I’ve been discreetly and randomly working on thetentative The Little Toilet Math Book in the bathroom, where my best thinking often takes place. I suppose a number of you too get your aha’s or eureka’s there, albeit understandably you wouldn’t admit it.
Yesterday, as I was passing by a community center, I happily saw a toilet rolls collection box. I immediately took a photo shot of its front and side views. And my mind started rolling in some real-world questions that could match the pictures.
Below are a sample of these toilet math (🧻🔢) questions:
If residents in the “fine” city of Singapore were to recycle their toilet rolls, guesstimate how many trees could be saved every year.
How much more space could be used if donors were considerate enough to flatten their toilet rolls before dumping them into the collection or recycle box?
If citizens and residents decided using water rather than toilet rolls to clean themselves up, how many millions of liters of water they would need per day after visiting a public toilet (excluding those hundreds of thousands of men who hardly ever wash their hands after relieving themselves or doing their dirty business)?
For a household, would using a bidet or water at home be dearer or cheaper than relying on toilet rolls in the long run (including medical bills for piles and other related health issues that are directly or indirectly due to paper uncleanliness or poor hygiene)?
Imagine that Singapore could no longer import toilet paper from its neighbors. Wouldn’t switching to NEWater—Singapore’s homemade drinkable water, which comes from polluted sea water and “toilet water” mixed with bacteria-killing agents, and which disputably smacks of or smells like sewage—cost for for the population than using toilet paper for doing their business?
Often times, for a community project to succeed, not only do we need that little extra effort but also an iota of thought to ensure that all stakeholders mindfully (or inconveniently) play their part.
Let’s all do the right thing and the thing right, because success often lies not so much in the doing but rather in the caring.
Remember: There is no Planet B (for Generations 𝛼, 𝛽, and 𝛾).
Pi recently took a page from Singapore’s only ruling party’s decades-long successful template how to stay in power perpetually, with quasi-zero public protests, strikes, and riots.
Will Pi win her viral legal case against the World Health Organization (WHO)? Millions of math teachers worldwide are unspokenly hoping that the WHO won’t alienate or betray Pi, just as it did for the marginalized and unrecognized variant Xi.
Would Pi be vindicated for unfairly being discriminated by those who’re playing politics to prevent her from being admitted as a bona-fide corona variant worthy of WHO’s recognition?
Imagine how excited math educators globally would be if Pi won her legal case against the WHO.
Come Pi Day or Pi Approximation Day, if the 16th letter of the Greek alphabet were officially declared a WHO-approved variant by then, schools and universities would be electrified in conducting an eclectic mix of pi talks and lectures to promote Pi’s ambivalent “murderous” new status.
I, for one, have started to work on Murderous Pi—the title of a math e-book to celebrate Pi’s evolution from a humble mathematical constant to a proud corona variant, which would be plagued with devilish or wicked problems on mathematics’s most beloved irrational number.
Are you looking forward for Pi’s long-overdue recognition by WHO’s health professionals in the Lunar New Year of the Rabbit?
Until she’s virally credited for her fatally mixed impact on earthlings before she’d rest in peace to make way for Rho and Sigma, who’re lining up to be WHO-recognized, Pi’s rejection would be perceived as an irrational [mathematical & viral] injustice or betrayal, whose aftermath paranoiac behaviors among math educators and virologists worldwide could potentially be unpeaceful, to say the least.
Like the “infidel” Zero, who’s ostracized by the Church Fathers of yesteryear, may the “agnostic” or “devilish” Pi be vindicated as she longs to gain formal approval to be in the company of fellow corona variants.
I can’t recall what prompted me to coin “mathemachicken” three-odd years ago. Was it the aftermath of setting or solving an unhealthy number of word problems on chickens or eggs, or both?
Not too long ago, in Organic Chicken Rice for the Rich, I hatched up a meme and offered some math questions on organic and kampong chickens. https://bit.ly/3y1fXvL
Early this month, the world read about Malaysia’s decision to ban the export of chickens (but not eggs) to its frenemy neighbor Singapore. In fact, even before the ban, the prices of chicken eggs were already skyrocketing in supermarkets, which sounds more like a case of synchronized profiteering strategies among exporters, distributors, and supermarkets than anything else, but after some Opposition members had denounced the unjustified inflated prices, things have since stabilized more or less.
Organic Chicken for the Rich & Wealthy
Ukrainian Eggs 4 Singapore
During Singapore’s “circuit breaker”—a PC term for “lockdown”—we’re blessed with white eggs flown from Ukraine. I recall that some supermarkets had promotions like “Buy One, Get One Free” or “Buy Two, Get One Free” to lure locals to try Ukrainian eggs. Since the war, the import of these bigger and cheaper eggs seems to have come to a halt.
