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Geoff Lehman

    Geoff Lehman

    The Parthenon and Liberal Education seeks to restore the study of mathematics to its original place of prominence in the liberal arts. To build this case, Geoff Lehman and Michael Weinman turn to Philolaus, a near contemporary of... more
    The Parthenon and Liberal Education seeks to restore the study of mathematics to its original place of prominence in the liberal arts. To build this case, Geoff Lehman and Michael Weinman turn to Philolaus, a near contemporary of Socrates. The authors demonstrate the influence of his work involving number theory, astronomy, and harmonics on Plato’s Republic and Timaeus, and outline its resonance with the program of study in the early Academy and with the architecture of the Parthenon. Lehman and Weinman argue that the Parthenon can be seen as the foremost embodiment of the practical working through of mathematical knowledge in its time, serving as a mediator between the early reception of Ancient Near-Eastern mathematical ideas and their integration into Greek thought as a form of liberal education, as the latter came to be defined by Plato and his followers. With its Doric architecture characterized by symmetria (commensurability) and harmonia (harmony; joining together), concepts explored contemporaneously by Philolaus, the Parthenon engages dialectical thought in ways that are of enduring relevance for the project of liberal education.
    Titian’s Allegory of Marriage depicts an equivocal moment of intimacy through a network of visual and tactile interactions. This dialectic of touch and vision evokes a range of embodied experiences that, through empathetic identification,... more
    Titian’s Allegory of Marriage depicts an equivocal moment of intimacy through a network of visual and tactile interactions. This dialectic of touch and vision evokes a range of embodied experiences that, through empathetic identification, also implicate the viewer and define a phenomenology of viewer response. Furthermore, the interplay of optical and haptic values invokes Titian’s painterly practice itself, mediating between the picture as window and the brushstroke as touch. The interpretive possibilities of this dialectic culminate in the crystal sphere, a discrete object receptive to human touch that also relates abstractly to the scattering of light in space, suggesting a more radical phenomenology of intimacy that transcends the limitations of bodily Gestalt and the separation between picture and viewer alike.

    Keywords:
    Intimacy, phenomenology, linear and painterly, the oneiric in art, viewer response
    Pieter Bruegel the Elder and William Shakespeare each create profoundly philosophical works through the representation of a broad range of human perspectives within a shared world. In Bruegel's pictures (the Procession to Calvary, the... more
    Pieter Bruegel the Elder and William Shakespeare each create profoundly philosophical works through the representation of a broad range of human perspectives within a shared world. In Bruegel's pictures (the Procession to Calvary, the Labors of the Months, and others), the variety of his figures' literal viewpoints suggests an equally wide range of physical, social, affective, and intellectual experiences. And the coordination of these viewpoints with each other, as well as their embeddedness in their spatial and landscape context, can define an epistemology (perspective as cognitive metaphor), an ethics (viewpoint in relation to compassion), or even a metaphysics (engaging the presence of the infinite in the physical world). Shakespeare's descriptions of perspective are equally charged with metaphoric resonances, creating something like Bruegelian painting in words. Perspectival pluralism in Shakespeare often suggests, in the epistemic register, the interplay of truth and deception (Richard II, Twelfth Night), while the coordination of (in)commensurable viewpoints raises questions of justice and of compassion (Twelfth Night, The Winter's Tale) analogous to those in Bruegel. In some of his later plays (King Lear, Cymbeline, The Winter's Tale), Shakespeare's ekphrastic descriptions of perspective views take on a phenomenological character, as the literal (optical) and metaphorical (cognitive, affective) aspects of this kind of looking are conceived in terms of an embodied experience with precise physiological effects. This phenomenology of perspective, a human encounter with the infinite through looking, metaphorically articulates moments of extreme affect in a style that is also, paradoxically, elaborately artificial, offering commentary on Shakespeare's art itself.
    This paper argues for reconsideration of two generally held views in the historiography of Greek mathematics, a narrow one about fourth and fifth-century Greek mathematics and a more general one about the continuity between Greek and... more
    This paper argues for reconsideration of two generally held views in the historiography of Greek mathematics, a narrow one about fourth and fifth-century Greek mathematics and a more general one about the continuity between Greek and earlier near Eastern mathematics. The narrower view called into question, owed to Knorr 1975, holds that two mathematical notions crucial for the development of Greek mathematics-(1) continuous proportion (and its non-reducible-to-a-unit-or-multiples-of-a-unit correlate, anthyphairesis) and (2) the reflective awareness of incommensurability owing to a misfit between magnitudes and multitudes-were understood for the first time in the mathematics of the first decades of the fourth century. Against this view, we propose to show that the Parthenon's construction displays at least a foundational comprehensive understanding of both of these mathematical ideas. Building on this narrower reconsideration, we further claim that the specific manner, which can be called 'algorithmic-problematic', of the Parthenon's engagement with these themes gives us reason to believe that the relationship of fifth-century Greek mathematics to its near Eastern precedents shows more continuity than is generally held.