Tuesday, May 30, 2023

Solving Simple Problems In Linear Algebra (3)

 One of the more interesting applications of linear algebra is to plane and solid geometry. Most of these applications entail computing the determinant D of a matrix. To recap, given a 2 x 2 matrix say:


The determinant D is computed:

D = (a11 x a22) - [(a12) x (a21)]

In geometric applications, one will take the absolute value x   of the result.

Let's take as an example finding the area of a parallelogram such as shown in Graph 1.

This figure is spanned by the vectors (2, 1) and (-4, 5) as shown. The area will then be the determinant D of the matrix formed. This matrix will be such that:

a11 = 2, a12 = 1, a21 = -4 and a22 = 5

Then: D = (a11 x a22) - [(a12) x (a21)] = (2 x 5) - [(1 x (-4)] = 10 + 4 = 14 sq. units

Example Problem:

Find the area of the parallelogram in Graph 2:


In this case, the spanning vectors are (3,2) and (-2, -3), so we have for the elements of the matrix:

a11 = 3, a12 = 2, a21 = -2 and a22 = -3.

Then: D =

 (a11 x a22) - [(a12) x (a21)] = [(3 x (-3)] - [2 x (-2)]

= -9 + 4 = -5    = 5 sq. units

Note that the absolute. value must be taken because the determinant is 

Suggested Problem:

Find the area of a parallelogram such that 3 of its corners are given by the points:

(1,1), (2, -1) and (4, 6)

Cocky House Dems' Bravado During 2022 Lame Duck Is Partly Responsible for the Debt 'Pickle' We're In


"No one should be surprised that the resolution of our most moronic fiscal policy, the federal debt ceiling, involved our stupidest social policy: work requirements for assistance programs.

Republicans showed they were willing to crash the U.S. economy to make some bog-standard complaints about the federal deficit, most of which they created themselves.  This through the 2017 tax cuts they created for the wealthy.   If Republicans were really serious about restraining federal spending they'd not have voted for those $1.7 trillion tax cuts." - Michael Hiltzik, LA Times yesterday, 'Debt Ceiling Tussle Was Supreme Waste Of Time', p. A2

Democrats, to put it very bluntly, lost the debt ceiling battle once they assumed - back in the lame duck session of 2022 - they could roll over Kevin McCarthy and his extremist 'Freedom Caucus' in any debt ceiling battle. So these daft twits even seemed to relish the oncoming 2023  confrontation, apparently believing it could be “won.

First, they assumed McCarthy might never get the votes needed to become Speaker and he'd need their help.  WRONG! McCarthy willingly became the forever 'bitch' of the MAGA extremists - promising them anything - even plum committee memberships, if only they'd elect him Speaker of the House.  By the 15th round it worked, and McCarthy got the position, but only after literally giving away the 'store'.  The "Taliban 20", including high school dropout Lauren Boebert e.g.

extracted almost every concession - large and small -  they could from the GOP's most notorious wuss.  Boebert, for her part,  announced in a tweet  back in January she had been appointed to the influential House Oversight and Accountability Committee.  The appointment gave the firebrand Trumper bimbo-  and Glock 9mm toter - an outsized influence on looming investigations, including: Fauci and the vaccines, Hunter Biden's taxes and his laptop, and investigations into "weaponization of government" by the CIA and FBI .

The balless wonder McCarthy wasn't done, also awarding Marjorie Taylor-Greene an appointment to the House Homeland Security Committee—which oversees the Department of Homeland Security.  Not to mention awarding Chairmanship of the Armed Services subcommittee to once accused sex trafficker and MAGA mutt Matt Gaetz .   This latter gift actually created a ruckus with Rep. Mike Rogers being restrained from punching out Gaetz on the House floor, e.g.

This was after Rogers learned the worm McCarthy surrendered his promised post to Gaetz.  

But even before that sordid scene erupted the House Democrats must have been sick to their core, by now realizing the depths McCarthy would go to in order to have power - and worse- that he basically ceded it all to the "Taliban 20" GOP terrorists. Who, at any time, could hold a vote to boot him out if he didn't give them what they want.

