Oneness, Aspects, and the Neo-Confucians

Confucius gave counsel that is notoriously hard to follow: "What you do not wish for yourself, do not impose on others" (Huang 1997: 15.24). People tend to be concerned with themselves and to be indifferent to most others. We are distinct from others so our self-concern does not include them, or so it seems. Were we to realize this distinctness is merely apparent--that our true self includes others--Confucius's counsel would be easier to follow. Concern for our true self would extend concern beyond the narrow selves we appear to be. The neo-Confucians held just such a view. They espoused an identity with the universe and everything in it, arguing that this identity explains a natural concern for everyone and everything, not just for our narrow selves. However, many things in the universe differ from each other, that is, some have qualities others lack. If they are all one and the same thing then that one thing differs from itself. I will suggest that the objection can be answered with some metaphysical innovation. I will address the objection by sketching a theory--call it the theory of aspects--that explains how numerically identical things can differ qualitatively

Hume on Substance: A Critique of Locke

The ancient theory of substance and accident is supposed to make sense of complex unities in a way that respects both their unity and their complexity. On Hume’s view such complex unities are only fictitiously unities. This result follows from his thoroughgoing critique of the theory of substance. I will characterize the theory Hume is critiquing as it is presented in Locke, presupposing what Bennett calls the “Leibnizian interpretation.” Locke uses the word ‘substance’ in two senses. Call substance in the first sense “individual substance” and in the second sense “pure substance.” I will discuss the seven main parts of Hume’s view: (I) that we have no idea of pure substance, (II) that there is no complex individual substance, except in a loose sense, (III) that the fiction of complex individual substance arises in a way parallel to that of the fiction of identity through time, and (IV) results in the fiction of pure substance, (V) that simple qualities and perceptions satisfy the definition of individual substance, (VI) that there is no such thing as inherence, and (VII) that there is no such thing as pure substance. Hume’s views on substance are often mentioned without being discussed in detail. Kemp Smith, Stroud, and Garrett, for example, mostly summarize various claims of Hume in the course of expounding on his theory of the idea of personal identity. In contrast, I will attempt to present a systematic treatment of Hume on substance as a refutation of Locke

Algebraic reduction of the Ising model

We consider the Ising model on a cylindrical lattice of L columns, with fixed-spin boundary conditions on the top and bottom rows. The spontaneous magnetization can be written in terms of partition functions on this lattice. We show how we can use the Clifford algebra of Kaufman to write these partition functions in terms of L by L determinants, and then further reduce them to m by m determinants, where m is approximately L/2. In this form the results can be compared with those of the Ising case of the superintegrable chiral Potts model. They point to a way of calculating the spontaneous magnetization of that more general model algebraically.Comment: 25 pages, one figure, last reference completed. Various typos fixed. Changes on 12 July 2008: Fig 1, 0 to +1; before (2.1), if to is; after (4.6), from to form; before (4.46), first three to middle two; before (4.46), last to others; Conclusions, 2nd para, insert how ; renewcommand \i to be \rm

Gaudin Hypothesis for the XYZ Spin Chain

The XYZ spin chain is considered in the framework of the generalized algebraic Bethe ansatz developed by Takhtajan and Faddeev. The sum of norms of the Bethe vectors is computed and expressed in the form of a Jacobian. This result corresponds to the Gaudin hypothesis for the XYZ spin chain.Comment: 12 pages, LaTeX2e (+ amssymb, amsthm); to appear in J. Phys.

Corner transfer matrices in statistical mechanics

Corner transfer matrices are a useful tool in the statistical mechanics of simple two-dimensinal models. They can be very effective way of obtaining series expansions of unsolved models, and of calculating the order parameters of solved ones. Here we review these features and discuss the reason why the method fails to give the order parameter of the chiral Potts model.Comment: 18 pages, 4 figures, for Proceedings of Conference on Symmetries and Integrability of Difference Equations. (SIDE VII), Melbourne, July 200

Role of Social Media and Digital Resources in Forage Education

Social media and digital resources are powerful tools that enable forage-livestock researchers and Extension specialists to connect with a wide audience of producers, Extension personnel, colleagues, and industry partners. This presentation in the thematic session on “Understanding the role of social media and digital resources in forage education and promotion” will focus on the role digital resources play in forage education

Role of Social Media and Digital Resources in Extension

Social media and digital resources can be powerful tools for Extension personnel as they can enable forage-livestock researchers and Extension specialists to connect with a wide audience of producers, Extension personnel, colleagues, and industry partners. Online platforms that provide a space for Extension personnel to deliver timely information and digital resources have been critical for continuing producer education in today’s environment. This presentation in the thematic session on “Understanding the role of social media and digital resources in forage education and promotion” will focus on the role social media and digital resources play in Extension. There are a host of programmatic methods used because each method will reach a different type of audience

The challenge of the chiral Potts model

The chiral Potts model continues to pose particular challenges in statistical mechanics: it is ``exactly solvable'' in the sense that it satisfies the Yang-Baxter relation, but actually obtaining the solution is not easy. Its free energy was calculated in 1988 and the order parameter was conjectured in full generality a year later. However, a derivation of that conjecture had to wait until 2005. Here we discuss that derivation.Comment: 22 pages, 3 figures, 29 reference

Some comments on developments in exact solutions in statistical mechanics since 1944

Lars Onsager and Bruria Kaufman calculated the partition function of the Ising model exactly in 1944 and 1949. Since then there have been many developments in the exact solution of similar, but usually more complicated, models. Here I shall mention a few, and show how some of the latest work seems to be returning once again to the properties observed by Onsager and Kaufman.Comment: 28 pages, 5 figures, section on six-vertex model revise

General scalar products in the arbitrary six-vertex model

In this work we use the algebraic Bethe ansatz to derive the general scalar product in the six-vertex model for generic Boltzmann weights. We performed this calculation using only the unitarity property, the Yang-Baxter algebra and the Yang-Baxter equation. We have derived a recurrence relation for the scalar product. The solution of this relation was written in terms of the domain wall partition functions. By its turn, these partition functions were also obtained for generic Boltzmann weights, which provided us with an explicit expression for the general scalar product.Comment: 24 page