A New Discovery About Matrices

The first time I studied linear algebra was when I was an exchange cadet at the Air Force Academy.  That was the only course in all of my college education in which everyone in the course failed.  Well, I earned a low 60-something percent, but since mine was the highest grade in the class, I got an A.  Yay me.

Not having learned anything in that course, and being petrified of linear algebra because of it (and perhaps because over 25 years had since passed), I convinced my advisor to let me retake the course in my master's program.  It was in that course that I learned a little bit about eigenvalues and eigenvectors, interesting components in the study of matrices.  It was when meeting a former student a few years ago, and telling him about what little we teach about matrices in pre-calculus class, that I learned from him about a YouTube video that explained eigenvalues.  That was when all those calculations I'd done made actual sense!

Physicists have now added to our understanding eigenvalues and eigenvectors:

The physicists — Stephen Parke of Fermi National Accelerator Laboratory, Xining Zhang of the University of Chicago and Peter Denton of Brookhaven National Laboratory — had arrived at the mathematical identity about two months earlier while grappling with the strange behavior of particles called neutrinos.

They’d noticed that hard-to-compute terms called “eigenvectors,” describing, in this case, the ways that neutrinos propagate through matter, were equal to combinations of terms called “eigenvalues,” which are far easier to compute. Moreover, they realized that the relationship between eigenvectors and eigenvalues — ubiquitous objects in math, physics and engineering that have been studied since the 18th century — seemed to hold more generally.

Although the physicists could hardly believe they’d discovered a new fact about such bedrock math, they couldn’t find the relationship in any books or papers. So they took a chance and contacted Tao, despite a note on his website warning against such entreaties.

“To our surprise, he replied in under two hours saying he’d never seen this before,” Parke said. Tao’s reply also included three independent proofs of the identity.

A week and a half later, the physicists and Tao, whom Parke called “a fire hose of mathematics,” posted a paper online reporting the new formula. Their paper is now under review by Communications in Mathematical Physics. In a separate paper submitted to the Journal of High Energy Physics, Denton, Parke and Zhang used the formula to streamline the equations governing neutrinos.

Experts say that more applications might arise, since so many problems involve calculating eigenvectors and eigenvalues. “This is of really broad applicability,” said John Beacom, a particle physicist at Ohio State University. “Who knows what doors it will open"...

Matrices do this by changing an object’s “vectors” — mathematical arrows that point to each physical location in an object. A matrix’s eigenvectors — “own vectors” in German — are those vectors that stay aligned in the same direction when the matrix is applied. Take, for example, the matrix that rotates things by 90 degrees around the x-axis: The eigenvectors lie along the x-axis itself, since points falling along this line don’t rotate, even as everything rotates around them.

A related matrix might rotate objects around the x-axis and also shrink them in half. How much a matrix stretches or squeezes its eigenvectors is given by the corresponding eigenvalue — in this case, ½. (If an eigenvector doesn’t change at all, the eigenvalue is 1.)

Eigenvectors and eigenvalues are independent, and normally they must be calculated separately starting from the rows and columns of the matrix itself. College students learn how to do this for simple matrices. But the new formula differs from existing methods. “What is remarkable about this identity is that at no point do you ever actually need to know any of the entries of the matrix to work out anything,” said Tao.

So cool.

Wind Turbines--Landfill Disaster

What good is wind power here in California?  When the wind blows, they shut the power off.

But what about the rest of the country?  Isn't wind the cleanest, least polluting form of energy generation there is, free of adverse effects?  Uh, no:

But the upgrades for Iowa’s growing wind industry, which is already among the nation’s largest, are creating some unexpected challenges.

MidAmerican’s retired blades, destined for the Butler County Landfill near David City, Nebraska, about 130 miles away, are among hundreds that will land in dumps across Iowa and the nation. Critics of wind energy say the blades’ march to a landfill weakens the industry’s claim it’s an environmentally friendly source of energy.

“This clean, green energy is not so clean and not so green,” says Julie Kuntz, who opposes a Worth County wind project. “It’s just more waste going in our landfills"...

