On Physiological, as Distinguished from Geometrical, Space.

We have already seen Ernst Mach (1838–1916) in the first volume of this collection, as a representative of positivist approaches to scientific knowledge. Here, we see a continuation of Mach’s ideas applied to the same kinds of concerns about space and geometry with which Helmholtz engaged in the last excerpt. Mach explores the concept of our visual space, the space in which our perceptions are found and which is given its structure by our subjective concepts of left, right, up, down, near, and far. He notes that this visual space “has but few properties in common with geometric space” (p. 150) – as, for instance, objects shrink and grow as they get closer to us or farther from us, and the apparent form of objects in the visual field sometimes radically belies their true shape. As Theodore Kneupper has noted, this is part of a broader concern with which Mach approached all these concepts: he “saw that the meanings of [‘space’ and ‘time’] are multiple, and carefully distinguished their diversity.” 1 While our different sense modalities don’t seem to take place in exactly the same space – the space of touch and of vision, for instance, seem to have different properties – Mach takes it that the demands of biological adaptation will ensure, at least, that these various “systems readily coalesce by association” (p. 154).

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