Wednesday, April 8, 2026

Solutions to Elliptic Curves and Their Rational Points Problems

1)  Construct the line L through any two points P1 and P2 such that they intersect a third point P3, by direct calculation or using Bezout's theorem:


Soln.



1) Sketch more of the elliptic curve (2) such that the section is shown for x = 4, y = ?


The y-coordinate occurs at: y (4)    = 

[(4)3   –    (4)  +  1 ½     =  [61 ½   =  7.8

2)  Use the short Weierstrass form to generate another elliptic curve and graph it. Then obtain the discriminant and ensure it is non-vanishing. Thence obtain h(E).

The short Weierstrass form is:  y2  =   x3     + Ax + B

Let A = -2   and    B = 10   then we will generate:

y2  =   x3    - 2x + 10

The equation when graphed appears:


Then the discriminant :  

D  = -16 (4 A3   +  27 B2 ) =   -16[( 4 (-2)3    + 27(10)2] = 

[ 512  +  (-16)2700 ] =    [512 -  43200]  = -42688


h (E) =   max (4 |A|3 ,   27 B2) =   (4 |-2|3 ,   27 (10)2) =  (32,  2700)

Tuesday, April 7, 2026

Harvard Opts To Put A Cap On A's To Temper Grade Inflation And Undergrad Students Freak Out

 "Bwahahaa! Please! I can't handle a B!"

According to a recent Wall Street Journal article ('A Harvard Cap On A's Has Students Smarting', p. A3, April 4):

"For years, Harvard has been handing out A's in abundance. Now, a proposed cap would pump the brakes-and students are up in arms. Harvard's faculty is set to vote next week on a proposal to cap the number of A's per course, which now make up more than half of undergraduate grades after years of inflation. The plan also suggests getting rid of GPA as an internal metric, instead using percentile rank to calculate honors like cum laude recognition."

There's nothing wrong with Harvard capping the A's as their overuse doesn't make the school look elite, as it purports to be. There's also nothing amiss in using percentile rank - say for honors calculation - which is also what the SAT and GRE exams use, i.e. one may place in the 92nd percentile in the verbal section and 90th percentile in math. 

Yet to read the reactions of the Harvard students polled you'd think they were being asked to flunk every course. Especially when one reads:

"Student-made memes depict the administration as 'Gandalf from Lord of the Rings saying 'You shall not pass!"

Talk about drama queens!  Of course you will pass, just not get an automatic A anymore. Hint: a D is - or used to be a pass mark - and an A used to be reserved as a superlative. But these snowflakes regard a 'D' the same way as being branded with a scarlet letter for 'failure'.

The WSJ piece goes on:

"A frenzied debate has gripped campus, with students protesting that the changes would increase stress, fuel competition and discourage academic exploration."

All of which is errant twaddle. Look, kiddies, stress has been part of college life since the year dot. If you're just coasting through courses with no stress then either the courses are way too easy, or the instructors way too generous (and perhaps intimidated by student evaluations).

As for fueling competition, wasn't that the hurdle you crossed to make it into Harvard in the first place?  You had to compete with tens of thousands to snag that acceptance, in terms of SAT scores, academic average at your HS and the number and stature of the clubs you joined - as well as how many European study ventures you went on to expand your cultural horizons.

Discouraging academic exploration? That's more poppycock. If you are truly interested in trying new courses outside your specialty (say astronomy instead of business), the risk of getting a B or even C should not matter. After all, Intertel's Dr. Stephen Mason had noted university education:

"teaches a person to live - not to earn a living" - and that living encompasses an incentive for learning for its own sake"

 But, of course, learning for its own sake is alien to these whiners. This is given all of these kids fancy themselves ultimately getting into the top 1 percent of this country, so anything that might dent a perfect 4.0 graduation average is anathema.

The administration's proposal follows a report showing that grade inflation at Harvard has grown dramatically over the past two decades. In the 2024-25 school year, roughly 60 percent of all undergraduate grades were A’s, a sharp increase from just 25 percent in the 2005-06 academic year. This prompted Amanda Claybaugh, the dean of undergraduate education, at Harvard, to tell the Journal:

“We have to do what’s in the interest of preserving the reputation of Harvard, and they all benefit from that.” 

