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Masterarbeit Universität Innsbruck 2023

von Lukas Gräupner, Masterarbeit Universität Innsbruck 2023

Halbtrockenrasen gehören zu den artenreichsten anthropogenen Lebensräumen der Gefässpflanzen in der Paläarktis. Jedoch ist in den inneralpinen Trockentälern des Wallis die Bewässerung der Halbtrockenrasen oft eine Grundvoraussetzung für die Ertragssicherung. Da bisher nur wenige Studien die langfristigen Auswirkungen der Beregnung mittels Sprinkler untersuchten, wurden Wiederholungsaufnahmen auf 12 Untersuchungsflächen in der Gemeinde Bettmeralp durchgeführt. Zusätzlich wurden weitere Flächenpaare (bewässert/unbewässert) im Gemeindegebiet aufgenommen. Das Ziel war die Biodiversitätsindizes, ökologischen Zeigerwerte, Arten der Roten Liste und die Lebensräume der Untersuchungsflächen zu quantifizieren sowie diese mit einem gepaarten t-Test und einer Co-Varianzanalyse statistisch auszuwerten. Die Dauerflächen veränderten sich geringfügig von 1988 bis 2021. Zwei Flächen entwickelten sich in nährstoffreiche Bestände und die Humuszahl nahm signifikant zu. Die unbewässerten und bewässerten Flächen unterschieden sich signifikant bei der Artenzahl und 10 gewichteten Zeigerwerten, wobei die Hangneigung bei vier Zeigerwerte einen signifikanten Einfluss hatte. Diese Ergebnisse zeigen, welche Auswirkungen die Bewässerung und teilweise die Düngung auf die Trockenvegetation hat. Die geringen Veränderungen auf den Dauerflächen deuten daraufhin, dass die Böden noch von der traditionellen Bewässerung, welche in den 60er Jahre aufgegeben wurde, geprägt waren.

In this paper we will deal with some aspects of the controversy between Wallis and Hobbes concerning the foundations of infinite mathematics and the use of infinite and infinitely small quantities in mathematics. Thus, after some initial clarification on Wallis’s arithmetic of infinities, we will focus particularly on three main topics of this discussion: the nature of infinitesimals and the validity of their use in mathematics; the infinite number and the supposition of what we will call “the completeness of the series”; and the conception that the “excess” disappears, taking the series to infinity., En este trabajo se abordarán algunos aspectos de la polémica entre Wallis y Hobbes en torno de los fundamentos de la matemática infinita y del uso en general de infinitos e infinitamente pequeños en matemática. Así, luego de algunas aclaraciones iniciales sobre la aritmética de los infinitos de Wallis, nos centraremos en especial en tres ejes de esta discusión: la naturaleza de los infinitesimales y la validez de su uso en matemática; el número infinito y la suposición de lo que llamaremos “completitud de las series”; y concepción de que el “exceso” desaparece llevada la serie al infinito.

Halbtrockenrasen gehören zu den artenreichsten anthropogenen Lebensräumen der Gefässpflanzen in der Paläarktis. Jedoch ist in den inneralpinen Trockentälern des Wallis die Bewässerung der Halbtrockenrasen oft eine Grundvoraussetzung für die Ertragssicherung. Da bisher nur wenige Studien die langfristigen Auswirkungen der Beregnung mittels Sprinkler untersuchten, wurden Wiederholungsaufnahmen auf 12 Untersuchungsflächen in der Gemeinde Bettmeralp durchgeführt. Zusätzlich wurden weitere Flächenpaare (bewässert/unbewässert) im Gemeindegebiet aufgenommen. Das Ziel war die Biodiversitätsindizes, ökologischen Zeigerwerte, Arten der Roten Liste und die Lebensräume der Untersuchungsflächen zu quantifizieren sowie diese mit einem gepaarten t-Test und einer Co-Varianzanalyse statistisch auszuwerten. Die Dauerflächen veränderten sich geringfügig von 1988 bis 2021. Zwei Flächen entwickelten sich in nährstoffreiche Bestände und die Humuszahl nahm signifikant zu. Die unbewässerten und bewässerten Flächen unterschieden sich signifikant bei der Artenzahl und 10 gewichteten Zeigerwerten, wobei die Hangneigung bei vier Zeigerwerte einen signifikanten Einfluss hatte. Diese Ergebnisse zeigen, welche Auswirkungen die Bewässerung und teilweise die Düngung auf die Trockenvegetation hat. Die geringen Veränderungen auf den Dauerflächen deuten daraufhin, dass die Böden noch von der traditionellen Bewässerung, welche in den 60er Jahre aufgegeben wurde, geprägt waren.