Second, the Dems assumed that despite such a shocking and implausible turnaround, they could still count on the "moderate" Reeps - i.e. such as the 4 who won seats in congressional NY districts won by Biden in 2020.  (This included the fraud George Santos.) Thus they banked on these moderates (minus Santos)  voting with them to defeat McCarthy's looneytunes in any debt ceiling vote. That also did not happen. The mushy moderates stuck with the MAGA rabble to vote for the horrific bill that basically gutted the poorest and most vulnerable.   This was through their voting for the horrific 'Limit Spend and Grow' act, e.g.

Which includes provisions - just voted on Saturday night - that have all single beneficiaries up to age 55 working to secure food stamps, Medicaid or both.  The idiot GOP terrorists believe they can carve out of people's hides up to $11 b in savings, but they are dreaming.   43 percent of those likely to be affected are already working - some at two jobs - and many of the others are either caretakers or partially disabled themselves.   This is why LA Times columnist Michael Hiltzik pointed out yesterday ('Debt Ceiling Tussle Was Supreme Waste Of Time', p. A2):  "By my calculations that savings comes to 17 thousands of a percent of the federal budget, which comes to about $6.4 trillion."

So there you have it. A colossal waste of time that merely enabled the Reeps to do more of their tacky performance art, posturing and bluster.  And which may lead to a debt default anyway because too many remain committed to play the role of financial terrorists.  But a lot of blame has to go to the House Dems who overplayed their hand - and overestimated their confidence - in getting the better of the Goops last fall.

See Also:

The full legislative text of the debt ceiling deal



Friday, May 26, 2023

Solutions To Simple Linear Algebra Problems (2)


1) Recall t^A, found in Ex. 1 and let =


a) Find AB and thence: t^(AB)

b) Verify that: t^AB = t^B t^A


A =


t^A =



And let =


Then AB = A  X =

(a11 a12) (b11 b12)
(a21 a22) (b21 b22)

= [{(a11b11) + (a12b21)} --{(a11 b12)+ (a12 b22)} ]
[(a21b11) + (a22b21) } --{((a21 b12) + (a22 b22)}]

AB =

Then the transpose:

t^(AB) =  


t^B  = 


t^A =  



Then:  t^B t^A  =

So that: 

t^AB = t^B t^A

2) Find the trace of: R3(Θ) =

(-sin (Θ)......cos(Θ)...........0)
(0 ..................0..................1)


Tr R3(Θ) =  cos(Θ)  +  cos(Θ)   + 1  = 1 +  2 cos(Θ)

Ignorant Attack On Amanda Gorman's Book (& Stature) Was Overt Racism, Pure And Simple


                     Amanda Gorman reciting her poem on Jan. 20, 2021
                       The lowbrow imp who had Gorman's book removed

One of the most memorable aspects of Joe Biden's presidential inauguration was to see and hear Amanda Gorman's recitation form her book, The Hill We Climb.   Gorman's place in history, lets us note, is sealed as the first National Youth Poet Laureate and the youngest poet to read at a presidential inauguration.  This is momentous, and the publication of her book equally so. A wonderful work that ought to be beyond the reach and ruin of Philistines in Florida, but evidently isn't.  Imagine, a work heralded by the U.N. General Assembly — but access to it is now restricted at a Miami-Dade County school.

This is also the latest casualty in the national fight over library books, driven by a handful of malcontents and racist agitators. Hell, as I posted back in December, we even have these Florida-based pseudo liberty reprobates invading Colorado Springs' school districts, e.g.

'Moms for Liberty' Open Local Chapter In Springs - With Book Banning Binge 

The Florida complaint filed against Gorman's book The Hill We Climb alleges that the work is "not educational," contains indirect hate speech and shouldn't be in schools. It emanated from a Miami Lakes resident named Daily Salinas, who has two children at Bob Graham Elementary. Oh, and before I continue, we've since learned this lowbrow genius has Proud Boy links, i.e.

