Later On

A blog written for those whose interests more or less match mine.

In a Single Measure, Invariants Capture the Essence of Math Objects

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Erica Klarreich writes in Quanta Magazine:

When Lisa Piccirillo solved a decades-old mystery about the “Conway knot,” she had to overcome the knot’s uncanny ability to hoodwink some of the most powerful tools mathematicians have devised. Known as invariants, these tools form the backbone not just of knot theory but of many areas of mathematics, extracting essential features of mathematical objects and detecting when two objects are fundamentally different from each other.

As the name suggests, an invariant is an attribute that doesn’t vary as you change an object’s inessential features (where “inessential” means whatever you need it to in a particular context). An invariant is a distillation of some innate quality of the object, often in the form of a single number.

To take an example from topology, imagine covering a ball with stretchy netting that partitions the surface into shapes such as triangles and rectangles. The number of shapes will, of course, depend on the netting you use, as will the numbers of edges and corners. But mathematicians figured out centuries ago that a certain combination of these three numbers always comes out the same: the number of shapes plus the number of corners minus the number of edges.

If, for example, your netting partitions the sphere into a puffed-out tetrahedron (with four triangles, four corners and six edges), this number works out to 4 + 4 − 6 = 2. If your netting instead forms the pattern of a soccer ball (with a total of 32 hexagons and pentagons, 60 corners, and 90 edges), you again get 32 + 60 − 90 = 2. In some sense, the number 2 is an intrinsic feature of sphere-ness. This number (called the sphere’s Euler characteristic) doesn’t change if you stretch or distort the sphere, so it is what mathematicians call a topological invariant.

If you wrap a netting around a doughnut surface instead, you always get an Euler characteristic of 0. On a two-holed doughnut, you get −2. The Euler characteristic for surfaces belongs to a series of invariants that allow mathematicians to explore shapes in higher dimensions as well. It can help topologists distinguish between two shapes that are hard to visualize, since if they have different Euler characteristics, they cannot be the same topological shape.

Invariants are also used to study the 15-puzzle, a classic toy consisting of square tiles numbered 1 through 15 that you slide around in a 4-by-4 grid. The goal is to put a mixed-up arrangement of tiles in numerical order from left to right, starting from the top row. If you’d like to know whether a particular arrangement is solvable, there’s an invariant that gives you the answer. It outputs either “even” or “odd” depending on the sum of two numbers: the number of slides required to carry the blank square to the bottom right corner and the number of tile pairings that are in reverse numerical order (with the blank square representing tile 16).

Whenever you slide a tile into the empty square, both these numbers switch parity (evenness or oddness). So the parity of their sum never changes, meaning that it is an invariant of the sliding process. For the solved configuration this invariant is even, since both numbers are zero. So any configuration with an odd invariant is utterly hopeless.

When it comes to knot theory, distinguishing between knots is a tricky business, since you can make a knot unrecognizable just by moving the strands of the loop around (mathematicians think of knots as occurring in closed loops rather than open strings, so they can’t be undone). Here, invariants are indispensable, and mathematicians have come up with dozens that distill different features of knots. But these invariants tend to have blind spots.

Take, for example, an invariant called tricolorability. A knot diagram is tricolorable if  . . .

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Written by LeisureGuy

4 June 2020 at 3:57 pm

Posted in Math

“Police Blinded Me in One Eye. I Can Still See Why My Country’s on Fire.”

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Linda Tirado writes in The New Republic:

I have been weeping since Friday night, because that is the night I was shot in the face. I have, since then, begun to piece together what happened to me: It wasn’t a rubber bullet, it was a foam bullet. I was standing near Minneapolis’s Third Police Precinct. I will not regain sight in my left eye. I will need more surgeries. But I have not been crying for my lost vision; rather, it feels as though my body is reacting to what is happening to my country.

This has been coming for years; anyone with wisdom has felt it in their bones. You cannot elevate to leadership the most base elements of humanity, the most amoral and reckless and cruel, and think that things will go well for the nation. Back in 2016, a week or so before the presidential election, I wrote a piece about how Donald Trump’s campaign speeches were openly fascist, how they spiked fear in those parts of my soul that remember being raised as a nativist. Back then, you couldn’t say Trumpism was a form of fascism—it was considered a bit hysterical.

