Wilson line breaking and gauge coupling unification

We estimate the effect of threshold corrections coming from Wilson lines to gauge coupling unification in the weakly coupled heterotic string with orbifold compactification. By expressing the corrections in terms of an effective field theory calculation we are able to estimate the minimal threshold corrections in a realistic model without constructing the full string theory. Using this we show that the effect of the gauge boson Kaluza Klein excitations is systematically to reduce the string prediction for the unification scale. In the case of discrete Wilson lines the effect of the Wilson lines on both the gauge and matter sectors is fixed. We show that the combined effect of the gauge and matter threshold corrections of the Kaluza Klein excitations of the MSSM states can readily bring both the prediction for the unification scale and for the strong coupling constant into good agreement with experiment.Comment: 15 page

Aeolian activity in a Urewera catchment

Analyses of sedimentary deposits on the Otapora flat and adjacent flood plain areas of Whakatane River demonstrate that aeolian activity is important even in a humid (BB'r) forested Catchment. The importance of relief and wind conditions are shown. A tentative assessment of potential feral pest damage and increased sheetwash from a forested Urewera catchment is advanced

Kant on teaching philosophy

[Introduction] In 1765, Kant issued an Advertisement for the four lecture courses he would be delivering in the winter semester of 1765/66, on Metaphysics, Logic, Ethics, and Physical Geography (Kant 1905). Instead of merely outlining the course syllabuses, Kant prefaced the document with what would nowadays be called a ‘statement of teaching philosophy’. As far as I am aware, this is the only place where he explains his approach to teaching,2 and it is an approach which (apart from the first point below) is remarkably consistent with what professional educationalists consider to be best practice in the 21st century. In view of the radical nature of Kant’s ideas, it is surprising how little attention has been paid to them. John Ladd (1982) summarises the Advertisement in a general account of Kant as a teacher, derived largely from Vorländer’s biography. His main purpose is to show that Kant’s approach to the teaching of philosophy presupposes that philosophy is very different from other disciplines, in that it fosters the independence of thought which is central both to the concept of enlightenment and to the concept of the autonomy of the will in ethics. Eugene Kelly (1989) provides a complete translation of the Advertisement into English, and prefaces it with a few brief remarks. Interestingly, Kelly is almost entirely negative about the Advertisement. He says that if Kant had submitted it for publication in the APA Newsletter on Teaching Philosophy (of which Kelly was editor at the time), he would have rejected it, on the grounds that it was too long-winded, it contained too much technical terminology and it said too little about the content of his lectures. Its only saving grace, according to Kelly, was that Kant showed a genuine concern for his students. The articles by Ladd and Kelly are the only two writings I have been able to find which discuss Kant’s Advertisement in any detail. In what follows, I shall give a much more sympathetic account of Kant’s approach to teaching philosophy, and relate what he says to current theories of good practice in university education

The PRS subject centre: four years on

At the AAPT International Workshop/Conference at Alverno College in 2000, I was invited to give a presentation on the recently established Philosophical and Religious Studies Centre of the Learning and Teaching Support Network. My presentation was published in AAPT News, 24/1, Spring 2001, pp.3–8. In the UK, there had never previously been a forum for publishing articles or conducting discussions specifically concerned with teaching philosophy. In those early days, I naively expected that there would be scores of philosophers scattered throughout the UK eager to share their ideas about teaching philosophy, and to publicise their innovative methods of teaching and assessment. This turned out not to be the case. Although we now have a growing resource of articles and reviews in our journal Discourse and on our website, these are mostly the outcomes of projects we have funded with grants of up to about $5k. We still have difficulty persuading people to write for us voluntarily, or to attend workshops and conferences — much more difficulty than subject centres covering other disciplines. It is worth considering possible reasons for this: (Continues..

Plagiarism in philosophy: prevention better than cure

[Introduction] Plagiarism more common than thought in student essays’ would make a good headline. Recent research suggests that students admit to much more plagiarism and other forms of cheating than teachers generally suspect, and it is widely believed that the problem is increasing as a result of the internet. The solution is to use a range of techniques to get the thought back into student essay writing, and to take more active steps to spot when this has not happened

One-Dimensional Diffusions That Eventually Stop Down-Crossing

Consider a diffusion process corresponding to the operator $L=\frac12a\frac{d^2}{dx^2}+b\frac d{dx}$ and which is transient to $+\infty$. For $c>0$, we give an explicit criterion in terms of the coefficients $a$ and $b$ which determines whether or not the diffusion almost surely eventually stops making down-crossings of length $c$. As a particular case, we show that if $a=1$, then the diffusion almost surely stops making down-crossings of length $c$ if $b(x)\ge\frac1{2c}\log x+\frac\gamma c\log\log x$, for some $\gamma>1$ and for large $x$, but makes down-crossings of length $c$ at arbitrarily large times if $b(x)\le\frac1{2c}\log x+\frac1c\log\log x$, for large $x$