Linear Algebra 101

Back in the 1960s most New Englanders' were loss at sea when asked to count beyond ten on their fingers. Multiplication and long division flummoxed college students. Calculus was the Black Plague, but I loved the intercourse between numbers and in 1966 I was awarded a scholarship to Xaverian Brothers High School on strength of my test score.

My father was an electrical engineer had been told by the Priests that they suspected that I might have cheated on the exam in which I scored an A+. Upon hearing my historical discourse on Ptolemy calculations, Archimedes' method of exhaustion, and Newton's errors on Gravity as well my problems with Einstein's Theory of Relativity my father was astounded by my knowledge, especially since I suffered from what was much later diagnosed as dyslexia.

"Why do you think Einstein was wrong?"

"Einstein calculated the speed of light as 186,000 MPS or miles per seconds. Do you drive 55 on the Expressway? No, so there is no speed limit. Not for your Oldsmobile or Light."

"Nothing?"

"Nothing, other than my love of Math."

Poetry was Math. This magic recreated time and shifted through a billion formalae seeking an ultimate truth.

E=MC squared equal 2.

That autumn I was placed in Xaverian's advanced Math program.

My grades hovered around B. My parents considered me an under-achiever. I strived to prove them wrong without success, yet I won a Math half-scholarship to a college based on my belief in Time, which saved me from tragic addition and subtraction of Vietnam.

Math as a major in college was a big mistake, since at night I drove taxi to finance my studies. I missed my 9am Multivariable Calculus class with regularity, however I aced my final and advanced to study Linear Algebra under Rene Marcus, a famed genius of telemetry, whom the Pentagon paid big money for his skill to mentally calculate missile attacks on Russia without a slide ruler.

NPR manufactured the first calculator in 1967. None existed in the marketplace until 1974, which then was sold by NPR for $170. Only the rich could afford that price.

On the first day of class I sat at my desk with a thin book for Linear Algebra, a pencil, and paper notebook. The text on flat differential geometry obtusely explaining the electromagnetic symmetries of space-time was as dense as Osmium. I read it in a day with Pene's daughter and invited her to the Phoenix Bar. As we played pinball, she asked,"Do you understand the importance of Linear Algebra."

"Only that it supports the Universe existence with lines, planes and rotations through complex functions."

"And you disagree?"

"I am not smart enough to argue its importance.

Rene's daughter had heard my beliefs on Time. She believed in Einstein's Theory of Relativity, while I argued that time wasn't not constrained by rules and I reiterated, "There are no speed limits on an empty highway."

"That means nothing."

"And nothing means much in Math and in life."

She laughed and said, "You are a fool."

"You are right about that."

That Fall I attended only four classes.

Four, which was two times two, the second prime number.

In December I arrived at the final and Professor Marcus pulled me to the side. The rest of the class stared at me as a stranger and the professor said, "You shouldn't be here. You might be my daughter's friend."

"Just friends."

"Either way that will not influence my grading you."

"I wouldn't expect anything else."

"You haven't been in class more than three times."

"Actually four times."

"Three or four. What the difference?"

"Three is a prime number."

"And what is the important of numbers."

"Numbers will never betray the ignorance, but will trap anyone else by their honesty."

"Do you really think you can pass this test?"

"Truthfully I suspect no is the right answer."

"Then what are you trying to achieve?"

"The impossible. Give me a test paper and let me place my hand on the textbook for ten seconds." I understood the value of a hand on a book.

"And this will help?" Mathematicians only believed in numbers.

"It can't hurt."

The professor held out the book. My hand touched the cover. My palm read nothing. I was fucked. If I failed this course, I might end up in Vietnam. I took the test. My score was 45. The whorls on my flesh were very sensitive. Rene was amazed by my idiot-savantism.

"I thought you'd get nothing right."

"I still failed."

"Yes, but if you drop out from Math, I'll give you a D+"

"It's a deal."I accepted his offer and dealt with my parents' disappointment.

"What will you study now?" asked my father.

"I don't know."

"Can't you plan for the future?"

"Not now."

"You fail next time and you'll end up in Vietnam."

"I know." The War was a meat grinder and I was no John Wayne. My new major was economics. I graduated sine laude or without praise in 1974. Nixon had pulled out most of our troops. I was safe and that summer I drove cross-country with my good friend AK to celebrate the end of my education.

It was a great trip and I haven't opened a math book since 1972, although I have learned that western man had no concept of zero until well until the end of the Middle Ages, while the Mayans always had zero or Pohp for their 20-based numeral system.

Presently I don't use my fingers for long math, but if you think you're smart just remember the words of Phil Pastoret.

"If you think dogs can't count, try putting three dog biscuits in your pocket and then giving Fido only two of them."

Arf Arf Arf equals three.

And three is a prime number