Justice as Self-Transmitting Power and Just Acts in Republic 4

In his influential paper “A Fallacy in Plato’s Republic,” David Sachs charged Plato with committing a fallacy of irrelevancy. Plato’s Socrates is asked to show that justice understood as acting in conformity with conventional morality, so-called vulgar justice, is beneficial to the just person. Socrates actually demonstrates something else, namely that psychic justice, a state of internal harmony between parts of the soul, is beneficial to its possessor. A generation of Plato scholarship has reacted to Sachs’ reading of the Republic by using discussions of moral psychology and education elsewhere in the dialogue to bridge the gap between psychic justice and a conception of justice centered on the performance of moral actions. This paper presents a different way of responding to Sachs’ paper. Republic 4 contains not two but only one conception of justice, according to which justice is a power in the soul of individuals. Justice is a power whose nature it is to transmit itself to cities which achieve civic justice as they are formed by just individuals. Just actions which promote the good of others are the medium by which justice transmits itself to cities

Eudaimonism and the Demands of Justice

The ancient eudaimonists were not misguided when they gave a prominent place to the human function in their ethical theory. Most modern reconstructions of eudaimonism do not employ the human function in this way. Though this gives them the appearance of being more streamlined and plausible, they fail to unify a life which respects the demands of justice. It is evident that in the Republic and other ancient ethical works humans are presented as acting out of concern for the good of others. They show respect for justice and act from altruistic motivation, and this is one source of value for a human life according to eudaimonism. But the question arises of whether this is the only sort of value a human life can have. Surely not; it matters as well whether a human life is flourishing and happy. How do these two aspects or areas of a human life combine? To present actions done from altruistic motivation as existing in splendid isolation from the actions done for the sake of happiness threatens to split a life and to fracture its overall structure. The better way is to propose that all actions, both those motivated by altruistic concerns and those motivated by the desire for happiness, are performed for the sake of happiness, with the caveat that the first set of actions need not be performed with any intention of achieving happiness. This respects the fact of altruistic motivation while integrating that motivation into the fabric of a happy life. But to achieve this unity, we must take seriously the notion of the human function and make room for it within the structure of eudaimonism. Only when we use the human function to develop a version of eudaimonism is it possible to describe the demands of justice as categorical, as making unconditioned demands on our practical rationality, and also to describe actions performed to meet these demands as being oriented to happiness as their end

Studying Mathematics for the Sake of the Good

In the Republic, Socrates describes the good as the end of all human action: “Every soul pursues the good and does what it does for its sake. It divines that the good is something but it is perplexed and cannot adequately grasp what it is or acquire the sort of stable beliefs it has about other things, and so it misses the benefits, if any, that even those other things may give.” I wish to examine how humans act for the sake of the good in the sections of the Republic following this passage. Human action is oriented toward the good in several distinct ways, one of which is illustrated by the procedures of mathematics in pursuing knowledge: without intending to achieve insight into forms such as the square itself, we can act for the sake of achieving this end

Impacts of Sea-Level Rise and Thin-Layer Deposition on Salt Marsh Elevation Dynamics in New Hampshire

The survival of salt marshes depends largely on their ability to build in elevation, thereby preventing increases in flooding due to sea-level rise, but the rate of marsh elevation gain depends on processes that are not well-understood, i.e. belowground productivity, sedimentation, and subsidence. The application of sediment to the marsh surface (thin-layer deposition) is a potential mitigation tool for increased flooding, but its effects on plant growth and elevation gain are understudied, especially in New England marshes. A marsh organ experiment was constructed and installed in the field to examine the effects of tidal flooding and thin-layer deposition on productivity. Feldspar Marker Horizons (MHs) were placed in the marsh to determine the effect of flooding on sedimentation rates and Surface Elevation Tables (SETs) were measured to determine elevation change. Without sediment addition, we found that belowground productivity decreased linearly as flooding increased for both Spartina patens and Spartina alterniflora. Belowground volume of S. alterniflora at the top elevation was around 4 times the amount of the lowest, most-flooded elevation. Planted treatments subsided significantly less than unplanted controls, indicating the importance of plants in reducing marsh subsidence. MHs showed that sedimentation decreased as elevation and distance from the creek increased, and SET measurements indicated high marshes in the Great Bay of New Hampshire are losing elevation relative to sea level at an average rate of 2.1 mm/year. This high marsh accretion deficit, combined with low sedimentation rates and a predicted decrease in productivity due to sea-level rise suggest that S. patens and other high marsh species will be replaced by S. alterniflora as flooding increases. Thin-layer deposition may help to slow this conversion, but our results show no significant effect of sediment addition on NPP in either S. patens or S. alterniflora over a 2 month period. More studies are needed to determine the long-term effects of thin-layer deposition in New England

