Category Archives: Mathematical Humor

The lightest side of Singapore math with a slight dose of irreverence

Formula One Singapore: Blessing or Curse?

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Since 2008, except in 2020 and 2021, when the night race was cancelled due to Covid-19, Singapore Grand Prix has had its highs and lows.

Most locals would hardly shed a crocodile tear should the three-day noise-pollution event cease to be held in the “fine” city in future, albeit a record 302,000 “fans” turned up for the 2022 F1 Singapore GP.

In 2019, when the hazy event venue was at an unhealthy level, race organizers were giving away thousands of free F1 tickets to beef up the number of attendees for the F1 night race to avoid the sight of empty seats. Who says that begging and betting are mutually exclusive?

The environmentally unfriendly event appeals mostly to diehard F1 fans, as F1 fatigue had already set in among locals who’d attended a few more canned events after 2008.

The Singapore F1 night race looks more like a curse than a blessing for a segment of the population, especially retail shop and restaurant owners (with cancelled meal orders and table reservations), and service providers (few gym or tuition classes, haircuts, etc.) in the Marina Bay area.

Some of them have their sales dwindled this week due to customers’ difficulties of navigating around road closures, or the latter’s decision to give their venue of choice a miss to avoid any inconvenience.

And religious services and recreational activities in the area had to be cancelled as a result of noise pollution from this weekend event. Even the holy souls or health freaks, who need to be in the vicinity, rain or shine, pollution or not, would have to find alternative parking space to attend to their weekly rituals.

A Hell of a Race

Deemed the “most difficult race of the year,” Singapore’s Marina Bay circuit is notorious for its plethora of 90-degree corners along the 23-turn lap. And F1 drivers’ annual complaining mantra is the sauna- or oven-like conditions of warm and sweaty Singapore.

God in the Wheels—F1 Goes Spiritual

Pray for the F1 Singapore Grand Prix

In the aftermath of F1 race organizers seeking protection from God, gods, or goddesses, back in 2016, I’d irreverently coined “F1 Blessing”:

F1 Blessing: When religious leaders from various faiths come together annually to pray for the Singapore Grand Prix and to bless the Formula One night race.

Example: The public has no idea whether the F1 blessing requires the holy men to go through a list of prayer items; if not, what exactly are they praying about?—safety of drivers? good sale of tickets? no crazy spectators crossing the racing track when the race is on? God knows!

by MathPlus September 09, 2016

F1 Prayers

Let’s pray these three F1 prayers for 2023:

1. Pray that few diehard (or better still, zero) fans at the Singapore Grand Prix would be infected with Pirola, the newly recognized variant of Omicron (Covid-19 virus strain BA.2.86), and that no foreign spectators would bring any WHO-undetected variants into the local community.

2. In past events, we’d had unexpected guests like lizards and snakes at the Formula One Singapore event. Pray that no reptiles, giant hornets, or extraterrestrials would show up on Sunday.

3. Pray that all corrupt men and women, be they billionaires, ministers-millionaires, or organizers, who’re behind the “success” of the F1 Singapore Grand Prix, would be exposed, fined, and imprisoned for their illicit financial gains.

F1 Math

A math quickie on Singapore’s “Highest Noise Pollution Day”: Local drivers have so far failed to make the grade at the Singapore GP. Which is more likely: A Singaporean F1 driver making it to the top ten, or Singapore getting into the World Cup final?

Prayerfully and environmentally yours

© Yan Kow Cheong, September 17, 2023.

The Clock Problem

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On July 12, @PicturesFoIder x-ed (or tweeted) the following picture:

Picture © Anon.

Is this another ill-posed math question? Or just another arguably creative solution that put the teacher or tutor in a catch-22 response?

Let’s look at a sample of comments for and against the given answer.

They don’t want a digital clock!
This is the correct answer for anyone that is somehow confused! 🤔

Teacher needed to say clock with hour and minute hands.

