Iterative modelling for stress analysis of composite laminates

The importance of interlaminar stresses has prompted a fresh look at the theory of laminated plates. An important feature in modelling such laminates is the need to provide for continuity of some strains and stresses, while at the same time allowing for the discontinuities in the others. A new modelling possibility is examined in this paper. The procedure allows for discontinuities in the in-plane stresses and transverse strains and continuity in the in-plane strains and transverse stresses. This theory is in the form of a heirarchy of formulations each representing an iterative step. Application of the theory is illustrated by considering the example of an infinite laminated strip subjected to sinusoidal loading.

Smoking from Adolescence to Adulthood : A 15-year Follow-up of the North Karelia Youth Project

The aim of the study was to examine the effects of a smoking prevention program and smoking from early adolescence to early adulthood by using longitudinal data. In addition, predictors of smoking, smoking cessation, and associations of smoking with socio-economic factors and other health behaviours were assessed. The data was gathered in connection with the North Karelia Youth Project follow-up study during 15 years. A two-year cardiovascular disease risk factor prevention program was carried out among students from grades seven to nine in four schools in North Karelia. Two schools were selected from Kuopio province for the control schools. The North Karelia Project, a community-based cardiovascular disease prevention program, was implemented in the same area. At the baseline in 1978 the subjects were 13-year-olds (n=903) and in the following surveys 15-, 16-, 17-, 21- and 28-year-olds. The parents of the subjects were studied twice, in 1978 and 1980. A two-year intervention based on social influence approach prevented the onset of smoking for several years. The continuity of smoking from adolescence to adulthood was strong: most adolescent smokers were still smoking in adulthood. Moreover, approximately half of the 28-year-old smokers had started smoking after the age of 15. Previous smoking status and smoking by friends were the most important predictors of smoking. One third of all adolescent smokers had stopped smoking before the age of 28, averaging at 2.3 % annual decline. The socioeconomic status of the subject and, especially, education were strongly related to smoking, the lower socioeconomic groups smoking the most. Parental socioeconomic status and intergenerational social mobility were not significantly related to the smoking of the subject in adolescence or adulthood. Smoking was associated positively with the use of alcohol and negatively with physical activity from adolescence to adulthood. The results support the feasibility of a school-based social influence program with a community-based program in smoking prevention among adolescents. Strong continuity of smoking from adolescence to adulthood supports the importance of preventing the onset of smoking in adolescence. It would be useful to continue prevention programs also after the comprehensive school, since so many young start smoking after that. It would likewise be important to develop cessation programs tailor-made for adolescents and young adults. Additionally, the results support the importance of using methods based on social influence in smoking prevention and cessation programs, targeting especially such risk groups as those with low socioeconomic status as well as those with other unhealthy behaviours.

Development of cat's claw creeper leaf-tying moth Hypocosmia pyrochroma (Lepidoptera: Pyralidae) at different temperatures: Implications for establishment as a biological control agent in Australia and South Africa

The leaf-tying moth Hypocosmia pyrochroma Jones (Lepidoptera: Pyralidae), a native of sub tropical South America, has been introduced as a biological control agent for cat’s claw creeper, Dolichandra unguis-cati (L.) Lohman (Bignoniaceae), in Australia and South Africa. So far there has been no evidence of its field establishment in either country. A narrow temperature tolerance is a potential limiting factor for the establishment of weed biological control insects in novel habitats. In this study, we evaluated the effect of seven constant temperatures (12–40 °C) on the survival and development of H. pyrochroma in temperature-controlled cabinets. Temperatures between 20 and 30 °C were the most favorable for adult survival, oviposition, egg hatching, and larval and pupal development. Adult survival (12–40 °C) and egg development (15–35 °C) showed tolerance for wider temperature ranges than oviposition, and larval and pupal development, which were all negatively affected by both high (>30 °C) and low (<20 °C) temperatures. The degree-day (DD) requirement to complete a generation was estimated as 877 above a threshold temperature of 12 °C. Based on DD requirements and an obligatory winter diapause of pupae from mid-autumn to mid-spring, the potential number of generations (egg to adult) the leaf-tying moth can complete in a year in Australia or South Africa range from one to three. A climate-matching model predicted that the inland regions of both Australia and South Africa are less favorable for H. pyrochroma than the coastal areas. The study suggested that H. pyrochroma is more likely to establish in the coastal areas of Australia where most of the cat’s claw creeper infestations occur, than in South Africa where most of the cat’s claw creeper infestations are inland.

