Education and Training

(Originally posted at on June 16, 2010 1:56 AM)

James P. Carse is the author of Finite and Infinite Games (New York:  Ballantine Books, 1986) which is, in my opinion, a very important book.  In it is a section on the difference between education and training:

To be prepared against surprise is to be trained.  To be prepared for surprise is to be educated.

Education discovers an increasing richness in the past, because it sees what is unfinished there.  Training regards the past as finished and the future as to be finished.  Education leads toward a continuing self-discovery; training leads toward a final self-definition.

Training repeats a completed past in the future.  Education continues an unfinished past into the future.

The book requires careful reading.  (It is unfortunate that my copy has a typographical error on the cover.  The cover states “If a finite game is to be won by someone, it must come to a definite end,” whereas the actual text in the book states “If a finite game is to be won by someone, it must come to a definitive end.”)


What Mathematicians Do

(Originally posted at on May 21, 2010 9:53 AM)

They ask and answer questions.  (Here is a more specific link for mathematics education.)

Top Philippine Universities

(Originally posted at on May 14, 2010 10:24 PM)

According to, four Philippine universities are in the list of the top 200 Asian universities.  (Also see this.)  For 2010, Ateneo de Manila University is at 58 (from 84 in 2009), University of the Philippines is at 78 (from 63), University of Santo Tomas is at 101 (from 144) and De La Salle University is at 106 (from 76).

Dr. Seuss’s 1977 Commencement Address

(Originally posted at on April 4, 2010 8:43 AM)

On June 1977, Theodor Seuss Geisel was invited to give the commencement address of Lake Forest College (outside Chicago). Here is his 75-second address entitled “My Uncle Terwilliger on the Art of Eating Popovers” (from Judith & Neil Morgan, Dr. Seuss & Mr. Geisel: A Biography. New York: Random House, 1995, pp. 234-235):

My uncle ordered popovers
from the restaurant’s bill of fare.
And when they were served,
he regarded them
with a penetrating stare …
Then he spoke great Words of Wisdom
as he sat there on that chair:
“To eat these things,”
said my uncle,
“you must exercise great care.
You may swallow down what’s solid …
you must spit out the air!”

And …
as you partake of the world’s bill of fare,
that’s darned good advice to follow.
Do a lot of spitting out the hot air.
And be careful what you swallow.

Judith and Neil Morgan add: “As Ted sat down, there was bedlam.  Students shouted, cheered and flung their caps into the air.  He was startled, for it was his first experience with the fervor with which many young Americans had begun to canonize Dr. Seuss.  These graduates were of the generation most critical of the Vietnam war, and from their earliest memories of Dr. Seuss books they had assumed that he too must be skeptical of the establishment.  Now they’d heard evidence from the master’s lips.”

On a related note, if ever you are asked to give a commencement address, try not to copy from others.  (See this, this, and this.)

Alice in Wonderland and Mathematics

(Originally posted at on March 25, 2010 9:18 AM)

Many people have tried to more fully explain details in Alice in Wonderland (and Through the Looking Glass), most notably Martin Gardner. There are many hidden references to what was happening during the time the books were written: spoofs of popular songs, how languages and dances were taught, comments on society and politics, Charles Lutwidge Dodgson’s feelings for Alice Pleasance Liddell, and so on.

It now seems that Lewis Carroll has also hidden some references to how he felt about the mathematical advances being made during that time. Helena Pycior (in 1984) and Melanie Bayley (in 2009) have found in Alice what they think are references to Victorian mathematics. Read more about it here.

Perelman Awarded First CMI Millenium Prize

(Originally posted at on March 23, 2010 10:13 AM)

In 2002 and 2003, Grigoriy Perelman posted three preprints on, which are now commonly agreed to provide a proof of the Poincaré Conjecture (pronounced “pwan ka RAY”). (He actually proved a more general conjecture of which the Poincaré Conjecture is a special case.)

In 2006, Perelman was awarded a Fields Medal, which he declined.

Last March 18, 2010, the Clay Mathematics Institute announced that it had awarded its first Millenium Prize to Perelman. (Read more about it here and here.) The prize includes an award of $1 million. Will he also decline this award?

Statistical Tools for Literature and Language Studies

(Originally posted at on March 21, 2010 9:28 AM)

Here are the slides for a seminar-workshop on statistics that I’m giving tomorrow to the faculty members of the Department of Literature and Language Studies, College of Arts and Sciences, Ateneo de Naga University.

In my experience, statistics is best learned using examples from one’s field of study. Admittedly, the slides do not contain as much information as I would like to teach. Unfortunately, as the seminar-workshop is limited to one day only, I am forced to limit my selection of topics to those which I think are most useful to the participants in general.

I hope that the participants will use the understanding and the skills that they learned in this seminar-workshop to better appreciate the research papers that they read and to better describe the results of their own research.