Brane Space

Wednesday, July 22, 2026

All Experts Redux: Gauge Fields Factor Into Solar Flares?

Solar eruption: Are gauge fields behind it?

Question: I recently read an article, I think in Scientific American, on the role of gauge fields in solar flares. How would gauge fields relate to powerful solar flares?

Answer: Lacking a specific citation (issue, date, title etc.) with the necessary elaboration, the question is not really answerable in a solar physics or astrophysics context. Basically, what you would need to do is present far more details from the piece you read and elaborate the case made. But it appears you are unsure of the source you actually saw it.

While it is true there is a fundamental relation between gauge fields and plasma physics, and plasma physics underlies solar flares, the objects of inquiry are vastly different. So while the electric and magnetic fields peculiar to plasma physics are themselves classical gauge fields, no solar physicist uses gauge fields to describe solar flare dynamics, nor will you see him using the term 'plasmons' (for the quanta of longitudinal plasma oscillations.)

In standard plasma physics, the dynamics are driven by Maxwell's equations which can easily be integrated into plasma dynamics of flares. However, specific gauge fields are far less amenable and out of place in flare theories. One could say the language is incompatible as well as the objects of inquiry.

One is more likely to find them in formulations like Quantum Electrodynamics (QED), and also references to electromagnetism as the simplest Abelian gauge theory (specifically, with a U(1) symmetry). The photons that mediate these interactions are the gauge bosons. But no one doing flare physics uses the term gauge bosons.

The problem in addressing it arises because the Wikipedia link you gave shows absolutely no citation reference for the term - so it is possible the author coined it himself- or interpreted it in a different context. Does it have special meaning? We may never know unless he himself explains it. I am in no position to since I have no idea what he means by "using gauge fields in flare physics"- anymore than if he used the term: "superflare plasma instability vortex".

However, if you are interested in pursuing the gauge field aspect, on consulting a book I have entitled 'Gauge Fields' there is a chapter on 'Asymptotic Freedom' in connection with energies associated with gauge fields.

It is noted that "grand unification" can be constructed on the basis of the SU(5) group. At this level of energy - "all interactions are combined". Meaning that we are probably looking at the very hottest temperature in the Big Bang itself where all the forces were still unified. (Again, this is all much more fundamental physics than solar flare plasma theory!)

How much more fundamental? In advanced group theory, objects such as spheres are identified with one or more planes of symmetry. The effect of this is to identify different symmetric groups through transformations. Among the most common such groups in physics are:

U(1) - > electromagnetic force

SU(2) -> weak nuclear force

SU(3) -> strong nuclear force

All of which have very significant importance in high energy and particle physics. For example, one might be looking at the transformation of a quantum wave function (U) such that:

U(t) = exp [-iHt/ħ]

Where U(t) is the unitary time-evolution operator, where i is the usual imaginary number, H is the Hamiltonian, ħ is the modified Planck constant (i.e. h/ 2p. ) Unitarity ensures that the total probability of finding a particle remains exactly 1.

In such a case, we say that the transformation of U is a unitary transformation and that the exponent (in brackets) is a (1 x 1) matrix. In effect, all such transformations form a unitary group, based on the 1 x 1 matrix, called U(1).

The (1) identifies one particle (boson) which mediates the associated field for this group. For U(1) that is the electromagnetic field, and the boson is simply the photon. For SU(2) and any SU(n) where n is a whole number , we can associate a unitary matrix of size (n x n) with determinant 1. Thus, SU(2), associated with the weak nuclear force (responsible for radioactive decay) requires a format such that a typical group member is:U = exp(-i M)

where M is now a 2 x 2 matrix of zero trace. Remember the trace of a matrix M is the sum of the diagonal entries, viz. Tr(M) = a11 + a22 + a33. The applicable matrix would look like this:

(a₁₁ ……a₁₂………a ₁₃)

(a₂₁…..a₂₂……….a₂₃)

(a₃₁……a₃₂……..a₃₃)

Following the same rubric as above, SU(3)- associated with the strong nuclear force, means that the matrix M (as defined in the earlier example for SU(2)) now has a 3 x 3 element size. This 3 x 3 matrix can now be resolved into eight (8) independent component matrices (instead of only three), each of which corresponds to a charge, so there are now eight charges in all: G1 .......G8, called 'gluons'. Putting all together:

SU(3) x SU(2) X U(1)

Note this represents lower energy than achieved at SU(5)!

One has a symmetry system which embodies all the gluons (for the strong nuclear force) as well as the vector bosons for the unified electro-weak force (SU(2) x U(1)) which subsumes the weak nuclear force as well as the electromagnetic force. This in turn can be subsumed under a 'grand unified' symmetry, ie. SU(5).

From the rubric we are using, SU(5) must have a defining matrix M of 5 x 5, that is 5 elements by 5 elements. Its resolution yields a total of 24 separate matrices which are associated now with 24 different bosons. This is but one example that would pertain to a GUT or grand unified theory.

Thus, the temperature referred to this (highest) energy embodied in SU(5) would be that associated with "extra-dimensional gauge freedom" - possibly because of all the extra dimensions needed to craft the SU(5) matrix.

Again, all of this is to show there is a vast and fundamental difference in the physics usually applied to gauge fields, compared say with the dispersion relation associated with plasma waves. Such a relation implies that a relationship exists between the plasma frequency w and the wave number k. If, on the other hand the group velocity the group velocity , V _gdoes not depend on wave number i.e.

V _g = ¶ w /¶k = 0

All of this is at a macroscopic level compared say to the behavior of gluons or bosons in a gauge field.

Hopefully, this makes sense!

With Congress Threatening To 'Fix' Social Security By 'Flattening' COLAs Why Hasn't The Least Toxic Solution Been Attempted?

The two Social Security cutters – Alan Simpson and Ernest Bowles - on Obama Deficit Commission in 2011

"Social Security is a “cow with 310 million tits”! - Alan B. Simpson, Feb., 2011

Back in 2011, one of Ernest Bowles and Alan Simpson's wonder “cure alls” for Social Security shortfalls was to raise the retirement age (at which full Social Security can be received) to 70. This was despite the fact that the newest demographic economic data showed that contrary to the myth that “all Americans are living longer”, elderly poor black women were seeing decreases in life expectancy.

Bowles and Simpson’s solution would not only have added 1.5 million seniors to the poverty rolls, but literally forced millions more poor black seniors (mainly women- to work until they literally dropped dead. (45% of black men were already dead by 66).

Thus, these two clowns would literally chop off an essential lifeline for millions of Americans, especially poor female minority Americans. In this context, one elderly female sent an email to Simpson – the top asshole on the commission, complaining about his denigrating reference to “pink panthers”- and dismissing Social Security as a "cow with 310 million tits."

Of course, the situation with Social Security has gotten worse since then given congress has basically sat on its hands, doing nothing to save this critical program. Indeed, 2 weeks ago the program's trustees warned that the trust fund that helps pay benefits to more than 75 million Americans will be depleted by the end oof 2032.

While Social Security wouldn't collapse, the incoming revenue from payroll taxes and taxes on benefits would cover only 78 percent of scheduled payments - which will force automatic benefit cuts. For a middle income household that could equate to a loss f up too $18,000 a year. Not small chunk by any means.

Basically, Social Security has paid out more than it receives since 2010. That shortfall has worsened in recent years because of drops in worker participation rate - owing to reduced immigration and fewer births - which result in fewer younger workers paying taxes (as well as the huge tax cuts passed last year in the Trump -GOP 'Big Beautiful Bill).

According to LZ Granderson in the LA Times, the "mess should be dominating midterm campaigns". Especially now as affordability fears ramp up owing to Trump's Iran War and tariffs. But weak-kneed politicos refuse to touch the issue out of fears they will scare voters with talk of benefit cuts or huge tax hikes.

Two changes, meanwhile, have been discussed - one mainly on the left, the other on the right. In the latter case "means testing" has been proposed, e.g. by Ted Cruz. This would reduce or eliminate benefits for millions who have paid into the system, but because they had much higher than average incomes over their earning years, they'd now be disqualified. Basically, Social Security would be then reserved for the lowest earning citizens which would turn it into a welfare program. And we know what happens to those.

Another cockeyed proposal reported in a Washington Post editorial piece yesterday is to resurrect a 1987 plan that freezes cost of living allowances for some deemed not to need it.