The question says “small clock”, not “analog clock”, therefore the answer is correct.

This is everything what’s wrong with current educational system.
It sure does prepare you.
To think in the frameworks they want you to think. For example “there is only one right solution to a problem and that ain’t it”

thats what happens when you let kids use ipads at a young age

This student should be transferred to art school immediately

On one hand I’m scared that the new generation can’t read physical clocks, on the other hand, I’m surprised by the out of the box thinking

If my child received a X for that answer, I would challenge it. There is nothing at all wrong. It is a small clock showing ten past eleven. 100% accurate. IF they wanted a conventional clock face that should have been stated. I’d have given 2 ticks for innovative thinking!

The question doesn’t specify that it meant “analog clock” plus it says “10 minutes past 11:00” which implies digital time as opposed to “10 minutes past 11 o’clock” which would imply analog time.

I would have drawn an analog and digital clock with a note saying the request was ambiguous and next time be more specific. Also how small? Another ambiguous request

How many of these responses would you agree or disagree with? Valid or invalid, or preposterous in some instances, most of these comments can’t be discounted offhand.

Followers or Oddballs?

At a time when politicians, pastors, or even prisoners are often hypocritically or insincerely pushing for an overhaul of their rigid educational system (from which they themselves benefited much)—which promotes rote learning or regurgitation, or prepares students to the test—are math teachers ready for students’ unconventional or disruptive solutions, which often border on the ridiculous or irreverent?

If a child (or a trained chimpanzee) presented the solution below to the above problem, what would your response or reaction be?

Picture © Anon.

Would you mark it wrong or partially correct, because he or she had failed to take account that time on a clock is determined by the hour hand alone, with the minute hand acting as a mere convenience? Or in layman terms, the hour hand had also moved when the minute hand took a sixty-degree turn.

Or would you take this opportunity to introduce nonroutine (or more subtle faux) questions like the ones below?

1. What is the angle measure between the hands of a clock at 10 minutes past 11:00?

2. A clock reads ten minutes past eleven. What time would the clock read if the hands of the clock were interchanged?

3. Are there other times of the day when the hands of a clock would also show the same angle measure as when they were at 11:10?

The Positives of Ill-Posed Questions

An ill-posed question, or the unexpected answers to such a flawed question, is a gold mine for creative mathematical problem posing. It not only provides an off-the-wall sense of humor, but also gives math educators an opportunity to address students’ mathematical loopholes or their half-baked understanding of concepts.

Positively & creatively yours

© Yan Kow Cheong, August 13, 2023.

Calculus for Mature Students

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Math Meme from Math Lady Hazel

Like math, calculus needn’t sulk (to any degree)! In the hands of an excited middle-school or high-school math teacher, or with access to some creatively written (or online free) resources, the ABCs of calculus can even be taught to elementary school kids.

Think of Mr. Jaime Escalante who had successfully taught calculus to cohorts of Mexican-American students. There is zero excuse why we can’t emulate him to teaching it to financially disadvantaged or minority groups.

What’s Calculus to You?

Do you parrot the textbook definition of calculus to your students? The mathematics of (instantaneous) change. Or do you share it as the branch of mathematics that measures “how far an object has been going fast,” and “how fast an object has gone far”?

Moons ago, I cheekily approached or indirectly defined calculus via the division of zero as follows:

0 ÷ 0: The Raison d’être of Calculus

With some dose of irreverence, the bête noire of high-school or college math could turn out to be a much beloved topic even among the so-called innumerates or mathematically challenged.

Calculus for the Numerati

It’s debatably said that without an exposure of some delta-epsilon calculus, no man or woman can honestly claim to be “mathematically educated” or “mathematically civilized.” Sounds like mathematical pride or arrogance, isn’t it?

Or just an example of “mathematical elitism” à la Trump for those fakes who declare themselves as being a “very stable genius.” Even Einstein had remarked that calculus was “the greatest advance in thought that a single individual was ever privileged to make.”

