Abstract
In 1917 Einstein viewed the universe (at any instant in time) as a 3-sphere. This chapter concerns Einstein’s comments surrounding the 3-sphere as expressed within his book Ideas and Opinions
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
Einstein’s book as published by Dell Publishing Co., Inc., ISBN: 0-440-34150-7, Fifth Laurel printing — June 1981, Copyright © MCMLIV by Crown Publishers, Inc. Author Albert Einstein, Based on Mein Weltbild, edited by Carl Seelig, and other sources with New translations and revisions by Sonja Bargmann. The quote begins on page 237 in the Geometry and Experience section of Part Five: Contributions to Science.
- 2.
The quote appears in the Foreword by Albert Einstein at the beginning of Lincoln Barnett’s book The Universe and Dr. Einstein. Barnett’s book is a Mentor Book published by The New American Library of World Literature, Inc. 501 Madison Avenue, New York 22, New York with Copyright 1948 by Harper & Brothers.
- 3.
To explain the projection of a 2-sphere into a plane Einstein uses the picture on page 283 of his book.
- 4.
Einstein also uses the words “Euclidean” and “non-Euclidean” to convey a distinction between geometries — Euclidean geometry is the geometry of human experience, i.e., the geometry of a line, a plane, or our visual 3-space that includes our usual “measurements.” Euclidean geometry is the geometry that Euclid documented circa 300 BC. In contradistinction, spherical geometry differs from Euclidean geometry as illustrated above: If you lived on the line, then to experience spherical geometry on the line both you and your “measuring rod” would expand as you moved away from the south pole. And you would not realize the expansion because you could not measure it!
- 5.
Einstein has a footnote at this point in his book. It reads as follows: This is intelligible without calculation — but only for the two-dimensional case — if we revert once more to the case of the disc on the surface of the sphere.
- 6.
Bing was a “President of the American Mathematical Society” and a world-class research mathematician who wrote extensively about 3-dimensional manifolds and the 3-sphere.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Lipscomb, S.L. (2014). Einstein and the 3-Sphere. In: Art Meets Mathematics in the Fourth Dimension. Springer, Cham. https://doi.org/10.1007/978-3-319-06254-9_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-06254-9_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-06253-2
Online ISBN: 978-3-319-06254-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)