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The Stones'"Ninguna Expectativa""No Expectation" Recorded With Friend "Cuco" Benitez


Creedence Clearwater's "Lodi" Recorded In Oaxaca With Friend Refugio "Cuco" Benitez

The Who's "Squeeze Box" ("La Caja") Recorded In Oaxaca With Friend Refugio "Cuco" Benitez

"Who's Going To Build Your Wall" ("El Muro") With Friend Refugio "Cuco" Benitez On Guitar

"La Chiquitita," Guitar Solo By Friend Refugio "Cuco" Benitez, Recorded In Oaxaca, March 2019

"Al Ritmo De La Lluvia" Recorded In Oaxaca By Friend Refugio "Cuco" Benitez

"Hey Jude" Recorded By Friend Refugio "Cuco" Benitez In Oaxaca

John Lennon's "Imagine" Recorded By Refugio "Cuco" Benitez In Oaxaca, Mexico


NPR: New Police Force From Scratch: Camden N.J. Proves It's Advantageous To Reform The Police

Rock And Roll Music "Made In Oaxaca" With Good Friend Refugio "Cuco" Benitez, 2019-2020

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"Something" Recorded In Oaxaca By Good Friend Refugio "Cuco" Benitez

I met Cuco when trying to locate supermercado Pitico. Out of the blue came the sweet sound of  "Something." I followed that sound for over a city block until I came upon my friend-to-be, playing under a palm tree in Jardin Conzatti. 
From then on, Cuco and I played as a duet six days a week in Jardin Conzatti and weekends in the Alameda de Leon (alongside Oaxaca's Cathedral) where Cuco was a member of the long-established Oaxacan band, Tunel del Tiempo. 

"Who's Going To Build Your Wall" ("El Muro") Recorded With Friend Refugio "Cuco" Benitez

The Stones'"Ninguna Expectativa""No Expectation" Recorded With Friend "Cuco" Benitez



John Lennon's "Imagine"
"Hey, Jude"

"Stand By Me" Recorded In Oaxaca, Mexico, With Good Friend Refugio "Cuco" Benitez On Guitar

Ritchie Valens' Sonámbulo/Sleepwalk Recorded In Oaxaca By Friend Refugio "Cuco" Benitez

The Who's "Squeeze Box" ("La Caja") Recorded In Oaxaca With Friend Refugio "Cuco" Benitez

"Al Ritmo De La Lluvia" Recorded In Oaxaca By Friend Refugio "Cuco" Benitez

"La Chiquitita," Guitar Solo By Friend Refugio "Cuco" Benitez, Recorded In Oaxaca, March 2019

Creedence Clearwater's "Lodi" Recorded In Oaxaca With Friend Refugio "Cuco" Benitez

The Stones'"Ninguna Expectativa""No Expectation" Recorded With Friend "Cuco" Benitez

"Para Mi Amigo Alan," A Gift Composition By Good Friend, Maestro Refugio "Cuco" Benitez

Music-Making With "Túnel Del Tiempo" And "Cuco" Refujio Benitez In Oaxaca, Mexico

Making Music In Oaxaca With Cuco Refugio Benitez


  

"Stand By Me" Recorded With Good Freind Refugio "Cuco" Benitez, Oaxaca, March, 2019

Trump Cultists "Beelining" In The Klondike

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 These People Are Miners "Beelining" During The Klondike Gold Rush. Almost None Of Them  "Struck It Rich" But Their Unfounded Credulousness  Recalls The Blind Faith Of Trump Cultists | made w/ Imgflip meme maker

The harsher things got, the more credulous these miners became.

After all, THAT many people "cannot be wrong."

"There's gold in them thar hills!"

Sadly, half of any population has double digit IQ and it is these people who are unusually inclined to believe rumors, gossip, and nonsense representing itself as wisdom.

No wonder Trump "loves the uneducated."

At the same time the "double digiters" are suckers for bullshit, doubling down on stupidity, ignorance and whole cloth lies as "proof" that they're the only people with real insight.

Here's "the flip side."

What "The Good Guys" Are Up Against | What The Good Guys Are Up Against... People Who Say "I Wouldn't Believe That Even If It Was True" | image tagged in aggressive ignorance,proud ignorance,boastful ignorance,evangelical ignorance,addlepated dimwits,the benighted | made w/ Imgflip meme maker

Video: "If You Don't Think Trump And Trumpistas Are Hypocritical, Dishonest And Stupid, You Will!"

"A Confession: I'm Starting To Write Off Stupid People As Incorrigible"
"The Demonstrable Stupidity Of Trump-Cultists"

We Know That Stupid People Exist. We Also Know Who They Are...

"Thinking Is A Learned Skill. Most Trumpistas Don't Understand This. In Fact, They Can't."
https://paxonbothhouses.blogspot.com/2019/11/thinking-is-learned-skill-most.html

Pax on both houses: "Farewell, America," The Post-Election ...
"Mark Twain, Adolf Hitler And The Dunning-Kruger Effect"

Barack Obama: "It’s Like These Guys Take Pride In Being Ignorant."

"Trump Is An Idiot's Idea Of A Genius": Find Out Why

Are We At That Point Where "The Sapiens" Are Again Separating From "The Neanderthals?"

"P.J. O'Rourke On Trump, Trumpistas And The Futility Of Drug Tests: Test For Stupidity, Ignorance, Greed And The Love Of Power"

Stunning Stupidity! (Not All Conservatives Are Stupid, But Most Stupid People Are Conservative)
"The Exquisite Stupidity Of Trump Supporters"
A Critical Mass Of American "Conservatives" Are Stupid, Ignorant, Hateful And Cruel

The Merger Of Stupidity And Racism Merge In This GIF Is Jawdropping - And Typical

"There's A Sucker Born Every Minute" | made w/ Imgflip meme maker
"There's A Sucker Born Every Minute"
Wikipedia
https://en.wikipedia.org/wiki/There%27s_a_sucker_born_every_minute
Pax on both houses: The Exquisite Stupidity Of Trump Supporters
"It Is Painful How Stupid People Are"
https://paxonbothhouses.blogspot.com/2020/05/it-is-painful-how-stupid-people-are.html

It Has Come To This: How Do Intelligent Citizens Deal With The Irredeemably Stupid, Ignorant And Self-Pithed People Who Have Taken Over? The Invasion Of The Body Snatchers Is Now Reality


"It's Like These Guys Take Pride In Being Ignorant." Barack Obama | made w/ Imgflip meme maker





"Demilitarizing" The Police Could Be A More Fruitful Rallying Cry For Reformers Than Defunding

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 There's a sign in there! "When At Last You Comprehend The Meaning Of The Universe,  You Will Worship Me.  Jesus Is Just The Official Story. | made w/ Imgflip meme maker

NPR: New Police Force From Scratch: Camden, N.J. Proves It's Advantageous To Radically Reform The Police

The Washington Post
The Daily 202
Intelligence for leaders.

When Liberals And Progressives Say "Defund The Police," Are They Trying To Lose Votes?

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"When Liberals And Progressives Say "Defund The Police,"  Are They Trying To Lose Votes? Proper Framing Would Say:  "Rebuild EVERY Police Force  FROM SCRATCH." | made w/ Imgflip meme maker
Alan: Maybe the motto for "Defund The Police" should be "Give Willie Horton More Weekend Passes."
If I were a Russian hacker employed by Putin to chip away "persuadable" voters, I would aspire with my head, heart, hands, soul and intellect to frame this debate under the title, "Defund The Police."

NPR: New Police Force From Scratch: N.J. Proves It's Advantageous To Reform The Police

Military Leaders Denounce President Trump: When "The Brass" Turn Their Backs - NPR's "1-A"

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"We Know That We Are Better  Than The Abuse Of Executive Authority...  We Must Reject And Hold Accountable   Those In Office Who Would Make A Mockery Of Our Constitution" Marine General James Mattis  Reflecting On Trump's Presidency | made w/ Imgflip meme maker

NPR's "1-A": When "The Brass" Turn Their Backs: Military Leaders Denounce President Trump

  https://the1a.org/segments/when-the-brass-turn-their-backs-military-leaders-retreat-from-president-trump/

"Marine General James Mattis  Describes Trump As A Near-Nazi Turncoat-Enemy  Of The American People" | made w/ Imgflip meme maker

General James Mattis Describes Trump As A Near-Nazi Turncoat-Enemy Of The American People


 General James "Mad Dog" Mattis  Does Not Use The Word "Traitor"   But He Describes Trump In Crystal Clear Terms  As A Near-Nazi Turncoat Enemy Of The American People. Google: "General James Mattis Denounces Trump's Nazi Attack On America" | made w/ Imgflip meme maker

Statement By General Mattis: If He's Not Saying Trump's A Traitor, What Does "Traitor" Mean?


General James Mattis Does Not Use The Word "Traitor" But Clearly Describes Trump As A Turncoat Enemy Of The American People |  “Donald Trump is the first president in my lifetime who does not try to unite the American people—does not even pretend to try. Instead, he tries to divide us... We are witnessing the consequences of three years of this deliberate effort... Instructions given by the military to our troops before the Normandy invasion reminded soldiers that ‘The Nazi slogan for destroying us … was “Divide and Conquer... When I joined the military, some 50 years ago, I swore an oath to support and defend the Constitution. Never did I dream that troops taking that same oath would be ordered... to violate the Constitutional rights of their fellow citizens—much less to provide a bizarre photo op for the elected commander-in-chief, with military leadership standing alongside.” Marine General James Mattis | image tagged in trump,traitor trump,treacherous trump,turncoat trump,sobmy trump,traitorous trump | made w/ Imgflip meme maker

Former White House Chief Of Staff John Kelly: "I Agree" With Jim Mattis On Trump


 White House Chief Of Staff General John Kelly Says:  "I Agree" With General James Mattis: "Donald Trump Is The First President In My Lifetime Who Does Not Try To Unite The American People - Does Not Even Pretend to Try. Instead He Tries To Divide Us."  In Fact, The White House Ordered Troops  To "Violate The Constitutional Rights Of Fellow Citizens." | made w/ Imgflip meme maker

 


"Taking A Knee"

"America Fails The Marshmallow Test," Paul Krugman

"Arabic Mathematics: Forgotten Brilliance?" University Of St. Andrews, Scotland

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Pax on both houses: Thomas Aquinas on Fear
Alan: I introduce this article on Arabic mathematics with reference to St. Thomas Aquinas since it is widely agreed that Aquinas "rescued" much ancient learning (particularly that of the Greeks) by way of Arab scholars who had preserved that body of knowledge.

John Ford, John Wayne, Aquinas And Theosis (Christian Divinization)
Aquinas, St. Symeon The New Theologian And Their Spiritual Kin
http://paxonbothhouses.blogspot.com/2013/08/aquinas-stsymeon-new-theologian-and.html

Pax on both houses: St. Thomas Aquinas, Natural Law, and the ...

Arabic mathematics : forgotten brilliance?

Alan: Thanks to friend Byron for bringing this article to my attention.

Recent research paints a new picture of the debt that we owe to Arabic/Islamic mathematics. Certainly many of the ideas which were previously thought to have been brilliant new conceptions due to European mathematicians of the sixteenth, seventeenth and eighteenth centuries are now known to have been developed by Arabic/Islamic mathematicians around four centuries earlier. In many respects the mathematics studied today is far closer in style to that of the Arabic/Islamic contribution than to that of the Greeks.

There is a widely held view that, after a brilliant period for mathematics when the Greeks laid the foundations for modern mathematics, there was a period of stagnation before the Europeans took over where the Greeks left off at the beginning of the sixteenth century. The common perception of the period of 1000 years or so between the ancient Greeks and the European Renaissance is that little happened in the world of mathematics except that some Arabic translations of Greek texts were made which preserved the Greek learning so that it was available to the Europeans at the beginning of the sixteenth century.

That such views should be generally held is of no surprise. Many leading historians of mathematics have contributed to the perception by either omitting any mention of Arabic/Islamic mathematics in the historical development of the subject or with statements such as that made by Duhem in []:-
... Arabic science only reproduced the teachings received from Greek science.
Before we proceed it is worth trying to define the period that this article covers and give an overall description to cover the mathematicians who contributed. The period we cover is easy to describe: it stretches from the end of the eighth century to about the middle of the fifteenth century. Giving a description to cover the mathematicians who contributed, however, is much harder. The works [] and [] are on "Islamic mathematics", similar to [] which uses the title the "Muslim contribution to mathematics". Other authors try the description "Arabic mathematics", see for example [] and []. However, certainly not all the mathematicians we wish to include were Muslims; some were Jews, some Christians, some of other faiths. Nor were all these mathematicians Arabs, but for convenience we will call our topic "Arab mathematics".

The regions from which the "Arab mathematicians" came was centred on Iran/Iraq but varied with military conquest during the period. At its greatest extent it stretched to the west through Turkey and North Africa to include most of Spain, and to the east as far as the borders of China.

The background to the mathematical developments which began in Baghdad around 800 is not well understood. Certainly there was an important influence which came from the Hindu mathematicians whose earlier development of the decimal system and numerals was important. There began a remarkable period of mathematical progress with 's work and the translations of Greek texts.

This period begins under the Caliph Harun al-Rashid, the fifth Caliph of the Abbasid dynasty, whose reign began in 786. He encouraged scholarship and the first translations of Greek texts into Arabic, such as 's Elements by al-Hajjaj, were made during al-Rashid's reign. The next Caliph, al-Ma'mun, encouraged learning even more strongly than his father al-Rashid, and he set up the House of Wisdom in Baghdad which became the centre for both the work of translating and of of research.  (born 801) and the three  worked there, as did the famous translator .

We should emphasise that the translations into Arabic at this time were made by scientists and mathematicians such as those named above, not by language experts ignorant of mathematics, and the need for the translations was stimulated by the most advanced research of the time. It is important to realise that the translating was not done for its own sake, but was done as part of the current research effort. The most important Greek mathematical texts which were translated are listed in []:-
Of 's works, the Elements, the Data, the Optics, the Phaenomena, and On Divisions were translated. Of ' works only two - Sphere and Cylinder and Measurement of the Circle - are known to have been translated, but these were sufficient to stimulate independent researches from the 9th to the 15th century. On the other hand, virtually all of 's works were translated, and of  and  one book each, the Arithmetica and the Sphaerica, respectively, were translated into Arabic. Finally, the translation of 's Almagest furnished important astronomical material.
The more minor Greek mathematical texts which were translated are also given in []:-
... ' treatise on mirrors, 's Spherics, 's work on mechanics, 's Planisphaerium, and ' treatises on regular polyhedra (the so-called Books XIV and XV of 's Elements) ...
Perhaps one of the most significant advances made by Arabic mathematics began at this time with the work of , namely the beginnings of algebra. It is important to understand just how significant this new idea was. It was a revolutionary move away from the Greek concept of mathematics which was essentially geometry.

Algebra was a unifying theory which allowed rational numbers, irrational numbers, geometrical magnitudes, etc., to all be treated as "algebraic objects". It gave mathematics a whole new development path so much broader in concept to that which had existed before, and provided a vehicle for future development of the subject. Another important aspect of the introduction of algebraic ideas was that it allowed mathematics to be applied to itself in a way which had not happened before. As Rashed writes in [] (see also []):-
's successors undertook a systematic application of arithmetic to algebra, algebra to arithmetic, both to trigonometry, algebra to the Euclidean theory of numbers, algebra to geometry, and geometry to algebra. This was how the creation of polynomial algebra, combinatorial analysis, numerical analysis, the numerical solution of equations, the new elementary theory of numbers, and the geometric construction of equations arose.
Let us follow the development of algebra for a moment and look at 's successors. About forty years after  is the work of  (born 820), who conceived the idea of reducing geometrical problems such as duplicating the cube to problems in algebra.  (born 850) forms an important link in the development of algebra between  and . Despite not using symbols, but writing powers of x in words, he had begun to understand what we would write in symbols as x^{n}.x^{m} = x^{m+n}. Let us remark that symbols did not appear in Arabic mathematics until much later. Ibn  and  used symbols in the 15th century and, although we do not know exactly when their use began, we know that symbols were used at least a century before this.

 (born 953) is seen by many as the first person to completely free algebra from geometrical operations and to replace them with the arithmetical type of operations which are at the core of algebra today. He was first to define the monomials x, x^{2}, x^{3}, ... and 1/x, 1/x^{2}, 1/x^{3}, ... and to give rules for products of any two of these. He started a school of algebra which flourished for several hundreds of years. , nearly 200 years later, was an important member of 's school.  (born 1130) was the first to give the new topic of algebra a precise description when he wrote that it was concerned:-
... with operating on unknowns using all the arithmetical tools, in the same way as the arithmetician operates on the known.
 (born 1048) gave a complete classification of cubic equations with geometric solutions found by means of intersecting conic sections.  also wrote that he hoped to give a full description of the algebraic solution of cubic equations in a later work []:-
If the opportunity arises and I can succeed, I shall give all these fourteen forms with all their branches and cases, and how to distinguish whatever is possible or impossible so that a paper, containing elements which are greatly useful in this art will be prepared.
 (born 1135), although almost exactly the same age as , does not follow the general development that came through 's school of algebra but rather follows 's application of algebra to geometry. He wrote a treatise on cubic equations, which []:-
... represents an essential contribution to another algebra which aimed to study curves by means of equations, thus inaugurating the beginning of algebraic geometry.
Let us give other examples of the development of Arabic mathematics. Returning to the House of Wisdom in Baghdad in the 9th century, one mathematician who was educated there by the  was  (born 836). He made many contributions to mathematics, but let us consider for the moment consider his contributions to number theory. He discovered a beautiful theorem which allowed pairs of amicable numbers to be found, that is two numbers such that each is the sum of the proper divisors of the other.  (born 980) looked at a slight variant of 's theorem, while  (born 965) seems to have been the first to attempt to classify all even perfect numbers (numbers equal to the sum of their proper divisors) as those of the form 2^{k-1}(2^{k} - 1) where 2^{k} - 1 is prime.

, is also the first person that we know to state Wilson's theorem, namely that if p is prime then 1+(p-1)! is divisible by p. It is unclear whether he knew how to prove this result. It is called Wilson's theorem because of a comment made by  in 1770 that  had noticed the result. There is no evidence that  knew how to prove it and most certainly  did not.  gave the first proof in 1771 and it should be noticed that it is more than 750 years after  before number theory surpasses this achievement of Arabic mathematics.

Continuing the story of amicable numbers, from which we have taken a diversion, it is worth noting that they play a large role in Arabic mathematics.  (born 1260) gave a new proof of 's theorem, introducing important new ideas concerning factorisation and combinatorial methods. He also gave the pair of amicable numbers 1729618416 which have been attributed to , but we know that these were known earlier than , perhaps even by  himself. Although outside our time range for Arabic mathematics in this article, it is worth noting that in the 17th century the Arabic mathematician Mohammed Baqir Yazdi gave the pair of amicable number 9,363,584 and 9,437,056 still many years before 's contribution.

Let us turn to the different systems of counting which were in use around the 10th century in Arabic countries. There were three different types of arithmetic used around this period and, by the end of the 10th century, authors such as  were writing texts comparing the three systems.

1. Finger-reckoning arithmetic.
This system derived from counting on the fingers with the numerals written entirely in words; this finger-reckoning arithmetic was the system used by the business community. Mathematicians such as  (born 940) wrote several treatises using this system.  himself was an expert in the use of Indian numerals but these:-
... did not find application in business circles and among the population of the Eastern Caliphate for a long time.
Hence he wrote his text using finger-reckoning arithmetic since this was the system used by the business community.

2. Sexagesimal system.
The second of the three systems was the sexagesimal system, with numerals denoted by letters of the Arabic alphabet. It came originally from the Babylonians and was most frequently used by the Arabic mathematicians in astronomical work.

3. Indian numeral system.
The third system was the arithmetic of the Indian numerals and fractions with the decimal place-value system. The numerals used were taken over from India, but there was not a standard set of symbols. Different parts of the Arabic world used slightly different forms of the numerals. At first the Indian methods were used by the Arabs with a dust board. A dust board was needed because the methods required the moving of numbers around in the calculation and rubbing some out as the calculation proceeded. The dust board allowed this to be done in the same sort of way that one can use a blackboard, chalk and a blackboard eraser. However,  (born 920) showed how to modify the methods for pen and paper use.  also contributed to improvements in the decimal system.

It was this third system of calculating which allowed most of the advances in numerical methods by the Arabs. It allowed the extraction of roots by mathematicians such as  and  (born 1048). The discovery of the binomial theorem for integer exponents by  (born 953) was a major factor in the development of numerical analysis based on the decimal system.  (born 1380) contributed to the development of decimal fractions not only for approximating algebraic numbers, but also for real numbers such as π. His contribution to decimal fractions is so major that for many years he was considered as their inventor. Although not the first to do so,  gave an algorithm for calculating nth roots which is a special case of the methods given many centuries later by  and .

Although the Arabic mathematicians are most famed for their work on algebra, number theory and number systems, they also made considerable contributions to geometry, trigonometry and mathematical astronomy.  (born 908), who introduced a method of integration more general than that of , and  (born 940) were leading figures in a revival and continuation of Greek higher geometry in the Islamic world. These mathematicians, and in particular , studied optics and investigated the optical properties of mirrors made from conic sections.  combined the use of trigonometry and approximation theory to provide methods of solving algebraic equations by geometrical means.

Astronomy, time-keeping and geography provided other motivations for geometrical and trigonometrical research. For example  and his grandfather  both studied curves required in the construction of sundials.  and  both applied spherical geometry to astronomy and also used formulas involving sin and tan.  (born 973) used the sin formula in both astronomy and in the calculation of longitudes and latitudes of many cities. Again both astronomy and geography motivated 's extensive studies of projecting a hemisphere onto the plane.

 undertook both theoretical and observational work in astronomy.  (born 850) made accurate observations which allowed him to improve on 's data for the sun and the moon.  (born 1201), like many other Arabic mathematicians, based his theoretical astronomy on 's work but  made the most significant development of 's model of the planetary system up to the development of the heliocentric model in the time of .

Many of the Arabic mathematicians produced tables of trigonometric functions as part of their studies of astronomy. These include  (born 1393) and . The construction of astronomical instruments such as the astrolabe was also a speciality of the Arabs.  used an astrolabe while  (born 835), al-Khazin (born 900) (born 965), and others, all wrote important treatises on the astrolabe.  (born 1201) invented the linear astrolabe. The importance of the Arabic mathematicians in the development of the astrolabe is described in []:-
The astrolabe, whose mathematical theory is based on the stereographic projection of the sphere, was invented in late antiquity, but its extensive development in Islam made it the pocket watch of the medievals. In its original form, it required a different plate of horizon coordinates for each latitude, but in the 11th century the Spanish Muslim astronomer az-Zarqallu invented a single plate that worked for all latitudes. Slightly earlier, astronomers in the East had experimented with plane projections of the sphere, and  invented such a projection that could be used to produce a map of a hemisphere. The culminating masterpiece was the astrolabe of the Syrian Ibn ash-Shatir (1305-75), a mathematical tool that could be used to solve all the standard problems of spherical astronomy in five different ways.

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Written by J J O'Connor and E F Robertson
Last Update November 1999


Meidas Touch Campaign Ad: "They Lie You Die"

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 Alan: To understand the last video clip in "They Live You Die" it is important to know that White House Press Secretary, Kayleigh McEnany, "promoted birther conspiracy theories about President Barack Obama in 2012At the start of the 2016 presidential election, she was critical of then-candidate Trump, calling his remarks about Mexican immigrants 'racist' and suggesting it was 'inauthentic' to call him a Republican."

Lest We Forget Kellyanne Conway's View Of Trump Before He Bought Her Off 




Court-Appointed Counsel Finds That Gen. Michael Flynn's Guilty Plea Should Not Be Dismissed

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Pax on both houses: What Flynn's Guilty Plea Could Mean For ...

Roger Stone: Members Of Trump's Inner Circle Are Unusually Likely To Be Convicted Felons

Flynn committed perjury and his guilty plea of lying to FBI should not be dismissed, as Justice asks, court-appointed counsel finds
Former New York federal judge John Gleeson was asked to argue against the Justice Department’s request to dismiss the prosecution of President Trump’s former national security adviser.
Michael Flynn was the highest-ranking official convicted in special counsel Robert S. Mueller III’s investigation of Russian interference in the 2016 U.S. election. In an extraordinary reversal, the Justice Department sought to undo its conviction after Flynn withdrew his guilty plea of lying to the FBI about his Russian contacts.
Read more »

Pax on both houses: Sentencing Judge Tells Michael Flynn "You May ...


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