A much more rational (and fairer) way to solve the problem is simply to raise the ceiling on income subject to the Social Security payroll tax. To fix ideas, that cap is now at $184, 500 which means anyone earning at least $1 million in wages stops paying any payroll tax from the beginning of March. That is $0.

Interestingly, if the payroll tax cap were raised to $400,000, i.e. all income in excess of that amount subject to the payroll tax, then Social Security's solvency would be ensured forever - or at least as long as this Republic lasts.

A simple solution, but you can be sure it will somehow escape the noggins of too many Reepo hardheads and wannabe Trumper crypto billionaires.

Excerpt:

A “new option” to reform Social Security turns out not to be so new. If it had been adopted when first proposed, Social Security today would be solvent for another 40 years or so.

In October, the Committee for a Responsible Federal Budget released a proposal to cap the Social Security cost-of-living adjustment (COLA) at a certain level of benefits. Rather than adjusting for inflation for every beneficiary, as the program currently does, it would do so only up to a certain point. They thought they had a fresh idea. But a CRFB blog post on Tuesday found that Reps. Tim Penny (D-Minnesota) and Arlan Stangeland (R-Minnesota) had introduced legislation along the same lines — in 1987.

As Penny said to Congress at the time, the bill would have created a “flat-dollar” COLA. Social Security would work the same in calculating the initial benefit level for seniors, based on their lifetime earnings. For the annual COLA, it would calculate the monthly increase for the beneficiary at the 20th percentile to account for inflation, then give that flat increase to all seniors.

And:

Hijacking Social Security: How Trump’s "Freedom 250" Grift is Draining Your Benefits

And:

Brane Space: A "Chained CPI"? Yes! For the CHAINSAW!

And:

Three Ma jor Myths That Undermine Social Security -...

Tuesday, July 21, 2026

Solving First Order Differential Equations By Eliminating The Dependent Variable (Part 1, Solving for y)

Many times in order to solve a differential equation, all that's needed is to eliminate the dependent variable (y or x). To that end, we look first at solving DEs for y, then for x.

If a first order DE can be solved for y, they n it can be written in the form: y = f(x, p)

The total derivative of this equation with respect to x is:

dy/dx = p = ¶ f/ ¶ x + ¶ f/ ¶ p (dp/ dx)

An expression involving only x and p. The objective now is to solve this equation to obtain:

F(x, p, c) = 0

To obtain the general solution of the original differential equation we need to form a pair of parametric equations with p as the parameter. Then p can be eliminated to obtain a solution in x and y along with an arbitrary constant.

Example: Solve:

p ² + 2 xp - 2y = 0

(1) Solve for y to obtain:

y = ½ p ² + 2 xp

2) Differentiate with respect to x:

dy/dx = p = p (dp/ dx) + x (dp/ dx) + p

Or: (p + x) (dp/ dx) = 0

From this result we see:

Either: dp/ dx = 0 or: p + x = 0

Hence: p = c or p = -x

3) Eliminate p between the last equations and the solution for y:

y = ½ c ² + c x

y = ½ x ² - x ² = - ½ x ²

Both of which satisfy the original differential equation. However, note that the 2nd solution does not contain c (an arbitrary constant) so is not the general solution. Rather it is what we call a singular solution.

Monday, July 20, 2026

Clearing the Air On Socialism In A Mensa Bulletin Letter

Frank Zeidler - Milwaukee's 3rd Socialist Mayor

Letter published in February Mensa Bulletin:

Socialism’s 20^th Century Track Record’ from John White (Nov./Dec., p. 10) perhaps needs some further expansion.

I was first introduced to socialism while living in 1950s Milwaukee. I was born in Milwaukee just two years before the city's third Socialist Mayor took office. Frank Zeidler was Milwaukee's third Socialist mayor (after Emil Seidel [1910-12] and Daniel Hoan [1916-40]), making Milwaukee the largest American city to elect three Socialists to its highest office.

Zeidler, a member of the then Socialist Party of America, served three terms from April 20, 1948, to April 18, 1960. During his time in office, the city built new fire stations, repaved roads, and established Wisconsin's first educational television station. He also oversaw the construction of low-income and veterans' housing and implemented city beautification programs.

