Calculus for Babies

A quarter-odd century ago, I came across Donald Cohen’s Calculus by and for Young People (Ages 7, Yes 7 and Up) (1989). The co-founder and teacher of The Math Program subscribed to the philosophy that children are capable of behaving as (little) mathematicians.

Apparently, kids could be exposed to a quasi-formal treatment of integration and differentiation without an ∫ or a dy/dx.

Little could I divine that three and a half decades later a physicist-mathematician-turned-science author would tease tiger or kiasu parents with his Calculus for Babies.

Photo © Anon.

Cal 4 Babies & Toddlers

After Chris Ferrie’s Pythagorean Theorem for Babies came out in 2022, I knew that it’d be just a matter of time before the author would give us Calculus for Babies (2024), under the “bestselling” Baby University series.

Two days ago, I finally laid my hands on the anticipated title, which claims to introduce babies (and reminds grownups!) to the basic concepts behind calculus, arguably “explained in an easy-to-understand and fun way!”

Sounds like when you’re a mathepreneur, no audience is ever too young to learn the basics of any abstract or advanced math. Or the unspoken assumption that nurturing a little genius at home is possible even if your baby isn’t born or blessed with the “mathematical gene.”

Yes, it seems that it’s never too early to become a mathematician or scientist (as long as you’d afford to pamper your child with the [best?] oft-dear math titles or resources).

Before Ferrie’s Calculus for Babies was published on July 2, 2024, Esmond Cooper had come with a similar title on June 28, 2023. Debatably, Cooper’s “simplified guide introduces young minds to the fundamental concepts of calculus in a way that is clear, engaging, and accessible.” 

Cooper’s Calculus for Babies “aims to make learning enjoyable and foster a love for math from an early age, providing a strong basis for future mathematical understanding.”

After the success of sexy titles like Calculus for Cats (2001) and How to Teach Quantum Physics to Your Dog (2010), publishers probably bet that the next wave of pop math titles targeting parents who think that they’ve been blessed with a “talented or gifted” child should focus on calculus—and for unknown reasons not on algebra or geometry or trigonometry.

Interestingly, as far back as 2011, Omi M. Inouye had published a 54-page Introductory Calculus for Infants, which is about the mathematical adventure of two buddies as they discover the wonders of calculus.

From Beethoven to Newton & Leibniz 

If pregnant women are already playing classical music or reading bedtime stories to their unborn, it’s not preposterous that in a-not-too-distant future, some pre-rich writers or publishers would give birth to Pre-Calculus or Calculus for Your Unborn Child.

Just because calculus is the bête noire of college math, it doesn’t mean that your [talented, gifted, or blessed] newborn or toddler or preschooler can’t handle it. They can if you think they can!

Differentially & integrally yours

© Yan Kow Cheong, December 2, 2024.

Murderous Pi

Political Pi
 

When π thought that she’d never want to be associated with gun violence and senseless death, was she just being politically positive or naive?

Pi’s fear has now come true. Without repeated funding from gun manufacturers and pollution-enabled organizations, an obscene number of morally corrupt halfwitted lawmakers in TrumpLand would never get elected or reelected.

Even as you’re reading this, the odds of another senseless shooting or tragedy currently being witnessed in some red-pilled states are anything but zero.

It looks like if only those GOP selfish lawmakers and their loved ones or friends were the victims, maybe then they’d eventually do something about gun control; otherwise, it’s all NATO (No Action Talk Only).

Should Math Teachers Be Armed?

The Blame Game

People are sick of hearing the years-long canned story from inept and morally bankrupt politicians, who simplistically blame mental health, inequality, racism, or whatever social ills, rather than the free flow of guns for the recurring senseless deaths. It’s like the political equivalent of scapegoating the forced learning of algebra for the nation’s high innumeracy rate.

The U.S. is the only “civilized” nation in the developed world that has continually shortchanged its schoolchildren and their teachers. When profits and politicians triumph over principles and people.

Or, only in TrumpLand do we read about these senseless school gun deaths—when students shoot teachers and their peers because they can do it. And those preventable school shootings have only got more frequent and resulted in higher casualties in recent years.

Murderous Statistics

Below are some “murderous statistics” I’d tweeted over the years following numerous school shootings:

Sadistic Statistics from the National Rifle Association (NRA): “No guns, very high murder rates; more guns, very low murder rates.”

Murderous Math: People in the U.S. are 20 times more likely to be killed by a gun than someone else in another developed country.

Gun Ownership: Singapore ranks among the bottom 10 for the number of privately owned guns per 100 people.

It’s said that the chance of a 15-year-old boy dying by the age of 50 is now higher in America than it is in Bangladesh. The odds might even be higher now with Trumpism and moral bankruptcy plaguing Trumpublicans.

Deadly Statistics: The positive correlation between the coronavirus and the growing gun sales in the U.S., which has the highest crime rate in the developed world.

Dark Problem Solving

Ironically, school and gun shootings in the U.S. have provided math educators with real-life math problems, which could be used to hone students’ guesstimation skills. Two such questions are:

Political Math: Guesstimate how many “corrupt zeros” Trump and his billionaires-donors (and the mostly morally corrupt GOP lawmakers) pocketed, by protecting profiteering guns, insurance, and pharmaceutical companies.

Death Statistics: How many students in the U.S. senselessly die every year from gun violence?

No Gun Reduction, but God’s Protection

Let’s end with a haiku I recently X-ed in the aftermath of Trump’s lackey saying that school shootings are a “fact of life.”

Serial School Shootings

Money politics
that support gun businesses.
That’s a “fact of life.”

If the U.S. is dead serious about protecting schoolchildren and teachers from gun shootings, maybe it’d do it the Singapore way: Zero tolerance for gun sale to 99.99% locals. Vote out politicians who’re funded by weapon manufacturers.

Safely & securely yours

© Yan Kow Cheong, October 14, 2024.

Risqué Math Cartoons

 @pickover on 9/23/24

What about a math joke that could in itself be treated as a kind of math joke? A so-called metamath joke.

Admit it! It’s not uncommon that sometimes it takes a while before you can get a math joke, especially if it relies on some basic knowledge of advanced or abstract (or abstruse) math.

Experiencing that aha! takes a little longer. For novices, a mature or sophisticated math joke wouldn’t spark much mathematical joy in them—it seems or sounds more like a boring math textbook or a vanilla math teacher than anything else.

Of course, there are some math jokes that are open to different interpretations, especially those bordering on poking fun at “oft-proudly self-professed nonmath” or semi-innumerate folks, which may arguably be perceived as being elitist, racist, or sexist (or all three) in some illiberal or puritan circles.

Cartoon by Mike Seddon

MAGA Math (or Haiti Math?)

Below are two political math jokes I recently X-ed in the aftermath of racist rhetoric perpetrated or repeated by a white supremacist, who once proudly self-proclaimed to be the “least racist person on the planet.”

Political Algebra: A MAGA equation that could lead to the loss of millions of conservative votes, as people have had enough of racist or nativist language, which divides rather than unites a polarized nation.

An equation à la Trump

Dog Math: How not to submit your math homework—thanks to Trump and Vance and MAGA ambassadors of bigotry, who forget that they themselves are the offspring of immigrants. Estimate how many millions of kids would get away from this racist excuse.

My Dog Stole My Homework (Again)

These days, it’s getting harder to share a math joke or a quasi-clean limerick without being labeled with all kinds of four-, five-, or six-letter adjectives in the “cancel culture” or “woke” world we live in.

Are the days of adult or mature math jokes numbered? Is vintage recreational math found in out-of-print math puzzles titles, periodicals, or journals—which is often inarguably colonialist, racist, or supremacist—heading the way of the dodo?

Humorously & irreverently yours

© Yan Kow Cheong, September 27, 2024.

Facebook’s “UK Best Jokes & Puns” (Feb. 13)

Is Age Just a Number?

Cartoon © Anon. (being memeified)

I admit that I’m guilty of ageism, but I make zero apologies for exposing criminality or hypocrisy, especially among (past and present) heads of state.

For the majority of us, oft-reluctant law-abiding citizens of the world, few would admit that the criminal mind is a “creative” mind in disguise—one that we’d learn a thing or two from if we put aside our prejudices.

A Tale of Two Senior Presidential Candidates

What are the odds that the world might soon witness a presidential debate between a patient and a prisoner? If reelected, could either folk serve his full term?

