Tag Archives: heaven

The Numerology about Mr. Lee Kuan Yew

In the aftermath of the death of Singapore’s founding father, Mr. Lee Kuan Yew (1923–2015), a number of numerological tidbits (or numerical curiosities, to put it mildly) floated on social media, which got a number of apparently self-professed innumerates pretty excited. Here are three such postings that I saw in my Facebook feed and on WhatsApp.

RIP: Lee Kuan Yew (1923–2015)

A numerological message that was circulated among WhatsApp users in Singapore
(© Unknown)—A numerological message that was shared among Singapore WhatsApp users

The WhatsApp message gives the impression that it was the works of some “pseudo-mathematician,” but it could very well have been the digital footprints of a “mathematical crank” or an amateur-numerologist, who wanted to tickle mathophobics with such numerical coincidences.

Did Singapore’s numerologists (or pseudo-mathematicians) fail to point out some of the following numerological absurdities?

The digital root of Mr. Lee’s birth year is 1 + 9 + 2 + 3 = 15, which stands for the last two digits of the year he experienced his last heartbeat.

The pollution index for that week was in an unhealthy range, and the average PSI for the six-day mourning period was about 91.

Or, were there exactly 91 priests on vigil at an undisclosed Roman Catholic Church, who were interceding for Mr. Lee to ensure that his heavenly destination is 100% secured, although his manifold deeds to the nation inarguably exceeds the number of his political faux pas, especially vis-à-vis his political enemies or opponents?

Or, did 91 senior monks and nuns (or did I mistake them for disciples of Shintoism?) resort to “synchronized chanting” to ensure that the highest level of enlightenment be bestowed on the late Mr. Lee, who might be reincarnated as a future Buddha for his numerous selfish deeds towards his oft-ungrateful and unappreciative fellow citizens?

And did any police personnel verify whether there were 91,000 odd mourners in black attire on that Black Sunday, not to say, 91 VIPs or Heads of States who attended the eulogy, depending on one’s definition of a VIP?

 

The Numerology of the Old Guard

One Facebook numerological factoid that circulated in the first post-LKY week was the following:

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Singapore’s political fathers who outlived the biblical three-scores-and-ten lifespan

At face value, these nonagenarians had their blessed lives prolonged up to “four scores and ten and one” years. Sounds like their good earthly or political deeds were good karma for their longetivity? Are they the recipients of the following success equation?

Sacrifice + Service + Incorruptibility + Risk  = Political Success + Longevity

Observe that simply taking the difference between the birth year and the death year of Mr. S Rajaratnam suggests that he died at the age of 91; however, if we look closely at the month dates (Feb. 25, 1915 – Feb. 22, 2006), he was still 90 years old, when he passed away. The same argument goes for Dr. Toh Chin Chye (Dec. 10, 1921 – Feb. 3, 2012), who wasn’t yet 91, when he died. So, always take the pseudoscience of numerology with a grain of salt. As with fengshui charlatans, a degree of skepticism towards numerologists of all sizes and shapes isn’t an option—wear your critical-thinking cap when meeting, or reading about, these paranormal folks!

 

Fortune via Misfortune—From 4D to 5C

(© Unknown) Punters used combinations of the digits related to Mr. Lee death date to lure Lady Luck.

To rational non-punters or non-gamblers, betting on someone’s death date, whether he or she was poor or rich on this side of eternity, seems like an extreme case of bad taste,  or simply showing zero respect for the deceased and their family members. However, in superstitious circles, that practice isn’t uncommon among mathematically challenged or superstitious punters, who think that bad luck paranormally translates into good omen, if they bet on the digits derived from the death date or age of a recently deceased person.

In fact, during the nation’s six-day mourning period for its founder, besides the long queues of those who wanted to pay their last respects to Mr. Lee at the Parliament House, another common sight islandwide were meters-long lines of 4D or TOTO punters, who wanted to cash in on the “lucky digits” to retire prematurely, hoping to lay hold of the traditional 5Cs (cash, car, condo, credit cardcountry club), coveted by hundreds of thousands of materialistic Singaporeans.

