Seeking Infinity: A Desperate Hunt for New Applied Math

On the run avoiding attacks, a team of high school students, along with their math teacher, methodically discover new math needed to reverse engineer alien engines. They examine applications, review division by zero, desperately look outside of math for fresh ideas, and remove positive actual infinity as the quantity of a set. Students Sam and Sally became committed to discovering the new applied math when student militia leader Amy asked the President for help. But cooperation fizzles when the President learns that Sam and Sally’s families had been seeking a buried treasure that the aliens want. The math in this book reads like a light textbook with symbols limited to high school AP math. Quick Discussion of the Book -- In its first draft, storybook Alien Invasion Math Story (retitled to Seeking Infinity: A Desperate Hunt for New Applied Math) was a chronological collection of essays and derivations written during the hunt for an actual infinity that would be useful in applied mathematics for theoretical physics. These essays and derivations had no place in the completed project’s textbook Special Algebra for Special Relativity. In the second draft a storyline was added to unite the essays and calculations and to depict the author’s emotional extremes, and to bring visualization to the confusion, frustration, misdirection, and stress felt by the author. Inspiration for converting the essays and derivations into a storybook came from the movie The Race for the Double Helix (Life Story, BBC Horizon) in which Crick and Watson mixed incomplete bits of data (mostly from Franklin) with staggered inspiration. They persevered past criticism and little failures to win the race. Their moment of success came with a revelation. The author sitting at a desk or standing in a store watching his wife shop while thinking through proofs is not nearly as exciting as Crick and Watson in their quaint apartments and labs, so his storyline is fiction. But at least the math and the essays on human will are real. And, for the revelation at the climax, well, you will just have to read the book. Please do. The author tried to make it fun. Previous Description -- Professionals and academics struggle in their attempt to reverse engineer alien technology, which they must to counter aliens who seek to exterminate life on Earth. Young students put their focus on math because applied mathematics limited to finite numbers excludes infinity, and if math, which is the language of physics, is to expand, then that expansion is out to infinity. State-of-the-art applied-mathematics only pertains to numbers that are finite, that is, that can be counted-to, because to be finite is to be logical, rational, solvable, and knowable. But because sqrt(2) is proven not rational, meaning its numerator and denominator cannot be finite, the students understand that numbers can be larger than finite, what is called infinity, and their mission is to expose and explain infinity. The students find that establishment axiomatic deductive logic of pure mathematics includes positive actual infinity as a quantity of a set, but there are holes-in-logic which suggest that version of infinity is incorrect. But what alternative is there? Frustrated and desperate when at their lowest, some of the students go where logical minds should not, wondering if contemplative artsy or philosophic / religious speculations hold a clue for what infinity really is. Half the chapters develop properties for a useful infinity in the context of geometry, irrational numbers, quantum mechanics, special relativity, and the reciprocal of zero. Other chapters have the students reviewing historical revelations that contrast rational with irrational, and logical with paradoxical. The students fight misdirection and find hope in unexpected clues. Failures provide lessons. And they are under pressure.