*Symbols for male gender, female gender, a not principally recognized symbol for birth, the Egyptian hieroglyphic symbol for life, ankh, and symbols for death and infinity. These symbols, without the ankh, were in the title sequence for the 1960s television series, Ben Casey. (Created using Inkscape*

Some years after middle school, I discovered that there were more than the one infinity I had learned. The principle that some infinities are greater than others was proved by the mathematician, Georg Cantor (1845-1918), in 1874, who published a general method of proof of such, his diagonal argument, in 1891. This proof, outlined in the figure, was used by Kurt Gödel (1906-1978) in his incompleteness theorems, one of which states that the truth or falsity of some mathematical statements cannot be determined; that is, there are limits to mathematical knowledge.

*Cantor's diagonal argument for the proof that there are more real numbers than natural numbers.Suppose that you create a table of real numbers, in this case the binary fractions shown, and associate each of these numbers with a natural number *

The technical term for the size of a set is its cardinality, and Cantor named a progression of infinite cardinalities using the Hebrew letter, aleph, א, with (א)

*The four classical elements, (Earth ΓΗ, Air ʾΑΗΡ, Fire ΠΥΡ, and Water ʿΥΔΩΡ), along with the four qualities of matter (Dry ξηρον, Wet ʿυγρον, Hot θερμον, and Cold ψυχρον).Earth is both cold and dry, Air is both hot and wet, Fire is both hot and dry, and water is both cold and wet.The particular properties of a composite material derive from an amalgamation of these element qualities in their proportion.(Created using Inkscape. Click for larger image.)*

Juliano C. S. Neves of the Universidade Estadual de Campinas (UNICAMP) and the Instituto de Matemática, Estatística e Computação Científica (Campinas, SP, Brazil), has recently published an article on arXiv in which he examines how conformal infinities in general relativity are analogous to the idea of natural places in Aristotelian physics.[4] While modern physicists don't consciously try to emulate Aristotle in their theories, it's interesting how the same ideas circulate in human thought in different forms. As an example, Neves gives the Carter-Penrose diagram for Minkowski spacetime, which combines the three Euclidean dimensions of space with an extra time dimension. A Carter- Penrose diagram is a two-dimensional representation of the causal relations between different points in spacetime where the horizontal axis represents space, the vertical axis represents time, and lines slanted at 45° correspond to light rays.

*Carter-Penrose diagram for Minkowski spacetime with r = 0 indicating the origin of the coordinate system.This diagram contains the following infinities: i*

Timelike, spacelike, and null geodesics lead to the concepts of timelike infinity, null infinity, and spacelike infinity as places for bodies along these geodesics. As seen in the diagram, bodies on spacelike geodesics have the point i

- Ben Casey Opening Credits - including Primal metaphysics, YouTube video by Irving Gribbish, May 24, 2011.
- Isaac Newton, "De Analysi per aequationes numero terminorum infinitas," MS/81/4, Royal Society Library (London, UK), via The Newton Project, of Oxford University, September, 2012.
- Newton, Chapter 1 of The Calculus Gallery Masterpieces from Newton to Lebesgue William Dunham by William Dunham, Princeton University Press, 2008, 256 pp., ISBN 9780691136264 (PDF File)
- Juliano C. S. Neves, "Infinities as natural places," arXiv, March 21, 2018