 

Number Theory over Numerology

Fengshui in the Gym
(© BBC) Chinese numerology in the gym? Or, is it just a mild form of deification of a political figure?

Instead of promoting a numerological or pseudoscientific gospel based on Mr. Kuan Yew’s death date or age, which only helps to propagate superstition and pseudoscience, perhaps a “mathematically healthy” exercise would be to leverage on the D-day to teach our students and their parents some basic numerical properties—for example, conducting a recreational math session on “Number Theory 101” for secondary  1–4 (or grades 7–10) students might prove more meaningful or fruitful than dabbling in some numerological prestidigitation, or unhealthy divination.

A Search for Patterns

91  is the product of two primes: 91 = 7 × 13

91 = 1² + 2² + 3² + 4² + 5² + 6²

91 is also the sum of three squares: 1² + 3² + 9²

Are there other ways of writing the number 91 as a sum of squares?

91 = 33 + 43

 

Non-Numerological Questions to Promote Problem-Solving Skills

Let’s look at an “inauspicious number” of elementary- and middle-school (primary 5–secondary 4) math questions, which could help promote numeracy rather than numerology among students and teachers.

1. Sum of Integers

Show that the number 91 may be represented as the sum of consecutive whole numbers. In how many ways can this be done?

2. The Recurring Decimal

What fraction represents the recurring decimal 0.919191…?

3. Palindromic in Base n

For what base(s) will the decimal number 91 be a palindromic number (a number that reads the same when its digits are reversed)? For example, 91 = 101013.

4. The Billion Heartbeat

Does a 91-year-lifespan last less or more than a billion heartbeats?

5. Day of the Week

Mr. Lee Kuan Yew (September 16, 1923–March 23, 2015) died on a Monday. Using the 28-year cycle of the Gregorian calendar, which day of the week was he born?

6. One Equation, Two Variables

If x and y are integers, how many solutions does the equation x² – y² = 91 have?

7. Singapore’s New Orchid

A new orchid—Singapore’s national flower—had been named after Mr. Lee: Aranda Lee Kuan YewUsing the code A = x, B = x + 1, C = x + 2, …, , does there exist an integer x such that ARANDA sums up to 91? In other words, does there exist a numerological system such that  A + R + A + N + D + A = 91?

8. Singapore’s Coin Goes Octal

Singapore's "lucky" octagonal one-dollar coin
The alleged involvement of Mr. Lee in Singapore’s “lucky” octagonal one-dollar coin

There is an apocryphal story that had circulated for many years linking Mr. Lee Kuan Yew with Singapore’s octagonal one-dollar coin. A high-ranking monk had apparently told Mr. Lee that Singapore’s fortune would continue to rise only if Singaporeans were to carry a bagua—the eight-sided fengshui symbol. That prediction allegedly prompted the Monetary Authority of Singapore to issue the octagonal shape of the nation’s one-dollar coin.

That rumor was later put to rest by no other than self-declared agnostic Mr. Lee himself in one of his books, Hard Truths. He remarked that he had zero faith in horoscopes, much less the pseudoscience of fengshui.

What is the sum of the interior angles of the Singapore’s eight-sided coin?

9. Show that the largest number k for which the decimal expansion of 2k does not contain the digit 1 is 91.

© Yan Kow Cheong, April 26, 2015.

Resurrection isn't an option in Singapore!
Resurrection isn’t an option in Singapore!

Selected Answers/Hints

1. One example is 91 = 1 + 2 + 3 +⋯+ 13.
2. 91/99.
5. Mr. Lee was born on a Sunday.
6. Hint: Show that x² – y² = 91 has 8 integer solutions.
9. Hint: Use a computer to verify the result.

Hungry ghosts don’t do Singapore math

In Singapore, every year around this time, folks who believe in hungry ghosts celebrate the one-month-long “Hungry Ghost Festival” (also known as the “Seventh Month”). The Seventh Month is like an Asian equivalent of Halloween, extended to one month—just spookier.