He acknowledges, though, that disposing of the blades is a challenge. Wind energy generation, now topping 100 gigawatts nationally, will create 1 million tons of fiberglass and other composite waste, said Laird, director of the National Wind Technology Center at the National Renewable Energy Laboratory in Colorado.

“The scale of the issue is quite large,” said Laird, whose group is working to develop new blade materials that will enable reuse. “It’s quite a bit of material. And it’s a larger sustainability issue. We would like everything that’s manufactured to be reusable or recyclable"...

Landfill operators thought the composite blades, cut in 40-foot or larger sections, could be readily crushed and compacted. “But blades are so strong — because they need to be strong to do their job — they just don’t break,” said Amie Davidson, an Iowa Department of Natural Resources solid waste supervisor.

“Sometimes pieces fly off and damage equipment” in the compacting process, she said. “Landfills are really struggling to manage them, and they just decide they can’t accept them.”

So far, only one facility in north Iowa is taking the blades, while other landfills are assessing whether they will.

Bill Rowland, president of the Iowa Society of Solid Waste Operations, said he’s unsure “we as a society” considered what would happen to the blades as older turbines are repowered.

“There wasn’t a plan in place to say, ‘How are we going to recycle these?’ ‘How are we going to reduce the impact on landfills?’” said Rowland, director of the Landfill of North Iowa near Clear Lake...

The difficulty in reusing blades adds to the complaints opponents make against wind energy. Some who live near the turbines complain that low-frequency noise and light flickering from the blades make them ill. And the spinning blades can kill migrating birds and bats.

Blade disposal is “just one of many factors we’re concerned about,” said Kuntz, the Worth County wind farm opponent.

Expensive boondoggles designed solely to line someone's pockets.

Buying The Rope That Will Hang Them

When newspeople don't value the 1st Amendment...:

Suppose you’re the editorial-page editor of a college newspaper, contemplating the big news on campus: protesters have silenced an invited speaker and gone on a violent rampage. Should you, as a journalist whose profession depends on the First Amendment, write an editorial reaffirming the right to free speech?

If that seems like a no-brainer, you’re behind the times. The question stumped the staff of the Middlebury Campus after protesters silenced conservative social thinker Charles Murray and injured the professor who’d invited him. The prospect of taking a stand on the First Amendment was so daunting that the paper dispensed with its usual weekly editorial, devoting the space instead to a range of opinions from others—most of whom defended the protesters. When a larger and more violent mob at the University of California at Berkeley prevented Milo Yiannopoulos from speaking on campus, students at the Daily Californian did write a forceful editorial—but not in favor of his right to speak. Instead, they reviled Yiannopoulos and denounced those who “invited chaos” by offering a platform to “someone who never belonged here.”

Free speech is no longer sacred among young journalists who have absorbed the campus lessons about “hate speech”—defined more and more broadly—and they’re breaking long-standing taboos as they bring “cancel culture” into professional newsrooms. They’re not yet in charge, but many of their editors are reacting like beleaguered college presidents, terrified of seeming insufficiently “woke.” Most professional journalists, young and old, still pay lip service to the First Amendment, and they certainly believe that it protects their work, but they’re increasingly eager for others to be “de-platformed” or “no-platformed,” as today’s censors like to put it—effectively silenced.

These mostly younger progressive journalists lead campaigns to get conservative journalists fired, banned from Twitter, and “de-monetized” on YouTube. They don’t burn books, but they’ve successfully pressured Amazon to stop selling titles that they deem offensive. They encourage advertising boycotts designed to put ideological rivals out of business. They’re loath to report forthrightly on left-wing censorship and violence, even when fellow journalists get attacked. They equate conservatives’ speech with violence and rationalize leftists’ actual violence as . . . speech.

It’s a strange new world for those who remember liberal journalists like Nat Hentoff, the Village Voice writer who stood with the ACLU in defending the free-speech rights of Nazis, Klansmen, and others whose views he deplored—or who recall the days when the Columbia Journalism Review stood as an unswerving advocate for press freedom. 