That remained true in mainstream consensus throughout 2017 and 2018. Sometime last year, more people started to realize that the norms were shattering, and they weren’t reassembling by way of any magnetic properties of self-healing constitutionalism. It was after we put migrant kids in camps and after the president started encouraging people to batter the press and after impeachment, but before the current stage of authoritarian collapse, which has us gassing clergy and desecrating churches for photo ops. Fascism is always a slow slide into routinized mayhem, noticeable to most people only in retrospect.

Since I was shot, I have been worldwide front-page news: China is using my bloodied face as propaganda, for instance. Hundreds, if not thousands, of interview requests have flooded in. All anyone wants to talk about is freedom of the press, if I am angry, what I will do next. I think that I am angry—but no more than I was this time last week, when I was watching America burn for the pleasure of our vainglorious leader. I lost an eye; George Floyd lost his life. What right do I have to rage on my own behalf?

I rage instead on behalf of my country, for the hundreds of millions of people who were appalled when Trump administration officials tried to change the words of Emma Lazarus into a brief for white resentment. I rage for the irony of the line “yearning to breathe free,” because we would not have our cities ablaze had our leadership cared an instant for the freedom or breath of those it considers its opposition, which is to say the citizenry.

If we must talk about press freedom, we must also talk about the First Amendment’s absolute guarantee of freedom of peaceable assembly—and the fact that it is the police, not some mythic rogue formation of antifa saboteurs, who are escalating conflicts. We know this because journalists keep documenting it, and because any person in a demonstration can become a momentary journalist if they have a cell phone and a data connection. We have seen the violent thugs in their stormtrooper uniforms joyfully unleashing violence, spitting on citizens during a pandemic, running civilians over with their SUVs, saying fuck your rights—and worse, fuck your life.

I have lost half of my vision, but I lack no clarity: There can be no peace without justice, and no justice without full-throated, damningly righteous anger. I am asked over and over again why are people burning and looting, and I wonder what anyone thinks they would do if they spent their whole lives being told they were lesser than and not equal, and then one day they woke up to a police state.

We saw this six years ago in Ferguson, Missouri, where I was embedded for weeks in the protest zone, sleeping in a tent with a group of youths who called themselves Lost Voices. It’s important to remember that the designated protest zone was about five blocks of a street called Florissant—and that people lived in cul-de-sacs off that street. That meant they had to drive through the tear gas and chaos to take their children home safely. Once police gassed the children, mothers broke down the glass door of the McDonald’s trying to get milk for their babies’ eyes. Employees were throwing milk to them, rushing to the back cooler to get more because tear gas is self-evidently bad for children. None of this got mentioned in the next day’s reporting from the mainstream press, which simply recited that the McDonald’s was looted.

A few days after that, I was taking photos on the highway where protesters were blocking traffic. Media were behind concrete barriers, clearly working as press rather than participants. An officer dressed all in black with plastic shin guards and elbow pads, dangling zip ties from his belt, pepper-sprayed me point-blank in the face. I have a picture of him somewhere, three feet away from me, shot when my camera was staring down the muzzle of his chemical weapon, and the hatred and glee twisting his face still gives me nightmares.

I am thinking about him a lot in recent days, as I watch footage of TV crews being arrested on live air and police spraying what they call “less lethal” rounds into crowds indiscriminately. I am thinking about him as I scroll Twitter, where brave men hide behind burner accounts to tell me “play stupid games win stupid prizes”—alt-right shorthand for calling me a traitor, to either the country or my race. In their discursive world, good white ladies are not supposed to scream that Black lives matter or point out the bigotry inherent in a system of law enforcement that started with slave patrols. White women, to those kinds of men, are not supposed to do much of anything except be quiescent until it is time to have babies or furnish a sexual pretext for some good old-fashioned racism. We are certainly not supposed to refuse to learn our lesson, even after we have been punished by having an eye put out.

Perhaps my best and worst quality is my defiance: I am . . .

