Metro Manila Traffic: It's Like Hell On Earth!

(Photo Caption: Rain or Shine, traffic situation in Katipunan Avenue near Ateneo. Source: Ateneo de Manila University Physical Plant Office.)

This morning (8/24/07) I had an unwelcome surprise. On my way to Ateneo I had to pass by the intersection of Xavierville Avenue and Abada Street. To my surprise, I encountered a DPWH (Department of Public Works and Highways) contractor digging portions of the narrow intersection. Since this intersection is a busy intersection (especially before 8:00 a.m. and around 3:00 p.m.) you can imagine the traffic jam that this unexpected work at the intersection has caused.

No warnings, no prior notices, and all of a sudden you will encounter road diggings not only in the Katipunan area but also practically everywhere in Metro Manila.

[Recently, it took me one hour just to get from Ateneo to the University of the Philippines in Diliman, which is a short distance away (without traffic, it will take only about 10 minutes!)
And this happened to me not only once but several times ): ]

To top it all, these DPWH contractors conduct road diggings and "repair work" (a misnomer) at the height of the rainy season!

It is no wonder why Metro Manila is filled with traffic-related incidents like car accidents, body injuries, fights, killings and even deaths.

When will our government get its acts together? (Wishful thinking!!!)

When will this madness end?

Metro Manila Traffic? It's like hell on earth!

Raffy
8/24/07

Helping The People Through Wireless Technology

(Photo Caption: Mr. Mahabir Pun, Source: http://www.himanchal.org/school-mahabir-pun.html)


Today (8/22/07), I received a forwarded e-mail from our Dean, Dr. Fabian "Toby" Dayrit about an article on Mr. Mahabir Pun, the 2007 Ramon Magsaysay Awardee for Community Leadership. The article is from SciDev.Net:

Nepali teacher wins 'Asian Nobel Prize': Mahabir Pun

(by Imelda Abano, 13 August 2007, Source: SciDev.Net)




"A Nepali teacher has been honoured with a prestigious Ramon Magsaysay Award, regarded as the Asian Nobel Prize, in recognition of his innovative application of wireless computer technology in Nepal.

Mahabir Pun, 52, from the remote village of Nangi in Nepal, will receive the 2007 Award for Community Leadership and a US$50,000 prize along with six other awardees in Manila, Philippines this month (31 August).

Pun started the project "The Nepal Wireless Networking Project" to meet the communication needs of his village, seven hours climb to the nearestroad and without a telephone connection.

"I believe that better communication systems are important for the overall development of a community and a nation," Pun told SciDev.Net. Under the project, villagers and a team of international volunteers initially powered several computers with small hydro-generators in an earby stream. They then linked them wirelessly to the Internet with a series of television dish antennas and mountaintop relay stations, usingthe nearest telephone connection in the town of Pokhara, a two-day trip away.

Pun said the project has so far provided 14 rural villages with access to services like telemedicine, distance learning, e-marketing of local products and telephone services.

"I strongly believe that all the people in the world have right to use and benefit from this technology. This has been a basic need in developed countries. Therefore one of my goals is to work hard to close the digital divide as much as I can," said Pun.

The Ramon Magsaysay Award Foundation writes that his innovation has brought progress "by connecting his village to the global village". Sandy Dela Cruz, the Ramon Magsaysay Award Foundation communications programme officer told SciDev.Net that Pun's dedication, innovative leadership and motivation in connecting the mountain villages of Nepal to each other and the outside world is magnificent." He is an inspiration to young people in Asia because of his courageous and ambitious goal for Nepal," Dela Cruz said.

The Ramon Magsaysay Award celebrates outstanding individuals and organisations working in Asia for the people of Asia."

