The concept of infinitesimal was beset by controversy from its beginnings. The idea makes an early appearance in the mathematics of the Greek atomist philosopher Democritus c. 450 B.C.E., only to be banished c. 350 B.C.E. by Eudoxus in what was to become official “Euclidean” mathematics. We have noted their reappearance as indivisibles in the sixteenth and seventeenth centuries: in this form they were systematically employed by Kepler, Galileo’s student Cavalieri, the Bernoulli clan, and a number of other mathematicians. In the guise of the beguilingly named “linelets” and “timelets”, infinitesimals played an essential role in Barrow’s “method for finding tangents by calculation”, which appears in his Lectiones Geometricae of 1670. As “evanescent quantities” infinitesimals were instrumental (although later abandoned) in Newton’s development of the calculus, and, as “inassignable quantities”, in Leibniz’s. The Marquis de l’Hôpital, who in 1696 published the first treatise on the differential calculus (entitled Analyse des Infiniments Petits pour l’Intelligence des Lignes Courbes ), invokes the concept in postulating that “a curved line may be regarded as being made up of infinitely small straight line segments,” and that “one can take as equal two quantities differing by an infinitely small quantity.”
However useful it may have been in practice, the concept of infinitesimal could scarcely withstand logical scrutiny. Derided by Berkeley in the 18th century as “ghosts of departed quantities”, in the 19th century execrated by Cantor as “cholera-bacilli” infecting mathematics, and in the 20th roundly condemned by Bertrand Russell as “unnecessary, erroneous, and self-contradictory”, these useful, but logically dubious entities were believed to have been finally supplanted in the foundations of analysis by the limit concept which took rigorous and final form in the latter half of the 19th century. By the beginning of the 20th century, the concept of infinitesimal had become, in analysis at least, a virtual “unconcept”. Continuity and Infinitesimals (Stanford Encyclopedia of Philosophy)
Trig teacher may have been my best HS teacher. Came in, sat down, and he’d do 50 minutes of blackboard work, very conceptual.
Took AP calc but also more advanced calc in college taught by a new Chinese asst prof with an impenetrable accent from an equally impenetrable text (by a prof in the department). Killed whatever limited interest I had in progressing further in math.
“Build back better—BBB. If you were going to imagine ‘666’ and you wanted to show it to people and disguise it at the same time, can you think of any letter that the numeral six would fit inside completely? Only capital B,” Adams said.
Even Joe Biden’s name, Adams said, has a satanic coincidence.
“Did you know if you took the capital letter J—just imagine the capital letter J in your mind—now think of the next letter in ‘Joe.’ It’s an O. Now just move with your mind the O to the left until it’s on top of the J. It’s a backward six,” Adams said. “Now suppose the next letter is the lowercase E. What does a lowercase E look like if you turn it upside down? Well, it looks like a six.”
He continued, “So you’ve got the J and O together. If you combine them it looks like a backward six. You’ve got this lowercase E that looks like an upside-down six, but that’s just two sixes. Six, six wouldn’t mean anything, right? But the next letter is capital B for Biden, and capital B is where you hide your six. So even J-O-E-B is 666.”
He surmised that the letters I, D, E, and N left in Biden’s last name is short for “identity.”
“666 identity. That’s what Joe Biden’s name actually is,” Adams said.
The question of age-gap dating is nuanced enough that I need to do some more thinking before actually weighing in either way. That said, it’s interesting to self-reflect on how differently I react to 20-year-old decision-making depending on the context. I celebrate it when - in a context filled with power differentials, fake news, and mal-intentioned old dudes - a college student exercises their agency to vote. But I have an instinctive “hmm, this might be terrible” response to a 20-year-old exercising similar agency within a widely age-gapped relationship.
A large part of this is because - on the individual level - the potential consequences to the latter are more significant and immediate. But since these are both theoretically exploitative contexts, is my thinking also shaped by historically-puritanical cultural influences re: relationships and sex specifically? I’m not sure yet where the balance is between developmental realism and an appropriate level of feminist empowerment.