Using Lifespan developmental theory and methods as a viable alternative to the study of generational differences at work

I agree with Costanza and Finkelstein (2015) that it is futile to further invest in the study of generational differences in the work context due to a lack of appropriate theory and methods. The key problem with the generations concept is that splitting continuous variables such as age or time into a few discrete units involves arbitrary cutoffs and atheoretical groupings of individuals (e.g., stating that all people born between the early 1960s and early 1980s belong to Generation X). As noted by methodologists, this procedure leads to a loss of information about individuals and reduced statistical power (MacCallum, Zhang, Preacher, & Rucker, 2002). Due to these conceptual and methodological limitations, I regard it as very difficult if not impossible to develop a “comprehensive theory of generations” (Costanza & Finkelstein, p. 20) and to rigorously examine generational differences at work in empirical studies.

Development of cat’s claw creeper leaf-tying moth Hypocosmia pyrochroma (Lepidoptera: Pyralidae) at different temperatures: Implications for establishment as a biological control agent in Australia and South Africa

The leaf-tying moth Hypocosmia pyrochroma Jones (Lepidoptera: Pyralidae), a native of sub tropical South America, has been introduced as a biological control agent for cat’s claw creeper, Dolichandra unguis-cati (L.) Lohman (Bignoniaceae), in Australia and South Africa. So far there has been no evidence of its field establishment in either country. A narrow temperature tolerance is a potential limiting factor for the establishment of weed biological control insects in novel habitats. In this study, we evaluated the effect of seven constant temperatures (12–40 °C) on the survival and development of H. pyrochroma in temperature-controlled cabinets. Temperatures between 20 and 30 °C were the most favorable for adult survival, oviposition, egg hatching, and larval and pupal development. Adult survival (12–40 °C) and egg development (15–35 °C) showed tolerance for wider temperature ranges than oviposition, and larval and pupal development, which were all negatively affected by both high (>30 °C) and low (<20 °C) temperatures. The degree-day (DD) requirement to complete a generation was estimated as 877 above a threshold temperature of 12 °C. Based on DD requirements and an obligatory winter diapause of pupae from mid-autumn to mid-spring, the potential number of generations (egg to adult) the leaf-tying moth can complete in a year in Australia or South Africa range from one to three. A climate-matching model predicted that the inland regions of both Australia and South Africa are less favorable for H. pyrochroma than the coastal areas. The study suggested that H. pyrochroma is more likely to establish in the coastal areas of Australia where most of the cat’s claw creeper infestations occur, than in South Africa where most of the cat’s claw creeper infestations are inland.

Indigenous cultural landscapes: Equitably defining the 'authenticity' of the intangible

Over hundreds of generations, indigenous groups around the world have passed down their traditional landscape associations, a number of which are intangible and therefore unquantifiable. Yet, these associative relationships with nature have been, and continue to be, pivotal in cultural evolution. Determining the authenticity of intangible landscape associations has caused much controversy, and in recent decades, indigenous groups have begun seeking protection of their places of significance. In response, the United Nations Educational, Scientific and Cultural Organisation (UNESCO) World Heritage Committee (WHC) developed a criterion that intended to assist in the identification and protection of cultural landscapes. The WHC has therefore become the global authority responsible for determining the authenticity of cultural landscapes, including those with intangible associations rather than material cultural evidence. However, even with the support of the United Nations, UNESCO and the WHC, it is unlikely that every tangible cultural landscape will be sufficiently recognised and protected. Therefore, this research paper explores the effectiveness of current approaches to gauging authenticity in instances where multiple landscapes are valued according to similar characteristics. Further, this work studies the inherent relationship between the indigenous Maori population of the South Island of New Zealand, in particular Kai Tahi peoples, and their significant landscape features, as a means of considering the breadth and depth of historic intangible associations. In light of these findings, this research challenges the appropriateness of the term 'authenticity' when analysing not only the subjective, but more pressingly, the intangible. It therefore questions the role of empirical data in demonstrating authenticity, while recognising that a prolific list of such intangible cultural landscapes has the potential to diminish integrity. This, this paper addresses an urgent need for increased social research in this area, namely in identifying cultural landscape protection methods that empower all local indigenous communities, not just those which are the most critically acclaimed.