NOTES:

1. Mr. Mahabir Pun is scheduled to give a public lecture at the Ateneo de Manila University on August 29, 2007.

2. Below are some links that I found (using Google, http://www.google.com/) about Mr. Mahabir Pun:

• http://www.nepalwireless.net/people.php
• http://www.since1968.com/article/50/nepal-wireless
• http://www.himanchal.org/school-mahabir-pun.html
• http://www.rmaf.org.ph/Awardees/Citation/CitationPunMah.htm

3. While writing this article about Mr. Mahabir Pun in my BLOG I remember one of my batchmates in Philippine Science High School (PSHS Class of 1977), Engr. Ramon "Mon" Castillo, president of INNOVATRONIX Inc. and a Gawad Lagablab Awardee. Mon is conducting a community project in a remote village in Tanay, Rizal (close to Metro Manila) which involves rural people's computer education and Internet access. I intend to write a blog entry about Mon and his community projects in the near future.

Raffy
8/22/07 in Quezon City

Mathematics, Reality, And Dr. Fidel Nemenzo

(Photo Caption: Dr. Fidel Nemenzo (sitting) together with his students at U.P. Diliman. Source: http://deesaster.blogspot.com)


Yesterday (8/21/07) I received an invitation from the University of the Philippines National Institute for Science and Mathematics Education Development (UP NISMED) about a public lecture to be given by a Filipino mathematician colleague, Dr. Fidel R. Nemenzo.




The title of the lecture is "Does Mathematics Reflect Reality?".

The lecture will be held on August 31, 2007, 9:00 a.m., at the STTC Auditorium, UP NISMED), Diliman, Quezon City.

Abstract:

"The great abstract ideas of mathematics are created by mathematicians out of sheer delight, independent of human experience. These ideas now help us predict weather and the ups and downs of stock market, understand the behaviour of birds in flight, design bridges and skyscrapers, and protect financial transactions done over the internet. Is it not puzzling that the abstract ideas of mathematics are precisely what are needed to understand and model social phenomena and the physical world?"

About the Speaker:

Dr. Fidel R. Nemenzo is an Associate Professor at the Department of Mathematics of the University of the Philippines in Diliman, Quezon City.

Dr. Nemenzo obtained the following academic degrees:

D.Sc. Mathematics. Sophia University, Japan. 1998
M.S. Mathematics. Sophia University, Japan. 1992
B.S. Mathematics. University of the Philippines, Diliman, Quezon City. 1985

At present Dr. Fidel Nemenzo is the president of the Mathematical Society of the Philippines (MSP).

My Notes on Fidel:

Fidel is the son of Dr. Franciso "Dodong" Nemenzo, former president of the University of the Philippines. In the past, I have invited Fidel to be one of our resource speakers in MODEL '99 (Workshop and Conference on Modeling, Simulation, and Scientific Computing), an event that I organized at the Ateneo de Manila University in November 1999. He gave a talk on data security using elliptic curves.

It would be very interesting to hear what Fidel has to say on the topic, "Does Mathematics Reflect Reality?"

Raffy
8/22/07 in Quezon City

Welcome Back, Dr. Ricardo Lim

1. 
2. (Photo Captions: Left - Ricky's high school picture (1977), Top Right - Ricky with his wife and kids, Bottom Right - Ricky's contemporary photo)

1. Yesterday (8/20/07) I had an e-mail communication with Dr. Ricardo "Ricky" A. Lim. Ricky and I belong to the same high school batch, Philippine Science High School Class of 1977. For a long time, Ricky has been "silent" in our batch e-group. So, perhaps he was not aware of our 30th batch anniversary project for PSHS (of which I am one of the coordinators).
   

According to him, he made a wrong press of the button (one of the keys in the computer keyboard) while surfing the Net the other night. The result: he had to apologize to most of the more than 1000 people in his address book for SPAM :) I guess, this kind of accident happens to many Net users, not only to Ricky.

However, because of that accidental pressing of the button one of the coordinators of our batch projects, Dr. Francis "Keku" Domingo (who is the medical director of Novartis Healthcare Philippines, Inc.), got in touch with Ricky. Keku forwarded to me the e-mail message from Ricky (Keku actually said it was "providential"). After that I e-mailed Ricky and requested him to reconnect to our batch e-group.

Ricky used to be one of the coordinators of our batch. He was active in the PSHS alumni affairs and even became the president of the Philippine Science High School Alumni Association.

During our high school days (1972-1977) Ricky stayed briefly at the PSHS boys' dormitory (I was also a dormer) during our freshmen year. We were classmates for two school years: during our sophomore year, our section was Champaca; and during our senior year, our section was Atom.

