Here’s a Guy Who Really Made Good Use of His Time!

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Image courtesy of pxfuel.com

 

Nobody would ever accuse me of being a math whiz, though I do feel I have skills some of my younger acquaintances lack: I eschew a calculator on occasion to make sure the various cortices of my brain responsible for addition, subtraction, multiplication, and division get a little workout.

You just never know when your battery may run down while you’re stranded on a desert island and have an immediate need to balance your checkbook.

Oh, and there’s another mathematical task that I’ve mastered.

An older friend told me not long ago that physicians who are concerned that a patient may be in the early stages of dementia will test mental agility by asking said patient to subtract backwards from 100—by 8s.

I’ve gotten quite facile at that effort—and have moved on to 7s with similar success.

Why am I telling you all this? Because I’m inviting you to join me in exploring a story that involves number theory—a deep dive that I have no business whatsoever attempting.

But my friend Allan, who excels in math, knows I like quirky stories and thoughtfully sent me this one, which appeared in Popular Mechanics.

So once again, Annie plunges ahead—undeterred by her total lack of experience. I promise, though, that I won’t go beyond what I understand, which means there won’t be a whole lot of number theory here.

I hope not too many of you will be disappointed by this limitation…

Christopher Havens (Chris) is the name of the guy in the title. He’d made quite a mess of his life: a high school dropout, he had become a homeless drug addict.

And then in 2010, he committed murder, killing a 25-year-old man with whom he’d been feuding; there was apparently a methamphetamine connection.

He was convicted and sentenced to serve 25 years in the Washington Department of Corrections.

He didn’t immediately transform himself into a model prisoner—far from it. Soon after being incarcerated in 2011, his behavior earned him a place in solitary confinement.

That’s where and when he “got math”—recognized his love for mathematics.

He’d spend as many as 10 hours a day studying, and then entered the Intensive Transition Program, ITP, which he described (with a vulgarity) as

“a one-year program which helps people get their minds right. It’s designed to effectively aid you into ‘taking your head from your backside.’

“This was my schedule. Eat, math, remove my head from my backside, brush, rinse, repeat. It was an important time in my life.”

After that, he sought information to help him with his studies by writing the following letter:

“To Whom It May Concern:

I’m interested in finding more information on a subscription to Annals of Mathematics for personal use.

I’m currently serving 25 years in the Washington Department of Corrections and I’ve decided to use this time for self-betterment. I’m studying calculus and number theory.

As numbers have become my passion, can you please send me any information on your mathematic journal. Thank you…Chris Havens.

P.S.: I am self-teaching myself (sic) and often get hung on problems for long periods of time.

Is there anyone I could correspond with, provided I send self-addressed stamped envelopes?

There are no teachers here who can help me so I often spend hundreds on books that may or may not contain the help I need. Thank you.”

(It isn’t clear where he gets the “hundreds” he spends on books, but that’s not central to our story.)

The letter circuitously reached a man named Matthew Cargo in January, 2013. Cargo, then production editor for Mathematical Sciences Publications, forwarded it to two mathematicians: the parents of his partner, Marta Cerrruti.

Cerruti wrote about the results of that connection in phys.Org.

“Initially, my father, Umberto Cerruti, a number theorist who was a professor of mathematics at the University of Torino, Italy, agreed to help Havens simply because we asked him.

“My father thought that Havens was likely one of the many cranks that fall in love with numbers and come up with a flawed theory. To test him, he gave Havens a problem to solve.

“In return, my father received a 120-centimetre-long piece of paper in the mail, and on it was a long and complicated formula. My father entered the formula into his computer and to his surprise, the results were correct!

“After this, my father invited Havens to work on a problem involving continued fractions he was working on.”

OK, here’s where I have to stretch a bit. Continued fractions, which Euclid discovered in 300 BC, enable the expression of all numbers through sequences of integer numbers, which are positive and negative numbers expressed without fractions.

Cerruti gives pi as an example: the ratio of a circle’s diameter and circumference is written as 3.14159…

“The sequence of numbers after the initial digit continues forever and is totally chaotic. But written as a continued fraction its expression is simple and beautiful.”