Florida mother behind ban on Amanda Gorman poem has Proud Boys links | Florida | The Guardian

Part of the form she completed is shown below:

Note the limited inputs to the extent that this dope admits to not even having read a single review.  That's really all you need to know, and disclosed she was merely carrying water for her Proud Boy associates or backers. And as The Guardian piece above notes, Salinas has also posted anti-Semitic content online and been present for several Proud Boys events."  In other words she's a low class loser and bigot - never mind her color.  We know blacks can be as perverted in their bigotry as whites, just look at Kanye West and his praise of Hitler.

Salinas specifically referred to two passages as inciting her ire:

"We’ve braved the belly of the beast.

We’ve learned that quiet isn’t always peace,

And the norms and notions of what ‘just is’

Isn’t always justice."


"And yet the dawn is ours before we knew it.

Somehow, we do it.

Somehow, we’ve weathered and witnessed

A nation that isn’t broken, but simply unfinished.”

Claiming they'd arouse hatred as well as cause confusion and indoctrinate children.    How she comes by these deductions we can't say.  But maybe she just has it in for Oprah, as the fool actually Winfrey was the author (or publisher).  In any case, as my Psych Prof niece Shayl believes: "She manufactured it in her head out of whole cloth paranoid delusions."

I agree and would add a large dollop of bigotry to her misfiring brain cells-  at least as much as the kooks seen in my blog post trying to ban books here in Colorado Springs.  Meanwhile, Janice's theory is that Daily just spotted the words "beast" and "broken". She then figured in her maimed brain these passages were "hateful" and/or "confusing".  Oh and might "indoctrinate" the kids who encountered them.  

 NPR for its part reviewed the complaint and other materials after they were obtained through a records request to the school district from the Florida Freedom to Read ProjectSalinas, true to being the simpleton she is,  did not fill out the forms entirely. And when asked if she had seen professional reviews she replied, "I don't need it."  Yeah, but it might have increased your low IQ by a couple apparent standard errors.

Meanwhile, a subsequent review by an eight-person committee from Bob Graham Elementary pointedly noted Gorman's book DID have educational value.  But it added that the "vocabulary used in the poem was determined to be of value for middle school students."  

Lest anyone think Salinas a one- off bigot wonder she also filed complaints about four other books: The ABCs of Black HistoryCuban KidsCountries in the News Cuba; and Love to Langston

Just one week after Salinas filed her complaints on March 29, the school committee decided most of the books on her list should not be seen by younger students. Salinas for her part had requested the materials be removed "from the total environment."  In other words, banished to oblivion. Process that: one moron with the power to remove a book from the purview of all kids at Bob Graham who could most benefit from it.  

Fortunately, the twit didn't get her way. After a review of Gorman's book the Bob Graham Education Center decided to retain the book — but only if it's shelved in an area reserved for middle school students. In their words: 

"The form, based on what has been provided and shared with us, does not even appear to be completely filled out or express a complete thought," Pierre said. "It is our collective goal to work on amending school board policy and effectuating changes to ensure that it takes more than one form to remove our history and heritage."

Small win though it was, Amanda Gorman hit back in a lengthy social media post, writing:

So they ban my book from young readers, confuse me with Oprah, fail to specify what parts of my poetry they object to, refuse to read any reviews, and offer no alternatives … Unnecessary book bans like these are on the rise, and we must fight back,

The poet then invited supporters to donate to the writer’s group PEN America, which she said had joined her publisher, Penguin Random House, to issue a lawsuit challenging book restrictions in FloridaAccording to PEN America, 565 books were banned in Florida schools in the 2021-22 school year.

Book bans have surged in Florida in the wake of a series of laws signed by GOOP Gubernator Ron DeSantis, who is determined to make Florida the place  where "woke goes to die".  Translation: The place where brains and consciousness go to die. What Janice and I continue to wonder is how this buffoon managed to graduate from Harvard, where evidently now reason goes to die.

See Also:

by Bill Berkowitz | May 13, 2023 - 5:59am | permalink


by Chris Wright | May 25, 2023 - 5:01am | permalink


Political discourse in the United States consists largely of lies and confusions. One of the greatest of lies and confusions, which I hope to help dispel in this article, is the common delimitation of the very concepts “left” and “right:” It is claimed that to be on the right is to value freedom above all—this is what “small government” is supposed to mean, for example—while to be on the left is to value equality, if necessary an equality enforced tyrannically by an enormous, Soviet-style government.