The son of the former Secretary of the Department of Social Welfare Dr. Estefania Aldaba Lim and the brother of media personality Che-Che Lazaro, Ricky is now a professor and an associate dean at the Asian Institute of Management. Below is a feature article about Ricky from the AIM website (Source: http://www.aim.edu/faculty/facultyresume.asp?id=228 ):

"Professor Ricardo A. Lim, PhD, is the Don Benigno Toda, Jr. Professor of Business Management. He is currently the Associate Dean of the W. SyCip Graduate School of Business (WSGSB) where he is a core faculty of the MBA Program. He was the former Associate Dean of the International Relations Group, and Editor-in-Chief of The Asian Manager. He specializes in information technology and management communication, and has published articles for MIS Quarterly and the Academy of Management.

Before joining the Institute, Prof. Lim managed ATM and branch automation projects for the Philippine National Bank; developed a telemarketing system for the Sears Roebuck Chicago Merchandising Group; and built an international securities monitoring and control system for the State Street Bank in Boston. He installed a nationwide claims litigation system for the American International Group in New York. He participated in manufacturing and financial systems development projects at Allied-Bendix Rhode Island, Hartz Mountain of New Jersey, Wang Laboratories and American Fund Raising Services in Boston, Massachusetts. He also worked for Nixdorf Computer Philippines, the CSC Consulting Group in Boston and the Bankers Trust Company in New York. He currently consults for local firms.

Prof. Lim has also taught management information systems in the MBA program of the Graduate School of Business of the University of the Philippines. He wrote The PHINMA Story (1996).

He received a Ph.D. in Business Administration from the Marshall School at the University of Southern California (2002), an MBA from the Darden School, University of Virginia (1989), and a B.Com. in Management Information Systems (Magna Cum Laude) from McGill University, Montreal (1982)."

To Ricky: this is what happens to you when you press a wrong button... You not only got to be found by us, you also got featured in my BLOG :)

Cheers,

Raffy
8/21/07 in Quezon City

Adding A Free Counter

Today (8/21/07) I found a website for adding a free counter to my blog. The source is http://easy-hit-counters.com/ . So, today I was successful in installing this counter in my blog. For the record, the start of the counter is zero on August 21, 2007. The number of "hits" or "visits" before August 21, 2007 are not included in the counter.

Cheers,

Raffy
8/21/07 in Quezon City

Innovation With Dr. Greg Tangonan

Today (8/21/07) I attended a meeting on industry-academe collaboration. One of the topics in the meeting is Innovation, with Dr. Gregory "Greg" Tangonan as the speaker. Dr. Tangonan is a co-faculty member at the School of Science and Engineering of Ateneo de Manila University.

Below are some information on Dr. Tangonan found in the UP-Ayala Technology-Business Incubator website ( http://www.up-ayalatbi.org/events.asp ).

===============================================================

Gregory Tangonan, PhD

President, Asia Pacific Technical Strategies

Retired Director of R&D, Hughes Research Laboratories (Los Angeles, CA)

Holder of 38 U.S. patents

Author/co-author of more than 100 published papers

Distinguished Inventor Awardee, Hughes Research Laboratories

in 2000, 2001, and 2002

===============================================================

"Dr. Tangonan joined Hughes in 1971 after receiving the Howard Hughes Doctoral Fellowship for studies at the California Institute of Technology. During his doctoral studies, he performed research in superconductivity and amorphous metals at Cal Tech and participated in optical device research at Hughes Research Laboratory. Dr. Tangonan has pioneered integrated waveguide detectors, Bragg modulators in LiTaO3 and LiNbO3, and glass-based couplers for wavelength multiplexing and coupling. He has been instrumental in developing applications of optoelectronics in radar, optical networking, and analog systems.

Dr. Tangonan was promoted to Director of Research in Communications and Photonics reporting directly to the President of HRL Laboratories. Dr. Tangonan Laboratory focused on the exploitation of wireless technologies for broadband access to interactive services, laser communications, optoelectronic devices and subsystems for RF systems, and novel inter-networking systems.