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Continued fraction of pi. Image courtesy of commons.wikimedia.org

Although this particular aesthetic is beyond my ken,  Cerruti’s point is that continued fractions show the power of number theory.

Much of this is theoretical, pure math, but number theory plays an important role in cryptography today.

Even I understand that its many uses are applicable in both financial institutions and the military, among other areas. It’s the reason you can buy something online or pay your bills in what are for the most part secure transactions.

Havens was so motivated that he started a Prison Mathematics Project in which he explained math to other inmates.

The group met biweekly and used books sent by Cerruti’s father. That change from the man who’d been in solitary confinement struck me as extremely impressive.

And the story gets dramatically better:

From his prison cell, Havens made a significant contribution to the field of continued fractions—so significant that he is named the first author in an article published in the January, 2020, issue of the journal Research in Number Theory.

(If you want to read the article, you’ll have to plunk down $99 for it.)

He reached this lofty spot using the highly sophisticated tools of pen and paper, “exchanging ideas with his co-authors in Italy though hard-copy letters mailed across the ocean,” Cerruti writes.

Cerruti describes Havens’ pathbreaking work: He “showed for the first time some regularities in the approximation of a vast class of numbers.”

In essence, he provided number theorists with an important new tool whose applications may be vast. According to Cerruti,

“finding new ways for writing numbers is one of the most important problems for a number theorist, although the results may not have an immediate application.”

She points out that some supercomputers are employed solely for computing pi digits into the trillions.

Havens’ achievement has also had a huge impact on his own outlook and future plans.

He’s studying for an associate degree through the mail and is determined to complete bachelors and graduate degrees in math and to pursue a career once he’s released from prison.

And he hopes to turn the Prison Mathematics Project he founded into a nonprofit organization to help inmates with a talent for math.

He told Cerruti:

“I definitely have plotted out a long term life plan to accommodate paying a debt that has no price. I know this path is permanent…and there never is a day that it’s finally paid off.

“But this longevity in debt is not bad. It’s inspiration. Maybe this will sound stupid, but I serve my time in the company of the soul of my victim. I dedicate a lot of my biggest accomplishments to him.”

Annie

Continue reading “Here’s a Guy Who Really Made Good Use of His Time!”

On Watching Michelle Obama Becoming…

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Image courtesy of commonswikimedia.org

She is an international icon, yet she talks with strangers as if they are her very best friends. She revels in her status, yet openly discusses her vulnerabilities. She moves deftly from riotous humor to wrenching soul-searching with an apparent spontaneity that’s surely grounded in practice. She’s a marvel.

If you’re fortunate enough to have Netflix access, you can watch the new documentary, Becoming, now. If you don’t have Netflix, I’m sure it will be more widely distributed in the near future.

I don’t think my description of the film will detract from your experience: Michelle Obama’s magnetism—and the poignancy of the recent trajectory of her life and that of President Obama—must be witnessed to be fully appreciated.

(The amazing orator, President Charisma, plays a relatively small part in this documentary.)

But if you’d rather watch it without a sense of deja vu, I excuse you from reading this post—with absolutely no hard feelings.

I viewed the documentary as a welcome antidote to the present. It combines snippets from Michelle’s 34-city 2018 book tour following the publication of her book Becoming, with shots from those often happy White House years filled with hope, and remembrances of her childhood and early years with Barack.

It reminds us that our national reality not so many years ago says much about who we are as a people—the good and the bad—but in better perspective than many of us can currently manage.

When asked what those last hours in the White House were like, she says they were very busy. Apparently, daughters Malia and Sasha often had sleepovers there with their friends, and the friends pleaded for one last visit the night before.

So the 44th First Lady of the United States ran around calling out to sleepy young girls,

“Wake up; the Trumps are coming and you got to get out!”

While we’re on the subject of the White House, I note two actions Michelle took early on.

She and Barack were dismayed they were being served by aging African American or Latino men dressed in tuxedos. These men could have been her uncles, she said.