Arguably, we’ve two power-hungry weak “leaders” that America could do without—when both seniors should be grandfathering (or con-sulting) rather than mis-leading or weakening the country for another four years (assuming their Creator doesn’t call them before their term is due).

Cartoon by Rick McKee (@Rick_McKee_Ink)

An Age Limit for Presidency

If the present president and his predecessor are too old to competently serve the challenges or demands of another term, shouldn’t lawmakers pass a constitutional law that no elected president shall be of a certain age on the date of inauguration?

What should that age limit be so that voters feel comfortable that any elected presidential candidate would fulfill his or her responsibilities of office? 65, 70, 75, or some other age?

Bitter Root ≡ Better Fruit?

If a bad tree can’t produce good fruit, it’s preposterous to see millions of voters expect a serial dishonest or corrupt “I-me-myself” candidate to deliver them from their years-old financial, social, and religious ills.

The theological or political argument that voters shouldn’t put too much emphasis on a candidate’s past manifold wrongs (who’s continually denied any wrongdoings) to assess or judge him sounds dangerously frightening. Understandably, the criteria to electing a president must be much lower than those used to choosing a pope. Really?

Cartoon by @DennisGoris (buff.ly/3VlEyaz)

King Saul 2.0

What are the chances that in Biden or Trump, we’d be witnessing a modern-day version of King Saul, whose rule would be cut short? Would those mostly morally bankrupt or corrupt appointees, who condone their lies and falsehoods, expect to operate in a blessed political environment? It looks more likely that political entropy would be the new normal come January 2025.

In politics, irrationality and hypocrisy often prove that a string of wrongs has near-zero bearing on the electability of a corrupt or rogue politician.

When one senior isn’t much younger than the other, the choice isn’t that difficult. You choose the one with (more) character, humility, and honesty. Voting for the alternative is flirting with ineptitude, dishonesty, and chaos—more pain and suffering for the majority of the population, who expect their next president to behave more like a priest or pope.

US Math: An Age Problem

Let’s end with a birthday joke on the two most senior presidential candidates in U.S. politics:

Q: Why even their diehard supporters see both Biden and Trump as old, who should be banned from taking part in a presidential election again?

A: At their last birthday, the candles cost more than the cake.

Electorally yours

© Yan Kow Cheong, June 27, 2024.

Thou Shalt Keep the Mathematical Sabbath!

The Weak Days of the Week

It’s said that working seven days a week makes one weak. Even workaholics who often wished they had an eight-day week couldn’t go on their routine hoping to ever be productive or creative sans experiencing a breakdown sooner than later.

Four-Day Work Week

Recently, there was much talk in the “fine” city about a four-day working week. Sounds like good news for tens of thousands of employees, especially those in the civil service, but bad news for profits-over-people employers or bosses in the private sector, who don’t subscribe to a workplace promoting a less than a 44-hour work week.

A recent poll found that around a third of Singapore workers surveyed expect a four-day work week to be the new normal in the next five years, with about twenty percents of them saying that their employers already offer such a work arrangement as an incentive to promote mental health at work.

Three-Day Weekend

What if schools switched to a four-day week? Would productivity (and creativity) for teachers and students go up? Would parents (and tuition or enrichment centers) support it?

Would the Ministry of Education dare to entertain such an idea in a tiger economy? As Singapore has evolved from a stigma-based streaming to a socially acceptable subject-based banding (a refined version of streaming) education system, it’s not a far-fetched idea of allowing students to come to school for just three or four rather than five days a week.

After all, the aftermath of Covid-19 had given them a foretaste of what schooling or blended learning might be in future, without depriving them of a formal education. A case of “less is more,” just like the politically correct “Teach Less, Learn More” mantra.

The Sabbath Mode

It’s never too late to put yourself in a Sabbath mode. You needn't be religious to see the benefits of the Sabbath—a mind-set that those in demanding jobs appreciate.

Think of those domestic workers in Singapore, whose employers expect them to work seven days a week, even if the Ministry of Manpower has mandated a one-day off for them every week.

A Mathematical Sabbath à la Singapour

Due to lack of understanding or wisdom, for a large part of my student and working life, I was often guilty of paying lip service to keeping the Sabbath, hoping to maximize my studying time, or minimizing my sleeping or resting time. A short-term success formula with long-term costly results.

Below is an attempt to define what a “mathematical sabbath” might entail for math educators around the globe, who long to be at their creative or productive best, week in, week out, without cutting corners on their rest or quiet time.