The way Leibniz applied his philosophy to mathematics has been the subject of longstanding debates. A key piece of evidence is his letter to Masson on bodies. We offer an interpretation of this often misunderstood text, dealing with the status of infinite divisibility in nature, rather than in mathematics. In line with this distinction, we offer a reading of the fictionality of infinitesimals. The letter has been claimed to support a reading of infinitesimals according to which they are logical fictions, contradictory in their definition, and thus absolutely impossible. The advocates of such a reading have lumped infinitesimals with infinite wholes, which are rejected by Leibniz as contradicting the partwhole principle. Far from supporting this reading, the letter is arguably consistent with the view that infinitesimals, as inassignable quantities, are mentis fictiones, i.e., (well-founded) fictions usable in mathematics, but possibly contrary to the Leibnizian principle of the harmony of things and not necessarily idealizing anything in rerum natura. Unlike infinite wholes, infinitesimals - as well as imaginary roots and other well-founded fictions - may involve accidental (as opposed to absolute) impossibilities, in accordance with the Leibnizian theories of knowledge and modality.

Aquest treball final de màster en arquitectura, renovació i rehabilitació tracta sobre com rehabilitar un tipus d’arquitectura vernacla a Valais, Suïssa, d’on sóc. Són petites construccions fetes de troncs de fusta, acoblades en sec, que es poden desmuntar. Aquestes construccions es consideraven com a béns mobles i no com a béns immobles i, de vegades, es movien segons les necessitats dels camperols. De fet, van adoptar ràpidament una forma de vida nòmada, movent-se en altitud per assolir diferents altiplans als Alps, depenent de la temporada. La tipologia constructiva bàsica varia en diferents tipus de construcció, depenent dels materials disponibles, les necessitats i l’altitud a la qual es troben. Poden tenir la forma d’un graner per emmagatzemar aliments, un Raccard on hi treballen les garbes de cereals, un graner-estable per a albergar el bestiar i el fenc; o fins i tot un Mayen, una construcció en altitud que es va utilitzar per albergar als camperols i al bestiar. A la primera part, el treball defineix aquestes diferents tipologies, buscant comprendre com i per què les coses s’han desenvolupat d’aquesta manera, definint els materials i les tècniques de construcció utilitzades al comparar construccions existents. A la segona part, es desenvolupa una anàlisi de rehabilitacions contemporànies duent a terme una valoració de les construccions, que permet presentar una mostra variada de casos reals, en els quals s’han aplicat diferents altituds. Com a resultat, vam descobrir que certes estratègies sovint es repeteixen, com aïllar les construccions des de l’interior, mentre es manté la pàtina exterior. També veiem que alguns edificis creixen, ja sigui per sota terra o amb annexos addicionals, el que ja s’ha fet històricament., Este trabajo final de máster en arquitectura, renovación y rehabilitación trata sobre cómo rehabilitar un tipo de arquitectura vernácula en Valais, Suiza, de donde soy. Son pequeñas construcciones hechas de troncos de madera, ensambladas en seco, que se pueden desmontar. Estas construcciones se consideraban como bienes muebles y no como bienes inmuebles y, a veces, se movían según las necesidades de los campesinos. De hecho, adoptaron rápidamente una forma de vida nómada, moviéndose en altitud para alcanzar diferentes mesetas en los Alpes, dependiendo de la temporada. La tipología constructiva básica varía en diferentes tipos de construcción, dependiendo de los materiales disponibles, las necesidades y la altitud a la que se encuentran. Pueden tener la forma de un granero para almacenar alimentos, un raccard en él que trabajan las gavillas de cereales, un granero-establo para albergar el ganado y el heno o incluso un mayen, una construcción en altitud que se utilizó para albergar a los campesinos y el ganado. En la primera parte, el trabajo define estas diferentes tipologías, buscando comprender cómo y por qué las cosas se han desarrollado de esta manera, definiendo los materiales y las técnicas de construcción utilizadas, comparando construcciones existentes. En la segunda parte del trabajo, se desarrolla un análisis de rehabilitaciones contemporáneas, llevando a cabo una valoración de las construcciones, que permite presentar una muestra variada de casos reales, en los que se han aplicado diferentes actitudes. Como resultado, descubrimos que ciertas estrategias a menudo se repiten, como aislar edificios desde el interior, mientras se mantiene la pátina exterior. También vemos que algunos edificios están creciendo, ya sea bajo tierra o por anexos adicionales, lo que ya se hizo históricamente., This final master’s thesis in architecture, renovation and rehabilitation deals with how to rehabilitate a type of vernacular architecture in Valais, Switzerland, where I am from. These are small constructions made of wooden logs, assembled dry, which can be dismantled. These constructions were considered as movable property and not real property and were sometimes transported according to the needs of the peasants. Indeed, they quickly adopted a nomadic lifestyle, moving in altitude to reach different plateaus in the Alps, depending on the season. The basic constructive typology varies in different types of construction, depending on the materials available, the needs and the altitude at which they are located. They can be in the form of an granary to store food, a raccard in which they work the sheaves of cereals, a barn-stable to house the cattle and hay or even a mayen, a construction in altitude which was used to shelter the peasants and the cattle. In the first part, the work defines these different typologies, seeking to understand how and why things have developed in this way, defining the materials and construction techniques used while comparing existing constructions. In the second part, an analysis of contemporary rehabilitations is developed, carrying out a valuation of the constructions, which makes it possible to present a varied sample of real cases, in which different attitudes have been applied. As a result, it is found that certain strategies are often repeated, such as isolating buildings from the inside, while maintaining the outside patina. We also see that some buildings are being enlarged, either underground or by complementary annexes, which was already done historically.