Fr: Ryan Truong on Facebook’s “Mathematical Mathematics Memes”

Recently, while working on the Urban Calculus manuscript, I forced myself to reread some of the out-of-print pop calculus titles like David Berlinski’s A Tour of the Calculus, Steven Strogatz’s The Calculus of Friendship, and Mary Stopes-Roe’s Mathematics with Love to get an intuitive feel of the subject again.

For a long time, the thought of taking up the challenge to read Newton’s The Principia (even its annotated version) frightens me, because the complexity of the content is beyond me. I’ve a good excuse not to borrow the thick copy from the university library unless I want to look like a “mathematical snob” carrying it around, or use it as a temporary doorstop.

When Comics and Calculus Converge

Calculus for All

Let’s play our part in sharing the mathematical gospel of Newton and Leibniz that calculus needn’t be a four-letter word—how these two mathematical greats had exorcized the demon out of the division of zero.

Why not strive to be the “James Escalante” of your school, state, or country? You’d be the changemaker or mathematical savior in motivating some undecided or mature students to read a calculus course or module in college?

Differentially and integrally yours

© Yan Kow Cheong, July 30, 2023.

A Question on Inequality

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Fr: Ralph McConahy on Facebook

Many years ago, I read about the co-authors of a handbook for mathematics teachers in primary schools warning readers not to use the sign “<” or “>” (because the symbols were removed from the primary school syllabus); instead, they suggested using phrases like “more than” and “less than.”

For example, teachers were to avoid setting questions in these formats:

34 is 6 > ☐
8 > 43 is ☐

Instead, they’d rephrase them as “34 is 6 more than ☐.” and “8 more than 43 is ☐.”

Similarly, they’d refrain from posing inequalities questions such as the following:

7 < ☐ is 15.
9 < 25 is ☐.

And also avoid problem sums like the one below:

What is the largest (or greatest) whole number that can be placed in the box to make the statement true? 8 + ☐ < 40

Why the Ban (with or without a Fine)?

Based on teachers’ feedback that young (or even older) schoolchildren are often confused about the similarity of the two symbols < and >, that’s likely a key why that prompted local curriculum math specialists in the “fine” city to ban these “unequal symbols” in primary school mathematics moons ago.

Inequality Metaphors from the Sunshine State

Over the years, to reduce the confusion between < and >, some elementary math authors have come up with some witty ways to help schoolchildren remember which is which.

For instance, students are often taught to see the symbols as hungry alligators or crocodiles with gaping mouths—these reptiles always want to eat the larger numbers, so the open mouth will always face this.

Observe that the < looks somewhat like a lopsided L, which reminds us that it denotes less than. Or, in any true statement, the large open mouth of the symbol is on the side of the greater quantity, and the small point is on the side of the lesser quantity.

No More Ban

Like last year’s repeal of Section 377A in pseudo-puritan Singapore, based on the CPDD’s Primary Mathematics Textbook 2A (2022), the inequality signs too are now free to roam the pages of any MOE-approved primary 2–6 textbooks and workbooks.

In the aftermath of zero ban on inequality signs, questions that involve comparing and ordering numbers would no longer be symbolically penalized or criminalized for using the “>” and “<” signs (until further notice).

Below are a sample of three “uninhibited” Singapore math primary two inequality questions:

Which sign will you use, > or <?
(a) 45 ☐ 42
(b) 81 ☐ 71
(c) 317 ☐ 407
(d) 734 ☐ 724

Fill in the boxes with ‘<’ or ‘>’.
(a) 35 ☐ 53
(b) 65 ☐ 62
(c) 79 ☐ 68

It’s not uncommon to see once-banned open-ended questions now gracing the pages of primary math textbooks, such as the following:

In 38 > 33 + ☐, what could the missing number be?

It looks like we’ve come some way in restoring the inequality signs in the (lower) primary school syllabus. Now that the mathematical resurrection of these symbols has taken place, does their confusion among schoolchildren still remain a concern for both teachers and parents?

An Inequality Quiz

Let’s end with a math quiz that tests our basic knowledge of inequalities.

1. How many types of inequalities in elementary school math are there?

2. Which metaphor(s) would you use to help children who are prone to mistake one inequality sign for another?

3. Name half a dozen math inequalities in real life that schoolchildren could relate to.

4. “An inequality is an equation that forbids the use of an equal sign.” True or False.

Symbolically yours

© Yan Kow Cheong, July 9, 2023.

Singapore’s PSLE Math Paper

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There is an educational (or psychological or emotional) price a country has to pay if it wants its students to continually rank among the top three in international comparative studies like TIMSS and PISA, or in regional or international math contests and competitions.

An irreverent definition of Singapore’s most dreaded school exam paper

Understandably, parents in Singapore are unhappy about the difficult PSLE (grade 6) math questions that are used to assess their children, before they’d graduate from primary (grades 1–6) school to secondary (middle) school.

And the oft-politically correct or modeled answers from the city-state’s Ministry of Education (MOE) hardly ever pacify or satisfy teachers, parents, and caregivers; in most cases, the canned suggestions or quasi-laughable solutions only make them angrier or more cynical.

PC Slogans for Kiasu Parents

Be it the mantra that “every (local) school is a good school,” or that parents need to help or educate their children believe that “their self-worth or value isn’t dependent on their exam grades” is easier preached than practiced.

When politicians or MOE officials preach to parents that they needn’t be paranoid about their children’s PSLE exam or math score, because it’s not the end of the world, it’s like ex-loansharks-turned-philanthropists or ethically challenged ex-CEOs- or ex-bankers-turned-preachers now telling the financially struggling public that money isn’t everything, or that they’d not make money their god. For the haves to tell the have-nots, it’s utter hypocrisy, to say the least.

Answers and oft-ill-edited half-baked solutions are usually from tutors or teachers-moonlighters.

Tuition: A Necessary Evil for the Nation

Without compulsory tuition or heavy parental involvement, the majority of elementary math students in local schools would likely struggle to score a decent grade in their PSLE math paper.

Singapore’s PSLE math paper with its quota of brain-unfriendly questions looks like a necessary evil that would help define or maintain the “fine” city’s high standard of mathematics regionally and internationally.

From Mid-Year to Mock Exams

This year, Primary 6 students didn’t have to sit for mid-year exams at school, because last year, Education Minister Chan Chun Sing had said that the move would allow them to “focus more on their learning and less on marks.”

In the aftermath of the MOE’s move to do away with all mid-year exams for primary and secondary schools, tuition centers saw a golden opportunity to lure kiasu parents with their mock mid-year exams, whose questions are generally harder (not better) than those set in the PSLE math paper.

Other than parental or peer pressure to excel, most students’ undue stress could be traced to the difficulty of math questions set by neighborhood schools (driven by school rankings) and tuition centers (powered by profits), which are generally harder than those that appear in the PSLE math paper. Yes, they’re the two big culprits that set an unhealthy number of nonroutine questions that often demoralize the kids, by making them feel like they still “aren’t that good in math.”

A Promised Land for Geeks—and Tax Fugitives

Singapore is a “promised land” for those who’re born or blessed with the “mathematical gene” or for those who’d afford a private tutor. However, for the majority of average or math-anxious school children, we can only pray that PSLE math wouldn’t become their bête noire, and that God would keep them motivated and focused as they go through this oft-stressful rite of passage of their schooling years.

I might sound like a mathocrite (short for “mathematical hypocrite”) in giving mathematical or parental advice; nevertheless, let me end with this educational slogan that is worth reiterating, because I believe that the sooner we put it into practice, the less stressful (or peaceful) our life will be: Our math scores or grades don’t define us—in or out of school, and certainly not in life.

