Learning to perceive the world in terms of four dimensions was the most challenging mental puzzle [of the
turn of the century]. Magazines like Scientific American sponsored contests to find explanations that could be easily
understood by the popular audience. The problem was that fourth-dimensinal consciousness could not be experienced
through the physical senses. Only the mind was capable of opening a frame of reference into this new realm of
comprehension.
Among those bringing logic and projective geometry to bear on the task was a New York architect named
Claude Bragdon (1866-1946). In an essay titled "Space and Hyperspace," he taught readers how to draw their own
mental portals into the fourth dimension called Tesseracts.(1) The resulting graphic device was the analog of a
fourth dimensional cube. Seen in the two-dimensional rendering of a line drawing, there were four squares set
equidistantly to one another. This implied a fifth yet invisible square, whose interior was a cross of open space
between the original four visible squares. The image represented a shift from external to internal perceptions of reality.
Bragdon called this a "higher level", explaining that the relationship of a higher space to a lower one is always an inner
state of recognition.(2)
To Purcell and Elmslie, the conceptual mechanics involved in this symbol perfectly described the process of unfolding
organic design. Whether drawn outright or indicated typographically by a pair of joined colons [::], the device appeared
on their presentation drawings, correspondence, advertising brochures, and in the issues of an architectural journal,
The Western Architect, which they designed to illustrate their work.
The Tesseract was the summa for all the geometric forms that played within their decorative designs, signifying the
creative process from which material objects crystallized. The tesseract declared that the physical, emotional, mental,
and spiritual elements of human consciousness interpenetrated in manifest unity at the moment of creation.

A Wrinkle in Time
Another explanation
Yet Another explanation
Best explanation yet!
Rotatable Tesseract.
Rotatable Tesseract.
Stereoscopic view
Source of image

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