Abstract
The authorities' version of events on September 11, 2001, is riddled with
ludicrous absurdities, suspension of the laws of physics, and vanishingly
unlikely coincidences. Although the mass media has gone along with the
official view of Muslim kamikaze pilots/hijackers, the ongoing Internet
expose of scores of problems with the suicide pilots scenario has led to
widespread recognition that it is false. Previous analyses have tended to
be qualitative rather than quantitative. By examining events whose
truth-value is closely correlated with that of a particular theory and
calculating the improbability of a false match with alternative theories,
we shall show the most likely apportionment of culpability, how the
conspiracy evolved, and what actually happened on the day. The available
evidence is more than sufficient to convict the principals in a criminal
court of law.
We find governments not guilty of conspiracy to mass murder their own
citizens, but guilty of conspiracy to wage illegal wars of aggression,
conspiracy to mass murder and maim unspecified foreign persons, conspiracy
to sacrifice their own military for profit, conspiracy to wilfully subject
hundreds of their own civilians to extreme danger to life and limb, culpable
negligence in failing to protect thousands of their civilians from death and
injury, and accessory to mass murder.
The Bush Administration was directly responsible for the Pentagon incident,
the state of Israel approved and organised the flying of planes into the
WTC, and a powerful real estate consortium arranged the demolition of three
skyscrapers. The recommendation is not that members of some specific race
be persecuted or exterminated, but that Lord Acton's famous maxim is so
important that civilisation is unlikely to endure short of a wholesale
reform of traditional institutions and organisation.
Methodology
We select two theories to weigh against each other, where we suspect that
Theory F is false and Theory T is true. It is assumed that Theories F and
T cannot both be true, although they could both be false. Specifically, we
are considering the truth or falsehood - the truth-value - of alternative
conflicting theories concerning the identities of the perpetrators of 9/11.
There will exist a particular set of events whose truth-value is very
closely correlated with that of a selected theory.
For example, if the official account of 9/11/01 events is true, then
it is associated with a set of events which are an integral part of the
theory and hence explicable. If an alternative theory is true, then another
set of events are likely to be true, having been generated by a causal
process inherent to the latter theory. Either way, events with a unique
causal link to the true theory are likely to occur, and if that theory were
false then those events could only occur as a result of a random generating
process and so would be very improbable.
Events must satisfy two conditions to quality for inclusion in the set with
a very closely correlated truth-value: (i) They are likely to have occurred
if Theory T is true (e.g. P greater than 0.1). (ii) They are very unlikely
to have occurred if Theory T is false (e.g. P less than 0.001), irrespective
of whether Theory F is true or false.
Let Theory F be the official version of events "Bin Laden Incited a Rabid
Satanism" (BLIARS), and let Theory T be "Operation Snowball" - the true
events of 9/11. (Once the conspiracy started rolling, it grew to a
magnitude totally out of proportion to the original plot. And those who
signed up to the original, limited casualties scheme hadn't a snowball in
hell's chance of turning back the tide.) Asking the question, "Did a flying
object hit the Pentagon on 9/11?" would not be useful, since it fails to
distinguish between alternative theories as to the perpetrators. The
question, "Did Flight 77, a Boeing 757, hit the Pentagon on 9/11?" is
useful, since this does distinguish between theories. The ideal type of
question would both distinguish between theories and feature an undeniable
event, such as, "Did three steel-framed skyscrapers collapse on 9/11?"
For a series of preselected independent events, the probability for all
events to occur is equal to the product of the individual probabilities for
each event to occur. However, when we become aware of a number of unlikely
occurrences after the event, these events have necessarily been selected
from a larger set of world events, many of which may be quite normal. Thus,
in such a case, the probability of the series may be considerably greater
than the product of the individual probabilities. The improbability will be
diluted to a degree which is determined by the size of the larger set, and
by the number of improbable events under analysis.
Acausal coincidences are regularly reported, such as X answering a ringing
telephone booth and finding Y is trying to phone X but dialled the wrong
number. Intuitively, such events can seem more frequent than chance would
dictate. In fact, the set of events is so vast that such improbable events
are included and their occurrence is consistent with a random generating
process. But we are concerned with a specific set of events that relate to
the identities of the 9/11 perpetrators. Since the truth-value of each
event must have a sufficiently high degree of positive correlation with that
of Operation Snowball, the set of events is very limited.
The argument approaches a reductio ad absurdum, if we consider Operation
Snowball as the conclusion and the set of positively correlated events as
the premises. When we assume BLIARS to be true and Snowball false, the
series of Snowball-correlated events approaches but stops short of
impossibility. In a criminal investigation, guilt can never be proven to
the same degree of certainty as our knowledge that two and two is four or no
mammals are cold-blooded. Witnesses can lie; 'evidence' can be planted.
