Current theorising in the area of cognitive arithmetic suggests that simple arithmetic knowledge is stored in memory and accessed in the same way as word knowledge i.e., it is stored in a network of associations, with simple facts retrieved automatically from memory. However, to date, the main methodologies that have been employed to investigate automaticity in simple arithmetic processing (e.g., production and verification) have produced a wide variety of difficulties in interpretation. In an attempt to address this, the present series of investigations utilised a numerical variant of the well established single word semantic priming paradigm that involved the presentation of problems as primes (e.g., 2 + 3) and solutions as targets (e.g., 5), as they would occur in a natural setting. Adult university students were exposed to both addition and multiplication problems in each of three main prime target relationship conditions, including congruent (e.g., 2 + 3 and 5), incongruent (e.g., 2 + 3 and 13), and neutral conditions (X + Y and 5). When combined with a naming task and the use of short stimulus onset asynchronies (SOAs), this procedure enabled a more valid and reliable investigation into automaticity and the cognitive mechanisms underlying simple arithmetic processing. The first investigation in the present series addressed the question of automaticity in arithmetic fact retrieval, whilst the remaining investigations examined the main factors thought to influence simple arithmetic processing i.e., skill level, surface form, problem type and split. All factors, except for problem type, were found to influence processing in the arithmetic priming paradigm. For example, the results of all five investigations were consistent in revealing significant facilitation in naming congruent targets for skilled participants, following exposure to Arabic digit primes at the short SOA. Accordingly, the facilitation was explained in terms of the operation of an automatic spreading activation mechanism. Additionally, significant inhibitory effects in incongruent target naming were identified in skilled performance in all of the studies in the present series of investigations. Throughout the course of these investigations, these effects were found to vary with operation, surface form and SOA, and in the final investigation, the level of inhibition was found to vary with the split between the correct solution and the incongruent target. Consequently, a number of explanations were put forward to account for these effects. In the first two investigations, it was suggested that the inhibitory effects resulted from the use of a response validity checking mechanism, whilst in the final investigation, the results were more consistent with the activation of magnitude representations in memory (this can be likened to Dehaene’s, 1997, ‘number sense’). In contrast, the results of the third investigation led to the proposal that for number word primes, inhibition in processing results from the activation of phonological representations in memory, via a reading based mechanism. The present series of investigations demonstrated the utility of the numerical variant of the single word semantic priming paradigm for the investigation of simple arithmetic processing. Given its capacity to uncover the fundamental cognitive mechanisms at work in simple arithmetic operations, this methodology has many applications in future research.

Current theorising in the area of cognitive arithmetic suggests that simple arithmetic knowledge is stored in memory and accessed in the same way as word knowledge i.e., it is stored in a network of associations, with simple facts retrieved automatically from memory. However, to date, the main methodologies that have been employed to investigate automaticity in simple arithmetic processing (e.g., production and verification) have produced a wide variety of difficulties in interpretation. In an attempt to address this, the present series of investigations utilised a numerical variant of the well established single word semantic priming paradigm that involved the presentation of problems as primes (e.g., 2 + 3) and solutions as targets (e.g., 5), as they would occur in a natural setting. Adult university students were exposed to both addition and multiplication problems in each of three main prime target relationship conditions, including congruent (e.g., 2 + 3 and 5), incongruent (e.g., 2 + 3 and 13), and neutral conditions (X + Y and 5). When combined with a naming task and the use of short stimulus onset asynchronies (SOAs), this procedure enabled a more valid and reliable investigation into automaticity and the cognitive mechanisms underlying simple arithmetic processing. The first investigation in the present series addressed the question of automaticity in arithmetic fact retrieval, whilst the remaining investigations examined the main factors thought to influence simple arithmetic processing i.e., skill level, surface form, problem type and split. All factors, except for problem type, were found to influence processing in the arithmetic priming paradigm. For example, the results of all five investigations were consistent in revealing significant facilitation in naming congruent targets for skilled participants, following exposure to Arabic digit primes at the short SOA. Accordingly, the facilitation was explained in terms of the operation of an automatic spreading activation mechanism. Additionally, significant inhibitory effects in incongruent target naming were identified in skilled performance in all of the studies in the present series of investigations. Throughout the course of these investigations, these effects were found to vary with operation, surface form and SOA, and in the final investigation, the level of inhibition was found to vary with the split between the correct solution and the incongruent target. Consequently, a number of explanations were put forward to account for these effects. In the first two investigations, it was suggested that the inhibitory effects resulted from the use of a response validity checking mechanism, whilst in the final investigation, the results were more consistent with the activation of magnitude representations in memory (this can be likened to Dehaene’s, 1997, ‘number sense’). In contrast, the results of the third investigation led to the proposal that for number word primes, inhibition in processing results from the activation of phonological representations in memory, via a reading based mechanism. The present series of investigations demonstrated the utility of the numerical variant of the single word semantic priming paradigm for the investigation of simple arithmetic processing. Given its capacity to uncover the fundamental cognitive mechanisms at work in simple arithmetic operations, this methodology has many applications in future research.

