Transreal logical space of all propositions

Transreal numbers provide a total semantics containing classical truth values, dialetheaic, fuzzy and gap values. A paraconsistent Sheffer Stroke generalises all classical logics to a paraconsistent form. We introduce logical spaces of all possible worlds and all propositions. We operate on a proposition, in all possible worlds, at the same time. We define logical transformations, possibility and necessity relations, in proposition space, and give a criterion to determine whether a proposition is classical. We show that proofs, based on the conditional, infer gaps only from gaps and that negative and positive infinity operate as bottom and top values.

Transmathematical basis of infinitely scalable pipeline machines

We describe infinitely scalable pipeline machines with perfect parallelism, in the sense that every instruction of an inline program is executed, on successive data, on every clock tick. Programs with shared data effectively execute in less than a clock tick. We show that pipeline machines are faster than single or multi-core, von Neumann machines for sufficiently many program runs of a sufficiently time consuming program. Our pipeline machines exploit the totality of transreal arithmetic and the known waiting time of statically compiled programs to deliver the interesting property that they need no hardware or software exception handling.

Boundaries and Bridges: the influence of James Cooksey Culwick on the development of the teaching and learning of music in nineteenth century Ireland

James Cooksey Culwick (1845-1907) was born in England. Trained as chorister and organist in Lichfield Cathedral, he moved to Ireland at twenty- one and remained until his death in 1907. Although his reputation as scholar, musician and teacher was acknowledged widely during his lifetime - he received an honorary doctorate from University of Dublin (1893) - little is known about the contribution he made to music education. This paper addresses this gap in the literature and argues that it was Culwick's singular achievement to pay attention to music pedagogy at secondary level, by recognizing that music could be seen as a serious career option for girls, and by providing resources for teachers which emphasised the development of an 'art-feeling' in pupils of all abilities. In addition, he considered Irish music as an art which had significance as music first, and Irish music second, and advocated a 'laudable tolerance' for opposing views on matters of cultural identity to Ireland at the end of the nineteenth century.