Pilipinas Forum 14: Math, Infinity and Limit

Here is another mind-twisting thread in pilipinasforum yahoogroups made in early December 2001. There was no political discourse here. And that's my point in posting these exchanges in this blog: We need little or no politics (and government) if we wish to expand our individual imagination and knowledge of math, logic and their applications. So, enjoy the 10-pages long exchanges on the subject.

Related articles in this blog are (1) An ever-expanding universe, June 25, 2011. It's about a lecture by an American cosmologist in UP about the "Accelerated History of the Universe". Also, (2) Pilipinas Forum 12: Origin of Zero, Nothingness, Big Bang..., September 25, 2011
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I was able to meet an old friend and a new friend - both Math professors in UP. My old friend, Fidel Nemenzo got his PhD in Sophia U. in Japan, and his specialization is "number theory", reputedly the purest of all math subjects.

Fidel's friend, Ernie, is really fantastic, academically i.e.: Monbusho scholar (like Fidel), finished MS and PhD Math in 5 years with "A" grades equivalent. At Sohia U, he was among the "wonder kids" by solving difficult math problems whle his Japanese classmates could only shake their heads. Undergrad, he finished BS Math in UP - Summa cum laude, in 3 years! High school, he came from Phil. Science HS; elem. he came from an obscure elem. school in an obscure town in Iloilo province. They're so poor that their house has no floor, that PSHS has to pay for his bus to Iloilo, his plane fare to manila. Yet this guy has no self-pity, nor hatred of the rich. He doesn't even see himself joining the corporate world, just a plain academic for the rest of his career. At 27, he's among the youngest professors in UP Math dept.

Fidel is moving to his friend's house, that of Mark Encarnacion, who took a temporary leave from UP for some stints in the US. Mark is another interesting kid. He got a PhD in "Computer Algebra" (!) from an Austrian university. The last time I talked to Mark in UP, about 4 years ago, he said he's the "only person in this country" who has that degree. Mark's father is UPSE's long-time dean, our dean that time, Dr. Jose Encarnacion. The Dean passed away about 3 years ago; his major works are often published in foreign academic journals, enough to be nominated for a possible Nobel prize in Economics.

OK, why am I sharing this? To show that there are such wonderful people in this country but our media and political and business leaders don't seem to notice. Every year we know who are the topnotchers in the bar exams, who are the valedictorians and salutatorians of the PMA, courtesy of the front page stories in our broadsheets and tabloids. But never has it occurred as far as I can remember, that Phil. broadsheets have given front page treatment to returning Filipino scientist or engineer or mathematician with distinguished PhD degree or astonishing research abroad. Which reflects the values and biases of Philippine media: future Filipino politicians and generals are hoorraayy! Future Filipino Einsteins are nobodies.

Of course I hope I'm wrong in this impression.

-- Nonoy Oplas

Inspired by Nonoy's post a few days back on our very own mathematicians in PilipinasForum, I decided to pick up a book, for leisurely reading, entitled, "A Tour of the Calculus" by David Berlinski. I wanted to be reminded as to why I fell in love with Math at one time in my life...

Math & life... the math of life...

From the book, "Some things were Greek to the Greeks. In the fifth century B.C., Zeno the Eleatic argued that a man could never cross a room to bump his nose into the wall...in order to reach the wall he would have first to cross half the room and then half the remaining distance again, and then half the distance that yet remains...this process...can always be continued and can never be ended..."

In the elevator, I always bump into the chief of another investment bank whose offices are in the same building as ours. He once asked me, "Gina, when do you think we can see the light at the end of the tunnel? You know, that one which is not from another train?" I answered, "Tomorrow!". Everytime I see him, we would look and smile at each other and we would, in perfect duet (seemingly practiced), say, "Tomorrow!"

In another instance, an analyst queried me, "Have we reached the bottom yet? How low can the market get?" Armed with calculus, I said, "We can never reach the bottom. The bottom will be forever unknown."

"...The plain fact is that we are capable of compressing those infinite steps..." and actually bump our noses into the wall. The truth is, for some businesses in the country today, tomorrow may not come. And I, a Trekkie, will uncharacteristically pass, on this voyage of discovery to the bottom of the Philippine markets. So much for infinity and continuity and the harsh concept of the limit.*

In case you have not noticed yet :-), this post has nothing to do with serious Math. I am just having fun with the concepts. May I end with this:

"The integral enables you
To do what you need not do. [ :-) ]
The theorem that will make this plain
Is one designed to spare you pain..."

- Mathematicians' Doggerel (quoted from the same book; the smiley, mine)

-- Gina L.