Jobs proliferated, especially in major manufacturing (Allis –Chalmers etc.) while the Breweries hired thousands with excellent pay and benefits, including health care. Housing abounded as well, affordable housing off of Greenfield Ave. and Teutonia and in other suburbs to the north and west. Parks, meanwhile, were the envy of many other cities for their beautiful layouts, amenities and services. I can still recall going to Washington Park (across the street from where my family lived on 48th and Cherry Streets) on the 4th of July for band performances and later fireworks. I also enjoyed going to the Washington Park Zoo as often as I could, especially to visit the denizens of the Reptile House.

Crime was almost non-existent, despite Milwaukee reaching a population of 747, 000 by 1960. Zeidler also provided health care through the city, so no one needed to go broke to get any treatment. Like all REAL Socialists, Zeidler believed health care was a right, not merely having health insurance!. Education also benefited, and Milwaukee’s schools became some of the finest – not just Catholic but public schools as well, thanks to a higher local taxation rate, and not merely property taxes, which Zeidler knew would hit the elderly hardest.

Even today, most of those who lived in Beer City back then remember what Zeidler did for the city, and are averse – as I am – to indiscriminately trash socialism. Too often just conflating it with Marxism or communism.

Philip A.. Stahl

Colorado Springs, CO 80917

#0011448529

--------------------------------

See Also:

Donald Trump

Trump’s National Socialism

by Robert Reich | July 16, 2026 - 5:25am | permalink

— from Robert Reich's Substack

Friends,

Quietly and without any fanfare, the Trump regime is becoming a shareholder or profit-sharer in an array of corporations thought to be critical to the nation’s security.

For example, in one of the most remarkable turnarounds in corporate history, the U.S. chipmaker Intel’s shares have more than quadrupled in value since March 2025. The stock has surged 464 percent in the past 12 months, with the company hitting a market cap of $608.7 billion.

A year ago, Intel was on life support. Many predicted its death. What happened?Intel’s rebirth is partly due to the AI boom, which requires huge quantities of computer chips known as CPUs, which are Intel’s specialty.

» article continues...

And:

Brane Space: Time for The Right/ Reepos To Stop Their Bedwetting About Mamdani's Socialism

Friday, July 17, 2026

First Felon President Spouts Mega Lies In Prime Time To Try To Subvert Midterms

Facial tics betray Trump's lies at a rate of 10 per minute

"Six bankruptcies, including casinos, which requires a special type of incompetence. Twenty four credible allegations of sexual assault. Thirty four felony convictions. The attempted assassination of American democracy on January 6th. Held civilly liable for rape. Amassing four billion dollars through sheer graft during term two. The destrucntion of NATO and our alliances globally and in the Gulf. Turning Iran into the hegemon of the middle east. " - WaPo comment

"When you commandeer prime time, or try to, you’d better have something prime to say. Trump didn’t. His speech on Thursday was a dud — a batty stew of whiny complaints stemming from an election that he claims was stolen that wasn’t, during a period when he was running the country. If something was wrong, dude, why didn’t you fix it? He still has no proof, and he muddied matters by releasing documents containing information already known and warning about “vulnerabilities” his administration has made worse" .- Maureen Dowd, ‘Low T, High Chair, NY Times

Whatever happens in November may not provide an adequate backlash to this criminal regime. Severe penalties, up to and including a possible life sentences in isolation (Guantanamo style) are not beyond consideration. Forfeiture of estates, blacklisting from jobs at any level of government, especially in law enforcement and education, should be the minimum. - NY Times comment

What is it with so many otherwise sober media mavens and commentators that they can't grasp Trump's clear derangement and malignant narcissism - which form the basis for his feral energy - as well as feeding his frenzy of nonstop lies? Especially concerning our election integrity - which the fungal orange cockroach attempted to savage last night. Claiming on the basis of "previously classified documents" he could prove the 2020 election was undermined by Chinese "interference". According to a WSJ account following the spin, errr speech:

" Trump addressed the nation Thursday from the White House, where he delivered allegations of foreign influence in U.S. elections. His administration began releasing what he described as previously classified documents to support his assertions, and he repeated some of the unsubstantiated claims he has made in the past."