This thesis makes a survey on conception of &ldquo / surface&rdquo / in the works of Peter Eisenman. In doing so, the concept of &ldquo / surface&rdquo / is discussed under three titles: &ldquo / Surface&rdquo / as an element of architectural vocabulary (as a formal element), as an analytical tool (as a grammar), and as a diagrammatic tool. Correspondingly, the thesis is intended to examine how &ldquo / surface&rdquo / is conceptualized and handled through the critical readings of Eisenman&rsquo / s writings, and projects are referred in order to support and visualize the discussions. In this context, Eisenman&rsquo / s dissertation, The Formal Basis of Modern Architecture (1963), reveals the definition of architectural surface in relation to the architectural language that is proposed by him. Through the formal analysis of Giuseppe Terragni&rsquo / s building, Casa Guiliani Frigerio, he utilizes surface as an analytical tool. Considering design processes of his projects, as discussed in the book Diagram Diaries (1999), surface becomes a dominant tool for generating architectural form. As a result, in this thesis, surface is evaluated in various aspects (as a formal, analytical and diagrammatic tool) that are essential for understanding of architectural form. In the case of Eisenman, its significance dominates the way of developing his architecture.

Ultraprecision single point diamond turning is required to produce parts with sub-nanometer surface roughness and sub-micrometer surface profiles tolerances. These parts have applications in the optics industry, where tight form accuracy is required while achieving high surface finish quality. Generally, parts can be polished to achieve the desired finish, but then the form accuracy can easily be lost in the process rendering the part unusable. Currently, most mid to low spatial frequency surface finish errors are inspected offline. This is done by physically removing the workpiece from the machining fixture and mounting the part in a laser interferometer. This action introduces errors in itself through minute differences in the support conditions of the over constrained part on a machine as compared to the mounting conditions used for part measurement. Once removed, the fixture induced stresses and the part’s internal residual stresses relax and change the shape of the generally thin parts machined in these applications. Thereby, the offline inspection provides an erroneous description of the performance of the machine. This research explores the use of a single, high resolution, capacitance sensor to quickly and qualitatively measure the low to mid spatial frequencies on the workpiece surface, while it is mounted in a fixture on a standard ultraprecision single point diamond turning machine after a standard facing operation. Following initial testing, a strong qualitative correlation exists between the surface profiling on a standard offline system and this online measuring system. Despite environmental effects and the effects of the machine on the measurement system, the capacitive system with some modifications and awareness of its measurement method is a viable option for measuring mid to low spatial frequencies on a workpiece surface mounted on an ultraprecision machine with a resolution of 1nm with an error band of ±5nm with a 20kHz bandwidth. / Thesis / Master of Applied Science (MASc)