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Written by LeisureGuy

4 June 2020 at 3:48 pm

Tactile Art

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John Lee Clark writes at the Poetry Foundation:

i

Downtown St. Paul is home to one of the most extensive skyway systems in the world. The sprawling maze connects buildings via enclosed bridges above the streets. The skyway solves one of our challenges as DeafBlind people traveling through a city: crossing busy intersections. My family lived there for as long as we could afford to because it was such a joy to be a mouse racing inside and out, up and down, plying my long single whisker. Following my nose, I found all the best places to eat and, following other instincts, I infiltrated all the cleanest bathrooms hidden away from the masses.

One day my partner, Adrean, an ASL Deaf artist, came home to tell me about something she’d spotted. It was a sculpture of a giant open Braille book. She had never gone that way before, but I’d passed by it several times. It stood in a building’s courtyard, some paces from the street. You had to see it to see it.

A few days later friends from out of town were visiting. We took them out to our beloved Ruam Mit Thai, and after our feast we gave them a tour of the city. I remembered Adrean’s sighting and asked her to show us the public work.

It turned out to be a huge sheet of metal propped up, its bottom edge near the ground and its top edge a foot taller than I. Each Braille dot was the size of a golf ball. This made it impossible to read the text, which was supposed to be a passage from a Walt Whitman poem. Although the sheet mimicked the open face of a book, with two facing pages, each line ran across both pages.

There was a plaque with the title, artist name, perhaps a statement. Did the statement pay tribute to Braille? This information was not available in regular Braille.

As I struggled to read what the golf balls had to say, a security guard trundled out of the building. He spoke no sign language but we got the message. One of the nice secret restrooms was close by, and we hurried there to wash our hands.

ii

Museums are difficult to get to. They don’t want me to touch anything. They require that I make an appointment—by phone, no less. So my information about mainstream aesthetics has largely come from ducks.

They rule over gift shops, Goodwills, and garage sales. Squeaking rubber versions have long been infants’ first encounter with artifice. Minnesota’s state bird is the loon, and many homes and stores here feature wooden, ceramic, metal, stone, plush, and glass loons. Waterfowl are a favorite of woodcarvers. There is even a DeafBlind Canadian who whittles, paints, and sells ducklings. What they all have in common is a flat bottom. A goodly portion of their natural anatomy is taboo. They are meant to appear floating on the still waters of a tabletop, a windowsill, or a bookshelf.

The hitch is that were I to handle a live duck paddling across a pond, I would be able to feel it as a whole, for water is not a tactile barrier as it is a visual one.

Small wonder, then, that one of my definitions of beauty is a certain stuffed wood duck in the nature center at Richfield, Minnesota. A piece of ordinary taxidermy, its feathers are ridiculously soft. “Wood duck,” I was inspired to write in a slateku, a form I invented using the Braille slate, “I feel for you/You never had hands to stroke/Your own wings.” Even more bewildering are its round velvet bottom and granular webbed feet, which bespeak a master creator.

iii

“Here, you can touch my face.”

“Thank you, no.”

“No, it’s fine. Really.”

“Nah. I just—”

“I want you to.”

Well, I want to tell them, what you are offering for my inspection is just a skin-covered skull.

“A head,” jokes the eighteenth-century British comedian George Alexander Stephens, “is a mere bulbous excrescence, growing out from between the shoulders like a wen; it is supposed to be a mere expletive, just to wear a hat on, to fill up the hollow of a wig, to take snuff with, or have your hair dressed upon.”

A friend once showed me a prized possession of his, an egg-shaped sculpture. I could feel its eyebrows, nose, and mouth, but they conveyed nothing. For my sighted friend, it had an exquisite expression of serenity. “Peace,” it’s called.

At least it was bald. The bust of Mark Twain in a museum I visited in New York had him wearing a futuristic helmet, with fantastical whorling grooves. A terrible tumor grows under his nose. Ulysses S. Grant was similarly helmeted but had an iceberg stuck up his jaw.

Helmets notwithstanding, sculptors were onto something with nudity and gesture until the Victorians began to manufacture a statue for every philanthropist and politician. Of these “leaden dolls,” G.K. Chesterton grouses, “Each of them is cased in a cylindrical frock-coat, and each carries either a scroll or a dubious-looking garment over the arm that might be either a bathing-towel or a light great-coat.”

iv

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Written by LeisureGuy

4 June 2020 at 3:43 pm

Posted in Art, Daily life

The Only Hospital in Town Was Failing. They Promised to Help but Only Made It Worse.

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This reports shows how capitalists can be blood-suckers. Brianna Bailey reports The Frontier and in ProPublica:

It was the sort of miracle cure that the board of a rural Oklahoma hospital on the verge of closure had dreamed about: A newly formed management company promised access to wealthy investors eager to infuse millions of dollars.

The company, Alliance Health Southwest Oklahoma, secured an up to $1 million annual contract in July 2017 to manage the Mangum Regional Medical Center after agreeing to provide all necessary financial resources until the 18-bed hospital brought in enough money from patient services to pay its own bills.

But about a month later, hospital board members were summoned to an emergency meeting.

Early one morning in August 2017, Alliance’s CEO Frank Avignone told hospital board members that his company, which had boasted of access to up to $255 million from well-heeled investors, was out of money.

Alliance needed a line of credit, and the bank required the board’s permission to use the hospital’s incoming payments as collateral. If board members didn’t agree, paying nurses and other health care workers would be a “slight miracle,” Avignone said, according to an audio recording of the meeting that was obtained by The Frontier and ProPublica.

“There were supposed to be so many millions available,” Staci Goode, chairwoman of the hospital board, said during the meeting, asking what happened to the promises made just weeks earlier.

Investors needed to see an improvement in the hospital’s finances before committing their money, Avignone replied.

“We’re in a bad spot right now with our investors just like you are,” he said. “We’re out over our skis a little bit.”

Exasperated, Mangum’s hospital board approved the line of credit.

Over the next year and a half, Alliance borrowed millions of dollars from the bank. The company paid itself and businesses tied to its partners a significant chunk of the money and then used $4 million from Medicare to help pay down the line of credit, according to interviews with town leaders and court records obtained by The Frontier and ProPublica.

Financial pressures have forced the closures of 130 rural hospitals across the country in the past decade, leaving communities grasping for solutions to avoid losing health care in areas with the most need. Rural health experts fear many more won’t survive the coronavirus pandemic.

An investigation by The Frontier and ProPublica found that some private management companies hired to save the most vulnerable hospitals in rural Oklahoma have instead failed them, bled them dry and expedited their demise.

It starts like this: Rural communities desperate to protect their hospitals hand the reins to management companies that portray themselves as turnaround experts and vow to invest millions of dollars.

Those companies are often hired without background checks or any requirement that they have experience running hospitals. They operate under nearly nonexistent state and local regulations with little oversight from volunteer governing boards. After they extract hefty monthly fees, they sometimes cut ties and leave rural communities scrambling.

In Mangum, a prairie town of 2,800 people in southwestern Oklahoma, the hospital is fighting several ongoing lawsuits stemming from Alliance’s management. It also has filed its own litigation, accusing Alliance of fraud and of siphoning away millions of dollars from the hospital. Alliance disputes the allegations and is countersuing to collect $1 million in management fees it claims the hospital still owes for its services.

Leaders from the Oklahoma towns of Seiling and Pauls Valley, who relied on Alliance’s assurances that it could revive their hospitals, similarly accuse the company of making lofty promises and leaving them deeper in debt.

Alliance’s failure to produce promised investments for the Pauls Valley Regional Medical Center made it harder for the hospital to escape the debt it had incurred under its previous management company, said Jocelyn Rushing, the town’s mayor. The hospital closed in October 2018 under Alliance’s management.

“What I can tell you is that Frank is a smooth talker, and he definitely knows how to play the media to his side,” Rushing said, referring to Avignone. “And he left Pauls Valley high and dry.”

Avignone denies wrongdoing. He said . . .

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Written by LeisureGuy

4 June 2020 at 1:41 pm

Contaminants Found in 90% of Herbal Supplements Tested

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The FDA does not jurisdiction over herbal supplements as it does over drugs, so it cannot act to ensure purity or validity of claims of efficacy. Thus the decision by Congress is to use the honor system, with corporations on their honor to ensure that their products are pure, safe, and efficacious. That works pretty much as one would expect. Dr. Michael Greger blogs:

The majority of dietary supplement facilities tested were found noncompliant with good manufacturing practices guidelines.

