Invariant lengths using existing Special Relativity

A field of random space-time events exhibiting complete spatial-temporal randomness appears statistically identical to all observers. Boost invariant lengths naturally emerge when we examine fluctuation scales of this field such as the nearest neighbor distance. If we interpret Planck's length as the characteristic fluctuation scale of quantum gravity, its boost invariance can then be understood without modifying Special Relativity.Comment: 5 pages, no figure

Verdi’s six-fours and la parola scenica

Verdi’s operas display many non-normative six-four chords. The question for the opera analyst, however, is not only what occurs musically, but why it does. Is there a dramatic function being served by this mix of harmonic-intervallic instability? We discuss four types of non-normative six-fours in Verdi: the arrival, wonder, evasion, and dissolving. But, even as we individuate these types, we note that they are all similar in one regard: they are all linked to a crucial dramatic statement that Verdi termed la parola scenica, a textual-musical signal that makes a dramatic situation suddenly evident

A Single-armed Manta-board as a New Diver-controlled Planing Board and Its Use for Underwater Surveys

Due to inadequacies of previous underwater towing techniques and the special needs of a recent underwater survey, a modified mania-board technique was developed. With this new technique, the diver holds on to the manta-board with one arm; consequently, the board is referred to as a single-armed manta-board (sam-board). The sam-board proved inexpensive and highly maneuverable, allowing the divers to freely collect samples or record information. Through some experimenting with the board and changing some of the variables, such as rope lengths, towing speeds, etc., a highly efficient towing method can be achieved. Preplanning and strict diving safety procedures must, however, be implemented to assure efficiency. This paper presents the materials, guidelines for board construction, equipment, and preplanning and diving safety procedures necessary for the sam-board towing operation

Geodesic systems of tunnels in hyperbolic 3-manifolds

It is unknown whether an unknotting tunnel is always isotopic to a geodesic in a finite volume hyperbolic 3-manifold. In this paper, we address the generalization of this problem to hyperbolic 3-manifolds admitting tunnel systems. We show that there exist finite volume hyperbolic 3-manifolds with a single cusp, with a system of at least two tunnels, such that all but one of the tunnels come arbitrarily close to self-intersecting. This gives evidence that systems of unknotting tunnels may not be isotopic to geodesics in tunnel number n manifolds. In order to show this result, we prove there is a geometrically finite hyperbolic structure on a (1;n)-compression body with a system of core tunnels such that all but one of the core tunnels self-intersect.Comment: 19 pages, 4 figures. V2 contains minor updates to references and exposition. To appear in Algebr. Geom. Topo