The universe is shaped like a yarmulke

Apparently, the space-time continuum of the universe can be visualized as a giant yarmulke, from book Steinmetz, Charles Proteus. (1923). Four Lectures on Relativity and Space (First ed). New York, New York: McGraw-Hill Book Company.

Figure 34: Two-Dimensional Analogue of the Universe:

and the footnote on p. 120:

Usually, physicists use the metaphor of a trampoline or a foam mattress to help people visualize the space time continuum, from the PBS NOVA (funded by the people Democrats consider evil: the Koch brothers!) documentary "The Elegant Universe" hosted by Brian Greene:





Not certain I agree with the Steinmetz's glib paraphrase of physics, p. 119:

"The relativity theory has reconfirmed the law of the conservation of energy, but has denied the law of conservation of matter by showing matter as kinetic energy"

People at the University of Colorado seem to share my ambivalence of Dr. Steinmetz's dubious paraphrase in their tutorial on "Mass and Energy Conservation in Nuclear Decay"

Encyclopedia Britannica further clarifies in their article "Principles of physical science :CONSERVATION OF MASS-ENERGY" by Sir A. Brian Pippard:

"Neither of two separate conservation laws, that of energy and that of mass (the latter particularly the outcome of countless experiments involving chemical change), is in this view perfectly true, but together they constitute a single conservation law, which may be expressed in two equivalent ways—conservation of mass, if to the total energy E is ascribed mass E/c², or conservation of energy, if to each mass m is ascribed energy mc²."

@slothrop23 @Lotus_F1Team how's that? pic.twitter.com/OEAZuvIME7
— L&T Motorsport (@LTMotorsportss) January 27, 2015

Steinmetz seems to preemptively exonerate himself in his introduction for any and all scientific and mathematical inaccuracies on page V:

Not to be rude to Dr. Steinmetz, but this hand waving seems something of a cop out.

Focusing on the aesthetics versus mathematics of Steinmetz's book, a number of the stereoscopic figures:

Such as Figure 22: Bent Euclidean Two-space:

Figure23: Elliptic Two-space:

Especially Figure 23, reminded me of Paul Klee paintings like his Twittering Machine:

or The mask with the little flag:

or Dawn One:

or Bust of a Child:

Figure 27: Projective Geometry in Elliptic Two-space:

Figure 28: Projective Geometry in Bent Elliptic Two-space:

Figure 24: Hyperbolic Two-space:

Figure 26: Projective Geometry in Bent Euclidean Two-space: