Friday, April 3, 2026

A Theology Test For Easter Weekend


What better way to get people- even blog readers-  to focus on Easter Weekend than a Theology exam?  And not any old basic exam but one prepared by the Jesuits at Loyola University, New Orleans.

Below, a 1964  final exam from a Loyola University 1st year course. Can't figure out an answer to the question? Enter the question in Google AI mode and be amazed at the comprehensive nature of the response. Then pack the answer away for future reference.

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1. Estimate the percentage of the Qumran scrolls that are copies of books of the Bible. Of which proto-canonical books were there copies or fragments? Of which deutero-canonical books? Define each type of book, making clear any unfamiliar terms.

2. WHY are the Qumran scrolls of such great importance? Why would it be erroneous to conclude that these scrolls provide us with the original reading of the New Testament books?

3.What aids did biblical scholars already possess toward reconstructing the original reading of the Old Testament books? How have the discoveries at Qumran enhanced the value of the Septuagint translation as a reliable aid for reconstructing the original reading of the Old Testament that appears in the scrolls?

4. How (not how much) have the Qumran scrolls contributed to our knowledge of the history of Judaism? What caution(s) must we keep in mind when reconstructing Israelite history from these scrolls?

5. Three fourths of the Dead Sea Scrolls are writings composed by the Essenes themselves, treating their religious views and way of life. What have we learned from them about the Essenes' beliefs to do with the "angel of light" and the "angel of darkness"? What have we learned about their beliefs concerning the Messiah?

6. Discuss the moral views and practices of the Qumran sectarians as they might have impacted their texts-scrolls. Give at least two specific examples and expand on them at length, including likely copyist errors.

7. Half the original manuscript witness sources, including a Bodmer papyrus and Beza's Codex, omit the last line (accorded to Jesus) from Luke 23:33-34. What does this omission convey concerning the textual tradition of this sentence? What general caution does this provide concerning exegesis for the synoptic gospels in general?

8. Some Protestant biblical scholars used to hold that St. John's Gospel could not possibly have been written by a Jewish Christian living at the time of Christ. They asserted it was more likely written in the 2nd or 3rd century A.D., because of the terminology and ideas in St. John's Gospel reflecting an abstract dualistic theology (e.g. emphasizing the conflict between light and darkness).

Explain how the Qumran documents smashed this theory. Why would Jesus (as reported in his speeches in St. John's Gospel) have used such terminology and ideas?

9.  Discuss fully the new insight for interpreting the 'Epistle to the Hebrews' which we get from the Qumran scrolls.

10. The word "mystery" (Greek 'musterion': 'what is known only to the initiated') occurs twenty seven times in the official New Testament and almost all these occurrences demonstrate the "secret infrastructure of a nascent cult". Further, a careful reading of the Pauline Epistles, and Gospels (supplemented by modern documentary discoveries- such as at Qumran) shows Christianity began as a mystery religion, replete with initiations, secrets and multiple levels of indoctrination.

The 'mystagogoue' element is also very evident in passages such as 1 Cor. 2:6 ff.

Explain the nature of a "mystery religion". Do you concur that Christianity - from the scriptural elements, passages noted- qualifies as such? Why or why not? If the negative, provide an alternative exegesis to make sense of 1 Cor. 2:6 ff.

Revisiting Elliptic Curves and Their Rational Points

 

                      Example of an elliptic curve under study for rational points

       Example 2 of an elliptic curve. Can you identify its rational points?


In an earlier post from 2010 , e.g.

http://brane-space.blogspot.com/2010/04/looking-at-groups.html


I noted the definition for an Abelian group, in respect of the commutative property i.e. Only if there exist elements a, b Î G such that (a · b) = (b · a), then G is said to be an Abelian Group.   
According to Mordell ('On the rational solutions of the indeterminate equation of the third and fourth degrees'Proceedings of the Cambridge Philosophical society, Vol. 21 (1922), 179),

The set E(Q) of rational points of an elliptic curve E defined over Q (the set of rational numbers) forms a finitely generated Abelian group such that:

E(Q) = Zr  ⊕ E(Q)tor


for some non-negative integer r and finite Abelian group E(Q)tor.  Where  'tor' denotes the torsion subgroup.

In general,  elliptic curves can be considered in long or short Weierstrass form. For the former, we know an elliptic curve over Q is isomorphic to the projective closure of the zero locus of the equation:

y2  + a1 xy  + a3y =  x3      + a2 x2   +  a4 x + a6

But when defining a nonsingular curve the preceding can be transformed over Q to the short form:

y2  =   x3    +  Ax   +  B


for A, B   Î Q   with non-zero discriminant   D = -16 (4 A3  +   27 B)

N.B. The non-vanishing of the discriminant ensures the curve is nonsingular.

And we say the elliptic curve given by the short form has height coordinate maximum:

h (E) =   max (4 |A|3 ,   27 B2)

Consider now two examples of elliptic equations with graphs for subsets of the real points shown above.  These are:

1) y2  =   x3     –       x  

And:

2) y2  =   x3     –     x  +  1


For each curve we can apply the short form for the Weierstrass equation. Thus, for (1) we have:    A = -1  and B = 0

Then the discriminant :   D = -16 (4 A3   +  27 B2 ) =   -16( 4 (-1)3    + 0) = 64

The height is:  h (E) =   max (4 |A|3 ,   27 B2) =  4 |(-1)|3 , 0   = 4, 0

For (2) we have: A = -1  and B = 1

Then the discriminant :   D = -16 [4 A3   +  27 (1)2]  =   -16[ 4 (-1)3    + 27]

=   [64 +   27(-16)]  =  [ 64 +   (-432)]  = -368

The height coordinates maximum is:   h (E) =   max (4 |A|3 ,   27 B2) =  4 |(-1)|3     = 4, 27

One peculiarity of such elliptic curves as noted by Ho (Bull. American Math Soc., Jan., 2014, p. 27) is that the elliptic curves occur in two separate domains: the complex points of an elliptic curve make up a one-holed torus, or "genus 1" curve, i.e. like a donut or torus given the genus specifies the number of "holes" or handles. Meanwhile, the real points are smooth curves in R2  with one or two components (compare the graphs shown above)

The "group law" applies, as Ho notes (ibid.) such that the set of solutions in a given field forms a group.

Ho goes on to say that "the group structure on the points of an elliptic curve uses the point 0 at infinity as the identity element and is most easily described geometrically."  Ho gives an example of this which I leave for the energized reader to actually work out using the curve shown in (2). His prescription, which the reader may use as a guide is:

"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, e.g. 

https://en.wikipedia.org/wiki/B%C3%A9zout's_theorem


The vertical line through P3 then intersects another point on the elliptic curve which is the composition P1 + P2 of P1 and P2"

Further elaborating (ibid.):

"In other words the three intersection points P1, P2, and P3 of any line L with the elliptic curve sum to the identity in the group law.(The identity point 0 may be one of these points,  e.g. a vertical line intersects 0, a point P and its negative. Moreover, if P1 and P2 are rational points then the line L has rational slope, so P1 + P2 is also a rational point."

To get the interested math reader started, you may use as point P1 the vertex of the curve shown in (2)

Suggested Problems:

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

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).


Thursday, April 2, 2026

Higher Tax Wealth Flight Is Irrational Given We Know Higher Tax Rates Generate Higher Productivity

 

                                 Burgeoning numbers of the Ultra-wealthy (WSJ, 3/28)


"Trump's war is causing unintended problems -- excessive military spending at the expense of most social programs. Considering that Trump, rich politicians, and billionaires rarely pay much (if any) taxes, the rest of us will be footing the bill. Considering the number of hospitals already teetering on the edge, this huge increase in defense is ridiculous -- and all because Trump's delusions and tantrums have led to Congress to allow him start a war to soothe his ego." - WaPo comment


The March 28-29 WSJ Editorial (p. A12): 'The Higher Tax Wealth Flight Continues' ) was eye-opening but did not convert me from my existing position that cutting tax rates for high income people douses productivity. Yet, according to the Journal:

"As Democrats across the country seek to raise income taxes, the IRS on Friday released new data on state income migration that is a reality check on their ambitions. Even after the pandemic high tax states continue to lose tens of billions of dollars in taxable income to low tax states."