Dr. Tangonan was responsible for setting the Strategic Technical Investments of the Owners of HRL - Boeing, General Motors and Raytheon.

After 31 years with HRL Laboratories, Dr. Tangonan retired from HRL Laboratories to pursue new interests. During the last few years at HRL Dr. Tangonan became very interested in the business side of technology and is the President of his Asia Pacific Technical Strategies. The company pursues strategic research and development projects that can be translated into Intellectual Property assets or start-up companies.

Dr. Tangonan joined the Ateneo de Manila University in the Philippines as Adjunct Professor in the Loyola School of Science and Engineering. He is responsible for research in the areas of biomedical engineering, wireless and optical communications and material science. He is very active in the development of Intellectual Property, and has, with several of the Ateneo faculty, filed U.S. Patents on their research.

In the last two years he has taught a class called Innovation and Technology to graduating engineering and science students. This class delves into the global competitive environment, the role that innovation plays in determining success or failure in almost every industry today, and how Filipino innovators can become successful through strategic planning of technology development.

Dr. Tangonan is co-author of >100 published papers and presentations in the fields of fiber optics, integrated optics, laser spectroscopy and amorphous materials. Dr. Tangonan has 48 U.S. patents. He has presented numerous papers at international forums in optoelectronics. Dr. Tangonan is a member of the Optical Society of America, IEEE Lasers and Electro-Optics Society and Sigma Xi.

Dr. Tangonan has received several major awards for his work. Among them are two R&D 100 Awards for New Products and Technologies. The first R&D 100 Award in 1994 was for Secure Fiber Optics Technology and the second R&D 100 Award was for Optical Networking Node Technology for All-Optical Switched Networks. Dr. Tangonan received several Published Paper- of-the-Year awards from HRL Laboratories. Dr. Tangonan received the Distinguished Inventor Award from HRL in 2000, 2001, and 2002. "

The Ateneo community and all Filipinos can truly be proud of Dr. Greg Tangonan, his achievements, and his contributions to science and techonology.

Raffy

8/21/07 in Quezon City

When It Rains, It Pours... And It Floods!

"When it rains, it pours..."

This is a common saying that you hear whenever one has a good fortune of having a series of good luck OR a misfortune of having a series of bad luck (like what happened to me last August 5, see http://raffysaldana.blogspot.com/2007/08/do-you-know-what-to-do-after-car.html).


But this saying may also be interpreted literally.

Early this month, the Philippines was faced with a problem of drought. It is already the rainy season but rains are hard to come by. Cloud seeding has to be done to prevent water shortage. In some areas of Central and Northern Luzon (Philippines), the rice fields have already been adversely affected.

To solve the problem of drought, the Catholic Church in the Philippines launched a campaign for Oratio Imperata Ad Petendam Pluviam (Obligatory Prayer To Request For Rain). So, millions of devoted Catholics in the country regulary prayed for rain.

And then the rains came.

But, as the saying goes, "When it rains, it pours..."

The rains were brought by one typhoon after another. Recently, we even had a supertypoon
(local name: Egay).

And with the rains, came the floods. The whole of Metro Manila and surrounding provinces were confronted with the problem of flashfloods brought about by continuous rain. Classes in schools and work in government offices were suspended.


Is this a case of "Divine Comedy"? People prayed for rain and the rain was given to the people. But then, it was excessive rain, which brought flooding in many parts of the country.

Perhaps, next time, when people pray for rain they have to state exactly how much rain they would like to have :)[Then, perhaps, people would need to consult scientists, and they would appreciate what scientists are doing :) :) ]

When it rains, it pours... and it floods!

Raffy
8/19/07 in Quezon City

Two Weeks After My Car Accident: Thoughts on Fatalism

It has been two weeks since I had a car accident at the C-5 flyover in Pasig City (See http://raffysaldana.blogspot.com/2007/08/do-you-know-what-to-do-after-car.html ) but still the damage to my car has not yet been repaired.

I'm wondering: does fate has to do with my car accident? It seemed to me that several events colluded so that I would be at the C-5 flyover in Pasig City at 8:45 a.m. on August 5, 2007, so that my car would be hit by another car. I could have avoided being there, but the fact is that I was there.