Ah yes, but try drilling that into the little lumpkins' craniums.  A survey conducted by Harvard’s undergraduate student government found overwhelming opposition to the proposed A-grade cap, with approximately 94 percent of respondents disapproving.  I'd wager this stat shows the preponderance of the entitled snowflake students, who would likely take a jump in the river if they got a C. "It would kill my chance of acing professional career!"

Whatever, kid.

But it also shows me exactly why this bunch at Harvard are furious over the proposed change, given they've been getting fat off the grade gravy train for so long. They're so used to it by now most probably don't have to study even an hour a night, if that. I mean, hell, we're looking at a change that could limit the number of A grades faculty can award in undergraduate courses, a move administrators say is necessary to curb rampant grade inflation. And as I have written before, the prevalence of grade inflation means a university's reputation craters - as well as its academic awards like 'Summa cum laude'. It can't be otherwise.  

When a school "doles out A's like peas" to use the Bajan expression, it signals that it regards excellence as little different from mediocrity. If so many undergrads  (3 out of 5) at Harvard have been getting A's the past two years then either: a) the courses were too easy, or b) the faculty are being intimidated by student evaluations.

One former Physics prof (William J. Veigele) writing in a 2020 issue of Physics Today (August, p. 12, 'Teacher Harassment and Loss of Respect'), wrote:

One protocol I've always disliked was the written student evaluations of professors."

Adding:

"A strong correlation holds between students earning low marks in physics and the ones submitting unfavorable remarks."

And let's face it, if this correlation applies in one academic course domain it is bound to apply in others.

The Harvard vote needs to fulfill that 20 percent cap in A's to retain respect for the institution. This would bring the number of A’s back down to the levels Harvard had in 2011. Hopefully also, the proposal won't be scuttled like Princeton did after implementing its own cap on A's in 2004, then repealing the  policy in 2014.  According to the report in the WSJ: 

"It had added a large element of stress to the students' lives"

Awwww...And these are the little puffkins who plan to run the world? Shape the universe? Try attending a really competitive Chinese university for a year. But then the Chinese are the ones who very soon will be the dominant movers and shakers.

See Also:

Thanks To Grade Inflation University 'Cum Laude' Honors Are Now Meaningless

And:

Brane Space: WHAT was that Harvard Twit Thinking?

And:

Brane Space: "Free Students From The Grading Curve"? - That Depends

Monday, April 6, 2026

Unbelievable: WSJ Editors Rip Trump For NATO Threats - Yet Still Can't Admit He's A Putin Asset

                                                                       

   "You are doing well, Donald, thanks for lifting the oil sanctions."


"Has any American action racked up so many costs for so little gain as this one?" - Fareed Zakaria, CNN,  Sunday.

"It's so glaring that our President has lost his mind. Doesn't he know that the Strait of Hormuz is closed because he started a war. It's his fault the strait is closed and he is going crazy about it. He also thought the rest of the world would need oil so much that they would be willing to help the US overthrow the Iranian government. Well after bad-mouthing NATO countries and the fact that they can get oil elsewhere, that didn't work either. The man has literally gone crazy and is coming apart at the seams."-  WaPo comment

"I don't get it, the Strait was open before Trump started bombing. Now he's going to claim victory because its going to be open again? He creates a crisis, works to defuse it, then claims victory for fixing something that wasn't broken in the first place. Epstein!" - WaPo comment


In their April 2nd Editorial (‘Bomb Iran But Blow Up NATO?’) the Wall Street Journal’s Pooh Bahs squawked:

Could the Iran War do what even Vladimir Putin couldn’t and blow up the North Atlantic Treaty Alliance?  That’s no longer an idle question as most of Europe  refuses to help the U.S. and Trump responds by threatening to leave NATO.  This would be the dumbest alliance breakup in modern history.”

Not only would it be the "dumbest alliance breakup" in modern history but the biggest gift to Putin in 30 years bar none. As the main story (not op-ed) in the same WSJ issue notes (p. A1, 'Trump Weighs Pulling U.S. Out of NATO'):

"Iran war tensions threaten to break up the alliance which has been the foundation of post -World War II order. Trump hasn't explicitly given the order to pull the U.S. out of this alliance that has stood for more than three quarters of a century but officials said he has discussed leaving NATO or finding potential ways to weaken U.S. commitment to it."