If you think that these spiritual vagabonds encircling the island are mere fictions or imaginations of some superstitious or irrational local folks who have put their blind faith in them, you’re in for a shock. These evil spirits can drive the hell out of ghosts agnostics, including those who deny the existence of such spiritual beings.

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Hell money superstitious [or innumerate] folks can buy for a few bucks to pacify the “hungry ghosts.”

During the fearful Seventh Month, devotees would put on hold major life decisions, be it about getting married, purchasing a house, or signing a business deal. If you belong to the rational type, there’s no better time in Singapore to tie the knot (albeit there’s no guarantee that all your guests would show up on your D-Day); in fact, you can get the best deal of the year if your wedding day also happens to fall on a Friday 13—an “unlucky date” in an “unlucky month.”

Problem solving in the Seventh Month

I have no statistical data of the number of math teachers, who are hardcore Seventh Month disciples, who would play it safe, by going on some “mathematical fast” or diet during this fearful “inaupicious month.” As for the rest of us, let’s not allow fear, irrationality, or superstition to paralyze us from indulging into some creative mathematical problem solving.

Let’s see how the following “ghost” word problem may be solved using the Stack Method, a commonly used problem-solving strategy, slowing gaining popularity among math educators outside Singapore (which has often proved to be as good as, if not better than, the bar method in a number of problem-situations).

During the annual one-month-long Hungry Ghost Festival, a devotee used 1/4 and $45 of the amount in his PayHell account to buy an e-book entitled That Place Called Hades. He then donated 1/3 and $3 of the remaining amount to an on-line mortuary, whose members help to intercede for long-lost wicked souls. In the end, his PayHell account showed that he only had $55 left. How much money did he have at first?

Try solving this, using the Singapore model, or bar, method, before peeking at the quick-and-dirty stack-method solutions below.

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From the stack drawing,
2 units = 55 + 13 + 15 + 15 = 98
4 units = 2 × 98 = 196

He had $196 in his PayHell account at first.

Alternatively, we may represent the stack drawing as follows:

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From the model drawing,
2 units = 15 + 15 + 13 + 55 = 98
4 units = 2 × 98 = 196

The devotee had $196 in his account at first.

Another way of solving the “ghost question” is depicted below.

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From the stack drawing,
6u = 55 + 13 + 15 + 15 = 98
12u = 2 × 98 = 196

He had $196 in his PayHell account at first.

A prayerful exercise for the lost souls

Let me end with a “wicked problem” I initially included in Aha! Math, a recreational math title I wrote for elementary math students. My challenge to you is to solve this rate question, using the Singapore bar method; better still, what about using the stack method? Happy problem solving!

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How would you use the model, or bar, method to solve this “wicked problem”?
Reference
Yan, K. C. (2006). Aha! math! Singapore: SNP Panpac Education. 
© Yan Kow Cheong, August 28, 2013.

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A businessman won this “lucky” urn with a $488,888 bid at a recent Hungry Ghost Festival auction.

Numbering Our Days

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Thou shalt remember thy PIN! © 2010 Summersdale Publishers Ltd

Teach us to number our days aright, that we may gain a heart of wisdom.
— Psalm 90:12

Every second counts. Every minute counts. These sound more like clichés to many of us that few would pay attention to. Most of us live our lives as if there’ll be many more tomorrows. For the rest of us who are nearing, or have lived past, the half life, mortality is no longer a topic we can conveniently dismiss. Some try to ignore it, or pretend that age is just a number, or that they’re young at heart—they “psycho themselves” to think or speak like folks from the Positive Thinking or New Age movement.

The Three-Scores-and-Ten Lifespan

The Holy Scriptures tell us that the majority of us are approximately given a three-scores-and-ten lifespan; for a blessed minority, it’d be extended to four scores and ten—90 years. The names of two ex-political ethical leaders cross my mind: Nelson Mandela and Lee Kuan Yew.

