On April 26, 2022, after reading in the local papers that almost 5,500 dengue cases were reported in high-GDP Singapore, exceeding last year’s total, I posed and posted the following quiz:
“Covid-🇸🇬: A True or False Quiz: “In living-with-Covid Singapore, people are more afraid of contracting the dengue virus (dubbed the ‘rich man’s threat’) than the coronavirus (coined the ‘poor man’s dread’).”
A Tale of Two Vectors
Last November, I’d somewhat asked a similar question: “What are the odds that in Singapore the wealthy are more likely to go to hospital due to a mosquito bite rather than due to a viral infection? The delta goes for the poor; the dengue targets the rich.”
A month earlier, I’d postulated the following scenario: “In the Singapore 2021 infection contest, the dengue is no match to the delta. Even with more biting opportunities to target potential work-from-home victims, the 🦟 blamed the 🦠 for failing to meet its target.” https://lnkd.in/d5TeNdUA
In fact, way back in 2020, I’d pondered about “Singapore’s double whammy: The dengue (9,261 cases) is catching up fast to give the coronavirus (36,405 cases) some fight. Which one will win the 🇸🇬 infection contest: the mosquito 🦟 or the virus 🦠?” bit.ly/36YIzbh
Fight for Your Life
Today, in a number of war-stricken or terrorism-sponsored countries, the battle cry is: “Be a peace fighter.” In SE Asia, the rallying cry is: “Be a dengue fighter.”
On Monday, Singapore’s Health Minister Ong Ye Kung reported that 80,000 seniors aged 60 and above have yet to take their Covid-19 booster shots, urging them to do so as the city-state is expecting a new wave of Omicron infections in the next few months.
The minister added that the first batch of Covid-19 vaccines were engineered more for the “wild-type” virus, and now that the coronavirus has mutated into the Delta and Omicron variants, we need at least three doses of vaccines for “effective” protection—and a fourth jab (or a second booster shot) is recommended for those who’ve so far lived on this planet for at least three scores and two tens (or four scores)—aged 80 and above.
Like thousands of my fellow skeptics, when we read or hear this kind of corona update from a local politician on a Monday, our skepticism index goes up at least twenty points. It sounds more like an indecent number of WHO-approved vaccines are nearing their expiry dates, so they need to come up with some creative eleventh-hour strategies not to waste away those tens of thousands of doses.
These days, even developing countries with low vaccination rates are likely to turn down any donated near-expiry vaccines from those high-GDP hoarders. They’d reply, “Thank you very much for your [“insincere”] donation!” followed by some PC excuses not to offend the donors.
One subtle way to salvage a fraction of these surplus doses is to use some mortality statistics to scare off those who’ve yet to be jabbed or boosted.
For instance, we’re statistically being told that the probability of unvaccinated seniors aged 60 and above ending in the intensive care unit (ICU) or dying from Covid-19 is 1/25, but the figure drops to 1/100 if they’ve been doubly jabbed, or nosedives to a mere 3/1000 if they’ve been boosted.
Minister Ong emphasized that “It makes a difference whether you have taken 0, 1, 2 or 3 shots.” So, the unvaxxed would better pay heed to his life-and-death warning unless they plan to journey to the other side sooner than later.
The sombre message is: Wake up to your minister’s advice if you don’t want to have a minister at your premature wake conducting nightly services to your loved ones and friends and colleagues. The decision is yours to act if you want to prolong your stay on this planet by an extra few years or decades.
Let’s pray that the unvaccinated or unboosted lot would fear Covid-19 more than Covid-🇸🇬, while not letting themselves be paralyzed by either one.
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.
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:
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!
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 card, country club), coveted by hundreds of thousands of materialistic Singaporeans.
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 Yew. Using 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
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.
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.
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.
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.
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.
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?
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.