Of course, either of these plays into Putin's hands, as just the weakening of NATO has been an aspiration of his since the end of the Cold War. In many respects weakening NATO would be as good a win as totally pulling out.  Fortunately, as the piece goes on to note:

"A law passed by Congress in 2023 prohibits a president from unilaterally withdrawing the U.S. from NATO. Doing so requires a two thirds in the Senate or a joint act of Congress."

But why would anyone believe that Biden-era law would stop Trump from doing it? He's flouted every other law, and the courts have barely made a dent in halting him. Especially given the Reep -GOP majority are no more than poltroons and quislings.  I mean he's rammed past every other norm, law and with only minimal opposition (Mostly from Dems as when they shut down the govt twice to try and control him). 

Hell, Trump has already started a devastating, unnecessary war on a whim with Iran which will have consequences for years to come. Even now, many nations are suffering emergencies owing to fuel and fertilizer shortages. But all the Reepo cowards and Dotard ass kissers do is whistle at the wind.

Meanwhile, Putin reaps big rewards. With the Strait of Hormuz closed, thanks to Trump's impetuous psychosis, Russia has already added an additional $150 million a day to its coffers. Add to that Trump easing sanctions on Russian oil providing Moscow with additional billions in revenue.

 Let's also recall this was the same traitor who basically gave Putin everything he wanted back in 2018 in their Helsinki summit meeting, including siding with the Russian on his denials of Russian interference in the 2016 election. Oh, and being willing to ship U.S. intel officers to Russia for questioning if Vlad so desired it!  See e.g.

Helsinki Summit: President Trump Backs Vladimir Putin On Election Interference | NBC Nightly News - YouTube

In the words of Sen. John McCain after the Helsinki debacle:

No prior president has ever abased himself more abjectly before a tyrant.  Not only did President Trump fail to speak the truth about an adversary; but speaking for America to the world, our president failed to defend all that makes us who we are—a republic of free people dedicated to the cause of liberty at home and abroad.

Former CIA director John Brennan, who was among the first to warn that Russia was waging a campaign to help Trump, said in a posting on his Twitter account at the time that Dotard's “press conference performance in Helsinki rises to & exceeds the threshold of ‘high crimes & misdemeanors.’ It was nothing short of treasonous.”  Brennan's term, not mine, but I absolutely concur.

Brennan more recently  ('Deadline White House') has lambasted Trump and his quislings for ignoring the WaPo news report from last month:

Russia is giving Iran intelligence to target U.S. forces, officials say - The Washington Post

As usual, Trump sounded like Putin's puppet in downplaying this. actually saying: "He may be helping them a bit, yeah. So what? He's helping us too selling us their oil, now that I removed sanctions."

But by choosing war with Iran, Trump is "helping Putin more than a lot", in the words of former  former Ambassador to Russia Michael McFaul.

Yet with all these 'receipts' piling up year after year the WSJ's editors prefer to see Trump only through their rose-colored glasses. Yeah, they will take the occasional shot, but then back off when he does something that suits them - like raising the defense budget by 43% to choke off public services spending.

Need more proof? After their initial lambasting of any move to leave NATO, the Editors then detach from reality as they write:

The immediate fault here lies with Europe. Spain and Italy are blocking U.S. military  flights to Iran from their bases.”

Errrr, no, there is no “immediate fault” with Europe.  The fault is all on Dotard Donnie for recklessly launching an attack, then war on Iran mainly to distract from the Epstein files brouhaha. The Europeans wanted nothing to do with it, and correctly saw it as a desperate brain fart from a senile orange fungus to distract from low polling and Epstein at home as well as a power grab after vanquishing Venezuela in 24 hrs. 

Fact:  If not for Trump’s insane and illegal actions, with no congressional approval, the Strait of Hormuz would still be open.  Oil would still be flowing and half the planet wouldn’t be on its knees declaring energy emergencies – like the Philippines has.  Let's also bear in mind NATO was formed as a defensive alliance, not an offensive one.  There was no NATO presence in Korea, Vietnam or Iraq as Fareed Zakaria noted yesterday on his CNN morning show.