The upper Rhone valley in the Swiss canton of Valais is one of the driest and most continental of the inner-alpine valleys and harbours a rich xerothermic flora. We studied syntaxonomy and ecology of dry grasslands and their species richness patterns. In 2018 we recorded 28 vegetation plots (10 m²) and three nested-plot series of 0.0001 to 100 m² on the south-facing slopes above the village of Ausserberg. Mean richness of all species ranged from 1.7 on 1 cm² to 47.3 on 100 m², with little contribution of bryophytes and lichens. The species-area relationship for total richness closely followed a power function. Modified TWINSPAN yielded a three-cluster solution, which could easily be matched with three orders of the class Festuco- Brometea: Stipo pulcherrimae-Festucetalia pallentis (xeric, rocky), Festucetalia valesiacae (xeric, non-rocky) and Brachypodietalia pinnati (meso-xeric). The subdivision of the xeric types into two orders is new for Swiss dry grasslands, where these types up to now had been joined in a single alliance Stipo-Poion within the Festucetalia valesiacae.

The upper Rhone valley in the Swiss canton of Valais is one of the driest and most continental of the inner-alpine valleys and harbours a rich xerothermic flora. We studied syntaxonomy and ecology of dry grasslands and their species richness patterns. In 2018 we recorded 28 vegetation plots (10 m²) and three nested-plot series of 0.0001 to 100 m² on the south-facing slopes above the village of Ausserberg. Mean richness of all species ranged from 1.7 on 1 cm² to 47.3 on 100 m², with little contribution of bryophytes and lichens. The species-area relationship for total richness closely followed a power function. Modified TWINSPAN yielded a three-cluster solution, which could easily be matched with three orders of the class Festuco- Brometea: Stipo pulcherrimae-Festucetalia pallentis (xeric, rocky), Festucetalia valesiacae (xeric, non-rocky) and Brachypodietalia pinnati (meso-xeric). The subdivision of the xeric types into two orders is new for Swiss dry grasslands, where these types up to now had been joined in a single alliance Stipo-Poion within the Festucetalia valesiacae.

