To: Nikola Chubrich

January 27, 2022

Dear Nikola,

It's inescapable that I have gone off the deep end.  Please don't report me to Dr. Delisi or any of her colleagues.  I have spent hours reading, What is Mathematics? (Courant), Was sind und was sollen die Zahlen? (Dedekind), reading about the travails of my Braunschweig compatriots Richard Dedekind with his asymmetrical cuts and Carl Friedrich Gauß with his hypotheses about non-Euclidean geometry which he declined to publish because he thought the critics would ridicule him. Non-Euclidean geometry was ultimately officially discovered (?invented) by János Bolyai in 1829 and published in 1832.  After seeing it, Gauss wrote to János' father Farkas Bolyai: "To praise it would amount to praising myself. For the entire content of the work ...  coincides almost exactly with my own meditations which have occupied my mind for the past thirty or thirty-five years." Gauß spent his childhood in a house within easy walking distance of the address where I lived from January 9, 1935, until March 20, 1939.

Predictably my irresponsible dabbling in mathematics has ignited my irrepressible do-it-yourself compulsions.  It turns out that I can't think about mathematics without injecting my own considerations into the maelstrom. I am determined not only to watch, but also to participate in the unbelievability marathon, even if I end up being the last across the finish line. Georg Cantor's fiddling with infinity gave me to think. If Cantor could postulate transfinite numbers which are neither finite nor infinite, and distinguish between infinity of denumerable and non-denumerable sets, and if Riemann and Hilbert could postulate innumerable instances of space with potentially infinite dimensions, why won't anyone permit me division by zero, where such division of positive real numbers would have a positive Meyer infinity as its limit, and division by zero of negative real numbers would have a negative Meyer infinity as its limit.

I understand that it's all about words, and the academic community claims "division", "infinity" and "zero" as its registered trademarks, the use of which it permits only in conformity with its hallowed, but nonetheless arbitrary rules. Division by zero is a no-no, infinity may not be designated as positive or negative, although it is forbidden to state the fact that an infinity so neutered is meaningless, and so likewise is a zero, for which there is no room on either side of a Dedekind cut.

From my perspective, the trademark issue is readily dealt with. Words are easy to come by, and by replacing "division" with "partition", infinity with apeiron, and zero with naught, I can say "Partition of plus one with decreasing real numbers down to and including naught, yields as a limit, positive apeiron," Partition of minus one with decreasing real numbers down to and including naught, yields as a limit, negative apeiron. Furthermore, since by definition apeiron is boundless, there can be no separation between positive and negative apeiron. Where there is no separation and in the absence of boundaries, fusion is inescapable. Positive apeiron must be presumed to consist of positive particles, and negative apeiron must be presumed to consist of negative particles. The positive and negative apeiron particles will attract each other with great force and annihilate each other in an energy-releasing cataclysm with consequences yet to be imagined.  The improved nomenclature will have the advantage of serving as seed for as many Ph.D. theses as the traffic will bear concerning the differences between "division" and "partition", between "infinity" and "apeiron", between "zero" and "naught".

I am relieved and comforted by the circumstance that mad mathematicians, and presumably also mad pseudo-mathematicians, are consigned to refuge in nothing more threatening than "sanatoriums", such as "Berghof" in Davos. Wikipedia reports that both Cantor and Gödel recuperated in sanatoriums from the stresses of their profession.

Stay well, and thank you for putting up with me. Give my regards to your parents.
EJM