Aspects of atomic decompositions and Bergman projections

The concept of an atomic decomposition was introduced by Coifman and Rochberg (1980) for weighted Bergman spaces on the unit disk. By the Riemann mapping theorem, functions in every simply connected domain in the complex plane have an atomic decomposition. However, a decomposition resulting from a conformal mapping of the unit disk tends to be very implicit and often lacks a clear connection to the geometry of the domain that it has been mapped into. The lattice of points, where the atoms of the decomposition are evaluated, usually follows the geometry of the original domain, but after mapping the domain into another this connection is easily lost and the layout of points becomes seemingly random. In the first article we construct an atomic decomposition directly on a weighted Bergman space on a class of regulated, simply connected domains. The construction uses the geometric properties of the regulated domain, but does not explicitly involve any conformal Riemann map from the unit disk. It is known that the Bergman projection is not bounded on the space L-infinity of bounded measurable functions. Taskinen (2004) introduced the locally convex spaces LV-infinity consisting of measurable and HV-infinity of analytic functions on the unit disk with the latter being a closed subspace of the former. They have the property that the Bergman projection is continuous from LV-infinity onto HV-infinity and, in some sense, the space HV-infinity is the smallest possible substitute to the space H-infinity of analytic functions. In the second article we extend the above result to a smoothly bounded strictly pseudoconvex domain. Here the related reproducing kernels are usually not known explicitly, and thus the proof of continuity of the Bergman projection is based on generalised Forelli-Rudin estimates instead of integral representations. The minimality of the space LV-infinity is shown by using peaking functions first constructed by Bell (1981). Taskinen (2003) showed that on the unit disk the space HV-infinity admits an atomic decomposition. This result is generalised in the third article by constructing an atomic decomposition for the space HV-infinity on a smoothly bounded strictly pseudoconvex domain. In this case every function can be presented as a linear combination of atoms such that the coefficient sequence belongs to a suitable Köthe co-echelon space.

Characteristics of Proportional Weirs

A theorem termed the Geometrical Continuity Theorem is enunciated and proven. This theorem throws light on the aspects of the continuity of the proportional portion with the base weir portion. These two portions constitute the profile of a proportional weir. A weir of this type with circular bottom is designed. The theorem is used to establish the continuity at the junction of the proportional and the base weir portions of this weir. The coordinates of the weir profile are obtained by numerical methods and are furnished in tabular form for ready use by designers. The discharge passing through the weir is a linear function of the head. The verification of the assumed linear discharge-head relation is furnished for one of the three weirs with which experiments were conducted. The coefficient of discharge for this typical weir is found to be a constant with a value of 0.59.

Theological Exegesis in the Canonical Context : Brevard S. Childs' Methodology of Biblical Theology

Modern Christian theology has been at pain with the schism between the Bible and theology, and between biblical studies and systematic theology. Brevard Springs Childs is one of biblical scholars who attempt to dismiss this “iron curtain” separating the two disciplines. The present thesis aims at analyzing Childs’ concept of theological exegesis in the canonical context. In the present study I employ the method of systematic analysis. The thesis consists of seven chapters. Introduction is the first chapter. The second chapter attempts to find out the most important elements which exercise influence on Childs’ methodology of biblical theology by sketching his academic development during his career. The third chapter attempts to deal with the crucial question why and how the concept of the canon is so important for Childs’ methodology of biblical theology. In chapter four I analyze why and how Childs is dissatisfied with historical-critical scholarship and I point out the differences and similarities between his canonical approach and historical criticism. The fifth chapter attempts at discussing Childs’ central concepts of theological exegesis by investigating whether a Christocentric approach is an appropriate way of creating a unified biblical theology. In the sixth chapter I present a critical evaluation and methodological reflection of Childs’ theological exegesis in the canonical context. The final chapter sums up the key points of Childs’ methodology of biblical theology. The basic results of this thesis are as follows: First, the fundamental elements of Childs’ theological thinking are rooted in Reformed theological tradition and in modern theological neo-orthodoxy and in its most prominent theologian, Karl Barth. The American Biblical Theological Movement and the controversy between Protestant liberalism and conservatism in the modern American context cultivate his theological sensitivity and position. Second, Childs attempts to dismiss negative influences of the historical-critical method by establishing canon-based theological exegesis leading into confessional biblical theology. Childs employs terminology such as canonical intentionality, the wholeness of the canon, the canon as the most appropriate context for doing a biblical theology, and the continuity of the two Testaments, in order to put into effect his canonical program. Childs demonstrates forcefully the inadequacies of the historical-critical method in creating biblical theology in biblical hermeneutics, doctrinal theology, and pastoral practice. His canonical approach endeavors to establish and create post-critical Christian biblical theology, and works within the traditional framework of faith seeking understanding. Third, Childs’ biblical theology has a double task: descriptive and constructive, the former connects biblical theology with exegesis, the later with dogmatic theology. He attempts to use a comprehensive model, which combines a thematic investigation of the essential theological contents of the Bible with a systematic analysis of the contents of the Christian faith. Childs also attempts to unite Old Testament theology and New Testament theology into one unified biblical theology. Fourth, some problematic points of Childs’ thinking need to be mentioned. For instance, his emphasis on the final form of the text of the biblical canon is highly controversial, yet Childs firmly believes in it, he even regards it as the corner stone of his biblical theology. The relationship between the canon and the doctrine of biblical inspiration is weak. He does not clearly define whether Scripture is God’s word or whether it only “witnesses” to it. Childs’ concepts of “the word of God” and “divine revelation” remain unclear, and their ontological status is ambiguous. Childs’ theological exegesis in the canonical context is a new attempt in the modern history of Christian theology. It expresses his sincere effort to create a path for doing biblical theology. Certainly, it was just a modest beginning of a long process.

