What do we know… of the world and the universe about us? Our means of receiving impressions are absurdly few, and our notions of surrounding objects infinitely narrow. We see things only as we are constructed to see them and can gain no idea of their absolute nature. With five feeble senses we pretend to comprehend the boundlessly complex cosmos. (H.P. Lovecraft, From Beyond, 1920)
- “Notes on the Fourth Dimension”, Public Domain Review. ~ This somewhat garbled introduction has the advantage of laying the ground and situating the fourth dimension in a wider cultural context, but fails to explain it. The links to Hinton’s works and illustrations are useful, but handle with care.
- “What is the Fourth Dimension?” (1884). ~ CH Hinton’s seminal “scientific romance”. In the words of one critic, it tries “to imagine and describe two-dimensional beings existing in a two dimensional space (that is, on a plane), as a way of helping us envision how there might be a space of spaces beyond our own perceivable three dimensions.”1
- “Speculations on the Fourth Dimension” (Dover, 1980) a selection of C.H. Hinton’s works.
- “Before Einstein: The Fourth Dimension in Fin-de-Siècle Literature and Culture”, Elizabeth L. Throesch (Anthem Press, 2017). ~ An interesting study of the fourth dimension an its wider aesthetic implications.
- The Annotated Flatland: A Romance of Many Directions, Edwin A. Abbott (Basic Books, 2008). ~ A wonderfuly dense and erudite annotated version of the popular geometrical novel by Abbott.
- Genealogía (1929), Felisberto Hernández. ~ An unexpected addition to this reading list is a short story by the Uruguayan writer Felisberto Hernández. It is, I must add, a masterful and perfect short story. I read —and was flabbergasted— by this little geometrical fiction many years ago, and while its geometry is entirely Euclidean (just as Abbott’s Flatlands and Hinton’s A Plane World, in any case) it’s clear that this story, published in 1929, was inspired by Hinton’s “scientific romances” and explores, in Felisberto’s characteristic succintness, the affectivity and pathos that can emerge from the movement of simple shapes along a line. But unlike Hinton’s bleak rejoinder that his conjectural two-dimensional human beings would be unable to experience “friendship or familiar intercourse”, Felisberto’s shapes experience something formaly akin to love, ecstasy and perfect communion.2
- A proper treatment of the influence of the fourth dimension in HP Lovecraft would require a lenghtier treatment, and in subsequent weeks I will add a list of his fiction that revolves around it. For now, I shall only quote this passage from “Notes on Writing Weird Fiction” (1937):
I chose weird stories because they suit my inclination best—one of my strongest and most persistent wishes being to achieve, momentarily, the illusion of some strange suspension or violation of the galling limitations of time, space, and natural law which for ever imprison us and frustrate our curiosity about the infinite cosmic space beyond the radius of our sight and analysis.
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Scott and Scott, The Love of Ruins, 100. ↩
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The difference is predicated on the possibility of two-dimensional shapes to behave, through purely two-dimensional means, as three-dimensional. Imagining a situation similar to Felisberto’s premise —two shapes moving along a line and crashing into one another— Hinton reflects: “The only way in which they can pass each other is by climbing over the other’s head,” and then concludes: “In this land no such thing as friendship or familiar interocurse between man and man is possible.” Genealogía, which start by refering the way in which a circle along a plane can in fact turn on its axis while remaining two-dimensional, devices another option: shapes can modulate their speed by changing their shape and, more importantly, shapes can fuse and even accomodate other shapes in their midsts. ↩