Inventing the Fourth Dimension

Ever since the latter part of the 19th century, the fourth dimension has been invoked in esoteric literature as an explanation for otherwise inexplicable phenomena such as ghosts and spirits (the picture on the left is taken from a book published in 1928 called Theosophy and the Fourth Dimension, by Alexander Horne). During the same period, mainstream scientists and mathematicians have embodied the fourth dimension (and other higher spatial dimensions) in various theories of cosmology and fundamental physics. As a general rule (despite what New Agers would like you to believe) there is very little common ground between the esoteric and scientific theories. But I’ve just discovered that the two “traditions” can arguably be traced back to a common origin in the 1870s.



There is a fascinating article in the latest issue of Astronomy and Geophysics (the monthly magazine of the Royal Astronomical Society) about a little-known 19th century astrophysicist named Karl Zöllner. If you look him up on Wikipedia you could be forgiven for thinking he was just a minor player on the fringes of science, who was only interested in things like optical illusions and spiritualism. But in fact he was a prolific mainstream scientist, who did innovative work in the fields of astrophotometry, instrument design, electrodynamics, solar physics and the theory of comets. He was the first person to consider that the three-dimensional space that we live in is not “flat” Euclidean space, but is curved on a cosmological scale. The idea of non-Euclidean geometry had been around as an abstract concept since earlier in the 19th century, but Zöllner—in 1872—was the first person to suggest the Universe itself was non-Euclidean. He was led to this conclusion as the simplest explanation of a well-known but puzzling astronomical observation known as Olbers’ Paradox.



What does “curved space” mean? The easiest way to visualize it is by analogy with a curved two-dimensional surface, such as that of a sphere. A normal two-dimensional surface is a flat sheet, which is Euclidean because the angles of any triangle drawn on it always add up to 180°. On the other hand, the apparently two-dimensional surface of a sphere is non-Euclidean because the angles of a triangle add up to more than 180°. This is because the sphere exists in a higher dimensional space—three dimensions—which is Euclidean. By analogy, Zöllner imagined that the universe was a four-dimensional Euclidean hypersphere that gives the illusion of being a curved, non-Euclidean three dimensional space because we cannot directly perceive the fourth spatial dimension that he believed to exist.



In 1877, a few years after Zöllner proposed his theory of curved space, he met William Crookes—a British chemist who had recently become interested in the scientific study of spiritualism. Zöllner quickly became convinced of the reality of “spirits”, but rather than believing them to be the souls of dead people he theorized that they were visitors from the fourth spatial dimension. He expounded this theory in an 1878 book entitled Transcendental Physics, which aimed to encompass both the physical and spiritual worlds with a single theory of four-dimensional space.





Unfortunately for Zöllner, the psychic medium he chose to carry out his spiritualist experiments with was a man named Henry Slade, who was subsequently exposed as a fraud who was adept at sleight-of-hand tricks. In one of Zöllner’s experiments (pictured on the right), Slade’s “spirits” allegedly tied knots in a string that was sealed at both ends. Zöllner interpreted this as evidence that the spirits could move freely in a fourth spatial dimension.



Although Zöllner’s theories of the fourth dimension are almost forgotten today, they preceded the work of Charles Howard Hinton: Pioneer of the Fourth Dimension (mentioned recently in my post on Esoteric Mathematics) by several years. And as I said at the beginning, they can be seen as the ancestor of all subsequent New Age theories about “extradimensional entities”, as well as mainstream cosmological theories involving higher spatial dimensions.

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