T E S S E R A C T


Start with a point. Make a copy of the point, and move it some distance away. Connect these points. We now have a segment. Make a copy of the segment, and move it away from the first segment in a new (orthogonal) direction. Connect corresponding points. We now have an ordinary square. Make a copy of the square, and move it in a new (orthogonal) direction. Connect corresponding points. We now have a cube. Make a copy and move it in a new (orthogonal, fourth) direction. Connect corresponding points. This is the tesseract. A tesseract has 16 vertices, 32 edges, 24 squares, and 8 cubes. What new (orthogonal, fourth) direction, you may ask. Well. . . any other direction! That is, to visualize the tesseract, there doesn't need to be a physical analogue of the fourth dimension. All you need is your imagination, and we hope you will enjoy this demonstration of just such an approach.
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



Still I Rise
I am a Phenomenal Woman
In Memoriam
How to Make a Tesseract
You Who Never Arrived.
Medicine and Sciences
Links
Tables Page
Frames Page
FractalsSwans
Butterflies
Hearts and Flowers