“The U.S. public is not well protected” by current dietary supplement recommendations, an issue I explore in my video Dangers of Dietary Supplement Deregulation. Sometimes, there is too little of whatever’s supposed to be in the bottle, and other times, there’s too much, as I discussed in my video Black Raspberry Supplements Put to the Test. In one case, as you can see at 0:20 in my video, hundreds of people suffered from acute selenium toxicity, thanks to an “employee error at one of the ingredient suppliers.” Months later, many continued to suffer. Had the company been following good manufacturing practices, such as testing their ingredients, this may not have happened. In 2007, the FDA urged companies to adhere to such guidelines, but seven years later, the majority of dietary supplement facilities remained noncompliant with current good manufacturing practices guidelines.

What are the consequences of this ineffective regulation of dietary supplements? Fifty-thousand Americans are harmed every year. Of course, prescription drugs don’t just harm; they actually kill 100,000 Americans every year—and that’s just in hospitals. Drugs prescribed by doctors outside of hospital settings may kill another 200,000 people every year, but that doesn’t make it any less tragic for the thousands sickened by supplements.

Sometimes the supplements may contain drugs. Not only does a substantial proportion of dietary supplements have quality problems, the “FDA has identified hundreds of dietary supplements…that have been adulterated with prescription medications” or, even worse, designer drugs that haven’t been tested—like tweaked Viagra compounds. About half of the most serious drug recalls in the U.S. aren’t for drugs but for supplements, yet two-thirds or recalled supplements were still found on store shelves six months later.

There is also inadvertent contamination with potentially hazardous contaminants, such as heavy metals and pesticides in 90 percent of herbal supplements tested, as you can see at 2:09 in my video. Mycotoxins, potentially carcinogenic fungal toxins like aflatoxin, were found in 96 percent of herbal supplements. Milk thistle supplements were the worst, with most having more than a dozen different mycotoxins. It’s thought that since the plant is harvested specifically when it’s wet, it can get moldy easily. Many people take milk thistle to support their livers yet may end up getting exposed to immunotoxic, genotoxic, and hepatotoxic—meaning liver toxic—contaminants. How is this even legal? In fact, it wasn’t legal until 1994 with the passage of the Dietary Supplement Health and Education Act. Prior to that, supplements were regulated like food additives so you had to show they were safe before they were brought to market—but not anymore. Most people are unaware that supplements no longer have to be approved by the government or that supplement ads don’t have to be vetted. “This misunderstanding may provide some patients with a false sense of security regarding the safety and efficacy of these products.”

This deregulation led to an explosion in dietary supplements from around 4,000 when the law went into effect to more than 90,000 different supplements now on the market, each of which is all presumed innocent until proven guilty, presumed safe until a supplement hurts enough people. “In other words, consumers must suffer harm…before the FDA begins the slow process toward restricting [a] product from the market.” Take ephedra, for example. Hundreds of poison control center complaints started back in 1999, increasing to thousands and including reports of strokes, seizures, and deaths. Yet the FDA didn’t pull it off store shelves for seven years, thanks to millions of dollars from the industry spent on lobbying.

What did the companies have to say for themselves?  . . .

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Written by LeisureGuy

4 June 2020 at 1:20 pm

Wee Scot on The Dead Sea, with iKon’s open-comb razor

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The Dead Sea recently arose (although only in a comment here), so I thought I’d bring it out. It’s always a pleasure to use, and the Wee Scot did a commendable job on the lather. This iKon open-comb is a first-rate razor and it did an efficient job with great comfort. A splash of Diplomat aftershave (despite the unprepossessing label, IMO a very fine aftershave) and I’m ready and williing for a new day.

Written by LeisureGuy

4 June 2020 at 10:08 am

Posted in Shaving

James Mattis Denounces President Trump, Describes Him as a Threat to the Constitution

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This is highly unusual. Jeffrey Goldberg writes in the Atlantic:

James Mattis, the esteemed Marine general who resigned as secretary of defense in December 2018 to protest Donald Trump’s Syria policy, has, ever since, kept studiously silent about Trump’s performance as president. But he has now broken his silence, writing an extraordinary broadside in which he denounces the president for dividing the nation, and accuses him of ordering the U.S. military to violate the constitutional rights of American citizens.

