“Space is not the vague and undetermined medium which Kant imagined; if purely and absolutely homogeneous, it would be of no use, and could not be grasped by the mind. Spatial representation consists essentially in a primary coordination of the data of sensuous experience. But this coordination would be impossible if the parts of space were qualitatively equivalent, if they were really interchangeable.”

— Émile Durkheim , book The Elementary Forms of the Religious Life

Source: The Elementary Forms of the Religious Life, 1912, p. 10

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Émile Durkheim 43

French sociologist (1858-1917) 1858–1917

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“Is the position tenable, that certain phenomena, possible in Euclidean space, would be impossible in non-Euclidean space, so that experience, in establishing these phenomena, would directly contradict the non-Euclidean hypothesis? For my part I think no such question can be put. To my mind it is precisely equivalent to the following, whose absurdity is patent to all eyes: are there lengths expressible in meters and centimeters, but which can not be measured in fathoms, feet, and inches, so that experience, in ascertaining the existence of these lengths, would directly contradict the hypothesis that there are fathoms divided into six feet?”

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“O'Keefe… argued that many forms of explicit memory (for example, memory for people and objects) use spatial coordinates… we typically remember people and events in a spatial context.”

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Context: A large part of mathematics which becomes useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so. By and large it is uniformly true in mathematics that there is a time lapse between a mathematical discovery and the moment when it is useful; and that this lapse of time can be anything from 30 to 100 years, in some cases even more; and that the whole system seems to function without any direction, without any reference to usefulness, and without any desire to do things which are useful.

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“Architecture is treated as crystallisation; sculpture, as the organic modelling of the material in its sensuous and spatial totality; painting, as the coloured surface and line; while in music, space, as such, passes into the point of time possessed of content within itself, until finally the external medium is in poetry depressed into complete insignificance.”

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Die Architektur ist dann die Kristallisation, die Skulptur die organische Figuration der Materie in ihrer sinnlich-räumlichen Totalität; die Malerei die gefärbte Fläche und Linie; während in der Musik der Raum überhaupt zu dem in sich erfüllten Punkt der Zeit übergeht; bis das äußere Material endlich in der Poesie ganz zur Wertlosigkeit herabgesetzt ist.
Part III https://www.marxists.org/reference/archive/hegel/works/ae/ch03.htm
Lectures on Aesthetics (1835)

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Émile Durkheim 43

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