But then, COULD I REALLY HAVE AVOIDED THE ACCIDENT?

This brings me to the subject of 'Fatalism'.

According to our friendly Wikipedia,

"[start of quote]

Fatalism is commonly referred to as "the doctrine that all events are subject to fate or inevitable predetermination."

More precisely, it can refer to at least one of three interrelated ideas:-

1. That there is no free will, and everything including human actions, could only have happened as it did. This version of fatalism is very similar to determinism.

2. That although human actions are free, they are nonetheless ineffectual in determining events, because "whatever will be will be".This version of fatalism is very similar to predestination.

3. That an attitude of inaction and passive acceptance, rather than striving, is appropriate. This version of fatalism is very similar to defeatism.

[end of quote]"

To me this is a frightening thought. That events would happen NO MATTER WHAT you do, they WOULD happen because they are predetermined.

Qe sera, sera. What will be, will be.

I tend to believe that we have free will, and that as human beings, we are responsible for our actions.

In every action, we have a choice. The decision we take is our responsibility.

But is this really the case? Can it be that even our manner of choosing and the choices we make are predetermined?

Raffy
8/19/07 in Quezon City

What Is the Meaning of Life?

Question: What is the meaning of life?

Answer: See cartoon -->

Cheers,

Raffy

8/18/07

(Cartoon Source: http://www.ericweisstein.com/)

Do You Want To Be Happy?

In an earlier entry (See http://raffysaldana.blogspot.com/2007/08/what-mathematicians-do-on-rainy-days.html) I mentioned that the Hungarian mathematician Alfred Renyi is probably the source of a famous quote ("Mathematicians are machines that turn coffee into theorems.") which is popularly accredited to another famous Hungarian mathematician Paul Erdos.





A Wikipedia article mentions that Renyi is also the source of another quote: "If I feel happy, I do mathematics to become happy. If I am happy, I do mathematics to keep happy."

(Photo caption: Alfred Renyi. Source: http://en.wikipedia.org/wiki/Alfr%C3%A9d_R%C3%A9nyi )

...

So, do you want to be happy?

Cheers,

Raffy
8/18/07

What Mathematicians Do On Rainy Days

Question: What do mathematicians do on rainy days?

Answer: Some drink coffee, some turn coffee into theorems :)

A famous mathematician, Paul Erdos is credited for having said that “mathematicians are machines that turn coffee into theorems". (However, a Wikipedia article states that this quote is most probably to have originated from a mathematician colleague of Erdos named Alfred Renyi.)

I wish that I can turn coffee into theorems during these rainy days :)

Cheers,

Raffy
8/18/07 in Quezon City

"Happy","Cute", "Sociable", "Weird" And Other Special Numbers

In a previous post (See http://raffysaldana.blogspot.com/2007/08/palindromes-and-palindromic-numbers.html) I talked about a special number called a palindromic number. In this article, I will discuss other special numbers...


“Abundant”, “amicable”, “cute”, “deficient”, “happy”, “narcissistic”, “perfect”, “semiperfect”, “sociable”, “square”, “weird”.

These adjectives normally pertain to people or, somehow, they are related to people.

But did you know that these adjectives also pertain to numbers?

In mathematics, there is such a field called number theory. Number theorists are mathematicians that study, among others, the characteristics of special numbers.

Here are some excerpts from a website “Math Forum@Drexel” ( http://mathforum.org/dr.math/faq/faq.number.glossary.html) on some kind of special numbers:


“Abundant Numbers

A number is abundant if the sum of its proper divisors is greater than the number itself. For example, the proper divisors of 24 are {1, 2, 3, 4, 6, 8, 12} and 1 + 2 + 3 + 4 + 6 + 8 + 12 = 36, so 24 is abundant."


"Amicable Pairs

You might think of an amicable pair as two numbers that are best friends. The sum of the proper divisors of the first number is the second number, and if you add up the proper divisors of the second number, you get the first number.

