Today is the last day of the annual 15-day Chinese New Year (or Lunar New Year) festival in China and Chinese communities around the world.
The Lunar New Year is so-called because the dates of celebration follow the phases of the moon—the new moon could fall on dates between January 21 and February 20, which is similar to Easter that could take place between March 22 and April 25.
Due to its “movable” date, the Lunar New Year (which is unspokenly steeped in superstition and divination, but unquestionably or expectantly celebrated by a billion-odd mainland Chinese and the forty-plus million faithfuls in the Chinese diaspora as part of Chinese tradition) serves as a rich recreational math or calendrical activity for teachers or educators worldwide.
In the Year of the Ox (or “Covidox”), which ushered in a palindromic date (12/02/2021), I pondered: “Any sexy formula that tells us when the Chinese New Year falls in a given year? Not calendrical recipes meant for symbol-minded geeks, but one for the majority of us, the simple-minded folks who’d key in the year and out come the CNY date & day of the week.”
With superstitious couples unfairly or irrationally treating baby tigers and bulls as “inauspicious,” but don’t mind baby bunnies, could supposedly conservative or puritan “fine” Singapore with a frightening low fertility rate of 1.2—below its replacement rate of 2.1, which could see its population heading the way of the dodo sans selective immigration and baby bonus cash incentives—expect a mini-baby boom in the Year of the Rabbit?
With few Covid restrictions still in place, would Singaporeans and permanent residents (and tax fugitives fearing political persecution or prison) be more excited this year to play their part in producing an above-average number of newborns-bunnies? And with Valentine’s Day around the corner, could the nation expect an overbooking of hospital beds or single wards in November?
I completely forgot that I wrote A Dozen Numerical Deeds for the Chinese New Year eight [sounds like a numerologically Sino-auspicious number?] years ago. If you want to keep the spirit of giving alive in the new bunny year, help yourself with some of the suggested gifts to bless others, Chinese and non-Chinese.
Moons ago, long before Trump’s MAGA slogan resonated among blue-collar workers and white evangelicals, I was surprised to read a parent’s guide mentioning that some American homeschoolers had mixed feelings about using foreign editions of Singapore math textbooks because of the lack of political freedom in the island-state.
No matter how value-for-money Singapore math titles are, or how impressive the “fine” city’s top ranking in both PISA and TIMSS is, some American parents and teachers would have nothing to do with a country that stifles freedom of speech, restricts political freedom, or cracks down on alternative views that often portray the government in a negative light.
Singapore is a partly free country.
This week, we read that in the new normal Singapore has fared worse than the previous year as far as political rights and civil liberties are concerned. If 50 were the passing mark, then the island-state fell short, by scoring a disappointing 48 out of 100 on political freedom.
Singapore’s Freedom in the World https://freedomhouse.org/country/singapore
Selective Internet Accessibility
Less well-known is Singapore’s average performance or ranking in terms of the public’s internet access, especially when both locals and aliens thought they could easily access the internet (except for some banned websites on politics, religion, and sex, or most political blogs that don’t depict the country’s political leaders positively), compared to their counterparts in China, where Google, Facebook, and Twitter are banned.
Singapore’s Freedom on the Net https://freedomhouse.org/country/singapore/freedom-net/2020
Political Freedom: Singapore vs. Others
Although we may not agree on the methodology used to compute the scores, which are calculated on a weighted scale, however, the global freedom ranking of most countries appears pretty accurate.
Let’s look at some freedom scores, by comparing how Singapore fares vis-à-vis some rich or rogue countries.
Since the start of the coronavirus pandemic, in the aftermath of more pseudo-free nations going rogue, or more institutions paying lip service to democratic processes, I remember less than three years ago coining tongue-in-cheek “Make Singapore Free Again.”
The Fear Factor in Singapore
The Fear Factor as a Common Denominator
What are some long-term consequences for math educators living in a politically semi-free milieu? Teachers who need to seek permission from their HODs or principals to start a blog or a Facebook page; or writers who need to consult editors or publishers before they start working on a politically incorrect or irreverent math title.
When I started blogging, I still recall that those who had a say in my pay wanted me to choose a different name that doesn’t include “Singapore Math” as part of the blog’s identity. Apparently, every time they Googled “Singapore math,” they landed on my site, and they’re uncomfortable with that. I refused to compromise because I thought then (and now) that the idea of censoring or threatening me for raising some unethical practices in educational publishing is laughably ridiculous, not to say, mathematically or educationally anti-democratic.
It’s not an accident or coincidence that high-GDP Singapore has probably the lowest number of math bloggers, or the least number of math teachers on Twitter, in the developed world.
For some of us, who look like an odd in a sea of evens, the “fear factor” of speaking up and speaking out is real, even if our audience is outside Singapore. As long as we are a “mathematical or political nobody,” it’s probably safe to say that we’re at quasi-zero risk of being banned or censored, while being aware that a small army of vigilantes are watching us 24/7/365 just in case we go “politically astray.”
POFMA Math
During the lockdown, when a few Opposition candidates appeared to be unfairly targeted for their “fake” comments, I entertained the possibility that soon the authorities would be targeting math bloggers or textbook authors, who poked fun at some MOE directives or policies, by irreverently christening POFMA Math.
What are the odds that Singapore math authors would be the next to be POFMA-ed?
Poverty or Democracy
For decades, the unspoken or unchallenged political message in Singapore for Singaporeans and foreigners is: High GDP or Low Political Liberty. You can’t have both!
Why can’t your say and your pay go hand in hand? The lie that a country’s economic prosperity and political freedom are inversely proportional needs to be debunked at all costs, because failure to do so would only perpetuate mediocrity, economic stagnancy, political apathy, and uncreativity among the citizenry.
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.