Conrad Summenhart's theory of individual rights and its medieval background

This study focuses on the theory of individual rights that the German theologian Conrad Summenhart (1455-1502) explicated in his massive work Opus septipartitum de contractibus pro foro conscientiae et theologico. The central question to be studied is: How does Summenhart understand the concept of an individual right and its immediate implications? The basic premiss of this study is that in Opus septipartitum Summenhart composed a comprehensive theory of individual rights as a contribution to the on-going medieval discourse on rights. With this rationale, the first part of the study concentrates on earlier discussions on rights as the background for Summenhart s theory. Special attention is paid to language in which right was defined in terms of power . In the fourteenth century writers like Hervaeus Natalis and William Ockham maintained that right signifies power by which the right-holder can to use material things licitly. It will also be shown how the attempts to describe what is meant by the term right became more specified and cultivated. Gerson followed the implications that the term power had in natural philosophy and attributed rights to animals and other creatures. To secure right as a normative concept, Gerson utilized the ancient ius suum cuique-principle of justice and introduced a definition in which right was seen as derived from justice. The latter part of this study makes effort to reconstructing Summenhart s theory of individual rights in three sections. The first section clarifies Summenhart s discussion of the right of the individual or the concept of an individual right. Summenhart specified Gerson s description of right as power, taking further use of the language of natural philosophy. In this respect, Summenhart s theory managed to bring an end to a particular continuity of thought that was centered upon a view in which right was understood to signify power to licit action. Perhaps the most significant feature of Summenhart s discussion was the way he explicated the implication of liberty that was present in Gerson s language of rights. Summenhart assimilated libertas with the self-mastery or dominion that in the economic context of discussion took the form of (a moderate) self-ownership. Summenhart discussion also introduced two apparent extensions to Gerson s terminology. First, Summenhart classified right as relation, and second, he equated right with dominion. It is distinctive of Summenhart s view that he took action as the primary determinant of right: Everyone has as much rights or dominion in regard to a thing, as much actions it is licit for him to exercise in regard to the thing. The second section elaborates Summenhart s discussion of the species dominion, which delivered an answer to the question of what kind of rights exist, and clarified thereby the implications of the concept of an individual right. The central feature in Summenhart s discussion was his conscious effort to systematize Gerson s language by combining classifications of dominion into a coherent whole. In this respect, his treatement of the natural dominion is emblematic. Summenhart constructed the concept of natural dominion by making use of the concepts of foundation (founded on a natural gift) and law (according to the natural law). In defining natural dominion as dominion founded on a natural gift, Summenhart attributed natural dominion to animals and even to heavenly bodies. In discussing man s natural dominion, Summenhart pointed out that the natural dominion is not sufficiently identified by its foundation, but requires further specification, which Summenhart finds in the idea that natural dominion is appropriate to the subject according to the natural law. This characterization lead him to treat God s dominion as natural dominion. Partly, this was due to Summenhart s specific understanding of the natural law, which made reasonableness as the primary criterion for the natural dominion at the expense of any metaphysical considerations. The third section clarifies Summenhart s discussion of the property rights defined by the positive human law. By delivering an account on juridical property rights Summenhart connected his philosophical and theological theory on rights to the juridical language of his times, and demonstrated that his own language of rights was compatible with current juridical terminology. Summenhart prepared his discussion of property rights with an account of the justification for private property, which gave private property a direct and strong natural law-based justification. Summenhart s discussion of the four property rights usus, usufructus, proprietas, and possession aimed at delivering a detailed report of the usage of these concepts in juridical discourse. His discussion was characterized by extensive use of the juridical source texts, which was more direct and verbal the more his discussion became entangled with the details of juridical doctrine. At the same time he promoted his own language on rights, especially by applying the idea of right as relation. He also showed recognizable effort towards systematizing juridical language related to property rights.