Nothing could be farther from the truth than this conventional wisdom. The opposite is closer to reality: To be on the right means, in effect, to advocate an enforced equality of nearly universal servitude and anti-democracy, while to be on the left means to value the greatest freedom for the greatest number


Archival Photos Remind Us That Book Burning Launched Third Reich's Savagery In 1930s 

Wednesday, May 24, 2023

The Hard Truth: Without Math Even 'Basic Concepts' In "Popular" Physics Books Are Meaningless


                           Seyda Ipek solving equation in her Carleton Univ. physics class

Among the most irritating remarks in any alleged “popular” physics book was undoubtedly Stephen Hawking’s in the Acknowledgements to The Brief History Of Time.  Therein he informs us that someone told him that "each equation included in the book would halve his sales.  Well he did include one, the famous Einstein equation  E = m c2 , but it hardly halved his sales.  This is given it was on The London Sunday Times bestseller list for no less than 237 weeks.  

All of which discloses that this circulating trope - still alive- amounts to a load of semi-erudite twaddle. And mostly emanating from nincompoops who either don't know physics, or are led astray by authors who claim the math just obscures the physics.  Not so with Physics Today (May, p. 51) reviewer Seyda Ipek in her review of Sean Carroll's book The Biggest Ideas In The Universe: Space, Time and Motion.  

As she rightly points out: "Carroll is aware that you need to understand the math to truly understand the physics that underpins our greatest brainchildren.  He diligently explains infinitesimal changes, for example, so that readers understand why Isaac Newton had to invent calculus to explain planetary orbits.

Over the course of the book readers go from learning how to take a derivative to gaining an appreciation of the metric tensor that describes spacetime.  That is also the path from Newtonian gravity to Einstein's general theory of relativity."

Is Carroll mad in his popularizing expectations? Or just optimistic to the point of skirting with physics fantasyland? What about reviewer Ipek? Is she grounded in her take or in La-La land?  I suspect she likely knows, perhaps even better than anti-math (in physics) curmudgeon ('Lost in Math')  Sabine Hossenfelder what is needed regarding communication of critical physics to the public.  As Prof. Ipek notes (ibid.):  

"Even physics majors in my classes are sometimes of the mindset if they just get the basic concepts they can understand topics as challenging as quantum mechanics."

But I can assert here this is preposterous given that a number of peculiarities of QM emerge in the mathematics behind it,and are next to impossible to grasp without it. For example, the issue of why complex numbers are needed to describe the wave function, e.g. 

Does Quantum Mechanics Really Need Complex Numbers? Yes!

And also why specialized statistics are needed to address the quantum measurement problem, e.g

Is There A 'Quantum Measurement Problem'? No - Provided One Adopts A Statistical Perspective

But there are vast areas even beyond these where math is essential for the student to grasp the concept.  For example, how a lower (kinetic) energy particle can surmount a higher energy barrier potential, i.e.


Consider a deBroglie (matter) wave arising from a single proton (p+) of form:

U(x) ~ sin(kx)

Where x is the particle's linear displacement (e.g. in 1-D) and k, the wave number vector(k= 2π/
l), where l  denotes the wavelength. Though the associated kinetic energy K < V (the barrier "height") the wavefunction is *non-zero* within the barrier, e.g.

U(xb)~ exp(- cx)

So using the math of wave mechanics  (and how a particle can be both wave and particle) we can visualize the particle of lesser energy K moving from the left side of the Energy-axis by"tunneling" through to the right side where it acquires the new wave function, U(x) ~sin (kx + φ), and φ denotes a phase angle.mNote that if the barrier is not too much higher than the incident particle energy, and if the mass is small, then tunneling is significant.

All the basic concept assimilation in the world won't enable the student to grasp the underpinning unless one also has the math under control. This is why Prof. Ipek's last point in her review is especially cogent, i.e.

"I don't want to make it sound like The Biggest Ideas In The Universe'  is solely a book about math.  But it's just so refreshing to read a popular science book that doesn't hide the math.  Instead of shying away from the nitty gritty calculations that led to the biggest leaps in our physical understanding of the universe."

