Wednesday, November 30, 2022

How Math Drives Our Understanding Of The Universe

The ASTRONOMY magazine article entitled 'Speaking the Language of the Universe' (December, p. 24) is one every math phobe needs to read- especially people who also appreciate the wonders of the night sky.

But sadly, as the piece by Bob Berman observes, while "professional astronomers use math all the time" - see e.g. some of the (free)  journal articles here:

Hobby astronomers generally "don't have math in their bones".  As Berman adds:

"They hate the subject. Perhaps it reminds them of school. Square roots and standard deviations bog down articles for them, and science writers oblige by leaving out equations altogether."

Which is sad beyond measure, because indeed, as Berman goes on to show, math is the language of the universe. Sure it's easy to simply stand beneath the stars and simply gaze at galaxies, planets and the Moon through a telescope - Oooh-ing and ahh-ing all the time. But while wonder and awe can be the keynote at that level, it can't lead to any deeper understanding of what those objects actually are, what they're made of, how they move or how they might affect our planet. For that,  deeper analysis is needed, i.e. into the relationships between physical parameters that define them.

Just to know how distant an object is - say a nearby star- depends on math, and it is critical given that the distance can allow other properties to be determined. Consider the famous "parallax method" to obtain the distance to nearby stars. This method  can apply to all stars within a distance of maybe 50 parsecs (1 pc = 3.26 Ly) or those for which a measurable parallax angle p exists.  The geometry shown below is useful to this end:

The angle p is obtained by taking photographs of the same star six months apart (i.e. from opposite sides of Earth's orbit) and comparing the two positions. One can thereby obtain the distance, D from:

D = r/ tan (p)

The relationship is such that for p = 1 arcsec the distance of the star would be 1 parsec (e.g. par-allax sec-ond). an angle of 1 arcsec = 1" = 1/3600 degree. So we see it is an extremely tiny angle. similarly, if the angle p = 1/10" then D = 10 parsecs, so we perceive a reciprocal relationship such that D = 1/p", though we must ensure the units are consistent.

In many applications, such as the budding undergrad student meets in 1st year Astronomy, the parallax angle p is merged with the equation for the "distance modulus" -  which makes use of the absolute magnitude M (see previous blog on this) and apparent magnitude m. In this way, estimates of the star's energy output, and brightness can be made.

Then, if D is the distance, the usual expression for distance modulus is:

(m - M) = 5 log (D/10) = 5 log D - 5 log 10 = 5 log D - 5

But: D = 1/p

(m - M) = 5 log (1/p) - 5

Or: (m - M) + 5 = 5 log p

A sample problem, such as an Astronomy 201-202 student would have to do for homework, is as follows:

Barnard's star has an absolute magnitude of +13.2 and an apparent magnitude m = +9.5. Find its distance in LIGHT YEARS.

The solution is based on using the parsec form of the distance modulus:


(m - M) = 5 log (1/p) - 5

(9.5 - 13.2) = 5 log(1/p) - 5

-3.7 = 5 log (1/p) - 5

5 log (1/p) = (5 - 3.7) = 1.3

log (1/p) = (1.3)/5 = 0.26

Taking anti-logs:

1/p = D = 1.81 pc

But 1 pc = 3.26 Ly, so D = (1.81 pc)(3.26 Ly/pc) = 5. 9 LY

Spherical Astronomy:

We are looking at how math drives our understanding of the universe from the perspective of a budding astronomy major at university. By the time the aspiring major reaches his sophomore year, he will be facing even more math in courses such as Spherical Astronomy.  The emphasis here is on astronomical time (sidereal time and position - the latter based on different coordinate systems used (equatorial, horizontal, ecliptic).  Each such coordinate system is defined by a different set of poles and equator. For example, the coordinate system depicted in the diagram below is known as the equatorial system.  