Grade-consciouslessly yours

© Yan Kow Cheong, June 18, 2023.

What’s Your Life PhD?

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For the majority of people around the world without a PhD, the academic title is often creatively or cynically assigned a different meaning. Talking of poking fun at those who make a living in an ivory tower—the image of an “ivory tower” is used in the Bible in the Song of Songs (7:4) to describe a woman’s purity—the lay public’s general impression or perception of most PhDs is often anything but positive. Could this be due to some subconscious “intellectual envy”?

Maybe because when they think of academics becoming politicians or of them serving as consultants or advisors for an oft-inept or corrupt government (or of an educational consultant for a publishing house hoping to boost their school adoption rate), many have mixed feelings about these exam-smart folks, who are mostly “un-street-smart,” when it comes to solving everyday life or real-world problems for their fellow citizens—their oft-halfwitted decisions often serve as a living proof of their (practical) unintelligence rather than their intelligence.

PhDs to Save the Planet from Covid-19

Below are three entries I submitted during the lockdown two-odd years ago.

Trump’s Covid-19 Con-sultant
Was Cummings, ex-PM Johnson’s “corona jerk”?
One rule for the Cummings and
one for the common people.

Be it the canned “Permanent Head Damage” or “Post Holiday Depression,” new meanings associated with the acronym are only limited by our imagination.

Boosted Jabs at PhDs

A few years ago, I started relooking at new meanings of a PhD. Two such revised definitions were:

Cheat PhD on the Cheap
God’s Doctorate Disciples

What’s your life’s PhD, especially when you respectfully compare yourself with those with big titles, most of whom often have infinitesimally positive or quasi-zero impact on those around them?

Meanwhile, why not pray, help, and do rather than just preach, hope, and delay?

© Yan Kow Cheong, March 25, 2023.

A North Korea without the Kims

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North Korea and the Kim Dynasty

Way back in 2017, when ISIS or radical Islamist ideologies were making inroads in a number of developing or war-torn countries, and North Korea then looked like the safest place on the planet from green terrorism, I coined North Korea as follows:

North Korea: Where jihadists daren’t go in trying to Islamize infidels unless they don’t mind going to hell sooner than later to meet up with ex-dictators Kim Jong Il and Kim Il Sung.

ISIS or the Taliban is no match for Dictator Kim Jong Un’s trained killers, if these Mohammedan jihadists dream of going to North Korea to set up their Caliphate.

by MathPlus May 31, 2017

The Kim Dynasty

The Kim dynasty is “like grandfather, like father, like son.” Would the world witness a gender change at the top, if a sister (and subsequently a daughter, legitimate or not) were to be reluctantly appointed, thus breaking the decades-long patriarchal political order? A modern-day Jezebel in waiting!

North Korea & Math Education

Imagine if North Korean students were to take part in TIMSS and PISA, what are the chances that they would outrank or outwit their Singaporean or mainland Chinese counterparts in both math and science?

Or, if you needed a part-time or freelance value-for-money coder (or licenced hacker), would you choose one from Singapore, India, or North Korea? The choice is pretty clear, isn’t it?

Dark Political Math

From Reel Trump to Real Kim

After Comrade Kim’s last heartbeat, what are the odds that the two Koreas might be reunited as one? Or would this reunification happen earlier, say, if the hermit nation was forced to surrender following a series of bombings on Pyongyang or on its nuclear sites by the Allies?

Broken Bromance Blossomed

Imagine that Donald J. Trump is miraculously re-elected in 2024, and the Trump-Kim lukewarm bromance is rekindled with a flurry of more “love letters.”

Reel Leaders Nominated for Nobel Peace Prize

What are the odds that they’d eventually have a tête-à-tête at the White House? A post-pandemic reunion between two vainglorious rogues that could help raise their chances of being nominated for the Nobel Peace Prize for the nth time, as their actions (or inactions) arguably prevented a WW3!

