Carl Sagan’s Infinite Fractal Vision: “Strange, Haunting, … The Most Exquisite Idea”
Carl Sagan offered the following comment in his book, Cosmos, which was linked to the TV series of the same name.
“There is an idea — strange, haunting, evocative — one of the most exquisite conjectures in science or religion. It is entirely undemonstrated; it may never be proved. But it stirs the blood. There is, we are told, an infinite hierarchy of universes, so that an elementary particle, such as an electron, in our universe would, if penetrated reveal itself to be an entire closed universe. Within it , organized into the local equivalent of galaxies and smaller structures, are an immense number of other, much tinier elementary particles, which are themselves universes at the next level, and so on forever — an infinite downward regression, universes within universes, endlessly. And upward as well.”
Sagan’s vision of an infinite self-similar cosmos resonated with me because several years earlier I had experienced a similar epiphany. It was an epiphany that had also occurred to Democritus in the 5th century BC, to Spinoza in the 17th century, to Kant in the 18th century, and to many others over the last 2500 years. In his last writing, for a 1955 conference in Italy celebrating of 50 years of relativity, Einstein noted the potential for solutions of his latest unified field equations that were “similar but not congruent”, i.e., that exhibited discrete self-similarity and dilation invariance. He was skeptical, however, because he noted that atoms appear to have fixed radii and masses, and this seemed to conflict with the concept of relative scale. Alas, he died about a month later that same year and never had a chance to fully explore the hint he found in those equations. Had he lived longer, Einstein might have considered Sagan’s “exquisite conjecture” of global discrete dilation symmetry, i.e., of a cosmos that repeats itself, but only in the case of almost unimaginably large and discrete (i.e., quantized) jumps of scale.
I have spent the last 44 years gathering evidence that supports this vision shared by Democritus, Spinoza, Kant, Einstein and Sagan. Here is an easy-going introduction to some of that observational evidence. No abstract smoke and mirrors. It’s a 19-minute read, but in the Covid-19 era we have plenty of time to branch out and explore new ideas.
I promise that you will learn more from this than in a gaggle of Umair’s repetitive screeds.