Read the whole thing.

The 4th Amendment

I agree with this ruling:

A federal judge ruled Tuesday that Border Patrol agents need “reasonable suspicion” before they can search international travelers’ electronic devices at airports or other U.S. ports of entry, delivering a big win to civil rights activists.

Federal Judge Denise Casper of the District Court of Massachusetts ruled that Customs and Border Protection (CBP) officials must have a specific reason for searching an individual’s smartphone, laptop, or other electronic devices, according to a 48-page decision...

The two agencies, which operate under the umbrella of the Department of Homeland Security, argued that such searches were necessary as they can lead to successful “fishing” expeditions — leading to apprehensions of child pornography or other illicit material from those attempting to enter the U.S.

Fishing expeditions cannot pass constitutional muster, and Judge Casper ruled correctly.

Having said that, I'm left to wonder under what constitutional authority Customs can search suitcases at airports--or my travel trailer at ports of entry.  From a 4th Amendment standpoint, why can my suitcase (or trailer) be rummaged through but not my phone?

I Care About As Much As My District Seems To

I received the following as an attachment to an email today:

Ignore for a moment the robotic tone of the message and the email it came with.  Does anyone in their right mind think that saying it's mandatory that I read all those policies (each year) is going to get me to read them?  Does this reading look like a great Thursday night at home? 

You can argue that I should know some of the contents of, or even just about the existence of, some of them, but really, Guidelines For Hazardous Ozone Episodes?  Does anyone really read these, except when they need to?

This is one of the things that frustrates me about my current employer.  My time, my competence, these are of no value to them.  Darren, take your time and read all these policies!  Oh, and let's not forget all the "important" trainings that I have to find time for--they're all online trainings.  They must be really important!  The 45 minutes I spent on the sexual harassment training online was oh so valuable (not).  At least I scored 100% on the sexual harassment training, so I am an expert in sexual harassment.  I know how to do it perfectly!

What frustrates me is they say something is important, but they don't treat it as important.  I'm supposed to treat it as important, but for the suits, these emails and trainings are just checking off a box.  Want to train me in something?  Pay me for the training.  My time is valuable.  Don't just tell me to find time in my work day to fit this in, I don't sit around on Facebook all day while students crank out worksheets.  I teach, often bell-to-bell.  And I conduct at least one formal assessment in each class each week.  And I grade those papers and get them back to students with a quickness so they can take advantage of the feedback I offer.  Colleagues and students both know I'm anything but a slacker in the classroom.

Our district had planned a (voluntary) training day this week.  It was canceled.  I'm not complaining about a 4-day weekend for Veteran's Day, but they could have gotten a lot of this training out of the way on that day and paid me for my time rather than expect me to stuff 10 more pounds of crap into a 5 pound bag.  Such training would have been better than whatever "social justice" or "equity" training they were considering.

Rejecting Diversity and Equity

This article is exceedingly logical--which is why lefties will never even hear of it.

Here is the argument against so-called diversity:

The theory driving diversity pursuits encourages us to value certain immutable characteristics over others. This is troubling for the following reasons:

1. Benefiting an individual at the non-consensual expense of another individual is inherently immoral.
2. Valuing one individual over another on the basis of race, gender or other immutable characteristics is inherently immoral.
3. Valuing diversity of immutable characteristics means valuing some individuals over others on that basis.
4. Crafting selection criteria that ensure diversity of immutable characteristics necessitates harming one group of individuals at the expense of another group on that basis.

Points one and two are basic moral principles. Points three and four are the logical conclusions of pursuing diversity as a value in itself.

Here is the argument against so-called equity:

If selection criteria are designed to promote equity, some individuals must benefit at the expense of others, on the basis of their immutable characteristics. Given a finite number of positions, this is a mathematically necessary and indefensible consequence.

Read the whole thing.