Here's an example. One amicable pair is 2620 and 2924. The proper divisors of 2620 are {1, 2, 4, 5, 10, 20, 131, 262, 524, 655, 1310}. Their sum is 1 + 2 + 4 + 5 + 10 + 20 + 131 + 262 + 524 + 655 + 1310 = 2924. Next we check whether 2924's proper divisors add up to 2620. 2924's proper divisors are {1, 2, 4, 17, 34, 43, 68, 86, 172, 731, 1462}. 1 + 2 + 4 + 17 + 34 + 43 + 68 + 86 + 172 + 731 + 1462 = 2620, so the pair of numbers really is amicable."

"Cute Numbers

If a square can be cut into n squares of at the most two different sizes, then n is called a cute number. For example, 4 and 10 are cute numbers."

"Deficient Numbers

If the sum of a number's proper divisors is less than the original number, it is called a deficient number. For instance, 16 is deficient. The proper divisors of 16 are {1, 2, 4, 8}, but 1 + 2 + 4 + 8 = 15."


"Happy Numbers

A happy number is a number for which the sum of the squares of the digits eventually equals 1.

For instance, 203 is happy:

2^2 + 0^2 + 3^2 = 13
1^2 + 3^2 = 10
1^2 + 0^2 = 1.

Numbers that are not happy, such as 16, are called unhappy numbers."


"Narcissistic Numbers

A narcissistic person is only interested in himself; a narcissistic number might seem a little self-centered, too. A narcissistic number is an integer equal to an expression that uses the same digits. For example, 36 = 3! * 6. Sometimes a narcissistic number is defined as a number equal to the sum of its digits raised to a certain power, or, more specifically, as an n-digit number equal to the sum of its digits raised to the nth power. For instance, 371 is narcissistic because 3^3 + 7^3 + 1^3 = 371, and 9474 is narcissistic because 9^4 + 4^4 + 7^4 + 4^4 = 9474."


"Perfect Numbers

The numbers that divide evenly into an integer are called its divisors. For example, the divisors of 6 are {1, 2, 3, 6}. Proper divisors are the divisors less than the integer you started with: the proper divisors of 6 are {1, 2, 3}. A number is perfect if it is equal to the sum of its proper divisors. 6 is perfect, because 1 + 2 + 3 = 6."


"Semiperfect Numbers

A semiperfect number is the sum of some of its proper divisors. For instance, 18 is semiperfect because its proper divisors are {1, 2, 3, 6, 9} and 3 + 6 + 9 = 18. If a semiperfect number is the sum of all of its proper divisors, it is called a perfect number."

"Sociable Numbers

Sociable numbers are like amicable numbers, but they come in larger groups. The proper divisors of the first number in the group add up to the second number, the proper divisors of the second number add up to the third number, and so on. The sum of the proper divisors of the last number in the group is equal to the first number. Sociable numbers tend to be quite large, so they are hard to find without using a computer. One example of a sociable group is 12496, 14288, 15472, 14536, and 14264."

"Square Numbers

Square numbers are the result of multiplying a number by itself once. These are the same as the "perfect squares": 1^2 = 1, 2^2 = 4, 3^2 = 9, and so on. (The small ^2 means 'squared' and in e-mail we write it ^2, so that 2^2 is 'two squared'.)

The square of 5 is 25, and working backward, we say the square root of 25 is 5. "

"Weird Numbers

A number is weird if it is abundant without being semiperfect; 70 is the first weird number."


Cheers,


Raffy
8/17/07 in Quezon City

How To Turn Numbers Into Palindromic Numbers

Still on the subject of palindromic numbers (See http://raffysaldana.blogspot.com/2007/08/palindromes-and-palindromic-numbers.html):

A palindrome is a word that's the same read either forward or backward, such as "rotor" or "tenet". Palindromic numbers, like 22 and 12321, have the same digits forward and backward.

Do you know that most numbers can be converted into palindromic numbers? How? Here is an answer (source: http://mathforum.org/dr.math/faq/faq.number.glossary.html )


"1. Pick a number.
2. Reverse its digits.
3. Add them together.
4. Repeat the process until you get a palindromic number.

