The episcopal complex of Eio-El Tolmo de Minateda (Hellín, Albacete, Spain). Architecture and spatial organization. 7th to 8th centuries AD

The episcopal complex of Eio, located in El Tolmo de Minateda, was built between the end of the 6th century and the beginning of the 7th century, possibly as a political decision taken by the ecclesiastical authority in the capital of the Visigothic kingdom (Toletum). With the comprehensive study of the whole complex presented below (construction cycles, furniture, decoration and location of spaces), we can interpret the function of each space in the basilica and the domus episcopi, the liturgical and general movement routes, the existence of some hierarchical environments, and specify the chronological development of the buildings. After the Arab-Berber conquest of Hispania in the early 8th century, the whole complex will experience a series of transformations that will convert the religious and monumental public area into a private, residential and industrial Islamic quarter.

Topological structures of complex belief systems

The concepts of substantive beliefs and derived beliefs are defined, a set of substantive beliefs S like open set and the neighborhood of an element substantive belief. A semantic operation of conjunction is defined with a structure of an Abelian group. Mathematical structures exist such as poset beliefs and join-semilattttice beliefs. A metric space of beliefs and the distance of belief depending on the believer are defined. The concepts of closed and opened ball are defined. S′ is defined as subgroup of the metric space of beliefs Σ and S′ is a totally limited set. The term s is defined (substantive belief) in terms of closing of S′. It is deduced that Σ is paracompact due to Stone's Theorem. The pseudometric space of beliefs is defined to show how the metric of the nonbelieving subject has a topological space like a nonmaterial abstract ideal space formed in the mind of the believing subject, fulfilling the conditions of Kuratowski axioms of closure. To establish patterns of materialization of beliefs we are going to consider that these have defined mathematical structures. This will allow us to understand better cultural processes of text, architecture, norms, and education that are forms or the materialization of an ideology. This materialization is the conversion by means of certain mathematical correspondences, of an abstract set whose elements are beliefs or ideas, in an impure set whose elements are material or energetic. Text is a materialization of ideology.

Topological structures of complex belief systems (II): Textual materialization

Mythical and religious belief systems in a social context can be regarded as a conglomeration of sacrosanct rites, which revolve around substantive values that involve an element of faith. Moreover, we can conclude that ideologies, myths and beliefs can all be analyzed in terms of systems within a cultural context. The significance of being able to define ideologies, myths and beliefs as systems is that they can figure in cultural explanations. This, in turn, means that such systems can figure in logic-mathematical analyses.