Veterans Day

It started as Armistice Day, commemorating the end of World War I--which until that time had been the bloodiest war in human history.  Thus we get this video from the British Army:



Coincidentally enough, I recently purchased this movie--only $15 at Target.  The "Making Of" featurette was as interesting as the movie itself.

Two wars later, President Eisenhower signed a law changing Armistice Day to Veteran's Day.  The holiday is to honor all veterans, Memorial Day in May is to honor those who died.

I recently read about the 1946 movie The Best Years of Our Lives, about 3 World War 2 servicemen who return home and have some difficulties adjusting.  Watched it Saturday night.  It was much more realistic than other movies of the time and addressed themes of alienation, of trying to reintegrate into society, of PTSD, of burying problems in alcohol.  It should be shown every Veterans Day.

For years my mother, a retired Army Reserve Sergeant Major, and I have gone to Applebee's on Veteran's Day.  This year she's in Cancun.  Not sure if I'll go to Applebee's or somewhere else, or if I'll go anywhere at all--but here's a list of restaurants offering free and discounted meals to veterans today.

You Are To Be Silent

Much like "OK Boomer" is nothing more than a comment designed to shut down discussion, so is mention of "privilege":

In an effort to encourage dialogue, the president of Skidmore recently invited a scholar named Fred Lawrence to give a lunchtime lecture to faculty and staff. As author of a book called Punishing Hate and the secretary of Phi Beta Kappa, the nation’s oldest honor society, Lawrence seemed suited to offer advice about the troubles we’d been going through on campus. How could we better differentiate between offenses serious enough to warrant concern, and the more minor slips or unintentional derogations sometimes called “microaggressions”?

“To be unable to tell the difference between kicking a dog and accidentally tripping over one is to have little hope of successfully navigating life on a college campus,” Lawrence said, in a talk that was mild and notably free of polemic.

The first faculty member to raise a hand after the lecture asked Lawrence whether he was aware of the privilege he had exercised in addressing us. She spoke with conviction, and suggested that Lawrence had taken advantage of his august position by daring to offer his advice. Lawrence replied with courtesy, conceding that, like everyone else assembled, he was of course the beneficiary of several kinds of “privilege”, and would try to be alert to them.

Though nothing further came of this exchange, it seemed clear that “privilege” had been invoked as a noise word to distract from the substance of Lawrence’s remarks and from his suggestion that some of us had failed to make the elementary distinction he had called to our attention. More, the “privilege” charge had been leveled with the expectation that he was guilty – not because of anything particular he had said, but because he was a white male.

Yep.

Of course there really is such a thing as “privilege”, and of course it is distributed unequally in any society. You’d have to be a fool to deny that whiteness has long been an advantage, however little some white people believe that their own whiteness has given them what others lack. Can anyone doubt that privilege is a real and legitimate issue when certain groups in a society enjoy ready access to good healthcare and schooling when others do not? There was a time, not so long ago, when to speak of privilege was to identify forms of injustice that decent people wished to do something about.

But you’d also have to be a fool to deny that the idea of privilege has been weaponized in contemporary discourse, often by people attempting to seize rhetorical advantage. The privilege call-outs increasingly common in the culture entail a readiness to rebuke people simply because their gender, ethnicity or rank makes them an apt target for shaming and condemnation. The charge of “privilege” is usually directed at its targets not with the prospect of enlisting them in some plausible action to combat injustice but instead to signal the accuser’s membership in the party of the virtuous. Accusations of “privilege” have become a form of oneupsmanship, and a charge against which there is no real defense.

Read the whole thing.

The Day The Wall Came Down

Thirty years ago today the Berlin Wall came down.  Do you remember that night?  I do.

In this post I talk about what it was like to grow up and live in the Cold War, and how I ended up with a piece of the Berlin Wall.

Have you ever seen The Lives of Others?  It's about a Stasi agent who surveilled a playwright in East Germany.  Parts of it are dry, but from what I've read I have no doubt that it accurately describes life in a real police state.  It's sickening.

This morning I read this:

Thirty years later, Germany is reunified, a powerhouse country once again, but the story is not over. East Germans are still seeking answers for some of the bad things that happened to them. The Records of the State Security Service of the former German Democratic Republic — commonly called the Stasi Archives — is open to the public. But in the frantic final days of the regime, the secret police began tearing up files. The public moved on them, blocking further sabotage but the Stasi managed to fill 17,000 bags with shreds of paper.

The Germans are putting them all back together. They want all who lived in former East Germany to be able to find out exactly what had been done to them.

Do you want more government?  That's what happens when you get more government.

Ukraine-gate

I'm Surprised It Took This Long

President Reagan gets some well-deserved recognition:

(AP) — The U.S. Embassy in Berlin unveiled a statue of Ronald Reagan on Friday at a site overlooking the location of the former president’s iconic speech imploring the Soviet Union to remove the Berlin Wall.

Secretary of State Mike Pompeo called the inauguration of the work a “monumental moment” before helping remove the cover from the larger-than-life statue on the Embassy’s terrace, at eye-level with the top of the landmark Brandenburg Gate.

Saturday marks the 30th anniversary of the fall of the Berlin Wall....

Too bad it's only at our embassy and not at the actual site, especially since the current German Chancellor is from the former East Germany.

I loved President Reagan for his conservative ideals.  President Trump, no Reagan he, is succeeding at conservative actions.  I'm privileged to have lived in such times.

Try Mine

Our school is built in a typically Californian "ranch style", which means it's several one-story buildings spread out over a couple acres.  It's spread out enough that we have 3 different staff lounges.

Today in the staff lounge that I have frequented for the past 16+ years, we had a "try mine" at lunch.  Anyone else would call it a potluck, but in that lounge it's been a "try mine" since long before I got there.

Chow mein.  Ziti.  Chinese Chicken Salad.  Cornbread with corn kernels.  Potato soup.  Hot apple cider.  And my homemade apple sauce, made with some of the super sweet apples I picked up at Apple Hill this past weekend (even if I can't remember what the super sweet ones are called).  And so many desserts.

Talk about a feast!

My Favorite Topic To Teach

In pre-calculus?  Easy.  Matrices, including Gauss-Jordan Elimination as an algorithm for solving systems of linear equations.  Started that topic today.

If students' ability to learn were proportional to my excitement in teaching the material, they'd all be matrix gurus.

OK, Boomer

Much like "racist" was before it was overused to the point that it's lost its power to shock and awe, "OK, Boomer" is a retort that's sole purpose is merely to shut down the recipient.  I'm reminded of a comment mentioned by Jonathan Haidt:  That's a slur, not an argument.


(3:56-4:26)

The older I get, the more I find this to be true:  The reason the left celebrates a cult of youth is that young people tend to be ignorant and gullible, and that’s the kind of people who tend to buy the left’s bullshit.

Update, 11/20/19:

Update, 12/3/19:  This too:

The remark doesn’t bother me in the least; indeed, it gives me a good chuckle since it typically comes from someone who’s never paid a bill, raised a family, or planned and made sacrifices for retirement...

You want boomers and Gen Xers to take you seriously? You forget yours is the generation of grade inflation. Of minimal discipline, in and out of school. Of being carted around to sports and social functions by helicopter parents who cater to your every whim. In college, you run and cry to “bias response teams” when the slightest little thing offends you. Then you demand “safe spaces” and other measures to make you feel “welcome” and “wanted” …  like therapy animals, etc.

Impeachment

I thought this was pretty spot on so I'll quite the entirety of the Instapundit post.  It's all about the election--nullifying the last one or spoiling the next one.

ANALYSIS: TRUE. Bureaucrats’ Hurt Feelings On Foreign Policy Don’t Justify Impeachment.

You see, it’s perfectly fine for Hillary Clinton to use her campaign funds to hire foreign national Christopher Steele to investigate Trump using (probably made-up) Russian sources. And there’s nothing wrong with the FBI using those partisan Steele smears to investigate the Obama administration’s political opponent.
Crossfire Hurricane, the official operational title for the investigation, employed assistance from the British government and an Australian diplomat. So the left believes there’s nothing wrong with asking a foreign government for help to investigate a domestic political opponent — so long as that opponent is Trump. After all, “Nobody is above the law, not even Donald Trump.” But if the shoe ends up on the other foot and Trump is the one investigating, it’s a constitutional crisis!
If you listen for more than a few minutes, you realize what’s really going on here is that Trump failed to prostrate himself before the “dedicated career professionals” who possess the “experience and expertise” that Trump supposedly lacks in foreign policy. Read your Constitution. Article II vests the power of foreign policy in the elected president. These “dedicated career professionals” aren’t even mentioned in the Constitution.
Maybe the framers made a drafting error in the Constitution? Or maybe we shouldn’t have a national impeachment circus over the hurt feelings of bureaucrats.

To me, the fuss indicates that this is over much more than “hurt feelings,” but actual criminal activity at risk of exposure.
UPDATE (FROM GLENN): Flashback, March 2017: “Hypothesis: The spying-on-Trump thing is worse than we even imagine, and once it was clear Hillary had lost and it would inevitably come out, the Trump/Russia collusion talking point was created as a distraction.”

$2 Bills

A lady at work was going through her mother's stuff and came across 45 $2 bills from the 50s and 60s.  Honestly, they aren't worth much more than face value, and she didn't know what to do with them, so I bought them from her for face value today.  I'm telling others at school they make great stocking stuffers for their kids, and cheap, too!

These notes have a red seal as opposed to today's green seal.

Apple Hill

Yesterday I made my annual fall pilgrimage up to Apple Hill, an area with several apple orchards.  October and November are the months to go, and I was able to pick up 10 pounds of Arkansas Black apples for me, as well as some Mutsu apples for my dad's wife.  Sure, I like Red Delicious and Honeycrisp as much as the next guy, but I can get those at the grocery store.  That I like the Arkansas Blacks is surprising, given that they're considered quite tart, but like them I do.

I also picked up an apple pie and some apple turnovers.  They maintain well in the freezer, and the turnovers are a treat throughout the year.

Tri-tip sammich lunch up there, life is good!

Two-fer

Not only do I get an extra hour of sleep tonight, but I've swapped the warm-weather Egyptian cotton bed sheets for the fleece.

Life is good :-)

Current Meme

Goliath Backs Down

Three months ago I wrote about a math curriculum company who sued a North Carolina parent for defamation for commenting negatively about the company's product:

I admit to knowing no specifics at all, but on its face this seems like Goliath trying to stomp David.

In an email Tuesday, Dillard said MVP's lawsuit "is an attempt at intimidation and bullying to silence my and other parents' free speech advocating for our children's education." Dillard's supporters have created a GoFundMe page to raise money for his defense against MVP.

I've long believed that we should have sort of a "loser pays" system in our courts.  If you sue someone and lose, and the judge/jury finds your case so weak that the most logical conclusion is that you attempted to use your lawsuit and the court's time as merely a means to harass the respondent, then the judge/jury would have the option of requiring you to pay the respondent's legal fees.  I have to believe that such a Sword of Damocles would stop many unnecessary lawsuits.  I don't know if this is one of those lawsuits or not--I hope to learn the outcome of this case. 

Case dropped:

This summer, a math curriculum provider made a surprising move against one of its most vocal parent critics—the company sued him for defamation and interference with business relations.

Now, after three months, the company has dropped its lawsuit.

Mathematics Vision Project, a Utah-based provider of open-source math curricula, and the parent, Blain Dillard, released a joint statement about the lawsuit's dismissal this week. Dillard also dismissed his countersuit against the company, which was for lawyers' fees and damages. 

After 3 years of using this program, the school district is going to evaluate its effectiveness:

Wake County schools is in its third year using Mathematics Vision Project. In response to formal parent complaints, the district has hired an external third party to conduct a review of the curriculum, which includes conducting parent experience surveys, the Raleigh News & Observer reports. 

Not a bad ending.