As the WaPo’s Kathleen Parker writes in her Friday column ('NATO is refusing to help Trump with his Iran fiasco. Cue the tantrums'):

"President Donald Trump’s latest tantrums against NATO remind us that toddlers love repetition. Trump has threatened to pull out of the transatlantic alliance so many times — it’s become, well, a joke. He recently called America’s European allies “cowards” for refusing to race to his command and seize the Strait of Hormuz.

All of this is because Trump and Israel decided to bomb Iran for reasons that vary day-to-day. Remember when Trump said last June that the United States had “totally destroyed” Iran’s ability to create nukes (false)? Well, now he says Iranian nukes remained imminent (false), and that America has already achieved victory through “regime change,” even though the war is stretching into its second month, with ground troops headed to the region.”

Even the WSJ editors acknowledge this two paragraphs down, writing:

“Europe’s frustration with Mr. Trump is understandable given his failure to consult about the war in advance and his taunts about occupying Greenland, as well as his refusal to help Ukraine resist Russia – which is another gripe.”

And therein, the last sentence, lay the key to the WSJ's infernal coddling of Trump. To consider Trump’s refusal to help Ukraine just another “gripe” – as opposed to playing Putin’s game, giving him what he wants.  Like removing the sanctions on Russian oil. Sheesh, WSJ Editors, how much more do you need to see that Trump is Putin’s Puppet?  Indeed, I already trotted out all the evidence that Trump is a traitor and a Putin asset in a previous post:

The 'Tragedy of Robert Mueller'? The Real Tragedy Is How The U.S. Right Media Keeps Coddling A Putin Asset & Traitor

Yet the WSJ and its related minions at FOX News (also in the Rupert Murdoch empire) continue to treat the guy as relatively normal - just a bit bombastic - who makes the occasional bad judgment call.  

But at least Ms. Parker isn't buying that codswallop as she writes:

"Suddenly Trump wants European allies he spent years insulting to join a war he started without a clear plan — or apparently any idea that decapitating Iran’s leadership would instigate a regional crisis and risk millions of lives. At least three NATO allies have told Trump, in so many words, to take a flying leap"

Bingo! So why the hell do it?  Well, because in a subsequent editorial ('Trump’s Budget Breakthrough for Defense ) the editors reveal their actual motivation:  More trillions for defense in Dotard's budget to starve any chance of public services support!  Meaning preserving Social Security and Medicare as well as Medicaid.  The latter more immediately impactful given the  trillion dollar hit from the grotesque 'Big Monstrous Bill' e.g.

‘Massive Blow’: Analyst Reveals How Trump’s Budget Bill Would Hurt His Base the Most

Hell's bells, the misfit Wack job recently has gone on record as saying the government ought to stop funding Medicare and Medicaid as well as childcare across the board:

Trump says government should stop funding Medicare, daycare to focus on war


Trump, like too many of his ilk, believe any tax money for public services is wasted, or "welfare". When in fact the Preamble to the Constitution itself notes that "promotes the General welfare" is one of the core purposes.  NOT military welfare or Dotard ballroom building welfare!

Even here in the U.S. we've known for decades that any increase in Pentagon spending limits the taxes allocated for critical social programs like Medicare, Social Security. Indeed, in a 2002 PBS NOW interview with Bill Moyer, former Pentagon Finance Analyst Chuck Spinney noted every increase of defense spending past a 2 percent of GDP threshold risked the stability of Social Security, Medicare.  In his words, any such increase:

"was nothing less than a war on domestic programs, including Social Security and Medicare".

The so-called European "welfare states" (a term invented by WSJ cowboy capitalists) know this which is why they are not interested in "boosting" defense spending.

So why is Trump doing it, all in on it? Two possibilities, both of which could be true:

First, the fucker has lost his mind totally, i.e.:

by Chuck Idelson | April 7, 2026 - 5:06am | permalink

`

There are almost no words to adequately convey the horror being unleashed by a mad king who wants to be the one king to rule them all. The menace in our midst is President Donald Trump, the Nobel Prize winner wannabe whose words of faith and rebirth to mark the holy day of Easter were, “Open the Fuckin’ Strait, you crazy bastards, or you’ll be living in Hell — JUST WATCH! Praise be to Allah.”

