Monday, April 24, 2017

Math Revisited: Looking At Linear Algebra

In earlier posts we looked at examples of linear algebra in terms of the behavior of lines and planes, e.g.

http://brane-space.blogspot.com/2010/05/analyzing-lines-planes.html


Now, we examine this fascinating branch of advanced math at deeper levels. Some aspects will resonate from when we were looked linear solutions of certain differential equations, i.e. http://brane-space.blogspot.com/2011/01/homogeneous-linear-de-systems-breaking.html

In this linear algebra context, let a 3 x 3 matrix A =

(a 1.....0.......0)
(0.......a 2.....0)
(0.......0.......a n)


We're first  interested in obtaining its characteristic polynomial from:

P_A(t) =

(t- a 1.....0.......0)
(0.......t – a 2.....0)
(0.......0....... t - a n)


Or:

P_A(t) = (t – a1)(t – a2) (t – a n)

The eigenvalues can be obtained via solving for a1, a 2, a n, in the equation:

(t – a1)(t – a2) (t – an) = 0

Example:

Given the matrix:

A =

(1.. ..i)
(i.......-2.)

Find the characteristic polynomial as well as the eigenvalues.

We have:

P_A(t) =

(t - 1…… i)
( i....... t + 2)

Whence: P_A(t) = (t – 1)(t + 2) – (i)2  


P_A(t) = t 2 –t + 2t -2 - (i) 2 = t 2 +t -2 + 1= t2 + t – 1

Since this is a quadratic equation, so we can find the eigenvalues (E1,2) using the quadratic formula:

E1,2 = Ö{- b +  [b 2 – 4 ac]} / 2a

Where  a, b, c denote the coefficients for the quadratic, with a the numerical coefficient for the exponent 2 term (t2), b for the exponent 1 term(t) and c the exponent 0 term. Thus: a = 1, b = 1, c = -1


Then:  E1,2 = Ö{- 1 +/- [12 – 4 (-1)]} / 2(1)


E1,2= Ö{-1 +/- [5] } / 2

So that:

E1 = Ö(-1 + [5] ) / 2 = 0.618

E2=Ö (-1 - [5] ) / 2 = -1.618


Practice Problems:

Find the characteristic polynomials and eigenvalues for each of the following matrices:

 X =

(1.. …. .2)
(2.......-2)


 Y =

(3.. ……2)
(-2...... 3)

Trump's Praise of Neo-Nazi Le Pen Doesn''t Work

Never let a good foreign crisis go to waste without some kind of an authoritarian tweet! That's the motto of  Donald Trump, who has yearned for his little Neo-Nazi Marine LePen to also get into power in France. Of course, with that "Frexit"  added to the Brexit, it would make the collapse of the EU almost a certainty.   Fortunately, that didn't materialize as Centrist Independent Emmanuel Macron just topped Le Pen yesterday by two percentage points. ('France Chooses Hope Over Fear mongering', The Financial Times, today). This marks the 3rd time right wing nationalists have been beaten back, following elections in Austria and the Netherlands. But....Macron still has to put Le Pen away on May 7th in the runoff.

In the lead up to the French elections yesterday Trump- as is his wont- was quite active. For example, on Friday morning Trump tweeted about the possible impact of the Paris shooting the previous day resulting in one police officer dead and 2 wounded.  Trump wrote:

"Another terrorist attack in Paris. The people in France will not take much more of this. Will have a big effect on presidential election!"


No surprise Trump - the Hitler wannabe - would tweet this offal, attempting to interfere in the French election like he enlisted the help of the Russkies to do so in ours.  After all, recall another incident in Paris - the November 2015 mass shooting at the Bataclan theater -  helped solidify his lead in the polls going into the GOP primaries. But this is how authoritarians work: they prey on each and every act of terror to ramp up fear to support their shticks.  At that time Trump tweeted:

"Everyone is now saying how right I was with illegal immigration and the wall. After Paris, they're all on the bandwagon."

Of course, as the results from yesterday revealed,  this is ineffable codswallop. First, not "everyone" was saying any such thing.   At least half the French electorate Is not on his "bandwagon" just as ours wasn't when he invoked each and every terror and quasi-terror incident (like the mass shooting in Orlando) to try to ramp up fear and consternation.  Second there is NO evidence "illegal immigration",  as per the Dept. of Homeland Security's own stats, shows any link to an uptick in terrorism.   The DHA report showed no terror attacks transpired from any of the six nations Trump put on his de facto Muslim ban.

 Third, the "wall" will not do anything to halt terror even if some element could use illegal (Mexican) immigration as a vehicle. What the wall will do is cost American taxpayers upward of $40 b if ever passed into law, and also - because of its putative design along river borders (like the Rio Grande) leave hundreds of Americans on the Mexican side.   (Look for Trump's wall funding to trigger a shutdown later this week)

Again, this is what authoritarian narcissists do to  consolidate power, as Hitler did after the Reichstag fire. (In that case, turning the power of the authoritative Nazi state against the Jews.)

In the case of the recent Paris attack, recall Trump labeled it such in advance of what French authorities acknowledged. During a joint press conference with Italian Prime Minster Paolo Gentiloni,  Trump quickly called it a "terrorist attack" before French authorities had done so. Such premature negative framing is common to most authoritarians who need a general terror meme to support their campaigns or future plans.   Trump went on to blab:

"It's a very very terrible thing that is going on in the world today. And what can you say? It just never ends. We have to be strong and vigilant and I've been saying that for a long time."

Once more, look at the buzzwords here: "strong and vigilant" - same words Hitler used after the Reichstag fire.  Also  Trump's words "it just never ends", expressing more the fondest hope of any proper  strong man because if it ever did "end" there'd be no use for his authoritarian prescriptions.

And more to the point, because authoritarians know sane people are skeptical of their governance or what passes for such, they seek to gather other confirmed authoritarians into their fold. Hence, Trump praising the Turkish strongman Recep Tayyip Erdogan as he's now egging on Le Pen.  He'd like nothing better than to be sitting in the middle of such a triumvirate by the end of the summer. And yes, I call a spade a spade, so Marine is a neo-Nazi, given the apple never falls far from the tree, and her notorious dad (Jean-Marie) once said the holocaust was just a "detail of history". (It is true that he was expelled from the National Front party by his daughter, but this wasn't done out of some noble motive or respect for the Jews. She did it to pave the way for a credible campaign run using the PR that she'd 'disavowed' Poppy's hate". Don't buy it for a second!)

That Le Pen is as shamelessly exploitative of attacks as Trump, to firm up her authoritarian bona fides, was evident in the wake of the Paris shootings. That is, referencing "incredible lapses in the justice system" such that the current French government and its predecessor "had done everything to make France lose the war on terrorism".  Immediately following her angst-provoking blurtations, Prime Minister Bernard Cazeneuve blasted her for exploiting the attack.

Although Trump has never formally met Le Pen, a little known but sordid fact is that she is close to some of the same advisors who helped craft Trump's pseudo-populist message during the U.S. campaign.  (And recall Le Pen was spotted in Trump Tower during the transition in January. The skinny is that they discussed mutual authoritarian governance in a post Brexit, post-Obama world)

Obviously, for Trump and Le Pen, the "populist" blather ....errr...message, is just that, all hollow bloviation with no substance. They tossed out words to console the feelings and infirmities of the poor, native working class blokes but don't really give two craps about them. If Trump really did, why would he have supported a health plan that tossed 24 million off their health care? 

Interviewed in a NY Times piece last week, many pro=Trump voters asserted ongoing commitment even if Trump fulfills none of his campaign promises. Why is this? Because he was the "first" to speak to their cultural "persecution" and being "left at the back of the bus for societal priorities".   Really, you can't make this shit up. So even after their health care is gone, and their homes foreclosed because the jobs promised never materialize, they will stick with their hero looneytune.

The French just have to ensure that in the runoff election THEY don't get stuck with Trump's psychotic female counterpart!


Friday, April 21, 2017

"Red Team" Exercise For Earth Day - But NOT Steve Koonin's Way!


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Image showing rift in Pine Island Glacier Ice Shelf in West Antarctica, the second to form in past three years. A sound "red team" exercise would seek to account for such changes on the basis of I) anthropogenic warming, or ii) "natural cycles"

With Earth Day now upon us, it has been suggested  by theoretical physicist Steve Koonin (WSJ today, 'A Red Team Exercise Would Strengthen Climate Science') that  we conduct a "red team" exercise to finally banish most of the doubts concerning anthropogenic climate change.  As he puts it:

"Summaries of scientific assessments meant to inform decision makers - such as the United Nations Summary for Policy Makers - largely fail to capture the vibrant and developing science. Consensus statements necessarily conceal judgment calls and debates, so feed the 'settled', 'hoax' and 'don't know' memes that plague the political dialogue around climate change. We scientists must better portray not only our certainties but our uncertainties and even things we may never know."

He then goes on to describe the template for his version of the red team exercise:

"The focus would be a published scientific report meant to inform policy such as the UN's summary, or the U.S. Government's National Climate Assessment. A Red Team of scientists would write a critique of that document and a Blue Team would rebut that critique. Further exchanges of documents would ensure to the point of diminishing returns."

While this sounds like a rational and scientific approach, the problem is all such reports have been -pre-massaged to a) make them more understandable to policy makers, and b) often leave out the most direct evidence.  (Such as the increasing second rift forming now on the Pine Island Glacier Ice Shelf in West Antarctica.)

First, let's reference that Koonin himself is not an honest broker for the "true representation" of climate science. As per a Wikipedia entry on him we read:

"In Climate Science Is Not Settled a 2014 essay published in the Wall Street Journal, Koonin wrote that "We are very far from the knowledge needed to make good climate policy," and that "The impact today of human activity [on climate] appears to be comparable to the intrinsic, natural variability of the climate system itself." Koonin criticized the use of results from climate modelling to support the "scientific consensus" (quotes in original) about climate change, noting that, among other problems, "The models differ in their descriptions of the past century's global average surface temperature by more than three times the entire warming recorded during that time." Regarding climate sensitivity, Koonin wrote that "Today's best estimate of the sensitivity (between 2.7 degrees Fahrenheit and 8.1 degrees Fahrenheit) is no different, and no more certain, than it was 30 years ago. And this is despite an heroic research effort costing billions of dollars."

Ten days after Koonin wrote this, Jeffrey Kluger in Time called Koonin's piece disingenuous if not dishonest. Koonin simply used the old debating trick of setting up a strawman to knock down by misconstruing what climate scientists mean when they say the climate debate is "settled." "...they mean that the fake debate over whether climate change is a vast hoax is finished," writes Kluger. He goes on to state that every point Koonin made is and has for years been widely acknowledged by climate scientists, very few of whom utilize the kind of overzealous language their critics commonly use."

IN other words, Koonin's "red team" proposal as given is merely another strawman tactic.  I propose instead a red team exercise that puts the skeptics on the defensive. Let them defend  THEIR models and "theories". For example, we demand from the skeptic side an alternative model or full explanation for each of the following:

i)                    The correlation of higher CO2 concentrations in ice cores with warmer temperatures through geological time. (Hint: Volcanoes do not explain it given the ACM or anthropogenic carbon multiplier shows human CO2 concentrations are much more significant)

 ii)The increasing C14: C12 ratio from the time of the Industrial Revolution as indicated in the diagram below:




















According to solar physicist John Eddy (‘The New Solar Physics’, p. 17):


“The sharp upward spike at the modern end of the curve, representing a marked drop in relative radiocarbon, is generally attributed to anthropogenic causes—the mark of increased population and the Industrial Age”


iii)                    The increasing acidity (lower pH)  of the oceans, as a result of CO2 absorbed and then the formation of carbonic acid, e.g.  H2O + CO2 ->  H2 CO3

vi)                   The presence of  jokulhlaups in Greenland’s ice sheet. The paper Jokulhlaup Observed in Greenland ice sheet’, appearing in Eos: Transactions of the American Geophysical Union (Vol. 89, No. 35, 26 Aug. 2008, p. 221). specifically noted an increased frequency in occurrence of “jokulhlaups”or sudden glacial bursts of melting runoff from glaciers. It is this phenomena that has also played a role in the “unusual cracks" that set off the separation of a “chunk of ice the size of Manhattan” (19 sq. miles)from Ellesmere Island in Canada’s northern Arctic.

v) An altenrative explanation for the rifts forming on the Pine Island Glacier Ice Shelf in West Antarctica.
vi) An alternative explanation or model for the increasing release of methane from melting permafrost - plus an explanation for the more rapid melting of the permafrost.

Let's have a red team exercise all right, but one based on examining the actual direct
evidence as it manifests on our planet - as opposed to some bland, second or third hand policy report - which can be manipulated via subjectivity.

Lastly, the serious science oriented person must admit that the best red team exercise in the world will not convince true believers in "natural cycles" or other balderdash to come around to accept anthropogenic warming science.


Space Probe Reveals Novel Geology on Mercury With Abundant "Hollows"

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Mercury impact crater "de Graft"  showing numerous 'hollows'  -  shallow depressions that form via a process of volatile loss.

Relatively unknown to most planetary aficionados (but not planetary astronomers) are recent results of the MESSENGER ('Mercury Surface Space Environment, Geochemistry and Ranging') mission.  Among the new results has been the discovery of thousands of 'shallows': shallow, fresh -looking depressions up to a few kilometers wide- scattered over the planet's surface.

Having said that, the nature of these depressions remains a mystery and only one model has evidently come close to explaining their origin. Thus, while several lines of evidence indicate formation as a result of the loss of volatile materials (easily dissipated) in surface rocks, the specific process for this remains unknown.

A breakthrough has arrived via unprecedented, high resolution MESSNGER craft imagery.  From these, Blewett et al have proposed a new model for the growth and formation of the hollows. See e.g.

https://doi.org/10.1002/2016JE005070


Blewett's team used measurements of shadow lengths to calculate the depths of more than 2,500 hollows and found that the depressions' average depth was only 24 m. This is substantially less than the typical thickness of the layer of dark, volatile-rich material in which the features are most frequently found. This mismatch suggests an alternative process at work.  This alternate process had to account for the depressions not attaining the depth of the surrounding volatile materials. 

The key material to fill the role is known as low reflectance material or LRM. Generally, this is kilometers thick or much greater than the computed depths of the hollows.  The Blewett team interpreted this to mean the shapes of the shallow depressions aren't controlled by the thickness of the host LRM.  Hence, the depressions are halted before they reach the bottom of the LRM layer.

The Blewett team has argued that a volatile-depleted "lag" material protects the underlying (LRM) material once it becomes sufficiently thick. A fair indication the hypothesis is accurate is the observation that hollows often occur on the walls and central peaks of impact craters. These are formations too steep for lag to develop so consistent with the proposed model.

From this the team concludes the hollows' formation and growth can be traced to the volatilization of carbon. (Evidence suggests that carbon is an important constituent of Mercury's crust). Again, bear in mind that "volatilization" is an analogous process to vaporization. Thus, a substance can often be separated from another by volatilization and then be recovered by condensation of the vapor.  One of the mechanisms proposed for carbon volatilization is the conversion of graphite to methane (CH4) via proton bombardment,

E.g. because graphite is an allotrope of carbon, we write in succinct form:

graphite  +  H1 + H1 + H1 + H1   ->   CH4

It is also noteworthy that the Blewett et all team was able to estimate the lower limit for the rate of hollow horizontal growth, on account of the presence of hollows within several impact craters with ray systems. See e.g. the image of the impact crater de Graft. Therein, the dark blue central peak complex is presumed composed of LRM which may include graphite bearing crust material. 

The pace of horizontal growth is likely via the retreat of scarps that form the hollows' walls.  The authors estimate the rate of retreat at 1 centimeter per 10,000 years - not exactly blinding speed.  Of course, this rate itself places further constraints on the formation and history of Mercury's land forms. That is, we cannot expect the rate of  formation of Mercury's other land forms  to significantly outpace the hollows' horizontal growth rate.




Thursday, April 20, 2017

Math Revisited: Extending Permutation Groups to Transpositions

It's also interesting to explore a permutation "offshoot" known as a transposition. A transposition is a permutation which interchanges two numbers and leaves the others fixed. The inverse of a transposition T is equal to the transposition T itself, so that:


T2 = I (identity permutation, e.g the permutation such that I(i) = i for all i = 1,...n)

A permutation p of the integers {1, . . . n} is denoted by

[1 .. . .. n]

[p(1).. p(n)]


So that, for example:

[1 2 3]
[2 1 3]

denotes the permutation p such that p(1) = 2, p(2) = 1, and p(3) = 3.

Now, let's look at EVEN and ODD permutations:

Let  P  n  denote the polynomial of n variables x 1,  x 2 ……x n which is the product of all the factors  x i .. x j  with i < j. That is:

n ( x 1,  x 2 ……x n) = P(x i .. x j)

The symmetric group S(n) acts on the polynomial  P  n by permuting the variables. For p Î  S(n) we have:

n ( x_p(1), x_p(2). . .x_p(n)) = (sgn p)  P  n ( x 1,  x 2 ……x n)

where sgn p = + 1. If the sign is positive then p is called an even permutation, if the sign is negative then p is called an odd permutation. Thus: the product of two even or two odd permutations is even. The product of an even and an odd permutation is odd.

Back to transpositions! We just saw:

[1 2 3]
[2 1 3]


The above permutation is actually a transposition 2 <-> 1 (leaving 3 fixed). Now, let p' be the permutation:

[1 2 3]
[3 1 2]

Then pp' is the permutation such that:

pp'(1) = p(p'(1)) = p(3) = 3

pp'(2) = p(p'(2)) = p(1) = 2

pp'(3) = p(p'(3)) = p(2) = 1


It isn’t difficult to ascertain that: sgn (ps) = (sgn p) (sgn s) so that we may write:
pp' =

[1 2 3]

[3 2 1]

Now, find the inverse p^-1 of the above. (Note: the inverse permutation, denoted by p - 1  is defined as the map: p - 1  : Zn -> Zn),  Since p'(1) = 3, then  p - 1 (3) = 1


Since p'(2) = 1 then p - 1 (1) = 2

Since p'(3) = 2 then  p - 1 (2) = 3


Therefore:  p - 1   =

[1 2 3]
[ 2 3 1]


Problem: Express  p =

[1 2 3 4]
[2 3 1 4]


as the product of transpositions, and determine the sign (+1 or -1) of the resulting end permutation.

Let T1 be the transposition 2 <-> 1 leaving 3, 4 fixed, so:

T1 p =

[1 2 3 4]
[1 3 2 4]


Let T2 be the transposition 2 <-> 3 leaving 1, 4 fixed, so:

T2 T1 p =

[1 2 3 4]
[1 2 3 4]

Then:

T2 T1 p = I (identity)

TWO transpositions (T1, T2) operated on p, so that the sign of the resulting permutation (to reach identity) is +1.  The permutation is therefore even.

A Note on Disjoint Permutations:

Expressing a permutation as a product of disjoint cyclic permutations is not hard at all, once one gets the hang of it. The key is to “cycle through” the mapping in the original to yield the different disjoint cycles, taking care to stop when the end element leads to a number (on the top of the original) that repeats. For example:

Express as disjoint permutations:

[1 2 3 4  5  6   7]

[4 5 6 7  3  1  2]

Solution: 1 goes into 4, 4 goes into 7, 7 goes into 2 – STOP! (Since 2 commences new cycle in next top position). So first disjoint cycle is: (1, 4, 7, 2).

Now, 2 goes into 5, 5 goes into 3, STOP! (3 repeats) So cycle is: (2, 5, 3). Then 3 goes into 6, and 6 into 1. Stop.

Answer: (1, 4, 7, 2)(2, 5, 3)(6).

German Telecommunications Authority To Parents: "Destroy That Doll!"

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The WSJ article 'German Officials Order Parents To Execute A Spy - Cayla The Doll' (April, 12, p. A1) wasn't making sport.   In the eyes of German authorities - who take seriously the protection of citizen privacy unlike the U.S., the doll "Cayla" was an unwanted intruder into the German landscape. And that meant it had to be destroyed.

As the article notes, on Feb. 17th, after a lengthy investigation, Germany's top telecommunications watchdog: the Federal Network Agency (Bundesnetzagentur) , issued a binding order to parents to find this plastic entity and destroy it. Parents who ignored the order faced a fine of up to 25,000 euros (about $26,500) an also faced up to two years in prison under paragraph 90 of Germany's telecommunications law.  And no, the word of parents was insufficient to get a pass.

The agency, on its website, posted a template for a destruction certificate that had to be faithfully completed - no bull. It then had to be signed by personnel at a waste management company as proof of destruction.  

The Bundesnetzagentur investigation found that while the spy doll can't connect directly to the internet it can be accessed via Bluetooth using any mobile device loaded with the 'My Friend Cayla' app.  Such access then is not protected so that any conversation a child might have, say with the doll or her parents, could be intercepted and eavesdropped on by a malicious outsider, or even neighbor, so the Germans weren't taking chances.

Nor is this doll the first spy toy to meet such a fate. As the WSJ article notes, "a toy robot was sent to the scrap yard because its head was embedded with an internet-enabled camera concealed behind a black visor." The agency also exposed a panda bear last year "with a camera hidden in its nose that operated as a nanny cam and could connect to a mobile phone" to enable outsider access.

So we see the Germans are not simply being paranoid and over reacting. According to one law student (Stefan Hessel) - who penned the legal opinion used by the agency:

"It's pretty bad bringing a doll on the market that anybody within a 30 foot radius can connect to. A regular Bluetooth loudspeaker is better protected."

Of course, the doll's distributor - Vivid Germany GmbH - insists it didn't "break the law" - but that's not the point. The point isn't that the doll "broke the law" any more than a legal gun lying on a desk has broken the law. But when the doll is accessed via Bluetooth and the connecting app, it can certainly be used for nefarious reasons - just like that gun when picked up and fired at someone's head.

Hyperbole - by comparing an activated spying doll to a fired gun?  Not to the Germans who've imposed prison sentences for failure to comply with 'Cayla's destruction. As I noted, the Germans take their citizens' privacy seriously - unlike the U.S. - where citizens' data, including medical - can be sold to the highest bidder.

See also:

http://brane-space.blogspot.com/2017/04/gop-congress-now-has-your-privacy-for.html

Good Riddance To Billo And His "Spin Zone"

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The news yesterday that FOX finally got rid of the obnoxious, fulsome, condescending Bill O'Reilly and his "No Spin Zone" ('The O'Reilly Factor'")  was music to the ears and brains of all sentient beings. This noisome, pretentious bloviator clogged cable airways for nearly 20 years with distorted takes on any subject you can imagine while stoking the meme of white identity.  On the side, it appears he  sought to parlay his FOX profile "fame" into a sexual harassment shtick,  as news reports have established such as this one from 'The Hill':

http://thehill.com/blogs/blog-briefing-room/news/329567-oreilly-accusers-lawyer-fox-news-host-fired-because-we

The upshot being that advertisers - perceiving a latent toxic mix - bailed in droves from the one time big mouthed big shot, leaving him with barely 4 minutes of adverts before he left on a trip to Italy April 11th.

O'Reilly's early career included teaching at my high school, Mgsr. Edward Pace, as per a Wikipedia reference 'Early life':

"O'Reilly moved to Miami, where he taught English and history at Monsignor Pace High School from 1970 to 1972."

When I attended a Pace High Class Reunion (class of '64) in December, 1971, all the buzz from the fellow Spartans focused on this "history teacher" who was making a name for himself trying to insert his ideology into class content.  Evidently, the skinny was he had some way out notions on a number of historical events including the JFK assassination. It seems he also used some of the class periods to hone his white identity shtick that figured so prominently on 'The Factor'.  One guy who had a sister in O'Reilly's English class asserted(according to his sis)  the approach and teaching style was mostly irritating - often barking incoherent questions at random. Half the time he didn't even know the students' names.

All of this preceded his mostly annoying jabber once he arrived at FOX. It seems - as one commentator observed last night on MSNBC,  O'Reilly "pitched his 'Factor' to an imaginary 70 year old white male who felt  besieged on all sides by cultural enemies".   Oh, and black and brown races! 

Some may disagree but I think O'Reilly using his prominent FOX  'Factor' profile to peddle his absurd history books was an even more outrageous insult. Indeed, I skewered his farcical book, 'Killing Kennedy' . Perhaps the biggest and most easily disproven lie of O'Reilly's  was his claim of tracking George de Mohrenschildt (Oswald's Dallas  handler for the CIA), to his Florida home then being there to hear the gunshot that killed him.

To paraphrase investigator Jefferson Morley: "No way could O'Reilly have heard a gunshot from 1200 miles away." 

As I  observed, if O'Reilly would lie about this event what would stop him from lying about any aspect of the JFK assassination?

There were also these additional distortions and misrepresentations:

 -  O'Reilly's claim that the death of de Mohrenschildt was a "suicide" when it was a hit, to keep him quiet so he couldn't testify before the HSCA about his mentoring of Oswald for the CIA;

- Describing an argument between Oswald and Cuban consulate officer Eusebio Azcue. (p. 219). Omitted is that Azcue went to the movies two weeks after the assassination and saw a newsreel of Oswald being shot by Jack Ruby. Azcue was stunned because the man he saw being shot in the newsreel was not the man he argued with in Mexico City.

- Totally leaving out any mention at all of the Zapruder film which, despite some nominal defects, IS the real time recording of the assassination.  It can be argued that ANY author that omits this film - often called the "Rosette stone" of the assassination - can't be considered a serious contributor to body of knowledge about the Kennedy assassination.

- Unable to come to grips with the fact Oswald was a lousy shot (called "Maggie's drawers" by Cpl. Nelson Delgado- most familiar with his ability) O'Reilly and co-author Dugard simply changed the facts and wrote that “Oswald was a crack shot in the military.” (p. 15)  Total absolute nonsense. See, for example:

http://brane-space.blogspot.com/2013/11/frequently-asked-questions-on-fhe-jfk.html

As author Jim DiEugenio notes: "The authors source this to the Warren Report. However, upon finding the relevant section — pages 681-82 — the reader will see that nothing even approaching this kind of description appears on those pages."

To be blunt, O'Reilly and his writing assistant Dugard were making it all up.

O'Reilly fared no better in his later book 'Killing Reagan' in which even the title betrays a wrong-headed take since Reagan didn't die from the assassination attempt on him! But O'Reilly used the same lies and sloppy scholarship to translate wounds into a "death" - meaning he construed the wounds to Reagan were so traumatic they converted Reagan into a member of the walking dead for the next 23 years.

 George Will, in his article 'Bill O'Reilly Slanders Ronald Reagan.', delivered an initial takedown of this piece of trash in his WaPo piece. He wrote::

"The book’s pretense of scholarship involves 151 footnotes, only one of which is even remotely pertinent to the book’s lurid assertions. Almost all contain irrelevant tidbits (“Reagan’s hair was actually brown”). At the Reagan Library, where researchers must register, records show that neither O’Reilly nor Dugard, who churn out a book a year, used its resources. The book’s two and a half pages of “sources” unspecifically and implausibly refer to “FBI and CIA files,” “presidential libraries” and travel “around the world.” They also cite Kitty Kelley’s scabrous 1991 Nancy Reagan “biography,” a sewer of rumors and innuendos that probably is the source of the sexual factoids O’Reilly and Dugard recycle."

All this alone would put the book on the same level of faux history as the earlier Kennedy book. But what would you expect from a clown that had been the star at  FAUX News?

All one can say is 'good riddance' especially as Billo will no longer be able to annoy and sexually harass female co-workers or use his privileged perch at FOX to hawk  his faux history crap.