Example:

1) 19
2) 91
3) 110
4) 011
5) 121

Nobody knows whether or not this works for every number. People have used computers to try the flip-and-add process on 196 nearly ten million times, without finding a palindrome-- but it might still be possible. We do know that it won't work for every number written in every base: Try 10110 in base 2."

Try this, it's fun :) { Challenge: Can you turn this into a theorem? }

Cheers,

Raffy
8/17/07 in Quezon City

When Is A Palindromic Number Prime?

(Figure Caption: The number of palindromic numbers less than a given number n. Source: http://mathworld.wolfram.com/PalindromicPrime.html)................................................................................

While seriously thinking about palindromic numbers (See http://raffysaldana.blogspot.com/2007/08/palindromes-and-palindromic-numbers.html) I thought that writing a program to determine whether a given palindromic number is prime would be a good programming exercise.

Then, by searching the Web using Google (http://www.google.com/) I found a website discussing palindromic primes (http://mathworld.wolfram.com/PalindromicPrime.html).

From the website, I found some interesting facts:

1. The first few (base-10) palindromic primes are 2, 3, 5, 7, 11, 101, 131, 151, 181, 191, 313, 353, 373, 383, 727, 757, 787, ...

2. The number of palindromic primes less than a given number are illustrated in the plot above.

3. The number of palindromic numbers having n=1, 2, 3, ... digits are 4, 1, 15, 0, 93, 0, 668, 0, 5172, 0, ...

4. The total number of palindromic primes less than 10, 10^2, 10^3 , ... are 4, 5, 20, 20, 113, 113, 781, ...

5. Gupta (2006) has computed the number of palindromic primes up to 10^19.

6. Banks et al. (2004) proved that almost all palindromes (in any base) are composite.

7. As of Jan. 2006, the largest proven palindromic prime is found by P. Jobling (2005), which has 150007 decimal digits.

Very interesting!

Cheers,

Raffy

8/17/07 in Quezon City

Palindromes and Palindromic Numbers

This morning (while thinking about what to do in case Supertyphoon Egay hits Metro Manila) I received a text message from a mathematician colleague who asked for my landline phone number. When I mentioned my phone number to him, he remarked that it is interesting because my phone number is a palindromic number. It was only then that I realized that indeed I have a palindromic phone number!

So what are palindromes and palindromic numbers?

A quick visit to Wikipedia ( http://www.wikipedia.org/ ) gave the following answers:

1. "A palindrome is a word, phrase, number or other sequence of units that has the property of reading the same in either direction (the adjustment of punctuation and spaces between words is generally permitted). The word "palindrome" was coined from Greek roots Greek πάλιν (palin) "back" and δρóμος (dromos) "way, direction" by English writer Ben Jonson in the 1600s. Composing literature in palindromes is an example of constrained writing."

(Source: http://en.wikipedia.org/wiki/Palindrome)

Examples of palindromes are the words: "rotor" and "tenet".

2. "A palindromic number is a 'symmetrical' number like 16461, that remains the same when its digits are reversed. The term palindromic is derived from palindrome, which refers to a word like rotor that remains unchanged under reversal of its letters.

Palindromic numbers receive most attention in the realm of recreational mathematics. A typical problem asks for numbers that possess a certain property and are palindromic. For instance,
the palindromic primes are 2, 3, 5, 7, 11, 101, 131, 151, … (sequence A002385 in OEIS)
the palindromic perfect squares are 0, 1, 4, 9, 121, 484, 676, 10201, 12321, …

Buckminster Fuller referred to palindromic numbers as Scheherazade numbers in his book Synergetics, because Scheherazade was the name of the story-telling wife in the 1001 Nights.

It is fairly straightforward to appreciate that in any base there are infinitely many palindromic numbers, since in any base the infinite sequence of numbers written (in that base) as 101, 1001, 10001, etc. (in which the nth number is a 1, followed by n zeros, followed by a 1) consists of palindromic numbers only."

(Source: http://en.wikipedia.org/wiki/Palindromic_number )


Now, I have a problem: Is my phone number a palindromic prime number or is it a palindromic perfect number (or both)?

Oh well, I guess having a palindromic phone number makes me special, especially on a rainy day like this :)

Cheers,

Raffy Saldana
8/17/07 in Quezon City