And if that wasn’t clear enough, he told ABC News’ Rachel Scott that if no deal is made, “we’re blowing up the whole country.” Scott asked if there’s anything off limits. “Very little,” he said.

“Very little.” Let that sink in. The same mad king who on April 1, promised in a prime time address to the nation to bring Iran “back to the stone ages where they belong.”

Who, along with his partner in crime, Benjamin Netanyahu, this week bombed the Bushehr nuclear plant in Iran for the fourth time. This attack led Iran’s foreign minister Seyed Abbas Araghchi to warn “radioactive fallout will end life in GCC capitals, not Tehran.”

» article continues...

Second: Putin knows Dotard is demented, therefore mentally weaker, and is playing him even harder.

Trump falling into the Iran trap also has a side benefit: it makes the U.S. even weaker, makes its population weaker (and unhealthier). Which is exactly what Vladmir Putin wants -and why he helped catapult Pvt. Bonespurs into power in the first place back in 2016. 

Recall here Christopher Steele's words from his 2024 book, Unredacted:

 "Presently the gravest threat to Western democracy and the rule of law comes from Donald Trump and the U.S. Republican Party, increasingly the willing handmaidens for Putin." 

See Also:

Youtube videos:

Iran GETS Satan-2 Nuclear 15-Ton Warhead From Russia — Israel Has 24 Hours, U.S PANICS

&

CNN analyst: 18 reasons why Trump may be a Russian asset

&

Prof. Jiang Xueqin: What If Trump Wants America To Lose The Iran War.. GROUND INVASION IS COMING

And:

by Peter Bloom | April 7, 2026 - 5:00am | permalink

`

When Donald Trump ordered military action against Iran, the response from much of the political commentariat followed a familiar script. Reckless, they said. Destabilizing. A dangerous distraction from domestic failures. A president lashing out. All of these characterizations may be true. But they miss what may be the far more consequential story, one that connects the bombs falling on Tehran to a calculated, if desperate, effort to make democratic accountability in the United States structurally impossible.

This is not hyperbole. This is what the evidence, taken together, begins to suggest.

To understand why, we need to step back from the fog of the immediate crisis and ask a harder question: what does Donald Trump actually need right now? Not rhetorically. Not ideologically. Politically and structurally, what does a president with cratering poll numbers, a midterm catastrophe on the horizon, and a plutocratic agenda that depends entirely on his continued hold on power actually require to survive?

» article continues...

And:

by Thom Hartmann | April 8, 2026 - 4:43am | permalink

— from The Hartmann Report

`

Trump is tearing America apart with his threats against Iran and comment that domestically, “It’s not possible for us to take care of day care, Medicaid, Medicare, all these individual things.” He’s also succeeded in intentionally pitting Americans of different races, religions, and across the rural/urban divide against each other.

As Michael Corthell noted on the Essay X² Substack:

“There was a time when Americans expected political leadership to involve sobriety, judgment, and at least a passing acquaintance with reality. That time now feels like one of those lost civilizations historians whisper about, somewhere between Atlantis and the Republican Party of 1956.”

» article continues...

And:

by William Hartung | April 4, 2026 - 4:49am | permalink

`

It has been reported that the Pentagon on Friday will release a proposed budget for Fiscal Year 2027 of almost $1.5 trillion, with approximately $1.15 trillion in discretionary spending contained in the department’s regular annual budget and an additional $350 billion dependent on Congress including it in a separate budget reconciliation bill.

Whatever vehicles the administration chooses to promote this huge increase, it will be doubling down on a failed budgetary and national security strategy. If passed as requested, $1.5 trillion in Pentagon spending—in a single year–will make America weaker by underwriting a misguided strategy, funding outmoded weapons programs, and crowding out other essential public investments.

The current war in the Middle East is a case study in the ineffectiveness of an overreliance on military force in seeking to make America or the world a safer place. In his first term, President Trump abandoned a multilateral agreement that was effectively blocking Iran’s path to a nuclear weapon. Six years later, in his second term, the president initially justified his disastrous intervention against Iran as being motivated by fears of that very same program.

» article continues...

And:

by Dean Baker | April 3, 2026 - 5:11am | permalink

— from Beat the Press

`

Our Secretary of Defense (or War) Pete Hegseth seems to be having a really great time killing people in Iran, but his live action video games come at a big cost, not just in lives, but in budget dollars. To be clear, the main reason to be opposed to this pointless war is its impact on the people of Iran and elsewhere in the region. But it also has a huge economic cost that is seriously underappreciated.

The short-term cost is the shortage of oil, natural gas, fertilizers, and other items that would ordinarily travel through the Straits of Hormuz. This shortage has already sent prices of many items soaring. The impact is not just on the goods themselves, but there is a large secondary impact due to higher shipping costs, and if fertilizer supplies are not resumed soon, higher food prices, due to lower crop yields. This is a big hit to people in wealthy countries, but it is life-threatening to people living on the edge in Sub-Saharan Africa and South Asia.

» article continues...

And:

by C.J. Polychroniou | April 4, 2026 - 4:57am | permalink

`

by Alexandra Boutri and C.J. Polychroniou

Does President Donald Trump have an endgame in Iran? Are personality traits a factor in Trump’s foreign policy behavior? How different is Trump from his postwar predecessors? Will he end US democracy? Political scientist, political economist, author, and journalist C. J. Polychroniou tackles these questions in an interview with the French-Greek journalist and writer Alexandra Boutri, but does not hesitate to point out that whoever thought that some of the acts associated with mad Roman emperors (like Caligula’s war on Neptune) belong to a bygone era probably hasn’t been paying attention to how crazy and disruptive things are in the Trump era.

Alexandra Boutri: The war in Iran has entered its second month and one cannot rely on the US president for when it might end. Trump refuses to give a clear timeline, although he has boasted on numerous occasions that his war was won. In your view, what is Trump’s endgame in Iran?

» article continues...

And:

by Thom Hartmann | March 12, 2026 - 5:18am | permalink

— from The Hartmann Report

`

Eight of our American service members are dead and over 140 wounded because Iran’s military has suddenly gotten really good at targeting our soldiers, Airmen, and Marines. News reports say they’ve been able to hit us with such precision because Russia is using their extraordinary spy satellite, spy plane, and advanced radar capabilities to help Iran’s military.

The Washington Post, which first reported on this, quoted a Russian military expert as saying that Iran is now “making very precise hits on early-warning radars or over-the-horizon radars,” seeming to validate the concern. The article added:

“Iran possesses only a handful of military-grade satellites, and no satellite constellation of its own, which would make imagery provided by Russia’s much more advanced space capabilities highly valuable — particularly as the Kremlin has honed its own targeting after years of war in Ukraine…”

» article continues...

And:

by Thom Hartmann | February 3, 2026 - 6:25am | permalink

— from The Hartmann Report

The British newspaper Daily Mail is out with a deeply researched investigative report, the result of a long collaboration between columnists Glen Owen and Dan Hodges, along with Mark Hookham (Assistant Editor Investigations), and Daisy Graham-Brown (Investigative Reporter).

It’s shocking in its detail and its implication that Putin has basically owned Trump for years, even before he ran for president in 2016.

They note of last week’s partial (about 50%) Epstein document release:

The files include 1,056 documents naming Russian President Vladimir Putin and 9,629 referring to Moscow. Epstein even seems to have secured audiences with Putin after his 2008 conviction for procuring a child for prostitution.”

» article continues...

And:

by Robert Reich | April 6, 2026 - 5:26am | permalink

— from Robert Reich's Substack

`

Yesterday morning, Trump posted:

“Tuesday will be Power Plant Day, and Bridge Day, all wrapped up in one, in Iran. There will be nothing like it!!! Open the Fuckin’ Strait, you crazy bastards, or you’ll be living in Hell - JUST WATCH! Praise be to Allah. President DONALD J. TRUMP”

Now, I ask you: If you were in the Iranian regime, would you be: (1) frightened by this post or (2) relieved that you were finally causing Trump to melt down?

I’d guess (2). You’d see his post and figure that Trump — posting on Easter Sunday — has finally gone utterly and definitively bonkers. You’ve done it. He’s mad as a hatter.

» article continues...

And:

The ‘Putinization’ of US foreign policy has arrived in Venezuela | Venezuela | The Guardian