Not surprisingly, his deranged new twist was to claim evidence of foreign machines altering votes but didn’t present a speck of hard evidence. Why would he when the only real thing he has to work with are his own lies. And since he knows he cannot get the votes of normal, rational voters, then as a traitor and felon he must resort to propaganda and misinformation to try t bend the minds of as many as he can. As Lawrence O'Donnell put it in blunt terms following the pathetic performance:

"Donald Trump believes his voters are the stupidest in the world, not just in America. Because he believes he can spend the rest of his life lying to them about anything."

And getting them to prop him up. Don't laugh. In a NY Times piece yesterday, featuring "ten young Trump voters",

one beheld a good chunk of the 10 interviewed still view him favorably in terms of his deportations and "business acumen". "Affordability" was the one area they're down on him (but only 2 of 10 interviewed delivered the lowest rating of 1 out of 5. (5 others were 3 or above) This doesn't bode well for the Dems snatching back constitutional checks and balances in the November elections if these Gen Z's fell for his lies last night.

A particular voter vulnerability, in fact, came up for discussion yesterday morning on Stephanie Ruhle's 'Money, Power and Politics'. There at least one guest insisted Trump's incessant lies were disabling many people's ability to see the truth. I point the finger at the Gen Z's especially after reading the book Hollowed Out, where the author (Jeremy Adams) highlighted the extraordinary political and historical ignorance of young Americans, many even unable to distinguish the Declaration of Independence from the Constitution. The fact the Gen Z's went for a liar, insurrectionist and felon in the first place, shows me they lack the wherewithal to see through his manipulation efforts.

Meanwhile, the usual Trump lackeys, like the cheerleader Karoline Leavitt - who fancies herself a "press secretary" - continued to reel off lies ahead of Trump's primetime fiasco, insisting: "His so-called obsession is only because he cares about the sanctity of our elections."

Hey, Bimbo, if that was true he wouldn't be trying to blow up our elections with his cognitively dissonant 'Save America Act'! See e.g.

Brane Space: Needing A U.S. Passport To Vote? Why The Misnamed 'SAVE' Act Is Not "Partisan Hype" -

But my main beef has been with the so-called "legacy media" - especially the right-leaning Wall Street Journal, as I noted a month ago (June 12 post)"

"Are the nabobs at the WSJ so devoted to his deformed agenda that they're willing to hurl this nation down the shit can to keep coddling him while castigating critics? Can't they see he's not firing on all cylinders, or even half?"

And the refusal to accept reality, i.e. that you lost a goddamned election, factors into that insanity. That plus incessant late night posting - citing former Trump lawyer Ty Cobb, attesting to Trump's brand of insanity:

Trump Lawyer Calls For 25th Amendment Over PSYCHOTIC MELTDOWN

But now, as Paul Krugman has noted, Trump's attacks on elections, combined with his shit-faced stupid attempts to control the Strait of Hormuz, are carrying us into far more dangerous territory, e.g.

The Forever War Gets Scary

This needs to be watched in entirety, as it also makes sense out of deranged Dotard's prime time lie time last night. As Krugman notes:

"What's really scary here is Trump looks like he's given up on trying to extract something that looks like victory."

The implication being he's willing to go to more extreme means to get it, despite the fact this comports with his madness - the inability to grasp the reality that the Strait is not his to control. And even bombing the nuclear reactor at Isfahan (reported in the FT some time ago) will not get him that control. So the only other distraction he can use to try to manipulate public opinion is to attack our election integrity - traitor that he is. As Krugman goes on to note:

"This is ominous because what is Trump's plan for the midterm elections? Here we have just as Trump is prepared to give u0p on trying to spin the Iran war as a positive outcome we have reports he's going to give a prime time speech Thursday about election fraud in 2020. And he may also try to declare the two Democratic Senators from Georgia as somehow illegitimate.

That's not going to actually work and nobody's going to be convinced he actually won the 2020 election. But what is happening is that he's setting up the pretext, the groundwork, for massive interference in the voting this November. And we're basically seeing some kind of attempt to block fair elections. So it's pretty clear now that Trump and those around him have actually given up on trying to win over voters.

They've decided instead that some combination of propaganda, misinformation and disinformation and possibly massive illegality is their way forward. And to say 'they'd never do that' has been the best way to be wrong about everything, every step of the Trump administration.