Rukous on perintöä suvusta sukuun : Ikääntyneet ja uskonto vuosituhannen vaihteen Suomessa

"Prayer, a heritage from generation to generation" The elderly and religion in Finland at the turn of the 21st century The strong demographic changes in Europe mean that research on the elderly is highly needed, and also from the viewpoint of their resources and opportunities. Further, it is important to determine, how the elderly could find a meaningful place as members of the chain of generations in our rapidly changing society. The aim of this study was to find out how the elderly build and perceive their place in the society through religious texts. The study was based on religious texts written by elderly people in the study groups of the Finnish pensioners organization Pension Union (Eläkeliitto). These 943 short prayers, poems, and aphorisms were collected during the Tree of Life (Elämänpuu) project in 1998-1999 and were then analysed applying qualitative content analysis and grounded theory methodology. The social construction of aging and the view of communication as a collective signifying process were used as the mainstays of the research perspective. The themes brought forward by the elderly writers were grouped around three key themes: the self, the world and religion. In this examination religion with its forms of expression appeared to be deeply rooted to each of these themes and thus seems a vital part of the elderly writers' culture. In connection with the theme of the self, the religious forms of expression provided a means of building a coherent and culturally accepted self-image which is further supported by positive views of personal history and current life situation. In relation to the world theme, the elderly writers stressed the importance of close social relationships and at the same time expressed anxiety with regard to the changing world. Concerning the theme of religion, the religious forms of expression were first and foremost used in building and creating a sense of personal safety and a belief in the future. The study suggests that skill in the use of religious language enable the elderly to cope with equivocal life events and cognitive dissonance. At the social level the religious forms of expression seemed to connect the writers to the Finnish linguistic culture and identity, as well as to the collective memory, where religion plays a central part. By using religious language the elderly both exploit and maintain these considerable social resources. The key result of the study is that the elderly were found to have a significant and separate role in the continuity and well-being of society. Bound to the religious tradition, the elderly seem to carry significant information as regards the identity of the Finnish people, information which is essentially passed on to future generations. By sustaining traditions and thus the collective identity, they perform a uniquely productive task and their life experience could be seen as a particular type of capital in the society. This result also raises a grave question: Will the elderly of the future be able to undertake this task that so profoundly requires religious literacy?

Towards an understanding of the information dynamics of the handover process in aged care settings: A prerequisite for the safe and effective use of ICT

Background Poor clinical handover has been associated with inaccurate clinical assessment and diagnosis, delays in diagnosis and test ordering, medication errors and decreased patient satisfaction in the acute care setting. Research on the handover process in the residential aged care sector is very limited. Purpose The aims of this study were to: (i) Develop an in-depth understanding of the handover process in aged care by mapping all the key activities and their information dynamics, (ii) Identify gaps in information exchange in the handover process and analyze implications for resident safety, (iii) Develop practical recommendations on how information communication technology (ICT) can improve the process and resident safety. Methods The study was undertaken at a large metropolitan facility in NSW with more than 300 residents and a staff including 55 registered nurses (RNs) and 146 assistants in nursing (AINs). A total of 3 focus groups, 12 interviews and 3 observation sessions were conducted over a period from July to October 2010. Process mapping was undertaken by translating the qualitative data via a five-category code book that was developed prior to the analysis. Results Three major sub-processes were identified and mapped. The three major stages are Handover process (HOP) I “Information gathering by RN”, HOP II “Preparation of preliminary handover sheet” and HOP III “Execution of handover meeting”. Inefficient processes were identified in relation to the handover including duplication of information, utilization of multiple communication modes and information sources, and lack of standardization. Conclusion By providing a robust process model of handover this study has made two critical contributions to research in aged care: (i) a means to identify important, possibly suboptimal practices; and (ii) valuable evidence to plan and improve ICT implementation in residential aged care. The mapping of this process enabled analysis of gaps in information flow and potential impacts on resident safety. In addition it offers the basis for further studies into a process that, despite its importance for securing resident safety and continuity of care, lacks research.

