Fermat Reals - Nilpotent Infinitesimals and Infinite Dimensional Spaces

F.: Good morning Hermann, I would like to talk with you about infinitesimals. G.: Tell me Pierre. F.: I'm fed up of all these slanders about my attitude to be non rigorous, so I've started to study nonstandard analysis (NSA) and synthetic differential geometry (SDG). G.: Yes, I've read something ... F.: Ok, no problem about their rigour. But, when I've seen that the sine of an infinite in NSA is infinitely near to a real number I was astonished: what is the intuitive meaning of this number, if any? Then, I've seen that to work in SDG I must learn to work in intuitionistic logic ... You know, I love margins of books, and I don't want to loose too much time, I have many things to do ... G.: In SDG they also say that every infinitesimal is at the same time positive and negative, what is the meaning of all these? And why does the square of a first order infinitesimal equal zero, whereas the product of two first order infinitesimals is not necessarily zero? And do you know that from any single infinitesimal in NSA is possible to construct a non measurable set? Without using the axiom of choice! F.: Yes, I know, I know ... Ok, listen: why cannot we start from standard real functions of one real variable and use ... This work is the ideal continuation of this dialogue: a theory of actual infinitesimals that do not need a background of formal logic to be understood, with a clear intuitive meaning and with non trivial applications to differential geometry of both finite and infinite dimensional spaces

A virus created radical moment: Not to be missed?

I'm sitting in splendid isolation on a lush hillside above a Cretan village, where even the patriarchal kafeneio is closed. Outside its shuttered face a group of old men sit, less than socially distant, defying spasmodic police surveillance. A few kilometres away people queue obediently outside the supermarket, clutching in their plastic gloved hands the required Out-of-Home pass and their ID. There are health concerns, even though the island of 650,000 souls has precious few Covid-19 cases and only one death, but such melancholia is hardly new. Crete is awash with chemists, testing one's blood pressure a daily routine. Notwithstanding the benefits of the Mediterranean diet it’s tempting to note that Hippocrates hailed from hereabouts and that hypochondria stems from Ancient Greek. There is real fear, though not so much of the virus per se but of what lies ahead. As I write the island is closed for business. The tourism-oiled life blood of the local economy congeals. With cafes, tavernas, hotels, even beaches, empty of purpose, unemployment and debt soars. The Orthrus-headed threat of poverty and hunger hangs in the air. The questions on everybody's lips are 'when will this end?' and ‘will we, do we, want to return to normal?' At this moment, if assuredly we are not all in this together, from capitalist to peasant, humanity faces a fragile future

Transcript of keynote speech, "Don't Lecture Me"

Keynote speech given by Donald Clark at “Into something rich and strange” – making sense of the sea-change, the 2010 Association for Learning Technology Conference in Nottingham, England. In the chair, Vanessa Pittard, Bect

THE SEXUAL ORIENTATION OF CELIE IN ALICE WALKER’S THE COLOR PURPLE

The objectives of this research are to reveal the factors that cause Celie to become a lesbian and to describe Celie‟s homosexual identity development. The researcher used sexual orientation, lesbianism and other related theories to answer the formulated research questions. The method used in this research is qualitative content analysis. The subject of this research is a novel entitled The Color Purple by Walker. The data are some phrases, clauses, and sentences related to the factors that cause Celie to become a lesbian and process of Celie‟s homosexual identity development. The key instrument of this research is the researcher herself employing sexual orientation theory by Giddens and lesbianism theory by Rich as explained in the conceptual framework. Sexual orientation and lesbianism are used as the grand theories for the analysis. The indicators made are based on the employed theories to gain the research data. To gain the trustworthiness, the researcher used data triangulation technique by crosschecking the data with her consultants and other researchers. The findings of the research show two important points. First, the factors that cause Celie to become a lesbian are psychological and social/environmental factors. Second, Celie‟s homosexual identity development process covers four stages: sensitization or emergence, identity confusion, identity assumptiopn and first relationship

The Freedom of the Christian for Culture

(Excerpt) It is somewhat surprising for Timothy Lull to be invited to address a liturgical conference of any sort. I was talking to several of my colleagues at Pacific Lutheran Theological Seminary this week about what I would be saying, and one of them said, Ah! Is Lull among the liturgists? He seemed surprised These colleagues wondered if you knew, for example, that I describe myself as a recovering evangelical catholic, or if you would know that I have the reputation in my congregation as being the great complainer about matters like the length of service, the fact that we sing no hymns written after 1750, that the basis for preaching almost never includes either the Old Testament or the Epistle lesson, and the kind of frightened anxiety with which we do things liturgical in our very liturgical parish