So the fact Trump is back to bombing Iran - mentioning it - is not because I have any fear that America is going to be at risk from a foreign power. But rather it signals an enormous risk to us from our own president, our own government. And you know, be afraid, be very afraid."

Meanwhile, some nine hours before Trump's performance, Sen. John Ossof (GA) best summed up what the orange maggot would do:

"Here's what's going to happen tonight. The world's most famous sore loser will deliver a prime time address to pursue his six year old grievances on losing the 2020 election while his war in the Middle East spirals out of control and the cost of living continues to rise for Americans across the country.

I also expect him to re-heat the debunked conspiracy theory about the repeatedly litigated, audited and confirmed 2020 presidential election result that Donald Trump LOST. Let me make this very clear. If he declares Georgia's election illegitimate and Georgia's two Democratic Senators illegitimate then he is declaring Georgia's voters illegitimate. Remember it was Donald Trump who committed election fraud when he phoned the Georgia Secretary of State on January 2, 2021 and said: 'I just need to find 11,780 votes, which is just one more than we have."

Which as Lawrence O'Donnell stated afterward, constituted a "crime in progress".

But what the hell do you expect of the first ever felon (and traitor) president? Last night continued that crime in progress. Including demanding licenses for ABC, NBC to be revoked for not airing his endless horse shit lies, e.g.

Trump says ABC, NBC licenses should be revoked over refusal to air speech on election integrity - The Washington Post

This is the liar, criminal and madman - in charge of a criminal regime (not a government) who should have been removed a year ago.

And:

Donald Trump

The Real Message of Trump’s Address to the Nation

by Robert Reich | July 17, 2026 - 5:06am | permalink

— from Robert Reich's Substack

Friends,

The real message to be drawn from Trump’s address to the nation tonight is that he will call into question the votes of every state and city that chooses a Democratic senator or representative in the 2026 midterm elections. He’ll push Republican governors and mayors not to certify the results. He’ll demand recounts and audits.

We’ve been here before, but this time he’s even less restrained than he was in 2020 and is surrounded by people who will do his bidding.

His address tonight was absurd. It was riddled with so many lies that I’m reluctant to dignify them with rebuttals, but you should have them.

» article continues...

And:

Trump doesn't realize how much he just embarrassed himself

And:

IHIP News:🚨 Trump Says CHINA STOLE Election In INSANE Speech?! FOX News FREAK'S DISGUSTING Rant!!

And:

ALL HELL BREAKS LOOSE As BALLISTIC MISSILES RAIN On US Bases & Iran ENDS ALL TALKS!! | Kyle Kulinski

And:

‘Uncle Donnie's’ brain MALFUNCTIONS on world stage

And:

"The Greater COLLAPSE Has Begun..." - Douglas MacGregor

And:

Trump has declared the Strait of Hormuz open. The facts say otherwise. - The Washington Post

Excerpt:

The Strait of Hormuz is now open for “ALL Ship traffic,” except Iran’s, President Donald Trump said on social media this week. But a presidential tweet does not make it so. “The United States [is] on course for perpetual conflict” in the Middle East, even without “a real, serious escalation,” said Seth Jones, president of the defense and security department at the Center for Strategic and International Studies.

And:

2026 Elections | Donald Trump

Midterm Elections: The Con Always Works, Right Up Until the Moment it Doesn’t

by Thom Hartmann | July 16, 2026 - 5:03am | permalink

— from The Hartmann Report

Tonight at nine o’clock Eastern, Donald Trump will look into a television camera and tell America he’s rescuing democracy. He teased the address to reporters this week, promising “really big news” about “free and fair elections” and adding that “it doesn’t get bigger.” For once, he and I agree. It doesn’t get bigger.

An administration official told Reuters that the speech will center on newly declassified intelligence about the 2020 election and what the White House calls voting machine vulnerabilities open to foreign hackers; multiple election experts quoted in that same reporting warn he’s laying the groundwork to contest Republican losses this November.

To understand what we’ll actually be watching Thursday night, we have to go back to 1973, to a Manhattan night spot called Le Club, where a 27-year-old Donald Trump, freshly sued by the Justice Department for refusing to rent apartments to Black families, met the most feared lawyer in New York. It’s a story I tell in detail in The Last American President.