“I didn’t want them [her daughters] seeing grown men serving them in tuxedos.”

So they changed the dress code.

Additionally, she begged the housekeepers not to make Malia and Sasha’s beds. As she explained:

“They won’t be living here forever. I am not raising girls who don’t know how to make a bed!”

The last day in the White House was highly emotional, but she knew she had to keep her feelings hidden for fear her tears would be misunderstood. But once on the plane, she says:

“I sobbed for thirty minutes—eight years of trying to do everything perfectly.”

Elsewhere she notes that

“It was hard to wake up every day and maintain the level of perfection absolutely required of Barack and me as President and First Lady.”

She recalls the first campaign, in 2008. She had become an effective campaigner, and the opposition knew it. She was depicted as “the angry black woman,” and Fox News commentators asked: “Does Michelle Obama hate America?”

The fun “fist bump” the Obamas shared became a nefarious sign of their alleged radicalism, their “otherness.”

This barrage had an impact: she began to talk less freely and became “more scripted than ever before.”

Being so falsely portrayed wasn’t easy. She is candid about the impact.

“That does hurt. That changes the shape of a person’s soul.”

If anyone wonders whether Michelle Obama will ever run for office, which is an oft-heard liberal dream, I believe she has definitively provided her answer.

With Obama’s election, she recalled:

“Life changes instantly—we were shot out of a cannon and didn’t have time to adjust. Every blink of eye is analyzed. Your life isn’t yours anymore.”

There’s surely a measure of irony in the fact that she chose this very public book tour as a time to reflect on what she’d just been through, to be “unplugged for the first time in a long time.”

I don’t think it’s a stretch to suggest that it was also a thoroughly justified means of reminding the public of Barack and Michelle Obama’s many solid accomplishments in those eight years—at a time when they have—in public, at least—silently watched the White House’s current occupant systematically seek to destroy every one of them.

There’s no mention in the film of Michelle’s famous “kitchen” garden, that tangible evidence of her successfully launching a campaign to improve the health of Americans, especially school children, which included improvements in the quality of school lunches.

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Image courtesy of letsmove.obamawhitehouse.archives.gov

To me, the destruction of that garden and all its bounty was an early and potent symbol of the senseless cruelty and disregard for the public’s health that Donald Trump has demonstrated (an attitude writ large in our present disastrous situation).

But back to our heroine. On the book tour, she greets each admirer with warmth and humor. They love her, and she basks in that affection. She challenges young people, urging them to ask themselves these questions: Who are you? What are you about? And what gives you joy?

They tell her how profoundly she’s affected them. One young woman says that Michelle’s discussing her postpartum depression helped her get through her own. Michelle describes the benefits she derives:

“Sharing somebody’s story gives me what I don’t have because all my actions are so sanitized. It helps me stay connected.”

Watching her connect with each book buyer on those interminably long lines was one of my favorite parts of the film.

Notably, in one gathering she met with the members of two book clubs who had read Becoming: one comprised of all African American women; the other all white women. The book “creates bridges.”

One of the white women describes her family’s being part of the “white flight” from Chicago neighborhoods as the racial composition changed. Michelle observes that it was her family from whom they were fleeing.

She points to her class photos: the kindergarten class has many white faces; the 8th grade class is entirely African American.

When an African American teenage girl asks her how she’s able to avoid feeling invisible, she pays tribute to her parents: at the dinner table on the South Side of Chicago, she and her brother were always encouraged to speak up, ask questions.

“My parents always made me feel visible,” she says. “We can’t afford to wait for the world to regard us as equal. I have high expectations of young people.”

She describes in detail a searing occasion on which—without the confidence her parents’ instilled—she might have been invisible. Her brother had gone to Princeton, but the high school guidance counselor told Michelle she was not Princeton material.

She did go to Princeton, where she learned on arrival that one of her intended roommates had moved out after hearing she was African-American, believing she was dangerous.

Still, she excelled there, graduated from Harvard Law, and learned that not everyone in these hallowed institutions is as special as one might think.

She makes a similar observation based on world travels and being in some of the most rarefied meetings among leading, exalted individuals.