Illumination waveform optimization for time-of-flight range imaging cameras

Time-of-flight range imaging sensors acquire an image of a scene, where in addition to standard intensity information, the range (or distance) is also measured concurrently by each pixel. Range is measured using a correlation technique, where an amplitude modulated light source illuminates the scene and the reflected light is sampled by a gain modulated image sensor. Typically the illumination source and image sensor are amplitude modulated with square waves, leading to a range measurement linearity error caused by aliased harmonic components within the correlation waveform. A simple method to improve measurement linearity by reducing the duty cycle of the illumination waveform to suppress problematic aliased harmonic components is demonstrated. If the total optical power is kept constant, the measured correlation waveform amplitude also increases at these reduced illumination duty cycles. Measurement performance is evaluated over a range of illumination duty cycles, both for a standard range imaging camera configuration, and also using a more complicated phase encoding method that is designed to cancel aliased harmonics during the sampling process. The standard configuration benefits from improved measurement linearity for illumination duty cycles around 30%, while the measured amplitude, hence range precision, is increased for both methods as the duty cycle is reduced below 50% (while maintaining constant optical power)

Proof of concept of diffuse optical tomography using time-of-flight range imaging cameras

Diffuse optical tomography is an optical technique to create 3-dimensional images of the inside of highly scattering material. Research groups around the world have been developing imaging systems using various source-detector arrangements to determine optical properties of biological tissue with a focus on medical applications. In this paper we investigate whether a range imaging camera can be used as a detector array. We used time-of-flight range imaging cameras instead of the conventional source-detector array used by others. The results provided in this paper show reconstructed images of absorption and reduced scattering of an object submerged in a tissue simulating phantom. Using the ranging camera XZ422 Demonstrator and the NIRFAST software package, we reconstructed 2D images of a 6 mm metal rod submerged in the centre of a 5 cm deep tank filled with 1% IntralipidTM. We have shown for the first time that range imaging cameras can replace the traditional detectors in diffuse optical tomography

Development of a Full-Field Time-of-Flight Range Imaging System

A full-field, time-of-flight, image ranging system or 3D camera has been developed from a proof-of-principle to a working prototype stage, capable of determining the intensity and range for every pixel in a scene. The system can be adapted to the requirements of various applications, producing high precision range measurements with sub-millimetre resolution, or high speed measurements at video frame rates. Parallel data acquisition at each pixel provides high spatial resolution independent of the operating speed. The range imaging system uses a heterodyne technique to indirectly measure time of flight. Laser diodes with highly diverging beams are intensity modulated at radio frequencies and used to illuminate the scene. Reflected light is focused on to an image intensifier used as a high speed optical shutter, which is modulated at a slightly different frequency to that of the laser source. The output from the shutter is a low frequency beat signal, which is sampled by a digital video camera. Optical propagation delay is encoded into the phase of the beat signal, hence from a captured time variant intensity sequence, the beat signal phase can be measured to determine range for every pixel in the scene. A direct digital synthesiser (DDS) is designed and constructed, capable of generating up to three outputs at frequencies beyond 100 MHz with the relative frequency stability in excess of nine orders of magnitude required to control the laser and shutter modulation. Driver circuits were also designed to modulate the image intensifier photocathode at 50 Vpp, and four laser diodes with a combined power output of 320 mW, both over a frequency range of 10-100 MHz. The DDS, laser, and image intensifier response are characterised. A unique method of measuring the image intensifier optical modulation response is developed, requiring the construction of a pico-second pulsed laser source. This characterisation revealed deficiencies in the measured responses, which were mitigated through hardware modifications where possible. The effects of remaining imperfections, such as modulation waveform harmonics and image intensifier irising, can be calibrated and removed from the range measurements during software processing using the characterisation data. Finally, a digital method of generating the high frequency modulation signals using a FPGA to replace the analogue DDS is developed, providing a highly integrated solution, reducing the complexity, and enhancing flexibility. In addition, a novel modulation coding technique is developed to remove the undesirable influence of waveform harmonics from the range measurement without extending the acquisition time. When combined with a proposed modification to the laser illumination source, the digital system can enhance range measurement precision and linearity. From this work, a flexible full-field image ranging system is successfully realised. The system is demonstrated operating in a high precision mode with sub-millimetre depth resolution, and also in a high speed mode operating at video update rates (25 fps), in both cases providing high (512 512) spatial resolution over distances of several metres