Your Mathematical Rest Day

Which Weekday Are You In?

On average, we’ve a three-scores-and-ten lifespan, or 70 years. If every day lasts a decade, which day of the week in your life are you in?

Sometimes God gives us an extra Monday, Tuesday, or Wednesday. How many souls do we want to bring along for the remaining days we’ve left with?

On a similar note, recently, I semi-poetically X-ed (or tweeted) the following:

@MathPlus on 3/28/24

Remember the keep the Sabbath day holy—and also the mathematical sabbath wholly.

Restfully & creatively yours

© Yan Kow Cheong, April 22, 2024.

Thou shalt not use an arrow for an equal sign!

Shot from Tiesha Sanders/Facebook

The above grade one math question from Texas is debatably ill-posed. However, the child answer of “7 ones” is “non-mathematically creative” or “irreverently correct.”

The teacher’s reply to the mother that “… this is the new math they have us teaching.” would puzzle many math educators outside TrumpLand. Arguably, the correct answer to this routine question has little or nothing to do with “new math” or “new new math” or whatever politically correct mathematical term we want to christen it.

The child’s “correct” answer that was marked wrong by her teacher defies logic. The use of an equal sign instead of an arrow would have minimized any misunderstanding whatsoever.

In “fine” Singapore, few teachers and parents would disagree that similar grade one place values questions are deemed routine. The chances of any local school teacher or tutor using arrows rather than equals signs for these drill-and-kill questions are quasi-zero.

Even for this ill-posed elementary math question, in the first part, if a child has correctly inserted the digit 7 under the ones column, and to expect them to give the same answer for the fill-in-the-blanks for the number of ones, it doesn’t sound too logical or commonsensical. The problem poser is unlikely to ask (or expect) for “7 ones” twice!

MAGA math: 7 ones ✔️

Insisting that the answer of “7 ones” is equally valid as “27 ones,” or denying that “7 ones” is incorrect, due to the way the question is posed, sounds like the mathematical equivalent of an ex-president insisting that he didn’t lose the election, albeit all the facts or results proved otherwise.

If the child isn’t wrong (because the parent isn’t wrong), and the teacher, too, isn’t wrong, so who’s right then? Could two conceptual negatives give a concrete positive?

Logically & truthfully yours

© Yan Kow Cheong, February 19, 2024.

Did You Commit a Prime Murder?

More than half a dozen years ago, I coined “Prime Murder” as follows:

What proportion of integers are prime? What are the odds that you might commit a prime murder at some point in your mathematical career, be it in teaching, editing, or writing?

Over the centuries, both professional and amateur mathematicians weren’t spared from it. Think of Pierre de Fermat who erroneously thought that 2^(2⁵) + 1, or 2³² + 1, was a prime.

So, for the majority of us, whether we’re born or blessed with the “mathematical gene” or not, the chances of being found guilty of a prime murder might not be limited to a single-digit percent. 

A 2019 graphic novel that explores two most basic mathematical objects: integers and permutations

Below is a simple exercise that might help reduce the odds of someone being a “prime murderer.”

1. Which of the following numbers are prime?

a) 919     b) 1,001     c) 1,763     d) 3,221     e) 8,081     f) 123,321

2. MAGA Math

a) The Pinocchio-in-Chief faces 91 criminal charges across four indictments, all of which he had pleaded not guilty. What are the chances that he is a prime suspect to these charges?

b) A “very stable genius” claimed to have an IQ of 211 (base p). Find the value of p.

c) The “MAGA-in-Chief” wanted a Secretary of State to find 11,780 votes, which would have given him one more than his Democratic opponent. Show that the requested number is not a prime number.

d)  A judge determined that the ex-“Commander in Cheat” had overvalued his Mar-a-Lago property by 2,047% besides claiming that his penthouse in New York was three times its actual size. Is this a “prime percent”?

In Prime Suspects, when Prof. Gauss & team looked at the autopsies of the victims of two seemingly unrelated homicides, they discovered the shocking similarity between the structures of each body.

Let’s end with a prime factoid: The writers of The Simpsons and Futurama have been smuggling complex mathematical ideas into prime-time television for over a quarter of a century.

Primely yours

© Yan Kow Cheong, December 18, 2023.