“I’ve been at the most powerful tables in the world. I’m coming down from the mountaintop. Don’t listen [to the naysayers who may question these young people’s worth]; they don’t know how they got there.”

Of the guidance counselor’s misguidance, she says she’s “still a little salty about that one.”

In the course of the book tour, she fills large venues—with people exuding happiness and good feeling.

“What I experience in those big arenas is the power of gathering: we’re sharing a set of experiences.”

The image of those diverse, highly civilized audiences is in stark relief to the Presidential rallies marked by hatred and divisiveness that we’ve been witnessing in the past several years.

Michelle provides a stunning insight into her thoughts, feelings, and White House life in detailing the day that marriage equality became the law of the land.

It happened to be the same tragic day as the funeral services for the African Americans gunned down in church by a white supremacist in Charleston.

When the Obamas returned from Charleston to the White House, now illuminated with the appropriate equality colors, they saw joyous people congregating in front. “I need to be a part of this,” she said, dragging Malia as her partner in crime to get outside.

After pulling on the locked front doors, she persuaded the Secret Service to let them slip out the back, where they saw some of the celebration from the steps.

“I had to have some indicator that all this is worth it,” she says—“we’re moving the country forward.”

She expresses sadness about the voters in 2016.

“A lot of our folks didn’t vote. It was almost like a slap in the face. I understand those who voted for Trump. But people who didn’t vote at all—young people, women—thought this was a game. They just couldn’t be bothered at all. That’s my trauma.”

I sure hope that sentiment resonates broadly this November.

Does she still feel that “when they go low, we go high?” she was asked. “I try,” she says, with a wry smile. But she does still feel there’s a desire to overcome “the racialism and tribalism that are tearing this country apart.”

“If we’re gonna get anywhere with each other, we have to say who were are…I am the former First Lady, and the descendant of slaves…

“The energy that is out there is much better than what we see. This country is good; the people are good.”

When Stephen Colbert interviews her about filling arenas with people from all different backgrounds, she says,

“I’m not alone. I like this not being divided. Share stories; be vulnerable. I remain hopeful that people want better…”

She has been doing just that. And now,

”My life is starting to be mine again. There is another chapter waiting for me out there.”

I haven’t yet read her book Becoming. But I look forward to reading every chapter. And then watching her evolve into her next chapter…and the next…

Annie

Continue reading “On Watching Michelle Obama Becoming…”

Another Trip to the Lighter Side…and a Message of Hope

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I guess I’m making a large leap in assuming that a) you haven’t seen this photo before; and b) you’ve had the Zoom online experience that so many of us have been introduced to in this time of social distancing.

At any rate, this image makes me laugh, and I hope you’ll enjoy it too. Even if you haven’t “Zoomed,” with so many of us worldwide living in isolation, I can tell from various posts that there have been some pretty weird changes in our daily routines. For example: It’s 5 pm. Is it really necessary for me to exchange my pajamas for sweat pants and a T-shirt?

I send good wishes to you all, and hope things are as pleasant as possible as we make our way through the specter of the pandemic during this time of Easter, Passover, Vaisakhi, Vishu, the Bengali and Tamil New Years, the Buddhist Theravada New Year, and Spring.

(I just learned that one of the traditions of Theravada is to build sand castles, with the belief that the waves’ washing away the effort symbolizes the removing of one’s mistakes and enables personal renewal. It’s a reminder of our impermanence, which by coincidence was my theme when I wrote this poem quite recently.)

All these occasions call forth the hope for better days ahead–something that whether or not we follow a religion is sorely needed these days. I am especially thinking of those among us who are in pain, mentally and/or physically, or have suffered a loss.

Though we’re separated, we know what we must do to speed the process that will enable us to emerge from this pandemic and be together once again. To that extent, we do have a measure of control, even if it seems that events have overtaken us.

And then, I fervently hope, we can begin the important efforts to work together–locally, nationally, internationally–to make this a more just world, where we care for one another, ensure that extra attention and resources are provided to those who have been hardest hit,  and at last give Mother Nature her due.

Annie