Probably no animal is more popular than the chicken in math word problems—even the beloved bunny comes a distant second. Be it the use of their heads, eyes, legs, or eggs, the chicken remains the animal of choice among mathematical problem posers.
Tens of thousands of brain-friendly and unfriendly math questions on chickens and eggs around the world make their way into canned and creative math textbooks every year, which makes millions of math-anxious students worldwide to “chicken out” to avoid being given all kinds of labels by peers and parents for their oft-irrational fear or failure to solving them.
Philosophically Speaking
If you were a chicken, would you feel privileged or pissed off by the way your name is being used, abused, or misused in school textbooks and workbooks?
Do you think it’s long overdue that you and your feathery friends and foes sue the publishers and the Ministries of Education around the world for showing disrespect or even disdain towards the chicken community?
On a lighter note, if it looks like a chicken and clucks and counts like a chicken, you never know: it might be a mathemachicken.
The day before, we read that a female Burmese python weighting 98 kg and nearly 5 m was caught in Florida. She’s the largest snake ever found in that state before her death, pregnant with an amazing 122 eggs; if stretched vertically, she’d be as tall as a giraffe.
In Florida, where now lives the Viper in Chief after being ousted from the White House, who’s since preoccupied himself with terrorizing those who refuse to propagate his lasagna of lies, pythons have become pests due to irresponsible pet owners of yesteryears releasing or allowing pet pythons to escape in the wild.
With no major predators, Florida’s subtropical climate has provided serpents and snakes a conducive breeding ground for them to multiply, often outcompeting native species. Who knows? Alien vipers might eventually outnumber local pythons, if left on their own to populate the land.
Recently, some human vipers mounted a “mathematical insurrection” against textbook publishers for allegedly promoting “woke math” to K–12 students. And a rising number of foreign pythons are set to keep Florida’s annual “Python Challenge” alive—this year, the event runs from August 5–14 and is expected to lure around 500+ python hunters from 25 different states.
🐍🔢: Math with Pythons & Pithons
Like math questions on vampires and zombies, those on pythons (and pithons) are no less frightening or exciting to problem solvers. Below are two examples:
It is estimated that the female Burmese python, which was caught after Floridian researchers used a male “scout” to find her, was up to 20 years old. In human years, would she be as old as the Viper in Chief?
Python Pies or Pizzas: In 2021, the winner of the “Python Challenge” captured 223 pythons, while the longest snake was 15 feet long. Imagine if this year’s captured foreign pythons were ethically killed and exotically used to make pies or pizzas, how many pieces of either one could be made by the chefs at Mar-a-Lago for the “Florida Python Food Festival”?
If you were given a chance to redefine a square, what would your new definition be other than it being another word for a geek, nerd, or bore? Or, a figure who refuses to do any of those immoral, illegal, or unethical things when pressured by peers: drug, booze, sex, porn, gang, scheme, graft, ….
Geometric Stereotype à la Singapour
In Chan Li Shan’s Searching for Lee Wen (2022), the author wrote:
“A well-known actress, Nancy Kwan once gave a talk at a conference of British-born Chinese. Having started in the film The World of Suzie Wong, she was talking about what it was like to be a Chinese actress working in Hollywood. Noticing Lee Wen [a deceased Singaporean artist who received the Cultural Medallion in 2005, Singapore’s highest award for the arts] at the back of the room, she said,
“Who’s that young man sitting behind? How come you’re so quiet? Where are you from?” “I’m Lee Wen from Singapore.” “Oh! Singapore… people there are all very square, right?”
Don’t you agree that there’s an iota of truth that people in the “fine” city don’t so much look like a square but do often behave like one? By this, I mean that they’re generally conservative, conformist, or compliant, or all three. Few would wish to be seen as an odd one in a sea of evens, because an oddball often creates waves, positively or negatively.
At work, few would step out of their invisible square to question, much less challenge, the oft-dated rules and regulations. Most hate their job, waiting for Fridays and dreading Mondays. They’ve subconsciously squared to live an uneventful or fearful life, because switching to an alternative career path looks pretty disruptive, not to say, (initially) painful.
Your choice of a meaningful life lies squarely on you. If you’re a math educator, are the math things you’re presently doing square with what you desire in future? For instance, are you waiting until you retire to write that book? Or until the kids go to college to start working on that manuscript? Whatever it is, just make sure that you don’t die with a book still inside you!
If you’ve been dubbed a square, or secretly see yourself as one, remember that squares are circles with corners, and over time, most of them do turn into a beautiful (imperfect) circle.
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.