The bejabbering WSJ editors than lay it on:

"By comparison, all states without an income tax besides Alaska gained income from inter-state migration, including Florida ($20.6 billion).'

Maybe before jumping into this drivel, the WSJ's mavens ought to have inquired why Florida is experiencing significant reverse migration. This after all the wealthy newcomers learned what many of us (former Floridians) knew: the state isn't for everyone - especially if you like efficient public services and hate excessive heat and humidity as well as overpaying for insurance.  Not to mention the bulk of available jobs are low productivity.  

The sad and sobering fact? Rising home and fuel costs, extreme summer heat, high insurance premiums, and, severe traffic congestion are driving a significant "reverse migration" of new residents out of Florida. Data from 2025 indicates more people were leaving Florida than moving in, with many relocating to the Midwest, Colorado, and the Northeast, reversing the pandemic-era boom.

How 'bout them apples, WSJ?

But seriously, if the WSJ editors had their heads less in the clouds of capitalism and more in reality, they might back off from the incessant yen to diss higher tax locations.  Recall here,  all tax cut "job creation" tripe emerged out of  "Supply Side Theory" which was actually invented by one Arthur Laffer, in 1974, when he purportedly drew a curve on a paper napkin at a restaurant, e.g.


 









and announced he'd found a "new theory that generates wealth" while it cuts income (tax). (See, e.g. James Medoff and Andrew Harless, The Indebted Society, 1995, p. 84, 'Let Them Eat Cake'.)

The curve, as Medoff and Harless noted, purported to show the relation between tax rates and revenues. A tax rate of zero naturally produces no revenue. As taxes rise from zero, revenues rise in tandem. But as the rates rise, they discourage the activities being taxed. So at some point, discouragement predominates in the curve. (Laffer showed this with a splash of catsup over the top of his curve, on the napkin.)

In fact, when Medoff and Harless removed the catsup stain from the graph, and looked at actual data, they found (p. 87) that "high tax rates are associated with higher productivity growth" There is a consistent and strong relationship. Moreover this relationship is historical, over decades and hence evidence -based, unlike Bush, Reagan and Romney's "tax cuts create jobs" malarkey! By contrast, for the years when supply side dogma held,  and tax cuts were implemented, productivity retreated by more than 30% and debt exploded- exactly the opposite of what we've been sold.

Based on Medoff and Harless' data, one can offhand predict that within four years of eliminating ALL the Bush - Trump tax cuts (middle class and for the wealthiest) our national productivity will enhance at least 25% and our GDP will actually GROW by 4-5% per year instead of the paltry 1-2% we've been seeing. Removing ALL the tax cuts will also stabilize the tax landscape and remove business uncertainty making corporations (still sitting on nearly $2.4 trillion in capital) invest not only in plant but labor! This labor investment is what will then drive the job creation!

Another aspect concerns the issue of percentage of GDP used for defense. For those who may not have been following all the recent news, the Trumpers have been pushing a number of European - NATO countries to boost military-defense spending.  Many have refused, including Spain's President Pedro Sanchez, because they grasp such a boost would force them to reduce social spending. 

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.  

By contrast, the orange buffoon in the WH now wants to increase defense spending by 40 percent -  to $1.5 trillion (WSJ, today 'Trump’s Budget Breakthrough for Defense'). This budget proposal, if passed, would put an even bigger target on Social Security and Medicare. (Especially if Dems don't win back the House to control Trump's militaristic spending insanity.)

The misfit wackjob recently has gone so far as to say the government ought to stop funding Medicare as well as childcare across the board, to focus on his war of choice with Iran. Oblivious to the fact he will only obliterate more taxpayer dollars that can help millions afford healthcare (as well as childcare and senior care) instead. 

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 welfare!