Still it may well be that contrarian Hossenfelder thinks Sean Carroll's book is "awash" in excess math computations and he may well pay the price in lost sales.  But at least those who will read his book will be well rewarded by a superior understanding of the most revolutionary concepts in modern physics.

See Also:


Monday, May 22, 2023

Newsflash, Mainstream Media! GOP Debt Ceiling Extortion Isn't About Spending OR Deficits!


                Edward Luce - Financial Times columnist who forecast GOP-incepted calamity in Oct.

"Moody’s Analytics estimates that even a short debt ceiling breach could cause a recession. An analysis by the White House’s Council of Economic Advisers modeled a more protracted default and foresaw a crash on the order of the 2008 financial crisis: The stock market falls 45 percent, unemployment rises by five points, and America’s long-term borrowing costs are much, much higher. All of this to pay money we already owe and can easily borrow. Madness."- Ezra Klein, NY Times yesterday

“My conservative colleagues for the most part support the Limit, Save, Grow bill and they don’t feel like we should negotiate with our hostage,” -  Rep. Matt Gaetz, two days ago

The clock is ticking and later today President Biden is scheduled to meet with Kevin McCarthy (GOP House Speaker) for what may be the last chance to nail a deal to raise the debt ceiling. Make no mistake that this is for all the marbles and anyone not paying attention is in for a brutal wake up call.

 Most serious financial experts believe if the debt ceiling isn't raised in 10 more days there will be an economic calamity.  We're talking a stock market crash of up to 45 percent wiping out trillions in wealth- with 401(k)s taking crippling hits, not to mention massive layoffs that could reach 8 million. Add in soaring inflation that may take years to tame, not months and a potential surge in homelessness and food insecurity and you have most of what is coming at us like a freight train. Adding even more ominous overtones, a recent survey by the National Low Income Housing Coalition showed a U.S. wide shortage of 7.3 million affordable rental homes, i.e. for extremely low-income renters.

This is germane as we learned yesterday - off the AP wires- that the razing of older mobile homes across the U.S. eliminates some of the already limited low cost housing stock - for the poorest of the poor. The bulldozing is going on at such a pace that residents, like in Phoenix, may soon have to double up with relatives or sleep in their cars.  And the Republicans will make it ten times worse if Biden and the Dems yield to their insane demands.

Amidst all the potential for economic horror, let's make damned sure we have our heads screwed on straight and know who the bad guys are.  Hint:  It is the cult determined to sink the nation if they don't have their insane demands met: the financial terrorists known as the GOP.

Let me also remind those still reading my blog, that during the last debt-ceiling standoff in 2011 investor confidence was shaken to the core. Analyses after that near-default showed that the plunging stock market vaporized $2.4 trillion in household wealth, which took years to rebuild, and cost taxpayers billions in higher interest payments. Today, credit is more even more expensive, and the banking sector is shaken after the collapse of the Silicon Bank SVB, i.e. 

The SVB Bank Collapse - Reasons For It - And Why It's Not A Good Idea To Panic 

And the desperate rescue of First Republic by Jamie Dimon's JP Morgan  bunch.  Add to that the fact the current economic expansion is tailing off rather than beginning and the outlook is far from sanguine.

Republican terrorists  have proposed pairing a debt-limit increase with sharp cuts in government spending. We are talking nightmarish stuff starting with stripping away protections for renters that could leave millions more sleeping in tents on the streets. And it doesn't stop there. Their "pledge" to spare Social Security recipients, Pentagon spending and veterans’ benefits would require steep reductions in other programs — like housing, toxic waste cleanup, air traffic control, cancer research and other categories that are economically important. The pain, in other words, would spread nationally to a much larger population - and the Democrats would likely be blamed for giving in and allowing it.  Which is why they can't give in now to the terrorists' demands.

They also well recall the 2011 Budget Control Act, which resulted from that year’s standoff, leading to a decade of caps that progressives have criticized for preventing the federal government from responding to new needs and crises. 

This has engendered the current mounting tension which could cause problems through a number of channels.  For one, rising interest rates on federal bonds will filter into borrowing rates for auto loans, mortgages and credit cards. That inflicts pain on consumers, who have started to rack up more debt — and are taking longer to pay it back — as inflation has increased the cost of living. Increasingly urgent headlines might prompt consumers to pull back on their purchases, which power about 70 percent of the economy.