En analyse af argumenter fra 1600-tallet for umuligheden af at kvadrere cirklen. Argumenterne angår først og fremmest umuligheden af at finde et algebraisk udtryk for cirklens kvadratur. Spørgsmålet om det indefinite cirkelkvadratur handler om muligheden af at finde et udtryk for arealet af et vilkårligt sirkeludsnit, medens det definite cirkelkvadratur omhandler arealet af hele cirklen. I artiklen analyseres bidrag af Wallis, Gregory, Leibniz og Newton., The classical problem of the quadrature (or equivalently the rectification) of the circle enjoyed a renaissance in the second half of the 17th century. The new analytic methods provided the means for the discovery of infinite expressions of and for the first attempts to prove impossibility statements related to the quadrature of the circle. In this paper the impossibility arguments put forward by Wallis, Gregory, Leibniz and Newton are analyzed and the controversies they gave rise to are discussed. They all deal with the impossibility of finding an algebraic expression of the area of a sector of a circle in terms of its radius and cord, or of the area of the entire circle. It is argued that the controversies were partly due to a lack of precision in the formulation of the results. The impossibility results were all part of a constructive problem solving mathematical enterprise. They were intended to show that certain solutions of the quadrature problem were the best possible because simpler (analytic) solutions were impossible.

En analyse af argumenter fra 1600-tallet for umuligheden af at kvadrere cirklen. Argumenterne angår først og fremmest umuligheden af at finde et algebraisk udtryk for cirklens kvadratur. Spørgsmålet om det indefinite cirkelkvadratur handler om muligheden af at finde et udtryk for arealet af et vilkårligt sirkeludsnit, medens det definite cirkelkvadratur omhandler arealet af hele cirklen. I artiklen analyseres bidrag af Wallis, Gregory, Leibniz og Newton., The classical problem of the quadrature (or equivalently the rectification) of the circle enjoyed a renaissance in the second half of the 17th century. The new analytic methods provided the means for the discovery of infinite expressions of and for the first attempts to prove impossibility statements related to the quadrature of the circle. In this paper the impossibility arguments put forward by Wallis, Gregory, Leibniz and Newton are analyzed and the controversies they gave rise to are discussed. They all deal with the impossibility of finding an algebraic expression of the area of a sector of a circle in terms of its radius and cord, or of the area of the entire circle. It is argued that the controversies were partly due to a lack of precision in the formulation of the results. The impossibility results were all part of a constructive problem solving mathematical enterprise. They were intended to show that certain solutions of the quadrature problem were the best possible because simpler (analytic) solutions were impossible.

Dans cet article, sont développés les acquis de Firth, Duranti et Salmond, qui montrent les dimensions interactionnelles, cognitives, sociales et politiques des salutations dans le Pacifique. Sont également considérés certains de leurs aspects plus proprement opératoires et rituels. Partant d’une ethnographie polynésienne sur les pratiques linguistiques et les conceptions locales du monde sociocosmique, je présente les modalités de l’action, notamment des actes de parole (énonciation des noms) en contexte cérémoniel. Le caractère instituant des salutations repose sur la nomination et sur les formes de coprésence que cette dernière reconnaît et établit, conférant aux actions leur bien-fondé et leur efficacité. Dans cette perspective, si les salutations participent de processus analysés par d’autres en termes de pouvoir et de politique, une entrée différente montre qu’il s’agit d’abord de définir le type d’interaction à venir, d’en préciser les coparticipants (vivants, ancêtres, Dieu), d’en déterminer, enfin, le cadre et l’étendue des résultats. Les salutations donnent à toute action son fondement et son efficacité., Formal greetings and exercise of authority in WallisThis article develops the results of Firth, Duranti and Salmond showing the interactional, cognitive, social and political dimensions of greetings in the Pacific. Some of their more strictly operative and ritual aspects are also considered. Starting from a Polynesian ethnography of linguistic practices and local conceptions of the socio-cosmic world, I present the modalities of action, especially of speech acts (names enunciation) in ceremonial contexts. Greetings have an instituting character based on the act of naming and on the forms of co-presence it recognises and establishes, conferring on the actions their legitimacy and their efficiency. If greetings are part of processes analysed by others in terms of power and politics, another way to look at it shows that it is mostly about defining the type of interactions to come, specifying the co-participants (human beings, ancestors, God), and eventually determining their framework and the extent of their results. Greetings give actions their foundation and efficiency.