In a Nov. 10, 2025 post I exposed how Oprah herself was as brainwashed about the value of higher taxes to support public services, or what constitutes "socialism" in this country'

This was in one episode of her eponymous show when she raised the misbegotten fear of socialism and the welfare state taking hold in the U.S., earning a robust response from two Danish citizens, e.g.:

Oprah got perfect response from Danish woman about their social welfare state PRESCIENT!



As Oprah rambled on about "socialism" with a fearful expression, the two Danish woman on Skype quickly informed her:

 "We think of it as being civilized. As taking care of each other...the elderly, the sick."   

The Danes had clearly exposed Oprah's brainwashing - and Oprah is not a dumb American.  But this same brainwashing is endemic in too many other Americans as well, infected with the rugged individualist bunkum.

The Danes response ties directly into higher taxation as opposed to tax cuts. Because democratic socialist nations use higher taxation - across the board not just on the rich - to make available the funding for public services whether education (free) or medical, or child care.  

In other words, their citizens - unlike too many Americans- understand you don't get something for nothing. Want free education, including up to college, free health care like in Canada, free child care like in Norway? Then you need to be willing to pay the higher taxes to fund them.  This is summed up in the highlight box below - from the exchange with the Danes:


So high taxation, often linked to socialism in this country, is really about having a civilized nation than a barbaric, i.e. 'dog eat dog' nation. 
Nor is this un-American. It was Supreme Court Justice Oliver Wendell Holmes Jr. who first said:

"Taxes are the price we pay for a civilized society."

Which was intended to justify taxation as investment in public goods. There is no reason why this cannot be implemented here in the US of A given the latest WSJ article (March 28-29, p. 2A): 'Gains by the Superrich Alter the Economy', noting:

"The number of Americans worth tens of millions  of dollars has boomed in the past few decades thanks to a rising stock market, lucrative private investments, and swelling valuations for small and midsize businesses."

But most Americans have not benefited for whatever reason. (I.e. "The wealthiest 10 percent account for 50% of consumer spending") Most can still not afford to buy a first home, far less a 2nd or 3rd, nor can they afford child care, or college. It is past time to share that wealth - via taxation on the "superrich" segment - as I am sure Oliver Wendell Holmes Jr. would advocate too.

See Also:

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:


Excerpt:

Due to availability or cost, 91,590 Colorado children can’t access child care — nearly one-quarter of all kids under 5 — and 40,000 parents report having made career changes to accommodate a lack of care. When they can get it, families pay, on average, $15,000 per child each year to place their kids in licensed facilities. Single parents can spend nearly half their take-home pay finding somewhere safe for their children to be during the day.



And:


And:
   

And:


Wednesday, April 1, 2026

Solution to Mensa Circle With Analytic Geometry Problem

 

The general equation of a circle is:


 (x - a) 2 -  (y - b) 2 =  r 2

Where (a, b) denotes the coordinate of the center, and r is the radius. See e.g.


For the circle in the problem, defined by:

(x - 132) 2 -  (y - 132) 2 = 24, 649  

The center is at:  (132, 132)  and the radius is:

Ö 24, 649   =    157

Then:  AO =  157

But the horizontal distance from A to O (see reconstructed diagram) is 132.

By the Pythagorean theorem:

(Vertical distance from A to O)2    + (132) 2 =   (157) 2     = 7, 225


Then:  Vertical distance from A to O  =   Ö 7, 225  =  85

Now,  <ACM  and  < ACN  are inscribed angles with both =  p/4  radians

The inscribed angle theorem states:

An inscribed angle is equal to one half the central angle that intercepts the same arc.

Therefore:  <ACM  =  ½  < AOM

And:  <ACN = ½  < AOM   +   < AOM

=  <AON  =    p/2  radians

NM is a diameter (in the reconstructed circle) since <AON and <AOM are on opposite sides of  AO  and < AOM + < AON =  p   radians

NM is perpendicular to AO, since < AOM and < AON are p/2  radians relative to AO.

Then:  The slope of AC =  85/ 132

The slope of NM =  132/ 85

M coordinates are: (132 + 85, 132 + 132) = (217, 264)

N coordinates are: (132 - 85, 132 - 132) = (47, 0)