## Conspiracy Theories and Mathematical Probabilities

26 May

Conspiracy Theories and Mathematical Probabilities

Richard Charnin
May 25, 2012
Updated: May 26, 2014

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It’s an interesting exercise to calculate mathematical probabilities of so-called “conspiracy theories”. The mainstream media and their cadre of online gatekeepers use the term “Conspiracy Theorist” (CT) as a derogatory label for those who seek the truth. According to the media, there are never conspiracies. But they avoid factual discussions based on the scientific evidence.

These myths are promoted non-stop in the mainstream media.
– Oswald acted alone in 1963 – with a magic bullet and defective rifle.
– Bush won Florida in 2000 and had a 3 million “mandate” in 2004.
– Nineteen Muslims armed with box cutters who could not fly a Cessna, hijacked four airliners and outfoxed the entire U.S. defense establishment – while Bin Laden was on dialysis, near death and hiding in caves.

But the media can’t refute the mathematics that proves beyond a reasonable doubt that there is a massive conspiracy to hide the truth of these events from the public.

Scientific notation is necessary to express the extremely low probabilities of the following events. For example, the probability P that at least 23 material witnesses would die unnaturally in the year following the JFK assassination is 7.3E-40 in scientific notation (less than 1 in a trillion trillion trillion).

To put the numbers in context: There are an estimated 300 billion trillion (3E23) stars in the universe. That’s 3 followed by 23 zeros: 300,000,000,000,000,000,000,000. There are an estimated 700 thousand trillion (7E17) grains of sand on earth or 7 followed by 17 zeros: 700,000,000,000,000,000.

The probability calculations are based on the Normal, Binomial and Poisson distribution functions.

The Normal Distribution (ND) is based on a sample of observations defined by the mean (average) value and standard deviation (a measure of volatility of the observations from the mean). The ND is used to calculate the probability that Kerry’s unadjusted 51.7% National Exit Poll (13660 respondents) share would deviate 3.4% from his 48.3% recorded national share.

The Binomial Distribution (BD) is used to calculate the probability P of n successes in N trials when the probability p of a success is constant in each trial. The BD is used to calculate the probability P that n= 86 of N=88 DRE voting machines would flip votes from Kerry to Bush.

The Poisson Distribution (PD) is used to calculate the probability P that a given number n of events with low probability will occur over a period of time. The PD is used to calculate the probability P that at least n JFK-related individuals out of a population of N witnesses would die unnaturally in the years following the assassination.

JFK Witness Unnatural Deaths

The probability analysis is straightforward; it’s not a theoretical exercise. It is a mathematical proof of a conspiracy based on factual data: number of witnesses, number of unnatural (murder, accident, suicide, unknown) deaths, corresponding mortality rates and the time period. The Poisson function calculates the probability. The average U.S. 1964-78 unnatural mortality rate was 0.000818. The average JFK witness mortality rate (0.000247) was lower due to the high proportion of homicides compared to suicides and accidents.

In the 1973 film Executive Action it was revealed that an actuary hired by the London Sunday Times calculated the probability that 18 material witnesses would die within three years of the assassination as 100,000 trillion to one.

This is a challenge to those who still claim that the deaths do not prove a conspiracy: To substantiate your claim, you must refute the database of witnesses, the unnatural mortality rates and the use of the Poisson formula.

Probabilities of Material Witness Deaths

Warren Commission Witnesses (1964-78):
– 15 official ruled unnatural deaths

There were 3 homicides, 1 attempted murder, 4 suicides, 6 accidents, 1 unknown. Given the 0.000295 weighted average mortality rate, the probability is
P= 5.08E-08 (1 in 20 million)

- 21 unofficial actual unnatural deaths
There were 17 homicides, 2 accidents, 1 suicide, 1 unknown. Normally, 7 unnatural deaths would be expected. Given the 0.000131 weighted rate, the probability is:
P = 3.65E-20 = POISSON (21, 1.08, false)
P = 1 in 27 million trillion

This graph shows the long-term trend in the U.S. homicide rate. Note that in 1963 the homicide rate was 5.4 per 100,000.

Deaths by Major Causes: 1960-2011 Source: U.S. National Center for Health Statistics. The average homicide rate for 1964-1978 was 8.4 per 100,000.

