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Full Description
To see objects that live in the fourth dimension we humans would need to add a fourth dimension to our three-dimensional vision. An example of such an object that lives in the fourth dimension is a hyper-sphere or "3-sphere." The quest to imagine the elusive 3-sphere has deep historical roots: medieval poet Dante Alighieri used a 3-sphere to convey his allegorical vision of the Christian afterlife in his Divine Comedy. In 1917, Albert Einstein visualized the universe as a 3-sphere, describing this imagery as "the place where the reader's imagination boggles. Nobody can imagine this thing." Over time, however, understanding of the concept of a dimension evolved. By 2003, a researcher had successfully rendered into human vision the structure of a 4-web (think of an ever increasingly-dense spider's web). In this text, Stephen Lipscomb takes his innovative dimension theory research a step further, using the 4-web to reveal a new partial image of a 3-sphere. Illustrations support the reader's understanding of the mathematics behind this process. Lipscomb describes a computer program that can produce partial images of a 3-sphere and suggests methods of discerning other fourth-dimensional objects that may serve as the basis for future artwork.
Contents
1. 3-Sphere.- 2. Dante's 3-Sphere Universe.- 3. Einstein and the 3-Sphere.- 4. Einstein's Universe.- 5. Images of S1 and S2.- 6. Four-Web Graph Paper.- 7. The Partial Picture.- 8. Generating the Hyper-sphere Art.- 9. Prelude to Chapters 10 and 11.- 10. Great 2-Spheres.- 11. Images of Great 2-Spheres.- Appendix 1.- Appendix 2.- Appendix 3. Inside S3 and Questions.- Appendix 4. Mathematics and Art.