The Peacefakers Sans Clothes

What if fearing that he’d end up on the wrong side of eternity, and also be remembered as a modern-day Hitler or Stalin, comrade Putin decided to return the annexed lands, including Crimea, to Ukraine? Would the world witness a peace prize being shared by the unholy Kim-Putin-Trump trio? Or would all three be re-nominated for the Ignoble Peace Prize instead?

The Leadershit Series for Rogue Leaders

Fake Missile for Anti-NATO*

Would the US and allies (yes-nations) only stop playing the more-sanctions game when Kim Jong-un’s patience ran out—when he decided to launch a “fake” missile targeting one of its neighbours, which would force them to take the rogue nation seriously or to treat the Kim dynasty with respect or reverence?

Peacefully & prayerfully yours

* NATO = No Action, Talk Only

© Yan Kow Cheong, March 3, 2023.

Numbers vs. Letters

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A while ago, I tweeted the following math or language or brain question, hoping for a layman answer from math educators or linguists or brain specialists, who might offer a quick-and-dirty explanation to that puzzle.

Tweet from @MathPlus

Another nontrivial question is: “For a number of us who’d no choice but to learn or master a few languages or dialects to survive, why do we feel at home decades later still vocalizing or reciting numbers in the (foreign) language we used while we’re growing up rather than in our mother tongue or lingua franca?”

Personally, I find it easier to recite or utter a sequence of consecutive numbers, or to work with mathematical symbols, in French rather than in English or Chinese—or in my Hakka dialect. I find it puzzling because French has now been relegated to my third or fourth language, and I hardly ever use it in my daily communication, or in any tête-à-tête meetings, other than occasionally dropping some French jargon in my writing to appear like a faux Francophone.

Although today English is my second language and lingua franca, French remains my language of choice when it comes to self-talking (or maybe even daydreaming or dreaming) in numbers or numerals.

It looks like if we learn numbers and symbols in a certain language or dialect in our formative years, we’re brainwired to recall or recite numbers in that particular language later in our adult life. This occurs especially when we’re on our own, even though we may be equally versed or quasi-fluent in other languages or dialects.

Like cycling, driving, or swimming, it appears that reciting numbers in the language of our childhood days in later years is something that stays with us for life.

When self-talking about numbers, do the majority of you who’re forced to be bilingual, trilingual, or multilingual to survive (or thrive) in school and in the workplace also share my experience? Sounds like it’s a neuro rather than a numero question we’re trying to address here!

Linguistically yours

© Yan Kow Cheong, February 11, 2023.

Lunar New Year

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The Spring Festival

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.

Generously yours

© Yan Kow Cheong, February 5, 2023.

Math Word of the Day: Formula Feeding

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On May 26, 2021, I hypocritically posed the following:

Family Math: The positives and negatives of formula feeding vis-à-vis breastfeeding. How to get millions of fathers involved in parenting, while giving the mother a break if formula feeding isn’t an option.

Below are three tweets, two of which are more than a decade old.

Got 🥛 : 🐄 or 🐐?

Lactose intolerant? Allergic to cow milk? Nature “next best thing to mother’s milk”: Singapore’s Goat Milk vine.co/v/i7OiHuQW62K (@MathPlus on 12/6/15)

Zero Fat ≠ No Fat

Beware of labels: Zero fat, no-fat (skim milk) contains 0.4 grams of fat per cup (or 86 calories per cup). A “zero lie”! #zero (@Zero_Math on 1/7/11)

Meeting & Milking the Cow!

You don’t get milk from a cow by sending a letter, or by calling on the phone. You get milk from a cow by sitting by its side & milking it. (@MathPlus on 12/2/12)

You may also be interested in Crime Watch and Crime Math, which is related to infant formula or powder milk.

Dutifully & responsibly yours

© Yan Kow Cheong, January 27, 2023

Formula Feeding ≡ Father Bonding