» article continues...

And:

Dr. John Gartner: Donald Trump is "the most pure incarnation of evil that I have ever encountered" - YouTube

And:

Donald Trump

Trump Just Made Some Wild Claims About America’s Election Security

by Adam Lynch | July 17, 2026 - 5:14am | permalink

— from Alternet

During a Thursday speech addressing his 2020 election loss, Donald Trump presented several claims about foreign interference and federal government actions he said affected the election results. Trump cited allegations involving Chinese acquisition of voter data, Deep State actors, Venezuelan interference, and concerns about voting machine security.

Here are some of his stranger claims:

1. China 'massaged' the election with manufactured ballots.

As predicted, Trump launched into his Thursday grievance speech over his 2020 election loss, complaining that Chinese government officials manipulated the race to hide his 2020 victory —despite no accusations of that panning out in 2021, despite the volume of Trump’s complaints.

» article continues...

Thursday, July 16, 2026

Solutions To D.E. Littlewood Non-Commutative Algebra Problems

1) Consider the parallelopipped below spanned by the vectors u, v and w in 3-space.

Find the volume of this solid given that:

u = (1, 1, 3)

v = (1, 2, -1)

w = (1, 4, 1)

Solution:

We let the volume be Vol(u, v, w) and:

Vol (u, v, w) = Det [u, v, w]

Then we need:

= [2 -(-4) - (1 - (-1)) + 3(4 - 2)] = 6 - (2) + 3(2)

Vol (u, v. w) = 12 - 2 = 10 cubic units

2)Show how the Grassman algebra formula for a single component of volume element k e₁e ₂e ₃can be used to find the volume of a tetrahedron.

Find that volume for this tetrahedron, given the concurrent vectors are:

a = (3, 0, 0)

b = (1, 4, 0)

c = (2, 1, 5)

Solution:

In Grassman algebra, the fundamental volume element V is represented by the wedge product of three basis vectors:

Then the product of the three concurrent vectors given (a,b,c) is the exterior product:

Then using the anticommutative property (identified in blog post):

The product of the linear combinations can then be evaluated:

Where det (a,b,c,) is the determinant of the vector components:

This scalar then gives the volume spanned by the vectors, much like the scalar in #1 (det) gave the volume for the parallelopiped.

Let D = det (a,b,c), then:

Volume of tetrahedron =

1/6 det (a,b,c) = D/ 6 = 60/ 6 = 10 cubic units

Wednesday, July 15, 2026

An Artificial 'Storm Wall' Could Shield Us From A Solar Superstorm - IF We Could Afford It

Solar eruption leading to solar storm that knocks out power grids

Chris Mims, writing in a Weekend WSJ article ('A Plan To Shield Earth From Solar Storms', p. C2) begins with this future flight of fancy:

"It’s the year 2040, and the Big One—a civilization-smashing solar storm of a scale not seen since the 19th century—is on a collision course with Earth. Far out in space, where geostationary satellites orbit, a half-dozen school-bus-size satellites crack open and start dumping barium, lithium or sodium. Within minutes, sunlight transforms this material into an ionized gas shield that slows the oncoming massive blob of plasma. Down on Earth, a would -be global catastrophe potentially knocking out all electric grids- is reduced to a nighttime display of aurora."

This provokes the question of what exactly Mims is writing about. Well, he (and others) envisage a "Storm Wall" to prevent such a mammoth CME (coronal mass ejection hurling us back into an electronic Stone Age). Translation: No working cell phones, no TV, no computers, no radios and no GPS.

The fancied project - not yet a reality- goes by the name 'StormWall'' and was "conceived by a trio of scientists: Daniel Welling, a space physics specialist at the University of Michigan, Brian Walsh, an associate professor of engineering at Boston University, and Allison Jaynes, a space physics professor at the University of Iowa.

Walsh and Welling are the co-authors and co-designers of the proposal, which - let's be clear - is still years in the future (assuming the money is available to complete it). According to Welling, quoted in the Mims' piece:

"Even in the best case scenario, just the research would require at least five more years."

Oh yeah, and "even if its costs $100 billion, that price tag is only one tenth of the amount tech companies are projected to spend on building AI infrastructure next year alone."