Good Lives, Hidden Miseries : An Ethnography of Uncertainty in a Finnish Village

This is an ethnographic study, in the field of medical anthropology, of village life among farmers in southwest Finland. It is based on 12 months of field work conducted 2002-2003 in a coastal village. The study discusses how social and cultural change affects the life of farmers, how they experience it and how they act in order to deal with the it. Using social suffering as a methodological approach the study seeks to investigate how change is related to lived experiences, idioms of distress, and narratives. Its aim has been to draw a locally specific picture of what matters are at stake in the local moral world that these farmers inhabit, and how they emerge as creative actors within it. A central assumption made about change is that it is two-fold; both a constructive force which gives birth to something new, and also a process that brings about uncertainty regarding the future. Uncertainty is understood as an existential condition of human life that demands a response, both causing suffering and transforming it. The possibility for positive outcomes in the future enables one to understand this small suffering of everyday life both as a consequence of social change, which fragments and destroys, and as an answer to it - as something that is positively meaningful. Suffering is seen to engage individuals to ensure continuity, in spite of the odds, and to sustain hope regarding the future. When the fieldwork was initiated Finland had been a member of the European Union for seven years and farmers felt it had substantially impacted on their working conditions. They complained about the restrictions placed on their autonomy and that their knowledge was neither recognised, nor respected by the bureaucrats of the EU system. New regulations require them to work in a manner that is morally unacceptable to them and financial insecurity has become more prominent. All these changes indicate the potential loss of the home and of the ability to ensure continuity of the family farm. Although the study initially focused on getting a general picture of working conditions and the nature of farming life, during the course of the fieldwork there was repeated mention of a perceived high prevalence of cancer in the area. This cancer talk is replete with metaphors that reveal cultural meanings tied to the farming life and the core values of autonomy, endurance and permanence. It also forms the basis of a shared identity and a means of delivering a moral message about the fragmentation of the good life; the loss of control; and the invasion of the foreign. This thesis formed part of the research project Expressions of Suffering. Ethnographies of Illness Experiences in Contemporary Finnish Contexts funded by the Academy of Finland. It opens up a vital perspective on the multiplicity and variety of the experience of suffering and that it is particularly through the use of the ethnographic method that these experiences can be brought to light. Keywords: suffering, uncertainty, phenomenology, habitus, agency, cancer, farming

Case management in action: An examination of two cases in the area of alcohol related brain damage

‘Practice Forum’ provides a forum for social work practitioners to share their practice with others; to describe what they are doing and assess its effectiveness. The practice of case management is applied in a wide range of service delivery models to meet complex client needs. Unfortunately, cost containment and lack of clarity of the role of the case manager has blurred the definition and practice of case management for both the consumer and professional providers. This article examines two cases of a small non-government agency in Melbourne called Alcohol Related Brain Injury Assessment, Accommodation & Support Inc. (ARBIAS) where case management services are delivered to people with alcohol acquired brain damage. The analysis presented here supports the view that continuity of care and intensive relationship building with clients is vital for successful client outcomes and has application to a variety of programs which service chronically disabled clients.

The Role of Abduction in Self-Similarity

Based on the Aristotelian criterion referred to as 'abductio', Peirce suggests a method of hypothetical inference, which operates in a different way than the deductive and inductive methods. “Abduction is nothing but guessing” (Peirce, 7.219). This principle is of extreme value for the study of our understanding of mathematical self-similarity in both of its typical presentations: relative or absolute. For the first case, abduction incarnates the quantitative/qualitative relationships of a self-similar object or process; for the second case, abduction makes understandable the statistical treatment of self-similarity, 'guessing' the continuity of geometric features to the infinity through the use of a systematic stereotype (for instance, the assumption that the general shape of the Sierpiński triangle continuates identically into its particular shapes). The metaphor coined by Peirce, of an exact map containig itself the same exact map (a map of itself), is not only the most important precedent of Mandelbrot’s problem of measuring the boundaries of a continuous irregular surface with a logarithmic ruler, but also still being a useful abstraction for the conceptualisation of relative and absolute self-similarity, and its mechanisms of implementation. It is useful, also, for explaining some of the most basic geometric ontologies as mental constructions: in the notion of infinite convergence of points in the corners of a triangle, or the intuition for defining two parallel straight lines as two lines in a plane that 'never' intersect.