“I have watched this week’s unfolding events, angry and appalled,” Mattis writes. “The words ‘Equal Justice Under Law’ are carved in the pediment of the United States Supreme Court. This is precisely what protesters are rightly demanding. It is a wholesome and unifying demand—one that all of us should be able to get behind. We must not be distracted by a small number of lawbreakers. The protests are defined by tens of thousands of people of conscience who are insisting that we live up to our values—our values as people and our values as a nation.” He goes on, “We must reject and hold accountable those in office who would make a mockery of our Constitution.”

In his j’accuse, Mattis excoriates the president for setting Americans against one another. . .

Mattis’s dissatisfaction with Trump was no secret inside the Pentagon. But after his resignation, he argued publicly—and to great criticism—that it would be inappropriate and counterproductive for a former general, and a former Cabinet official, to criticize a sitting president. Doing so, he said, would threaten the apolitical nature of the military. When I interviewed him last year on this subject, he said, “When you leave an administration over clear policy differences, you need to give the people who are still there as much opportunity as possible to defend the country. They still have the responsibility of protecting this great big experiment of ours.” He did add, however: “There is a period in which I owe my silence. It’s not eternal. It’s not going to be forever.”

That period is now definitively over. Mattis reached the conclusion this past weekend that the American experiment is directly threatened by the actions of the president he once served. In his statement, Mattis makes it clear that the president’s response to the police killing of George Floyd, and the ensuing protests, triggered this public condemnation. . .

Here is the text of the complete statement.

IN UNION THERE IS STRENGTH

I have watched this week’s unfolding events, angry and appalled. The words “Equal Justice Under Law” are carved in the pediment of the United States Supreme Court. This is precisely what protesters are rightly demanding. It is a wholesome and unifying demand—one that all of us should be able to get behind. We must not be distracted by a small number of lawbreakers. The protests are defined by tens of thousands of people of conscience who are insisting that we live up to our values—our values as people and our values as a nation.

We must reject any thinking of our cities as a “battlespace” that our uniformed military is called upon to “dominate.” At home, we should use our military only when requested to do so, on very rare occasions, by state governors. Militarizing our response, as we witnessed in Washington, D.C., sets up a conflict—a false conflict—between the military and civilian society. It erodes the moral ground that ensures a trusted bond between men and women in uniform and the society they are sworn to protect, and of which they themselves are a part. Keeping public order rests with civilian state and local leaders who best understand their communities and are answerable to them.

James Madison wrote in Federalist 14 that “America united with a handful of troops, or without a single soldier, exhibits a more forbidding posture to foreign ambition than America disunited, with a hundred thousand veterans ready for combat.” We do not need to militarize our response to protests. We need to unite around a common purpose. And it starts by guaranteeing that all of us are equal before the law.

Instructions given by the military departments to our troops before the Normandy invasion reminded soldiers that “The Nazi slogan for destroying us…was ‘Divide and Conquer.’ Our American answer is ‘In Union there is Strength.’” We must summon that unity to surmount this crisis—confident that we are better than our politics.

Donald Trump is the first president in my lifetime who does not try to unite the American people—does not even pretend to try. Instead he tries to divide us. We are witnessing the consequences of three years of this deliberate effort. We are witnessing the consequences of three years without mature leadership. We can unite without him, drawing on the strengths inherent in our civil society. This will not be easy, as the past few days have shown, but we owe it to our fellow citizens; to past generations that bled to defend our promise; and to our children.

We can come through this trying time stronger, and with a renewed sense of purpose and respect for one another. The pandemic has shown us that it is not only our troops who are willing to offer the ultimate sacrifice for the safety of the community. Americans in hospitals, grocery stores, post offices, and elsewhere have put their lives on the line in order to serve their fellow citizens and their country. We know that we are better than the abuse of executive authority that we witnessed in Lafayette Square. We must reject and hold accountable those in office who would make a mockery of our Constitution. At the same time, we must remember Lincoln’s “better angels,” and listen to them, as we work to unite.

Only by adopting a new path—which means, in truth, returning to the original path of our founding ideals—will we again be a country admired and respected at home and abroad.

See also: From the June 2020 issue: We are living in a failed state

And: From the July/August 2020 issue: History will judge the complicit

Written by LeisureGuy

3 June 2020 at 4:54 pm

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