not using these systems to measure physical world. So we propose to replace ‘geo’ with ‘cyber’ coining a new term ‘cybermetries’.

[2] Leyton M., Shape As Memory, A Geometric Theory of Architecture, Birkhäuser, 2006.

​[3] A. Wexelblat, ‘Semantic Dimension’ in Architects in Cyberspace.