* In process, June 17, 2019*

**1. As a result of his work, everyone began thinking about the origins of the universe.**

In 1927 Georges Lemaître observed the expansion of the universe and wrote his landmark article about the origin of the universe. Applying a simple logic, he assumed at one time the universe had a single originating point. That concept of an *initial singularity*, for many readers, was an expression of his Jesuit history and the story of Genesis.

**2. The finite-infinite bridge should not have been ignored.**

You will find within this website an appreciation for a wide latitude of singularities, however, it would seem that the concept and term does not apply to the “initial” singularity understood by many to the foundations of the hot big bang. Here the finite-infinite bridge is real and dimensionless constants are an inherent part of every transformation. Instead of singularities, there is always a nexus of transformation.

**3. The expansion of the universe is a key clue.**

Nobody questions that there is a well-ordered expansion underway. Perhaps the concept or an expanding universe originated with Alexander Friedmann in 1922. Russia, in the heinous aftermath of the 1917 revolution, would be a difficult place to build on theory and logic alone, nevertheless, using Einstein’s formula, he proposed the idea that the universe is expanding. Between 2001 and 2010 the Wilkinson Microwave Anisotropy Probe (WMAP) precisely measured the expansion and definitively confirmed Friedmann and Lemaître’s intuitions and observations.

**4. Homogeneous and isotropic are keys to understanding our universe.**

Most often, people attribute the cosmic microwave background radiation (CMBR) to a *massive explosion* and not to a geometric and exponentially-expanding universe in a highly-ordered, progressively-organized state. Yet, our explosive people will readily tout the fact that our universe is homogeneous and isotropic^{1}.

**5. The circle, sphere, and the dynamics of spheres is not appreciated enough.**

The 1948 Lemaître essay about quaternions and elliptical space does not engage the much earlier work of Fourier and his analysis of the sine and cosine functions within and around the sphere.

Much more to come…

# References

^{[53]}

William Kingdon Clifford

elliptic space

versors

Erlangen program

H. S. M. Coxeter

^{[54]}

*Mathematical Reviews*

# Cold Big Bang

atoms

expansion of the universe

Very low temperature

cohesion

acoustic peaks in the cosmic microwave background radiation^{[1]}

WMAP observations