It is based on the projection of the Earth's N. and S. poles into the sky, as well as its equator. The poles then become the North and South Celestial poles, and the equator becomes the celestial equator. If these poles are defined respectively at +90 degrees (NCP) and -90 degrees (SCP) and the celestial equator at 0 degrees, then a consistent system of celestial latitude and longitude  can be defined in a consistent system, to locate any celestial object. We call the longitude coordinate (Θ) the Right Ascension (R.A.) while the celestial latitude coordinate is called declination and is measured in degrees north or south of the celestial equator. (In the diagram, the complementary angle of the declination is shown, φ, which we call the zenith distance.)

One of the first things the astronomy sophomore learns is how to find directions around the celestial sphere, including how to relate the R.A. to time and time keeping.  He must also do exercises showing he can find the hour angle - and distinguish it from the Right Ascension. This starts with identifying the R.A. of his local meridian (the imaginary celestial longitude passing through his zenith or highest point.)  The Right Ascension of the star is clearly equal to the local sidereal time (L.S.T.) plus the hour angle. Thus, we can write:  HA = RA of observer meridian - RA of object

Of course, before he gets very far, he will be adept at sketching any number of diagrams to solve time and position problems, such as the diagram below - with perspective looking down onto the North Celestial pole:

For example, in the diagram shown, if the star's R.A. is 7h 00m and the observer is at a local sidereal time of 6h 00m, then the hour angle becomes: HA = 6h - 7h = -1h or -15 degrees. (Since every hour of longitude corresponds to 15 degrees angle, i.e. Earth turns through 15 degrees every hour, 360 degrees in 24 hours.)

The budding astronomy student will also have to know how to sketch a three dimensional diagram to enable conversion between coordinates, say from the horizontal (observer -based) to the celestial sphere. This will always include what is called the fundamental "astronomical triangle" (shaded region of Fig. 3 below):

 from which spherical trig relationships can be obtained and conversions can be made to different coordinate systems.  Using spherical trig, the student can write the law of sines and law of cosines for spherical triangles (such as shown in Fig. 3)which are analogs of the law of sines and cosines for triangles in plane trig.

We have for the law of sines:

Sin A/ sin a = sin B/ sin b = sin C/ sin c

where A, B, C denote ANGLES and a,b,c denote measured arcs. (Note: we could also have written these by flipping the numerators and denominators).

We have for the law of cosines:

cos a = cos b cos c + sin b sin c cos A

Where a, b, c have the same meanings, and of course, we could write the same relationship out for any included angle.

Now, we use Fig. 3, for a celestial sphere application, in which we use the spherical trig relations to obtain an astronomical measurement.

Using the angles shown in Fig. 3 each of the angles for the law of cosines (given above) can be found. They are as follows:

cos a = cos (90 deg - decl.)

where decl. = declination

cos b = cos (90 deg - Lat)

where 'Lat' denotes the latitude. (Recall from Fig. 1 if φ is polar distance (which can also be zenith distance) then φ = (90 - Lat))

cos c = cos z

where z here is the zenith distance.

sin b = sin (90 deg - Lat)

sin c = sin z

and finally,

cos A = cos A

where A is azimuth.

Let's say we want to find the declination of the star if the observer's latitude is 45 degrees N, and the azimuth of the star is measured to be 60 degrees, with its zenith distance z = 30 degrees. Then one would solve for cos a:

cos a = cos (90 deg - decl.)=

cos (90 deg - Lat) cos z + sin (90 deg - Lat) sin z cos (A)

cos (90 deg - decl.) =
cos (90 - 45) cos 30 + sin (90 - 45) sin 30 cos 60

cos (90 deg - decl.)= cos (45) cos 30 + sin (45) sin 30 cos 60

We know, or can use tables or calculator to find:

cos 45 =
Ö2/ 2

cos 30 =
Ö3 / 2

sin 45 =
Ö2 / 2

sin 30 = ½

cos 60 = ½

cos (90 deg - decl.) = {Ö2/ 2)(Ö3 / 2)} + {Ö2/ 2} (½) (½)

cos (90 deg - decl.)= [
Ö6/ 4 + Ö2/ 8]
= {2Ö6 + Ö2}/ 8

cos (90 deg - decl.)= 0.789

arc cos (90 deg - decl.)= 37.9 deg


decl. = 90 deg - 37.9 deg = 52.1 deg

Or,  decl. (star) = + 52.1 degrees
The student will also become familiar with matrix methods for converting between the different coordinate systems.
The basic principle involves relating the Cartesian coordinates (rectilinear) of a point on the celestial sphere (diagram) to the curvilinear coordinates measured in the primary and secondary reference planes. One has then, for example:

(z) u,v =

(cos v .....cos u)
(cos v .....sin u)
(sin v..............)

After conversion the curvilinear coordinates may be calculated according to:

u = arctan (y/x) and v = arcsin (z)

Now, consider conventional orthogonal matrices of 3 x 3 dimensions, given as functions: R1(Θ), R2(Θ) and R3(Θ), to rotate the general system by the angle Θ about axes x, y and z, respectively. Thus we obtain:

R1(Θ) =

(0.....cos(Θ)..... sin(Θ))

R2(Θ) =

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

R3(Θ) =

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

To fix ideas, say you wish to obtain the horizontal coordinates (A, a) for some object in the sky and you know its R.A. and decl. from an almanac.  Then the procedure is fairly straightforward, and entails writing:
R3(Θ) = R3(-180 deg)

R2(Θ) = R2(90 - lat.)

so that:

(z) A,a = R3(-180 deg) R2(90 - lat.) (XYZ(h, decl.))
where : (XYZ(h, decl.)) =

(z) h,decl.
Bear in mind: R3(-180 deg) =

(cos 180........-sin 180................0)
(sin 180........cos 180................0)

And:R3(Θ) =

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

Therefore: R3(-180) =


Obtaining R2(Θ) = R2(90 - lat.) is just as easy, if one recalls the basic trig identity:

cos (90 - φ) = sin (φ)
Not surprisingly, it is the sophomore year at which point most wannabe Astronomy majors change their minds and either drop out entirely or change their major - say to a less mathematically demanding subject. At the Univ. of South Florida, nearly 60% had dropped out by the end of the quarter which featured spherical astronomy.

By his junior and senior year, the Astronomy major who's survived thus far has much more math to look forward to, in courses such as: Introductory Astrophysics, Celestial Mechanics, Radio Astronomy, Stellar Constitution & Evolution, and Stellar Spectroscopy. In addition he will be expected to complete an undergrad research project, and attend Astronomy seminars in the department - in which visiting 'stars' present their latest research findings.

In Introductory Astrophysics, the primary emphasis is getting the student acquainted with the Planck function and applying it to simple, plane-parallel stellar atmospheres, such as depicted below:

The Planck function describes the distribution of radiation for a black body, and can be expressed:

B(l) = {(2 hc2)/ l5}  [1/ exp (hc/lkT) - 1)]

Of course, all stars are effectively black bodies, which are perfect radiators, or as close to that state as nature allows.  In the case of simple radiation transfer in a static model stellar atmosphere (e.g. nothing changes with time), we have the relation of specific radiation intensity I(l) to source function S(l):

dI(l)/ds = -k(l)  I(l) + k(l)  S(l)

 = k(l) [S(l) – I(l)] - 0   or I(l) = S(l)

For a black body, the student learns I(l) equals the Planck function:

B(l) :  i.e.  S(l) = I(l) = B(l)

And this is a condition which implies LOCAL THERMODYNAMIC EQUILIBRIUM or LTE   LTE does NOT mean complete thermodynamic equilibrium!(E.g. since in the outer layers of a star there is always large energy loss from the stellar surface) . Thus, one only assumes the emission of the radiation is the same as for a gas in thermodynamic equilibrium at a temperature (T) corresponding to the temperature of the layer under consideration.  Another way to say this is that if LTE holds, the photons always emerge at all wavelengths.  In the above treatment, note that the absorption coefficient was always written as: k(l) to emphasize its wavelength (l) dependence. 

The student will be required to do a number of challenging problems for homework, including the specific applications of the gray atmosphere approximation. In a particular integral, let the surface flux:

 p( Fo ) = 2 p (I(cos (q)) = p [a(l) + 2(b(l)/3 ] 

and Flo = S(lt(l) = 2/3 

which states that the flux coming out  of the  stellar surface is equal to the source function at the optical depth t = 2/3. This is the very important ‘Eddington-Barbier’ relation that facilitates an understanding of how stellar spectra are formed.  Once one then assumes LTE, one can further assume k(l) is independent of l (gray atmosphere) so that: 

k(l) = k;  t (l) = t  and Flo =  Bl (T(t = 2/3) )

Thus, the energy distribution of Fl is that of a black body corresponding to the temperature at an optical depth t = 2/3.  From this, along with some simple substitutions and integrations a wdie array of problems can be done. A few HW problem  examples:

1. Estimate the specific intensity I (q=p/4) if the surface flux from the Sun is  6.3 x 10 7 Jm-2 s-1.

2.  Find the effective temperature of the Sun and the boundary temperature (To) and account for any difference. (Hint: The effective temperature is related to the boundary temperature by: Teff  = (2)1/4 To   )

At some later stage sources' radiation characteristics will also be covered, and this will include treating the quantity known as the specific intensity i.e.

Il (0,q) =   òo z  Bl(t)  exp [(-tl / cos  q)] dt/ cos  q

where Bl(t)   is the Planck function.    The energy which flows per unit solid angle will then be based upon finding:

dE n =    I  cos  q   d dt  dn 

from which one will wish to obtain the total flux

By now radio astronomy will emerge, with  essentials of assorted radio telescope properties, especially for antennas, will also be introduced, along with many problems - including practical (i.e. designing a specific antenna to detect an object of given flux, and spectral output etc.).  To this end the student will distinguish between the flux emitted for an isotropic (lossless) antenna, and an anisotropic antenna with the gain (g) subject to the constraint:

ò 4p  g  dw   =   4p 

and the relation between the gain of the antenna and its effective aperture (A) such that:

g( (q ,  φ )  =   4p  A (q ,  φ)/ l2 

From here, the student will be expected to work out the beam width and beam efficiency of a given antenna, as well as compute the 'brightness temperature' for a localized source, and the antenna temperature:
Ta =  1/4p  ò 4p   g T(b)  dw

 where T(b) is the brightness temperature.

Sensitivity of the antenna will also be considered, as well as other details such as the amplification of high frequency signals.

By his senior year, the budding astronomy major will have to confront the theory of stellar structure.  In this case, the student will be introduced to a variety of differential equations which he'll later be expected to use in the construction of an actual stellar model (which may be 50 percent of his final grade.) He learns that the force of attraction between M(r) e.g. the mass enclosed inside the stellar sphere of radius, r and r dr  (the mass of an element) is the same as that between a mass M(r) at the center and  r dr at r.   By Newton’s law this attractive force is given by:

F = G M(r)  dr/ r2

Since the attraction due to the material outside r is zero, we should have for equilibrium: 
- dP = G M(r) r dr/ r2

Or:     dP/dr = - G M(r) r / r2

 Consider now the mass of the shell between an outer  layer of a given star  and a deeper stellar layer. This is approximately, 4p rr dr, provided that dr  (shell thickness) is small. The mass of the layer is the difference between M(r + dr) and M(r) which for a thin shell is:

M(r + dr) -  M(r) = (dM/ dr) dr

Equating the two expressions for the mass of the spherical shell we obtain:

dM/dr = 4p rr

The two equations, for dP/dr and dM/dr represent the basic equations of stellar structure, without which the innards of a star would be inaccessible to investigation. A third equation of stellar structure may be derived using by using the equation for dM/dr in combination with the fact that a star’s luminosity is produced through the consumption of its own mass. This may be expressed mathematically as:

dL/dM = e

where e denotes the rate of energy generation. For the proton-proton cycle (for stars like the Sun- and designed for cgs units!): 

e= 2.5 x 106 (r  X2).· (106 /T)2/3 exp[-33.8(106 /T)1/3]

Of course, to construct a stellar model as part of a course project, the student will more likely have to deal with a different 'critter' entirely -  say a star of two solar masses with a convective (as opposed to a radiative) core and with composition: X = 0.65 (i.e. 65% hydrogen), Y = 0.32 (i.e. 32% helium) and Z = 0.03 (i.e. 3 % heavy elements).  Say with an energy generation function:

e= 10-14.2 (r  X X(CN)).· (T20 )

where: X(CN) = 0.01   and :

X =  4.34 x 1025  Z(1 + X)  r  --3.5

This is none other than the stellar model problem construction I had to complete, and for which I received an 'A' and also an A in the course. The details of the problem were:

Neglect radiation pressure and degeneracy and assume the gas is nearly totally ionized. Utilizing Wrubel's interior integrations and Schwarzschild's and Harm's envelop solutions:

a) Construct a consistent stellar model utilizing the U-V plane fitting technique, and

b) Calculate the following physical properties of the star: L, R, Tc  ,  r c ,  Pc  , and the mass of the convective core,  m c .

Still want to become an Astronomy major?  Just make sure math is in your blood.

(This was published in 3 parts originally under the title 'Math Drives The Universe', in November, 2013)

Tuesday, November 29, 2022

The Skeptics Society Conspiracy Phobes - And Why They Discredit Themselves


Cover of new pamphlet received from the Skeptics Society,  purporting to expose conspiracy theories. 

Having just started reading Richard Charnin's new book, Reclaiming Science: The JFK Conspiracy, I can say I am already delighted on seeing the depth of the analyses to come, and the focus on science, making the book a nice complement to Prof. James Fetzer's Assassination Science. Because science is what we need here to counter the flood of disinformation that first arrived with the Warren Commission Report - not to mention the efforts of all its apologists to defend it.

"Reclaiming Science" is an apt title because it entails reclaiming the content that has hitherto been obfuscated and distorted under the specious science (or what I call pseudo-science) of the Warren Report as well as the apologists like Gerald Posner ('Case Closed') and Vince Bugliosi ('Reclaiming History') who have sought to reinforce that pseudo-science . I showed much of that in my FAQ (Part 5) addressing the bullets and wounds back  in in November of last year, e.g.

Today, the 51st anniversary of the JFK assassination,  is a good opportunity to re-examine the entrenched CT phobics, especially the more sophisticated ones that have surfaced in organizations like  The Skeptics Society. For example, via a little pamphlet (see cover image at top) put out recently - which I received in the post three days earlier. Perhaps 21 years ago I had a letter published in the journal of that organization wherein I warned that expressions of hyper-skepticism could backfire and were counterproductive. This was after the magazine took some initial critical shots at the claim for conspiracy in the Kennedy assassination - revealing like so many others before and since that they hadn't done their homework.

Before proceeding further let us remind ourselves of the definition of conspiracy (e.g. from the Webster's Encyclopedic Dictionary):

treacherous, surreptitious plan formulated in secret by two or more persons

Why this simple definition should cause so many heads to explode - especially in the US of A-   is frankly beyond me. It is elemental and has been demonstrated many times as I will show - hence, it's not as if we're talking or writing about ghosts, 
poltergeists, elves or fairies.

An easier question to address is: Why are so many would-be skeptical critics broken on the 'wheel' of the JFK assassination? Well, because they treat it frivolously - without the respect it is due  - more often conflating it with nonsense pseudo conspiracies (which shouldn't even be dignified by the name) such as the claim of the "faked Apollo Moon landing" or the UN seeking to take over the nation via black helicopters or the claim government agents are secretly using the Post Office to buy up all the ammo so gun owners can't get any. Each of these, by contrast to the JFK assassination, demonstrates ignorance or manifest paranoia.

Apart from the presumption of frivolity, without due diligence in approaching a controversial  political-historical topic, and with only uninformed, indiscriminate skepticism expressed - the whole exercise becomes one of merely academic pique, or "bullshit" in the parlance of Harry Frankfurt in his masterpiece, On Bullshit. According to Frankfurt:

"Bullshit is unavoidable whenever circumstances require someone to talk (or write) without knowing what he is talking (or writing)  about. Thus, the production of bullshit is stimulated whenever a person's obligations or opportunities to speak(or write) about some topic exceed his knowledge of the facts relevant to the topic."

Such is the case with the contents of the Skeptics Society pamphlet.. What is the error that threads its way throughout the book? While the authors specifically target ALL conspiracy theories - as if these were a form of general mental disorder- they are implicitly attacking the reality of actual conspiracies! (Bear in mind once a conspiracy exists it is no longer "theory".) Logically, then, if ab initio  all conspiracy theories are falsefoolish or invalid (meaning other explanations can suffice and the ones advanced are daffy) it means there can be no real conspiracies either!

But we know this to be false, because Watergate was certainly a real conspiracy,  exposed in Nixon's White House Tapes (get hold of them as I have and listen!) as was Iran-Contra. To refuse to label a crime, especially a political one,  a conspiracy -  is therefore to be dishonest in one's approach to historical or political knowledge and education. It is also to be guilty of spreading disinformation,

To fix ideas, let me offer some perspectives on the Iran –Contra conspiracy which was implemented by Reagan cronies such as Oliver North, John Poindexter, Albert Hakim and Caspar Weinberger. (Reagan always denied any involvement, though it is incredible that such a plan could have unfolded without topmost authority. But, being generous, mayhap Reagan's Alzheimer's had al
ready set in and someone like Poindexter was needed to oversee it!)

All the charges against the above-named characters and others are listed on page xiv of the Introduction to The Iran –Contra Report (1994) published by Random House at the behest of Independent Counsel Lawrence E. Walsh. (Note: Weinberger,  “charged with four counts of false statements and perjury,  was pardoned by George Bush” That would be George Senior).

The basic facts to take away concerning the  Iran-Contra conspiracy are these:

- Shipping Israeli Hawk and TOW missiles to Iran from 1985-86 to obtain the release of American hostages held in the Middle East. This was despite an embargo on such sales.

- The money from the sales of these arms was to be funneled into Nicaragua to support the Rightist “Contras’, a violation of the then 
Boland Amendment, and basically exposing the Reagan administration’s covert support for paramilitary activities conducted against the Sandinista government.

As noted in Walsh’s Introduction (p. xv):

The Iran and Contra operations were merged when funds generated from the sale of weapons to Iran were diverted to support the Contra mission in Nicaragua.  Although this diversion may be the most dramatic aspect of Iran-contra, it is important to emphasize that both the Iran and contra operations, separately, violated United States policy and the law.”

Violation of policy thus was via the violation of the Boland Amendment, named for Rep. Edward Boland (D-MA).  The amendment restricted U.S. aid to the contras and “
prohibited the use of U.S. funds for the purpose of overthrowing the government of Nicaragua.”

But even Rep. Boland likely couldn't have conceived of the dastardly lengths to which the Reaganites would go even before his amendment was in the public domain. I am referring, of course, to the “October Surprise” whereby Reaganites (known at the time also to be strongly supported by the Republican Heritage Council with Nazi links- see, e.g. Russ Bellant’s book: ‘Old Nazis, The New Right and the Republican Party’, 1991, pp. 41-44)) used back channels to make a secret deal with Iran to postpone release of the 52 American hostages in return for arms sales after the election.

Corroborating this, on July 18, 1981 the then USSR's TASS news agency reported the emergency landing near the USSR-Turkish border of an Argentine-registered transport aircraft leased and flown by Israelis, carrying a full load of US weaponry and military spare parts. The US Assistant Secretary of State for the Middle East, Nicholas Veliotes, subsequently investigated this occurrence and concluded that the downed aircraft was on its third such flight in a series of shipments of US weapons to Iran which had been authorized by high officials in the Reagan Administration.

Before people start talking “tinfoil hats” let’s examine what was at stake and in particular the federal conspiracy law as it would relate to the later arms-for-hostages dealings of Iran-Contra. As noted on p. 56 of The Iran –Contra Report:

“The federal conspiracy statute, 18 U.S.C. Sec. 371, states that ‘it is a crime to conspire to defraud the United States, or any agency thereof in any manner or for any purpose’”

This would have been violated under three criminal actions by the perpetrators identified by Walsh (ibid.):

1) “Using government resources, the conspirators conducted an unauthorized covert program in support of the contras.”

2) “North and Poindexter used their Government positions to create a hidden slush fund under the exclusive control of the conspirators

3) “By secretly pursuing their own ends, the conspirators outraged the Iranians they were attempting to persuade and thus jeopardized the success of the Iran initiative.”

In terms of the scale and scope of the deal, on p. 338 of the Iran-Contra Report we see: “3300 TOWs for hostages”, then on p. 339, we note: “In fact, 1,000 TOW missiles had been delivered to Iran between February 15 and 17, 1986.”

These facts are germane and important because they disclose the extent of the conspiracy as well as the people involved.  But this is the essential nature of all real conspiracies in the political realm - to somehow leverage power to the advantage of those seeking to impose their own agenda. It was applicable in the Iran-Contra conspiracy as it was in the Kennedy assassination conspiracy - the objective in the latter to implement a much larger national security state and permanent war state

The authors of the Skeptic Society's pamphlet, meanwhile, step into reeking heaps of virtual 'doggy doo' as they go their merry way making wild generalizations about all claimed conspiracies and conflating them indiscriminately. This is in addition to plenty of dime store psychology meted out such as  citing a waste of paper called 'American Conspiracy Theories' in which it is claimed "researchers have found that inducing anxiety or loss of control triggers respondents to see non-existent patterns and evoke conspiratorial explanations."

Proving again that a little knowledge is a dangerous thing especially in subjective areas like  psychology and psychiatry (for an excellent exposure of the Diagnostic and Statistics Manual and all the psycho-malarkey within it, check out 'The Book of Woe: The DSM and the Unmaking of Psychiatry')  Such psycho-babble also elicited the scorn and rebuke of my friend Rolf  (formerly a member of the Spezialdienst) when I emailed him a scan of the pertinent material. His rejoinder was that this anti-conspiracy crowd that relies on such babble  "needs their own heads examined".

In the case of the pamphlet, its lone (peripheral) foray into the Kennedy assassination occurs on page 4, under the header, 'Ingredients for Conspiratorial Thinking' (hmmmm.....was  Independent Counsel Lawrence E. Walsh guilty of "conspiratorial thinking" for pursuing Iran-Contra?) Therein, the authors  (Michael Shermer and Pat Linse) babble:

"Conspiracy theories connect the dots of random events into meaningful patterns (patternicity) and then infuse those patterns with intentional agency (agenticity). Add to this confirmation bias, the tendency to look for or find confirmatory evidence for what you already believe- and the hindsight bias (after the fact explanation for what you already know happened)  and we have the foundation for conspiratorial cognition."

Which is fulsome horse pockey. Indeed,  by the clever use of this pseudo-scientific,  dime store psychology template virtually any real conspiracy could be dismissed as nothing more then a combo of :  P (patternicity)+ A  (agenticity) + H (hindsight) + C (confirmation bias) nonsense!   

Think of it! In the case of the Iran-Contra conspiracy,  the shipping manifests revealing the assorted Hawk and TOW missiles  destined for Iran would be likened to "seeing a pattern".  This would then be "infused with agenticity"(sic)  because the missiles ended up with the Iranians - so someone had to be a bad guy in doing it- since the Iranians were bad guys holding American hostages.  The next step would be to accuse  Prosecutor Walsh of "looking for confirmatory evidence of what he already believed", i..e. the guilt of Oliver North, John Poindexter et al. because they "used their Government positions to create a hidden slush fund under the exclusive control of the conspirators”.  And finally, the coup de grace, Walsh would be accused of "hindsight bias" - advancing explanations after the fact for what he already knew happened. (Of course he knew, he uncovered the evidence in the course of his investigation!)

So, in other words, their bandying about of this pseudo-process is useless because it errs by proposing an excessively subjective and open-ended standard for parsing objective evidence. Hence, tying proof of conspiracy to sophisticated second guessing.

Shermer and Linse then move on to the Kennedy assassination (ibid.):

"Consider the Kennedy assassination: Knowing what we know now, film footage of Dealey Plaza from Nov. 22, 1963 seems pregnant with enigmas and ironies - from the oddly expectant expressions on the faces of the onlookers on the grassy knoll (What were they thinking?) to the play of shadows in the background (Could that flash of light have been on a gun barrel?) Each odd excrescence, every random lump in the visual texture, seems suspicious"

But here the authors invoke too much in the way of red herring, and not enough substance. Sure, there were random flashes and visuals appearing in the setting, i.e. in the Zapruder film as well as the Nix film. High tech investigation of one photo - from Mary Moorman- even disclosed the outline of a shooter behind the stockade fence on the grassy knoll, e.g.

This "Badgeman" photo above, compliments of Richard Charnin - from his blog- in contrast to the woolly speculations of the skeptic duo, was declared authentic by an MIT analysis team - as Charnin observes. (For the likely identity of 'Badgeman' see my Sept. 20th post: 'Switzerland: Destination for the Kennedy Assassins?' )

But even if one would claim to be so bleary-eyed or visually deficient as to see nothing peculiar in the image, or the evident outline of a gunman in the photo (including muzzle blast), the autopsy photos - fraudulent and real - shown below, ought to give pause. These are not based on random flashes or expectant expressions on living faces  but the stark consequences after the rifles were fired.
 These, along with the released CIA files about Oswald, seem to be what the hyper-skeptics have missed.

And perhaps this is why these skeptics who fancy themselves informed and smart enough to take on the JFK assassination,  ought to back away and regard it instead as the "fire breathing dragon of American history" - in the words of one Truthdig journalist who interviewed Tom Hanks for a supposed series he had planned on HBO (later cancelled). Hanks was ultimately gobbled up by this fire-breathing dragon because in the end he was too flippant in his approach to the facts, as well as arrogant in seeking to  "do the American public a service" - because they "have been snookered into believing that Lee Harvey Oswald was framed."

These lessons,  which occur from time to time,  ought to also steer other presumptuous fools clear of this event in any future forays where they go after ALL conspiracies. Oh, they might wish to stay away from Iran-Contra, Watergate and BCCI too!

Btw, I have no problem - not one, if this pair, Pat Linse and Michael Shermer (or the entire Skeptics Society),  want to go after those who suggest the Apollo Moon landings were faked or that the Air Force is secretly hiding aliens somewhere in Area 51. But if you plan to try to skunk those of us who've seriously investigated the Kennedy assassination - conflating us with the nutsos above-  you had best be loaded for bear!

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(This Post first appeared in November, 2014)