Interrupting the smooth functioning of federal institutions has already created a headache for state and local governments. Many issue bonds using a U.S. Treasury mechanism known as the “Slugs window,” which closed on May 2 and will not reopen until the debt limit is increased. Public entities that raise money that way now have to wait, which could hold up large infrastructure projects if the process drags on longer.

When do these consequences really start to mount? In one sense, only when investors shift from assuming a last-minute deal to anticipating a default, a point in time that is nebulous and impossible to predict. But a credit-rating agency could also make that decision for everyone else, as Standard & Poor’s did in 2011 — even after a deal was reached and the debt limit was raised — when it downgraded the U.S. debt to AA+ from AAA, causing stocks to plunge.

What if June 1 arrives with the Reeps still holding a gun to the nation’s head and no debt ceiling increase? Most experts say the Treasury Department would continue to make interest payments on the debt and instead delay fulfilling other obligations, like payments to government contractors, veterans or doctors who treat Medicaid patients. That would prevent the government from immediately defaulting on the debt, but it could also shatter confidence, roiling financial markets and leading to a sharp pullback in hiring, investment and spending.  

The worst case scenario would be a delay in payment of Social Security benefits to more than 63 million recipients, as well as a halt in VA benefits and possible Medicare support -remuneration of medical centers for delivered care.  At this stage I cannot see how this standoff ends well, and you can blame the unhinged demands of the Reepos for that   - whose tactics Edward Luce warned us about more than 7 months ago.  

Finally, let's get it straight once and for all this is not about controlling spending or lowering deficits, those are smokescreens. It can't possibly be because whenever the Reeps are in power - as they were for the first two years of the Trump administration - they didn't do jack shit about spending or deficits. Instead they blew through ever barrier, including a $1.7 trillion tax cut mainly for the rich, and other spending like the veritable drunken sailors.  Nope, this is about one thing only: trying to sink Biden's chances for re-election just like they tried to sink Obama's back with the near 2011 default.  Only the consequences of this default - if it happens - will be much much worse Again, bear in mind who the bad guys are!

See Also:

Biden uses good cop, bad cop against the GOP’s debt ceiling extortion




by Jeffrey D. Sachs | May 21, 2023 - 7:23am | permalink


In the year 2000, the U.S. government debt was $3.5 trillion, equal to 35% of the Gross Domestic Product (GDP). By 2022, the debt was $24 trillion, equal to 95% of GDP. The U.S. debt is soaring, hence America’s current debt crisis. Yet both Republicans and Democrats are missing the solution: stopping America’s wars of choice and slashing military outlays.

Suppose the government’s debt had remained at a modest 35% of GDP, as in 2000. Today’s debt would be $9 trillion, as opposed to $24 trillion. Why did the U.S. government incur the excess $15 trillion in debt?

The single biggest answer is the U.S. government’s addiction to war and military spending. According to the Watson Institute at Brown University, the cost of U.S. wars from fiscal year 2001 to fiscal year 2022 amounted to a whopping $8 trillion, more than half of the extra $15 trillion in debt. The other $7 trillion arose roughly equally from budget deficits caused by the 2008 financial crisis and the Covid-19 pandemic.


 McCarthy Confirms: GOP Will Crash the Economy Unless Democrats Agree To Destroy Social Security

by Joan McCarter | October 19, 2022 - 7:43am | permalink

— from Daily Kos


If the GOP regains the House, four of the leading Republicans contenders for the House Budget Committee chair have all vowed to demand cuts to Social Security and Medicare in return for their cooperation in raising the debt ceiling next year. To be clear, that’s Republicans saying they will crash the U.S. economy to force President Joe Biden to give into their demands.

Now would-be House Speaker Kevin McCarthy has confirmed that yes, that’s exactly what Republicans intend to do. That continues to generate yawns from the super savvy reporters in D.C. and New York, who largely ignored the first reports of this threat. Now they’re continuing to try to downplay it. But it’s as real and as dangerous as can be.