Last week, I read on Facebook that one glass of iced lemon tea at some coffeeshops is now selling at $1.80, up from $1.20. An obscene 50% rise (or ruse?). Or an outrageous 66.67% increase if they charge us $2.00 for takeaway (even before the GST or VAT kicks in next year).
For those of us who’ve already used up our S$100 government voucher in less than a week, which is meant to help us in our daily expenses as part of the Household Support Package, it looks like we won’t enjoy the next iced lemon tea until the next voucher. I wonder when the next one is coming. In late 2022 or early 2023?
Looks or feels like those in the “write” business might have chosen the “wrong” profession, including moonlighters in academia, especially if their royalties since the pandemic—and now the Ukraine-Russia war—have headed south.
For the majority of us who’re not born with a silver spoon in our mouth, I suppose it’s probably not too late to seriously consider selling or distributing slightly dearer home-made iced lemon tea, barley drink, honey tea, and chrysanthemum tea to health-conscious customers.
Pandemic or Putin? Or Both?
A FB netizen commented: “Tea 1% + 1% Lemon + 1% Sugar + ALL 97% Water imply hardly anything to do with FOOD Shortage so please don’t divert the blame to Pandemic, UN or what have you NOT.”
The profit margins for selling beverages are a hundred times better than the returns or royalties earned from posing and solving math questions in school textbooks or assessment (or supplementary) titles.
Not IQ Nor EQ, But FQ
Talking about being street-smart rather than exam- or book-smart! When financial quotient (FQ) is worth more than (IQ + EQ).
Inflation provides an oft-unseized opportunity (disguised as a problem) for mathepreneurs to generate unexpected sources of income to make up for any (potential) loss in royalty or consultancy.
The advent of cryptocurrencies like Bitcoin and Ether has provided math educators worldwide with fertile resources to indulge themselves in creative mathematical posing and solving.
Unfortunately, the negative perception that cryptocurrency or crypto is a vector for serious organized crime and money laundering has led millions of half-informed or risk-averse folks to adopt a wait-and-see attitude vis-à-vis Bitcoin transactions.
Who/What Is Satoshi Nakamoto?
Nobody knows the identity of Satoshi Nakamoto. If the name isn’t a he or she or it, could the name be a covert group of cryptographers and mathematicians?
Like the modern-day equivalent of the Bourbaki group—the collective pseudonym of a group of predominantly French mathematicians in the 1930s, who tried to axiomatize mathematics to make it more rigorous?
So far, the few suspects—digital-currency addict Nick Szabo, Japanese mathematician Shinichi Mochizuki, and Co.—all have denied being the founder of Bitcoin, except for Australian computer scientist who loudly but unprovenly claimed that he is Nakamoto.
Crypto Math
Posing fertile crypto math questions is only limited by our imagination. Thanks to Bitcoin or cryptocurrency, NFTs, and the Metaverse, I’ve toyed around with a number of crypto math questions.
Below are a sample of Bitcoin-related questions that I hope would make their way into a math booklet fit for publication in a-not-too-distant future.
Bitcoins are divided into Satoshis: one hundred million Satoshis in each Bitcoin. At the current Bitcoin price, what fraction of a U.S. cent is worth the smallest fraction of a Bitcoin?
In 2010, a pizza restaurant agreed to accept ten thousand Bitcoins in exchange for two large pizzas. At today’s exchange rate, how much would each pizza be worth?
In September 2021, El Salvador approved Bitcoin as a secondary currency; in April 2022, Central African Republic followed suit. Which rogue or war-torn nation in Asia or the Middle East would be the first one to make Bitcoin its official currency? Or would it be “fine” city Singapore that would lead the way in becoming SE Asia’s crypto hub?
Crypto Apocalypse: What are the odds that due to hyperinflation (or a possible WW3 in the aftermath of the senseless Ukraine-Russia war) people would start losing faith in Bitcoin to the point that it suffered the same fate as the Zimbabwean dollar bills?
A golf resort is rumored to have been gifted with 13.257 ETH and 12.5 bitcoin from a Middle Eastern prince. How much did the shady resort receive in cash donation from their criminal donor?
Crypto Winter Is Coming!
With news of a crypto winter in the horizon, let’s hope that the mathematics of Bitcoin or cryptocurrency wouldn’t deter math educators globally from getting involved in creative mathematical thinking and problem solving.
I don’t know about you, but I’m waiting for Bitcoin to drop under $10,000 as my next buy alert. The future lies in Bitcoin—or in blockchain.
In the aftermath of a Singapore permanent resident who was bitten 26 times by a romp of otters in 10 seconds at the Singapore Botanic Gardens, which attracted mixed reactions from both locals and foreigners, I entertained the idea how math teachers could use this once-in-a-lifetime incident to indulge in some problem posing for elementary math students.
