A Topos Foundation for Theories of Physics: I. Formal Languages for Physics

This paper is the first in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of space and time. Our basic contention is that constructing a theory of physics is equivalent to finding a representation in a topos of a certain formal language that is attached to the system. Classical physics arises when the topos is the category of sets. Other types of theory employ a different topos. In this paper we discuss two different types of language that can be attached to a system, S. The first is a propositional language, PL(S); the second is a higher-order, typed language L(S). Both languages provide deductive systems with an intuitionistic logic. The reason for introducing PL(S) is that, as shown in paper II of the series, it is the easiest way of understanding, and expanding on, the earlier work on topos theory and quantum physics. However, the main thrust of our programme utilises the more powerful language L(S) and its representation in an appropriate topos.Comment: 36 pages, no figure

Gene Expression Differences between Enriched Normal and Chronic Myelogenous Leukemia Quiescent Stem/Progenitor Cells and Correlations with Biological Abnormalities

In comparing gene expression of normal and CML CD34+ quiescent (G0) cell, 292 genes were downregulated and 192 genes upregulated in the CML/G0 Cells. The differentially expressed genes were grouped according to their reported functions, and correlations were sought with biological differences previously observed between the same groups. The most relevant findings include the following. (i) CML G0 cells are in a more advanced stage of development and more poised to proliferate than normal G0 cells. (ii) When CML G0 cells are stimulated to proliferate, they differentiate and mature more rapidly than normal counterpart. (iii) Whereas normal G0 cells form only granulocyte/monocyte colonies when stimulated by cytokines, CML G0 cells form a combination of the above and erythroid clusters and colonies. (iv) Prominin-1 is the gene most downregulated in CML G0 cells, and this appears to be associated with the spontaneous formation of erythroid colonies by CML progenitors without EPO

Topos theory and `neo-realist' quantum theory

Topos theory, a branch of category theory, has been proposed as mathematical basis for the formulation of physical theories. In this article, we give a brief introduction to this approach, emphasising the logical aspects. Each topos serves as a `mathematical universe' with an internal logic, which is used to assign truth-values to all propositions about a physical system. We show in detail how this works for (algebraic) quantum theory.Comment: 22 pages, no figures; contribution for Proceedings of workshop "Recent Developments in Quantum Field Theory", MPI MIS Leipzig, July 200

Renormalization : A number theoretical model

We analyse the Dirichlet convolution ring of arithmetic number theoretic functions. It turns out to fail to be a Hopf algebra on the diagonal, due to the lack of complete multiplicativity of the product and coproduct. A related Hopf algebra can be established, which however overcounts the diagonal. We argue that the mechanism of renormalization in quantum field theory is modelled after the same principle. Singularities hence arise as a (now continuously indexed) overcounting on the diagonals. Renormalization is given by the map from the auxiliary Hopf algebra to the weaker multiplicative structure, called Hopf gebra, rescaling the diagonals.Comment: 15 pages, extended version of talks delivered at SLC55 Bertinoro,Sep 2005, and the Bob Delbourgo QFT Fest in Hobart, Dec 200

Quaternionic Electroweak Theory

We explicitly develop a quaternionic version of the electroweak theory, based on the local gauge group $U(1, q)_{L}\mid U(1, c)_{Y}$. The need of a complex projection for our Lagrangian and the physical significance of the anomalous scalar solutions are also discussed.Comment: 12 pages, Revtex, submitted to J. Phys.

Elective Modernism and the Politics of (Bio) Ethical Expertise

In this essay I consider whether the political perspective of third wave science studies – ‘elective modernism’ – offers a suitable framework for understanding the policy-making contributions that (bio)ethical experts might make. The question arises as a consequence of the fact that I have taken inspiration from the third wave in order to develop an account of (bio)ethical expertise. I offer a précis of this work and a brief summary of elective modernism before considering their relation. The view I set out suggests that elective modernism is a political philosophy and that although its use in relation to the use of scientific expertise in political and policy-making process has implications for the role of (bio)ethical expertise it does not, in the final analysis, provide an account that is appropriate for this latter form of specialist expertise. Nevertheless, it is an informative perspective, and one that can help us make sense of the political uses of (bio)ethical expertise

Physics, Topology, Logic and Computation: A Rosetta Stone

In physics, Feynman diagrams are used to reason about quantum processes. In the 1980s, it became clear that underlying these diagrams is a powerful analogy between quantum physics and topology: namely, a linear operator behaves very much like a "cobordism". Similar diagrams can be used to reason about logic, where they represent proofs, and computation, where they represent programs. With the rise of interest in quantum cryptography and quantum computation, it became clear that there is extensive network of analogies between physics, topology, logic and computation. In this expository paper, we make some of these analogies precise using the concept of "closed symmetric monoidal category". We assume no prior knowledge of category theory, proof theory or computer science.Comment: 73 pages, 8 encapsulated postscript figure

cohesion and conflict in transnational merchant families

How do people negotiate the diversity of positionalities within kin groups? Through a diachronic approach, I investigate how Ali and Jalal, two merchants with Azeri and Gilaki ethnic identifications who came to Hamburg in the 1930s, mobilized kin to generate capital along the lines of generation, gender, and age. The reader simultaneously learns about the local history of Iranian immigration. Building on literature about historical merchant networks, the social organization of the Iranian marketplace (bazaar), the anthropology of kinship and transnational families, I question the social cohesion on which Aihwa Ong's study of flexible capital creation relies. The material suggests that the experience of family relations influences agents' positioning in the local Iranian social field