At least 78 deaths were ruled unnatural (17 were expected) out of an estimated 1400 JFK-related individuals (see Benson’s Who’s Who in the JFK Assassination). The probability is based on the JFK-weighted unnatural death rate (0.000247):
P = 2.8E-62 = Poisson (78, 15*1400*0.000247, false)
P = 1 in a TRILLION TRILLION TRILLION TRILLION TRILLION.

Convenient deaths spiked in 1964 (Warren Commission) and 1977 (House Select Committee).

1988-2008 Election Fraud

To believe that Bush won fairly in 2004, you must believe.. http://richardcharnin.wordpress.com/2011/06/22/to-believe-that-bush-won-in-2004-you-must-also-believe-that%E2%80%A6/

1. In 2004, the Election Incident Reporting System (EIRS) indicated that 86 of 88 DRE voting machines in various states flipped votes from Kerry to Bush. The probability P is calculated as:
P = 1E-23 = Binomdist (86, 88, .5, false) + Binomdist (87, 88, .5, false) + Binomdist (88, 88, .5, false)
P = 1 in 79 billion trillion

There were massive discrepancies between the average Democratic/Republican recorded vote split (48-46%) and the 274 unadjusted state and national exit polls (52-42%). The True Vote Model (TVM) was developed before the exit polls were posted on the Roper UConn website. The 53-41% TVM split confirmed the polls.

2. In 2008, the unadjusted exit polls in 36 states red-shifted beyond the margin of error (MoE) to McCain in the recorded vote.
P = 2.4E-39 = Poisson(36,.025*50,false)
P = 1 in 400 trillion trillion trillion!

3. In the 1988-2008 presidential elections, 232 (85%) of the 274 state exit polls red-shifted to the Republican. Normally, an even split (137) would be expected. The probability is:
P = 4.7E-39 or 1 in 1 trillion trillion trillion!

4. The probability that at least 55 of 57 state elections would flip from the Democrats in the polls to the Republicans in the recorded vote is given by the Binomial distribution:
P = 1-Binomdist(54,57,.5,true)
P = 1.1E-14 = 0.000000000000011 or 1 in 88 trillion!

5. In the 1988-2008 elections, there was an 8% discrepancy between the 274 state unadjusted exit poll aggregate (52D-42R) and the recorded votes (48D-46R). There were 375,000 exit poll respondents. Assuming an extremely conservative 1.2% margin of error, the probability of the discrepancy is:
P = Normdist(.52,.48,.012/1.96,false) = 3.51E-08 or 1 in 28 million.
Assuming a plausible 0.8% MoE, the probability is P= 1.37E-19 or 1 in 7 million trillion!

6. The exit poll margin of error (MoE) was exceeded in 131 of the 274 exit polls in favor of the Republican – and just 4 for the Democrat. The probability that the MoE would be exceeded in any state is 1 in 20. Therefore, the MoE would normally be expected to be exceeded in 7 states for the Republican and 7 for the Democrat.

The Poisson function calculates the probability that the margin of error would be exceeded in 131 of 274 state exit polls in favor of the Republican:
P = 3.7E-116 = Poisson (131, .025*274, false)

P = .0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 0000000000 000001

Microbiologist Mystery Deaths

The unnatural deaths of 16 world-class microbiologists (8 homicides) in the four months following 9/11 and the anthrax scare cannot be coincidental. Assuming 10,000 world-class microbiologists, the probability of 16 unnatural deaths in 4 months is:
P = Poisson(16,.33*.0002*10000,false)
P = 1 in 30 trillion
Assuming 100,000 microbiologists, P= 1 in a thousand
.

Eight International Bank Executives Mystery Deaths in Jan. 2014
This is a probability sensitivity analysis over a range of 5,000-500,000 bank execs: https://docs.google.com/spreadsheet/ccc?key=0AjAk1JUWDMyRdFRYUERxNDkwNGRlZkVndkc5TWFXREE&usp=drive_web#gid=0

9/11 Scientific Evidence vs. the Official Conspiracy Theory

To believe the official conspiracy theory (OCT) requires a belief in miracles. It requires cognitive dissonance of obvious explosive (WTC1 and WTC2) and symmetric (WTC7) destruction.

This group of professionals is dedicated to uncovering the truth about 9/11. http://www.consensus911.org/

Probability calculations are not applicable as free-fall collapse is physically impossible without explosives. Ask Isaac Newton. Office fires burn at 2000 degrees below the temperatures required to melt steel. Not one steel-framed building has ever collapsed due to fires, before or since 9/11. The probability is ABSOLUTE ZERO based on historical facts and Newtonian physics.

NIST claims that office fires caused 3 steel-framed buildings to collapse at near free-fall – a clear refutation of Newton’s Laws of Motion.
– Free fall can only occur by an instantaneous removal of all supporting columns (i.e. a controlled demolition).
– Lateral ejection of debris can only occur from explosions – not from fires.
– Jet fuel fires burn at a much lower temperature than is required to melt steel.
– No steel-framed office buildings have ever collapsed due to fires.

CNN reporter Barbara Olson was a passenger on AA Flight 11 (which allegedly crashed into the Pentagon). She called husband Solicitor General Ted Olson from her cell phone and told him hijackers were armed with knives and box cutters.
– It was later disclosed that cell phones could not work at 30,000 feet.
– Olson then said that she called from a seatback phone. But according to an American Airlines spokesman, there were no seatback phones on Boeing 757 airliners.
– At the 2006 Moussaoui trial, the FBI reported there was one attempted call that lasted zero seconds (“unconnected”)from Barbara Olson to Ted Olson.

The BBC reported that WTC 7 collapsed at 5pm, 20 minutes before happened.
– How did the reporter know that it would collapse? Was she psychic?
– All fires burned out long before 5pm.
– Silverstein, the owner, said “pull it”.

and there is much more…

A believer of the official conspiracy theory (OCT) must ask explain how…

- William Rodriguez, a WTC janitor, would hear a loud explosion seven seconds before the plane hit, but his testimony would be ignored by the 9/11 commission.
– The NIST would fail to acknowledge free-fall until David Chandler proved it.
– The collapse of WTC 7 would occur due to structural failure of one beam.
– The 9/11 Commission would fail to mention WTC 7 or note it their Report
– For the first time in history, not one but three steel-framed buildings would collapse due to office fires.

- Airline fuel burning at 1000F would melt steel.
– April Gallop would hear an explosion next to her office at the Pentagon but not see any aircraft debris.
– NIST would not consider explosives as a possible cause of the collapses.
– NIST would admit freefall and claim it was due to office furniture fires.
– There would be traces of thermite in the lungs of first responders.

- Over 118 firefighters would imagine that they heard explosions.
– Furniture would be ejected laterally 600 feet from office fires.
– Firefighters would know that WTC 7 would collapse before it did.
– When Larry Silverstein said “pull-it” he did not mean demolish WTC 7.
– At 5pm, the BBC would report WTC7 fell, 20 minutes before it did.

- The passport of an alleged hijacker would be found in the rubble of the WTC.
– There would be no manifest record that hijackers boarded the planes.
– Put options on airline stocks would rise dramatically a few days before 9/11.
– Osama Bin Laden would not be on the FBI most wanted list for 9/11.
– 9/11 Commission heads Kean and Hamilton would disavow their own report.

- There were multiple air defense exercises conducted on 9/11.
– Officials who ignored standard response procedures would be promoted.
– Not one of the four flight recorders would be retrieved.
– There is no video, airline debris or human remains at the Pentagon.
– There is no video, debris or human remains at the Pennsylvania crash site.

- The media would not investigate these facts.

April Gallop was working at the Pentagon and never saw a plane.

Barbara Honegger presents a detailed analysis of the Pentagon scam:

http://townhallseattle.org/911-truth-seattle-barbara-honegger-behind-the-smoke-curtain/

This is what a retired general in charge of intelligence had to say:

Posted by on May 26, 2012 in JFK, Uncategorized

### 15 responses to “Conspiracy Theories and Mathematical Probabilities”

1. May 26, 2012 at 1:53 pm

Good work, Richard. And, thanks for your contribution to the understanding of the polls surrounding the Wisconsin recall elections.

• May 27, 2012 at 12:58 pm

James,

Thanks. I appreciate your spreading the word. Try to post links to relevant posts of mine when you can. It’s a constant battle to expose the corrupt media. We need all the help we can get. I recently posted comments on the Washingon Post and NY Times websites and was pleasantly surprised that they were not taken down. Is that a sign of progress?

• October 16, 2012 at 9:25 pm

While in general this is an interesting and worthwhile article, a few things may not be correct:

1.”Not one of the four flight recorders would be retrieved.” It is my understanding that the flight recorder for AA77, the plane that crashed into the Pentagon, was retrieved, and that analysis of data from that recorder has contributed to our understanding of the the Pentagon events. See:
“Flight AA77 on 9/11: New FDR Analysis Supports the Official Flight Path Leading to Impact with the Pentagon” by Frank Legge and Warren Stutt, at the Journal of 911 studies web site.

2. “There is no video, airline debris or human remains at the Pentagon.” The video that has been released is, indeed, inconclusive. However, when it comes to airline debris, etc., Frank Legge has addressed this issue in his paper “What Hit the Pentagon? Misinformation and its Effect on
the Credibility of 9/11 Truth”, also at the Journal of 911 studies web site. There is indeed evidence for airliner debris and human remains found at the Pentagon crash site.

If you have not done so already, I hope you will take a look at the articles I have listed above. I think it important that we not spread misinformation about the events of 9/11, given the importance of understanding the truth about what happened that day.

Thank you for your informative and thorough work regarding elections, etc.

It has been proven beyond any doubt that that no passenger jet hit the Pentagon, but actually flew over it. There was no aircraft debris other than what was planted at the scene.

I refer you to the testimony of April Gallop, who was working next door to the “impact” and never saw a plane.

Also to the detailed analysis of Barbara Honegger:

http://townhallseattle.org/911-truth-seattle-barbara-honegger-behind-the-smoke-curtain/

An army general in charge of intelligence:

2. June 11, 2012 at 9:51 am

Brilliance like your pursuit of the truth is honorable to our nation and will soon help ensure integrity in our voting system. Thank you, Richard.

• June 11, 2012 at 3:15 pm

Laura,

Thank you very much for that.
It tells me that all of the hard work was well worth it.

• June 30, 2012 at 1:11 am

Thanks, Laura.

I appreciate your interest in my posts.

3. July 12, 2012 at 1:49 pm

Its always great to see conspiracy news!

4. September 7, 2012 at 8:10 pm

Beautiful job, Richard! You are a genius at work and just what the world needs at a difficult time in our hisory.

5. November 24, 2014 at 5:41 pm

The problem with reasoning about events using probability like this is that the arguments assume what they set out to prove, which is that the events are independent and not dependent, and thus statistically significant to a very high degree, thats how you get these ridiculously small p values.

Whereas if they were taken as a dependent chain of conditional events the p values get much, much larger.

For instance, its like stating that out of 5 people who knew Miss Jones 3 have died in a car accident and given she’s involved in some dubious activity, she must have been complicit in the deaths. You take some population data, the p(car accident death) = .05 and assume the events are independent and apply compound probability and find .05x.05x.05 = .000125 and propose that the odds of these individuals dying in a car accidents so unlikely to have occurred by chance that Miss Jones must have been involved.

Then you find some contingent factor, like they all met at AA and had convictions for drunk driving. You see then that probability here is applied just like a post hoc narrative and doesn’t lend any rigour from mathematical formalism because as a theory, the argument is constructed after the events and doesn’t lead to any testable prediction, but merely is another way of stating what you’ve already assumed. You find that the conditional probability of these deaths given the new information is much higher and you assumed a link to Miss Jones as an alternative way of explaining the data.

I could argue against the complicity of the US government in 9/11 on the basis that and these are arbitrary numbers,10,000 drill days have been conducted and only on 1 occasion has there been a terrorist attack and conversely, that on 10,000 days without drills there had been 10 terrorist attacks, thus that the hypothesis that drills cause attacks due the complicity of the government is patently wrong.

I’m skeptical about the events surrounding 9/11 too, but the truthers really need a good Bayesian prior to hang all these indeterminate events that have competing explanations on, actual proof of thermite would be one such prior. All of these key pieces of evidence the truthers think they have are subject to equally as likely and more likely competing explanations.

The fact remains that the international scientific community has not taken up 9/11 truth and it remains a fringe belief. As Chomsky said, you have a complex event that leaves many unresolved issue and its easy to hang a narrative on it, equally applicable is Sunstein Cass’s comment that truthers suffer from a “crippled epistemology”.

• November 24, 2014 at 11:49 pm

Chomsky? Sunstein?
You give yourself away by quoting those purveyors of disinformation.

You have not refuted any of the calculations in the post.
In fact, you do not even understand the basic methodology.
I do not use compound probability. I use the Poisson function. Have you ever heard of it? Poisson is the classic formula to calculate the probability of rare events.

It’s all about the STATISTICALLY EXPECTED vs. ACTUAL number of events.
Baysians, Priors? Much handwaving which is not applicable.

We have n events, each with a very low probability, occurring in a random N sample space. We would expect E events to occur based on the probability. But we have n events, where n is far greater than E. It’s that simple.

I suggest you read the definition of unnatural mortality (homicide, accident, suicide) and look up the corresponding rates. Or do you disagree with the London Times actuary who calculated a 1 in 100,000 trillion probability that 18 material witnesses would die (13 unnaturally) in the three years after the assassination. There were 552 witnesses who testified at the Warren commission in 1964.

When the actual number of ACTUAL events far exceeds the mathematically expected number, we calculate the probability of the occurrence. And if the probability is E-6 = .000001, we have proven a conspiracy. If the probability is E-50, that is just more icing on the cake. Compelling but overkill.

In a criminal trial, 0.01 is the mathematical definition of guilt beyond a reasonable doubt.

It is beyond a reasonable doubt that you do not understand the mathematical probabilities of rare events.

• November 25, 2014 at 1:41 am

Thanks for the response, but unfortunately you haven’t responded to my argument directly and have included a categorically false claim, and some irrelevant comments.

“In a criminal trial, 0.01 is the mathematical definition of guilt beyond a reasonable doubt.”

Wrong. Having studied criminal law I can tell you that there is no discrete value to BRD. It is a heuristic based on the anthropomorphic conceptualization of the courts or juries judgment in terms of a “reasonable man”.

“You have not refuted any of the calculations in the post.”

You’re absolutely right I haven’t refuted any of your calculations and I don’t have to, you’ve just post hoc arbitrarily assigned probability values to events and then claimed they are statistically significant. That is the extent that 9/11 has been mathematically “proved” to be a conspiracy.

You do have some O-E/E data on suspicious deaths which is interesting, but there is reason to think it’s methodologically flawed and significantly over represents the statistical significance of the occurrences, due to a small (n=16) observations with the microbiologists.

“In particular, the Poisson and normal distributions may provide poor approximations of the true probabilities when the numbers of the observed and expected deaths are small. This may lead to the incorrect interpretation of some situations as being “significant statisticaly” when they are not, and contrariwise, to the failure to detect statisticaly significant aberrations.”

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1069950/pdf/hsresearch00061-0038.pdf

You’re making big claims here, so you should expect to have to elaborate and thoroughly explain your reasoning.

6. November 25, 2014 at 1:48 am

I see you have edited your post after I responded.

• November 25, 2014 at 7:11 am

Yes, I reserve the right to improve my reply.
And your reply about Poisson was disingenuous: “distributions may provide poor approximations of the true probabilities when the numbers of the observed and expected deaths are small. This may lead to the incorrect interpretation of some situations as being “significant statisticaly” when they are not, and contrariwise, to the failure to detect statisticaly significant aberrations.”

You quote but you don’t analyze the mortality data or the exit poll data. Why not?

Refute the math; refute Poisson. I dare you to even try.
I use the binomial distribution for smaller N-samples.

Now you resort to attacking the use of Poisson.
Poisson is an approximation to the binomial, when N is large and p is small.

JFK: 1400+ JFK witnesses, 78 ruled unnatural deaths (probability of an unnatural death: 0.0008)
Probability of 78 unnatural deaths in 15 years from the 1400: E-30

Election fraud: 274 exit polls; 135 exceed the MoE (14 expected), 131 for the Republican (7 expected) Probability MoE exceeded in 131 of 135 exit polls for the GOP: E-116.

Andrew, what is your math background?
Have you developed/programmed mathematical models? If so, what were the applications.

Do you believe Sunstein is correct in his call to infiltrate “conspiracy” posters?
That appears to be what you are doing right now.
It won’t work.

You just exposed yourself.
Quoting Sunstein and Chomsky was a big boo-boo on your part.
Nothing you can say after that can be taken seriously.

Do you know the melting point of steel?
Do you know the maximum temperatures of the office fires caused by aircraft fuel?

Do you know what free fall acceleration is?.
Have you heard of Sir Isaac Newton?
Are you aware that the towers fell at near free-fall.

Do you agree with Chomsky that there is no proof there was an inside job on 9/11?

Your mentors Sunstein and Chomsky are not stupid, are they? Then they must be professional disinformationists. And you quote them. What does that tell us about you?

Time to end this “discussion”, but not before I remind you that I have written these books – which have been peer-reviewed and lauded by PhDs in Physics, Law, Statistics – and cited in books by JFK researchers: Belzer, Marrs, Kreig, Baker..

• November 30, 2014 at 1:18 pm

It’s trite to say because its so obvious but your arguments are riddled with ad hominem and appeal to authority. Carrying on that line of reasoning because you rest so heavily on it, has it ever occured to you why there is no broad based support for the 9/11 truth agenda among the international scientific community? It’s because the evidence is inconclusive and a conspiracy itself is a high sigma event, given how hard they are to prevent being exposed or leaked by allegedly large number of people involved. Similarly, there is no MIT, CalTech and Harvard professors for 9/11 truth, why? Reasonable, scientific minded people dont resort to teleological explanations like you do in furtherance of your narrative – again, applying occams razor here should be obvious.

Yes, I have studied calculus based probability and inferential statistics and have worked with the related chi2 distribution, but not the poisson. I have performed many hypothesis tests and know how it works. You have a more developed quantitative background than I do, but i dont have to “refute the math”, this a matter of knowing the difference between statistical and practical significance – simply showing the result is extremely unlikely doesn’t prove your narrative is an explanation of the events. The creationists have used this argument ad nauseum and it hasn’t gained much traction in the scientific community either, has it?

No, its not disengenous to point out the limitations of the Poission distribution for a small number of observations because you list a probabilty value for the expected number of deaths of Biochemists using that distribution. You say you used what, the bionomial distribution and this reduces the tendency to overstate significance?

Yes, I have looked at your other tables, but like the biochemists, what of your sampling methodology – your observations are not independent (random sample)? The potential for sampling error (bias) is very real. How do I know those biochemists werent all on a plane that crashed. In order to prove the results arent skewed by sampling error you should have to show that the probability of those inviduals dieing was average, based on medical / life history etc; analysed by type of death.

For cases in which you dont have a large number of independent observations, what sort of sampling problems have you encountered and how have you dealt with them?

As for this string of statements of the for “free-fall” – “issac newton”, etc. You should know that anything that falls is going to do so at the rate of the gravitational acceleration and this holds for all objects because their mass proportionally resists the force of gravitational acceleration. So its no surprise that the building fell at this speed once the support gave way. You may find the official reports from FEMA etc lacking, but this has been studied at top universities: http://dspace.mit.edu/bitstream/handle/1721.1/31114/61145960.pdf?sequence=1

I don’t know what you mean by “inside job” but maybe you could supply a more specifically operationalized definition – is it possible that the whole thing was orchestrated by agents inside the government? Extremely unlikely, there isn’t enough evidence to suggest this on balance of probabilty, never mind the standard of a criminal trial. Is it possible that some actors willfully bungled the initial response and let the attackes unfold? This seems more plausible, but still is unproven.

Has it occured to you that maybe Chomsky and Sunstein are making a valid argument that you need to listen to in order to further refine your position?

I think you’re a concerned citizen and I admire your enthusiasm, but you have to stay unrelentingly skeptical and interpret ambigous evidence in terms of the least complex theory.

You seem very adversarial in your approach to questioning and more inclined to use rhetoric and and an “us and them” mentality. Simply doubting your results and conlcusions doesn’t testity to me being part of some disinformation cabal. But it does demonstate your tendency to conflate purpose, motive, association and causation.

• November 30, 2014 at 1:48 pm

If its true that you have large n randomly sampled pole exit data that shows a significant difference with the official result, then you have a good argument for election fraud and I would be interested in your book.