Even with medical breakthroughs in recent decades, a look at the obituary pages in the papers every day shows that the average lifespan of a man or woman has remained fairly constant for centuries—even with women living an average of 3 to 5 years longer than men, depending on which continent of the world they live in.

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Is age a mere psychological figure? “I am seventy years young!”

The Billionth Heartbeat

For most part of human history, the billionth heartbeat has defined the length of a man’s days. Even today, that nine-zero figure remains fairly constant in a number of African or developing countries. But, thanks to medical advances and better standards of living, many in developed nations can live up to about two to three billion heartbeats.

A Satanic Alert

If you’re more of an apocalyptic type, then you’re more likely to define your mortality in terms of some multiple of the beast number. This means you’ve about 888 months during your earthly stay to live in a manner that could reduce your odds of joining folks like Idi Amin Dada, Saddam Hussein, and Adolf Hitler.

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Not all dozing folks on the bus are dead! © 2003 Summersdale Publishers Ltd

Mortality and Eternity

Show me, O Lord, my life’s end and the number of my days; let me know how fleeting is my life. —Psalm 39:4

It’s easy to count our age and the number of years we’ve lived, but it’s difficult to count the number of our remaining days—we simply can’t count from the future.

Perhaps, we need to pray the psalmist’s prayer: Teach us to number our days aright, that we may gain a heart of wisdom.

In Job 14:5, we read: Man’s days are determined; you have decreed the number of his months and have set limits he cannot exceed.

Elsewhere, Jesus told Peter: “I alone control the length of a man’s days.”

No doubt, our days are numbered, and how can we make wise use of them? How do we frame our finite days in the light of eternity? How do we break away from living unremarkably average lives? How can we plan not just for a big, meaningful day or event, but also for a big, meaningful life?

It’s high time we stop kidding ourselves: We don’t have 500 years to live. If we realize that our average lifespan of “three scores and ten” years on earth—about two to three billion heartbeats, depending on our location, position, or station in life—are insignificant in the light of eternity, we’ll value what are important: Love God and His people.

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What would you define as your “prime years”?

Math Educators, What’s Your Legacy?

With The Lord a day is like a thousand years, and a thousand years are like a day.
— 2 Peter 3:8

For us, math educators, how can we move more to the right side of the bell curve when it comes to impacting the lives of others in some areas of mathematics education? How can we say NO to living mediocre mathematical lives, although we may not presently have all the necessary tools in our mathematical toolkit to reach out to those whom we long to positively influence?

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Is fifty the new thirty-five?

A Spiritual Formula for Longevity

Let me leave you with some verses that may hold the key to seeing you live beyond the  billionth heartbeat—three verses that may be worth keeping in your heart.

Ephesians 6:2–3 

“Honor your father and mother”—which is the first commandment with a promise—”that it may go well with you and that you may enjoy long life in the earth.”

Exodus 20:12 (The 6th Commandment):

“Honor your father and your mother, so that you may live long in the land the Lord your God is giving you.”

Number your days. More than a million people die every single week. Think about it. You made it another week! You’re better off than a million folks. You can thank God that you’re alive. Make “numbering your days” a priority in your mathematical journey!

Practice

1. How many times does the heart beat in a person’s lifetime? How do the figures vary for those living in developed and developing countries?

2. Show that most folks have an average of 888 months to live on this side of eternity.

3. Based on a two- or three-billion-heartbeat lifespan, or depending on the continent you are living in, what fraction of your lifetime have you lived? How do you plan to spend the remaining of it meaningfully?

References

Solomon, R. M. (2012). Reflections on time & eternity. Singapore: Genesis Books.

Summersdale Publishers Ltd (2011). Old is the new young. UK: Summersdale Publishers Ltd.

Fraser, B. (2010). You know you’re having a senior moment when…. West Sussex, UK: Summersdale Publishers Ltd.

Fraser, B. (2003). You know you’re getting old when…. West Sussex, UK: Summersdale Publishers Ltd.

© Yan Kow Cheong, July 27, 2013.

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A funny book with a touch of seriousness.