As natural swimmers, Singapore’s smooth coated otters, once thought to be extinct, have made a comeback to the island-state. They are believed to have swum across the Straits of Johore and made their homes here. Their present “locations of choice” are: Bishan Park, the Kallang River estuary, Marina Bay, and Singapore Botanic Gardens—and the Singapore Zoo.
Singaponacci Numbers and the C-Word
Mathematically or theoretically speaking, without culling, Singapore’s otters could exponentially grow as fast as Fibonacci’s rabbits, although otter sexperts think there are alternative humane ways of family planning.
An “otterman” who was furious that netizens had uttered the C-word against the cute-looking furry creature blamed them for spreading white lies or fake news about these “critically endangered animals.”
The Fear Factor
These “urban pests” seem to be better protected under the Wildlife Act than we humans against the Delta and Omicron variants. They’ve the SPCA behind them, but we’ve the POFMA* and FICA** over us to police our online behaviors.
Can you distinguish an adult otter from a baby seal?
Co-Existing with Covid and Otters
Last week, in the light of Singapore’s otter saga making the headlines overseas, I tweeted the following:
Otter Math: If the present population of 150 otters doubles every leap year, while Singapore’s annual fertility rate continues to head south, with zero immigration allowed, when would otter babies outnumber human babies? https://lnkd.in/gVfqjEZ8
Animals’ cruelty against humans: Otters bit a Singapore Botanic Gardens visitor 26 times in 10 seconds. What are the chances that such a similar incident happening again are less than the odds of someone being abducted by an alien? https://bit.ly/3oH93IO
Canals, Condos & Churches
Singaporean river otters are notorious in devouring dear ornamental fish found in condominiums and churches. If the probability of rich people disliking otters is x folds higher than that of poor folks, guesstimate x.
What are the odds that someone from a middle-income family in Singapore is more likely to cross paths with an otter family thanks to a greening Singapore, which provides an ideal milieu for otters to breed stresslessly, compared to Singaporeans, who often can’t even find a little space to do their private business?
Otter: Singapore’s Unofficial Mascot
Think of Singapore as an otter, and its frenemies-neighbors as crocodiles and monitor lizards. When threatened by its natural resources-rich, but militarily weaker, neighbors, Singapore would hit back to defend itself. Sure, they’d use low-cost warfare tactics like forest haze and arsenic-polluted rainwater to frustrate their little-red-dot neighbor—a form of asymmetric warfare to neutralize the enemy by natural and man-made means.
How not to mismanage Singapore’s otter population
Thou Shalt Not Catch an Otter!Fine: S$X
How much is the fine for someone caught capturing or trapping otters in the “fine” city of Singapore? What are the odds that a repeated offender could get jailed or/and caned for their illegal activity?
What If? Exotic Singapore Cuisine
Does otter meat taste more like chicken, beef, or pork? What if Singapore started farming otters to satisfy the desire of adventurous gourmets? Like crocodile, deer, or frog meat, could the legalized consumption of otter meat be a lucrative food business for both locals and aliens, who are looking for an exotic dish (halal, kosher & vegetarian), if there were a mismanaged otter population control in future?
An Otters Naming Contest
In the past, Singapore had the famous or notorious romp of otters called the “The Marina 10.” Now, we’ve local groups like the Zouk Family. Has the raft of otters that bit the über-unlucky British man 26 times at the Singapore Botanic Gardens been christened? If not, why about having a national contest to name them following the recent biting incident, which could have potentially led to Singapore’s first case of “death by otters”?
Otter Math for Mature Students
Let’s end with a grades 1–2 otter math question to tickle actress Sandra Bullock’s two children and their peers, who’ve been jabbed (or maybe even boosted) with a dose or two of the Singapore math vaccine to protect them against the plague of innumeracy:
After seeing an otter family of twelve devouring the fish in their condominium pond, a number of children were traumatized for weeks. Five children had recurring nightmares about the attack. There were three fewer children having nightmares than those needing counseling.
a) If two boys and a pair of twin sisters met up with a school counselor, how many children were altogether affected by the otter invasion?
b) Guesstimate how many fish were eaten up by the hungry otters in a few minutes before they made their way to the swimming pool.
Answer: (a) 13 children (b) Hint: Think about the demographics of the condo residents.
A grades 4–6 Singapore math question
Answer: 1. 8 koi fish. Can you solve the question in more than one way without algebra?
* POFMA: Protection from Online Falsehoods and Manipulation Act ** FICA: Foreign Interference (Countermeasures) Act
