<Emphasis Type="Italic">The Mathematical Intelligencer</Emphasis> Flunks the Olympics

The Mathematical Intelligencer recently published a note by Y. Sergeyev that challenges both mathematics and intelligence. We examine Sergeyev’s claims concerning his purported Infinity computer. We compare his grossone system with the classical Levi-Civita fields and with the hyperreal framework of A. Robinson, and analyze the related algorithmic issues inevitably arising in any genuine computer implementation. We show that Sergeyev’s grossone system is unnecessary and vague, and that whatever consistent subsystem could be salvaged is subsumed entirely within a stronger and clearer system (IST). Lou Kauffman, who published an article on a grossone, places it squarely outside the historical panorama of ideas dealing with infinity and infinitesimals.     

Heidegger on <Emphasis Type="Italic">Verfallenheit</Emphasis>

The question of Heidegger’s reflections on technology is explored in terms of ‘living with’ technology and including the socio-theoretical (Edinburgh) notion of ‘entanglement’ towards a review of Heidegger’s understanding of technology and media, including the entertainment industry and modern digital life. I explore Heidegger’s reflections on Gelassenheit by way of the Japanese aesthetic conception of life and of art as wabi-sabi understood with respect to Heidegger’s Gelassenheit as the art of Verfallenheit.     

A Theory of Scientific Model Construction: <Emphasis Type="Italic">The Conceptual Process of Abstraction and Concretisation</Emphasis>

The process of abstraction and concretisation is a label used for an explicative theory of scientific model-construction. In scientific theorising this process enters at various levels. We could identify two principal levels of abstraction that are useful to our understanding of theory-application. The first level is that of selecting a small number of variables and parameters abstracted from the universe of discourse and used to characterise the general laws of a theory. In classical mechanics, for example, we select position and momentum and establish a relation amongst the two variables, which we call Newton’s 2nd law. The specification of the unspecified elements of scientific laws, e.g. the force function in Newton’s 2nd law, is what would establish the link between the assertions of the theory and physical systems. In order to unravel how and with what conceptual resources scientific models are constructed, how they function and how they relate to theory, we need a view of theory-application that can accommodate our constructions of representation models. For this we need to expand our understanding of the process of abstraction to also explicate the process of specifying force functions etc. This is the second principal level at which abstraction enters in our theorising and in which I focus. In this paper, I attempt to elaborate a general analysis of the process of abstraction and concretisation involved in scientific- model construction, and argue why it provides an explication of the construction of models of the nuclear structure.     

<Emphasis Type="Italic">k</Emphasis>-Adic Similarity Coefficients for Binary (Presence/Absence) Data

k-Adic formulations (for groups of objects of size k) of a variety of 2-adic similarity coefficients (for pairs of objects) for binary (presence/absence) data are presented. The formulations are not functions of 2-adic similarity coefficients. Instead, the main objective of the the paper is to present k-adic formulations that reflect certain basic characteristics of, and have a similar interpretation as, their 2-adic versions. Two major classes are distinguished. The first class is referred to as Bennani-Heiser similarity coefficients, which contains all coefficients that can be defined using just the matches, the number of attributes that are present and that are absent in k objects, and the total number of attributes. The coefficients in the second class can be formulated as functions of Dice’s association indices. The author thanks Willem Heiser and three anonymous reviewers for their helpful comments and valuable suggestions on earlier versions of this article.     

Cultural-Biology: Systemic Consequences of <Emphasis Type="Italic">Our</Emphasis> Evolutionary Natural Drift as Molecular Autopoietic Systems

Our purpose in this essay is to introduce new concepts (dynamic architecture and dynamic ecological organism-niche unity, among other) in a wide and recursive view of the systemic consequences of the following biological facts that I (Maturana in Biology of cognition, 1970, Unity and diversity of man. Le Seuil, Paris, 1978; Maturana and Varela in Autopoiesis and cognition: the realization of the living. D. Riedel Publishing Co, Boston, 1980, El Árbol del Conocimiento: Las Bases Biológicas del Conocer Humano, 1a Edición. Editorial Universitaria, Santiago, 1984; Maturana and Mpodozis in Rev Chil Hist Nat 73:261–310, 2000) and we (Maturana and Dávila in Habitar humano: en seis ensayos de biología-cultural. Juan Carlos Sáez Editorial, Chile, 2008) have presented that can be resumed as: (1) that as living systems we human beings are molecular autopoietic system; (2) that living systems live only as long as they find themselves in a medium that provides them with all the conditions that make the realization of their living possible, that is, in the continuous conservation of their relation of adaptation to the circumstances in which they find themselves; (3) that as a living system exists only in a relation of adaptation with the medium that operates as its ecological niche, its reproduction necessarily occurs as a process of systemic duplication or multiplication of the ecological organism-niche unity that it integrates; (4) that the worlds of doings that we generate as languaging beings in our conversations, explanations, reflections and theories are part of our ecological niche; and (5) that we human beings as living beings that exist in languaging, are biological–cultural beings in which our cultural and our biological manners of existences can be distinguished but cannot be separated. Of the systemic consequences of these biological facts that we consider in this essay, we wish to mention two as the principal: (1) that the diversification of manners of living produced in biological evolution is the result of differential survival in a changing medium through the conservation of adaptation, and not through competitive survival of the best; and (2) that we in our living as languaging human beings (observers) are the epistemological fundament of all that we do and know as such.     

Social Autonomy and Heteronomy in the Age of ICT: The Digital <Emphasis Type="Italic">Pharmakon</Emphasis> and the (Dis)Empowerment of the General Intellect

‘The art of living with ICTs (information and communication technologies)’ today not only means finding new ways to cope, interact and create new lifestyles on the basis of the new digital (network) technologies individually, as ‘consumer-citizens’. It also means inventing new modes of living, producing and, not in the least place, struggling collectively, as workers and producers. As the so-called digital revolution unfolds in the context of a neoliberal cognitive and consumerist capitalism, its ‘innovations’ are predominantly employed to modulate and control both production processes and consumer behavior in view of the overall goal of extracting surplus value. Today, the digital networks overwhelmingly destroy social autonomy, instead engendering increasing social heteronomy and proletarianization. Yet it is these very networks themselves, as technical pharmaka in the sense of French ‘technophilosopher’ Bernard Stiegler, that can be employed as no other to struggle against this tendency. This paper briefly explores this possibility by reflecting upon current diagnoses of our ‘technological situation’ by some exemplary post-operaist Marxists from a Stieglerian, pharmacological perspective.