But as I see it, the more serious problem - which may prevent even partial funding - is that Trump's 'Big Beautiful Bill' passed last year - has already blown past the debt doors by $5 trillion. So, the chance of passing a $100 b space project are more like slim and none. Which is a pity, given from what Mims spells out in his WSJ article it could work.

To reduce it to its ultimate simplicity one can think of an "airbag for the magnetosphere." According to co-designer Dan Welling:

"You can think of it as an air bag. It would be deployed only when all other measures have been deemed insufficient. And like an air bag for your car, deployment is a one-time thing. After all, if you use it in your car the entire steering column has to be replaced and the insurance company will declare your car totaled."

Of course, this 'one off' aspect is another reason I doubt there will be any budget allocations for it. I mean a one time project for $100 billion? Certainly not with any Reepo congress in place, and I suspect a Dem congress would give pause as well, given they will likely be in 'clean up; mode after the Goopers leave so much debt in their wake.

But again, this would be a pity given "the idea of StormWall is to help boost the magnetospheric defenses when bad stuff heads toward us."

Reviewing the function and nature of the magnetosphere we can refer to the artist illustration below:

Here, a CME from the Sun is headed toward Earth, with billions of charged particles en route. But most will get deflected by the magnetosphere (greenish field lines). A portion of the incoming particles are channeled to the Earth's poles and show up as the aurora when the solar wind is especially active.

StormWall would enhance the magnetospheric field, but the major expense would be in assembling at least 830,000 pounds (415 tons) of ionizable material (lithium, barium or sodium) to be launched to an altitude of 22,000 miles above the Earth's surface. Thus one would have a geosynchronous orbit. In this case, the altitude is critical given it's at the height the injected ionized material would be able to follow the 'natural highways' in space, according to the project designers. Obviously, to get this job done would require the most powerful rockets available.

Currently many launches would be needed to put that much material into the desired orbit. In truth, a mega-rocket like Space X's Starship would likely be needed to effect a single transfer of 415 tons into a 22,000 mile orbit. But I doubt Musk would endorse it.

Why all the expense and effort? To avoid the next massive disruptive event especially given the extent humans now depend on things like smart phones, computer and AI. The last truly disruptive even was in March, 1989 when the Quebec power grid was knocked out for 9 hours. Large direct currents arising from a red aurora at the time, triggered by a solar storm, were believed to be the immediate cause.

Then in 2012, a solar 'superstorm' more powerful than any in the past 150 years, narrowly missed Earth. i.e.

Monster Plasma "Blob" Headed for Earth: Is This the End?

But let's be clear that predicting a space weather event - say a massive CME erupting from the solar meridian - is not the same as correctly forecasting its effects on one particular part of a hodge-podge terrestrial power grid. In other words, you can't hold space physicists responsible for failing to forecast that field line currents generated - say like in the 1989 event- will have a similar impact now.

In the case of CMEs, a quantitative forecast strategy would revolve around obtaining the rate of increase of the poloidal magnetic flux (Φp) associated with a specific flux rope (e.g. that shows kink or other instability) e.g.

dΦp(t )/dt

Then, for a predictive basis one would require the related function be adjusted for each potential CME (dependent on its current heliographic location) that best fits the total observed data. This function would normally be given in terms of the electromotive force associated with the active region so that:

E(t ) ≡ −(1/c)dΦp(t )/dt

Where the preceding would constitute a forecast from the theory for each CME trajectory. According to Ian Cohen, head of solar and space physics at the Johns Hopkins APL,

"The challenge is that experts can't predict space weather the way they can predict weather on Earth. We don't have as many sensors in space, and the processes that trigger solar storms and make them devastatingly potent, are more complicated."

One only hope the challenges can be met, but time is not on our side, nor is the degree of human insight, critical thinking and support for science - having taken a massive hit since last January. If Mr. Mims's' fantasy rescue from electronic doom is to be averted using StormWall, we'll need a succession of fortuitous breaks before 2040. Most critical of all, will be the money and the will to put politics behind us and make a common goal the priority.

See Also:

http://www.spaceweather.com/

And:

Coronal Mass Ejections In The Context Of Collisionless Shocks

And: