The term “official 9/11 account” refers here to the account of the events of Sept. 11, 2001, as presented in June 2004 by the Commission of Inquiry appointed by President George W. Bush, and complemented by other official documents issued by US government agencies.  This account includes various details, such as identities of the alleged hijackers, identities of aircraft, timelines and other data used to prove that the crime of 9/11 was perpetrated by the named individuals under the orders or the inspiration of Osama bin Laden and other al Qaeda leaders.

It can be demonstrated by two straightforward mathematical techniques that the official account on 9/11 is not true.

The first method uses Boolean algebra. The second method is based on probability theory.

1. Boolean algebra used to invalidate the official 9/11 account

Boolean algebra deals not with numbers but with truth values. In Boolean mathematics we have only two values: True and false. One of the primary operations in boolean algebra is the operator AND.    In the equation A AND B we have:

Given A = true and B = true, then A AND B  = true
Given A = true and B = false, then A AND B = false
Given A = false and B = true, then A AND B = false
Given A = false and B = false, then A AND B = false

The AND relationship can be illustrated by three bulbs connected in series. The truth value for each bulb is ON or OFF.  In order for bulb C to be ON, both A and B must be ON.  If either A or B or both are OFF, C will not obtain electrical current and be OFF.  The same would apply to a longer series of bulbs connected in series.

Applying the AND relationship to the official 9/11 account, we posit that

in order for the official account to be true, a number N of fundamental allegations must be proved as true.  If any one of these fundamental allegations is false, the entire official account is false. 

Thus, it is only necessary to demonstrate that a single fundamental allegation in the official account is false for the entire account to be deemed false. Fundamental allegations include the following (a non-exhaustive list), all of which are part of the official version on 9/11:

1. No plans existed prior to 9/11 to protect the Pentagon and the White House against approaching aircraft.
   
2. The idea that the World Trade Center could be attacked from air, did not occur to any US government agency before 9/11.
   
3. All persons named by the FBI as hijackers actually boarded the four aircraft which crashed on 11 Sep. 2001.
   
4. The planes which crashed on 11 Sep. 2001 were flight number AA11 (tail number N334AA), flight number AA77 (tail number N644AA), flight number UA93 (tail number N591UA) and flight number UA175 (tail number N612UA).
   
5. Flight AA11, a Boeing 767, left from Logan Airport, Boston, and crashed into the North Tower of the World Trade Center in New York..
   
6. Flight AA77, a Boeing 757, left from Dulles Airport, Washington, D.C., and crashed into the Pentagon in Washington, D.C..
   
7. Flight UA175, a Boeing 767, left from Logan Airport, Boston, and crashed into the South Tower of the World Trade Center in New York..
   
8. Flight UA93, a Boeing 757, left from Newark Airport and crashed into a field near Shanksville, Pennsylvania.
   
9. The US military were not notified in time to scramble military jets and prevent the crashes of the hijacked aircraft.
   
10. President George W. Bush did not know that “America was under attack? before entering the primary school in Florida on the morning of 9/11.
    
11. The South and North towers of the World Trade Center as well as WTC no. 7 collapsed due to fire.
    
12. Numerous calls from hijacked passengers were made to family members and airline personnel from cell phones.

All of the above allegations have been disputed by independent observers. The US authorities have not provided credible evidence to support any of these allegations.  If any one of the above allegations is found to be false, the official account must be put in doubt or rejected and the suggestion of official deception or criminal complicity must be considered as justified.

2. Probability theory used to invalidate the official 9/11 account

It is also possible to invalidate the official 9/11 account by using probability theory. If it is shown that the probability of the official account is practically zero, it can be said with confidence that the official account is a lie.

The probability that a compound event has occurred is the product of all sub-events necessary to accomplish the compound event.  All of the following propositions, designated herein as sub-events, are part of the official account. They all refer to unlikely or extremely unlikely circumstances or events.   In order to simplify our demonstration, we arbitrarily assigned a probability of 0.1 (or 10 percent) to each of the following selected propositions which underpin the official account. Skeptics may try other combinations of probabilities, higher or lower, in order to test the methodology.  

1.  The probability that four young, healthy and educated Muslims with lots of cash and who like to party, would prepare for many months to sacrifice their lives for Allah in a complex hijacking operation, is 0.1.

2.  The probability that four groups of young Muslims would board four different aircraft in the United States on the same day without raising suspicion, is 0.1

3.  The probability that young, unmarried, Muslim men, known to have been in Afghanistan, would receive without problem a visa to the United States in order to learn to fly, is 0.1.

4.  The probability that foreign Muslims who plan to hijack planes in the United States, would choose to train in American, rather than in Arab, flight schools in order to prepare their hijackings, is 0.1.

5.  The probability that a person planning a hijack operation in the US would tell a US public official about his criminal motives, is 0.1.

6.  The probability that Muslims who meticulously plan a hijacking operation in the United States, would “forget” a Kor?an on a bar stool on the eve of their operation and a flight manual in Arabic on the morning of their operation, in a rented car left near the airport, is 0.1.

7.  The probability that hijackers who wish to be certain to arrive timely for their operation would fly from another town to the airport from which they intend to commit the hijacking rather than take a taxi or public transport to the airport, is 0.1.

8.  The probability that US military authorities will schedule for exactly the date of the murderous events, war games and exercises including simulated plane attacks on US facilities and planes crashing on government buildings, is 0.1.

9. The probability that passengers could pursue successful cell phone conversations from a passenger aircraft flying at 500 miles per hour at more than 6,000 feet, is 0.1.

10. The probability that hijackers would take their passports with them on their flight to Allah and that their passports would survive the hellish fires at the crash site and be found shortly after the attacks, is 0.1.  

11.  The probability that the US air force would bungle attempts to intercept four hijacked planes is 0.1.

12.  The probability that plans did not exist to protect the White House and the Pentagon against an accidental or malicious plane crash, is 0.1.

13.  The probability that neither the CIA nor the FBI could have possessed prior knowledge of the identities and whereabouts of the alleged hijackers before 9/11, is 0.1.

14.  The probability that a law enforcement agency, such as the FBI, would reduce their investigations of a mass murder merely four weeks after the events, is 0.1.

15.  The probability that a government would oppose an official investigation of a terrorist attack against its own country, is 0.1.

16.  The probability that terrorists would commit mass murder without making any demands, is 0.1.

17.  The probability that five individuals with only packing knives as weapons could overwhelm fifty adults in a plane without raising the awareness of the pilot, is 0.1.

18.  The probability that hijackers could successfully enter the pilot’s cabin in three different aircraft, without the pilot’s awareness, is 0.1.

19.  The probability that a person who had never flown a Boeing 757 or any other passenger aircraft could fly such an aircraft at 30 feet in the speed of 400 miles an hour into the back side of a building (the Pentagon), is 0.1.

20.  The probability that a crashed plane would leave no trace, is 0.1.

21.  The probability that a high rise steel building would collapse at free-fall speed on its own footprint after one hour’s fire, is 0.1.

22.  The probability that debris from a crashed plane would be found miles from the crash site is 0.1.

The compound probability of the above events to have occurred is the product of the individual probabilities, that is 0.1 in the 22 exponential, or 0,0000000000000000000001.   

Even by increasing the probability of the above propositions to 0.5, their compound probability will still near zero.  In fact, it suffices that a subset of any three of the above propositions be selected with a probability of 0.1 to make the official account on 9/11 highly improbable.  

While both methods demonstrate that the official account on 9/11 lacks minimal crediblity, the question arises why the US authorities have fabricated their account, what are they covering up, who exactly perpetrated the mass murder of 9/11 and how it was accomplished.  These questions are beyond the scope of this short essay.  As long as the above methodology and reasoning are not falsified, the U.S. administration would have to be suspected in covering up the crime and become the prime suspect in this crime against humanity.  The international community must demand answers and seek the truth on these horrendous events.