But, as we shall calculate below, given the limited size of the set into
which dilution of the historical improbable series has occurred, the series
can remain sufficiently improbable to furnish a reliable criminal
conviction. When BLIARS is assumed to be false and Snowball true, the
series of events turns from almost impossible to very reasonable. (The
events within the series will only have dependent probabilities if the
truth-values of Snowball and BLIARS are in a floating state. When we define
one or the other as true then the probabilities are independent and they may
be multiplied prior to the necessary correction for being selected after the
event.)
In the case of 9/11, the guilt of the principal perpetrators can be proven
to at least the same degree of certainty as a case involving DNA profiling
and multiple corroborative evidence.
Calculating the corrected probability
In order to demonstrate how the improbability of a series of improbable
events is diluted as elements are added to the set containing the series,
it will be useful to consider random number generators with integer outputs
from 00 to 99, or 000 to 999 etc. The output range corresponds to a sample
space of weighted outcomes, and the state of a particular digit denotes the
truth-value of a particular event. The findings will indicate whether it is
worth taking into account dozens of anomalies or more useful to concentrate
on a few highly aberrant events.
Suppose there are two independent events whose probability is 0.1 or 1 in
10. If these were the only two events in the set, the sample space of all
possibilities could be represented by the random generation of a two-digit
number. "0" denotes an occurrence; "N" denotes anything from 1-9 and
non-occurrence; "A" denotes any outcome from 0-9. So occurrence of both
events requires a 00 and has 0.01 or 1 in 100 probability as expected.
If the set contains three events, the possibilities for at least two
probability 0.1 events includes 00N, 0N0, N00 and 000 which is 3 x 9 + 1
= 28 from a total of 1,000 possibilities. With a four-element set, the
10,000 combinations offers 00NN, 0N0N, 0NN0, N00N, N0N0, NN00, 000N, 00N0,
0N00, N000, and 0000 which is 6 x 9 ^ 2 + 4 x 9 ^ 1 + 1 x 9 ^ 0 = 523. A
five-element set offers 00NNN, 0N0NN, 0NN0N, 0NNN0, N00NN, N0N0N, N0NN0,
NN00N, NN0N0, NNN00, 000NN, 00N0N, 00NN0, 0N00N, 0N0N0, 0NN00, N000N, N00N0,
N0N00, NN000, 0000N, 000N0, 00N00, 0N000, N0000, 00000 which totals
10 x 9 ^ 3 + 10 x 9 ^ 2 + 5 x 9 ^ 1 + 1 x 9 ^ 0 = 8,146 from 100,000.
A six-element set offers 00NNNN, 0N0NNN, 0NN0NN, 0NNN0N, 0NNNN0, N00NNN,
N0N0NN, N0NN0N, N0NNN0, NN00NN, NN0N0N, NN0NN0, NNN00N, NNN0N0, NNNN00,
000NNN, 00N0NN, 00NN0N, 00NNN0, 0N00NN, 0N0N0N, 0N0NN0, 0NN00N, 0NN0N0,
0NNN00, N000NN, N00N0N, N00NN0, N0N00N, N0N0N0, N0NN00, NN000N, NN00N0,
NN0N00, NNN000, 0000NN, 000N0N, 000NN0, 00N00N, 00N0N0, 00NN00, 0N000N,
0N00N0, 0N0N00, 0NN000, N0000N, N000N0, N00N00, N0N000, NN0000, 00000N,
0000N0, 000N00, 00N000, 0N0000, N00000, 000000 which totals 15 * 9 ^ 4 +
20 * 9 ^ 3 + 15 * 9 ^ 2 + 6 * 9 ^ 1 + 1 * 9 ^ 0 = 114,265 from 1,000,000.
With 4 events from a set of nine, for example, there are 126 combinations of
four zeros and five Ns, 126 of five zeros and four Ns, 84 of six zeros and
three Ns, 36 of seven zeros and two Ns, 9 of eight zeros and a single N, and
one combination of nine zeros. Allowing for the descending powers of nine,
this totals 8,331,094 combinations from a sample space of one billion.
With 2 improbable events from a set of three, the probability is increased
from 0.01 by a factor of 2.8; with 2 from 4 the multiplying factor is 5.23;
with 2 from 5 it is 8.146; with 2 from 6 it is 11.4265. In the previous
paragraph's example of 4 events from 9, the probability increases by a
factor of 83.31094 as a result of the five additional elements.
For our purposes, a useful approximation can be obtained from the formula
for the number of combinations of n elements taken r at a time, where:
n!
nCr = -------------
r! * (n - r)!
n is the number of elements or events in the set
r is the number of selected improbable events within the set.
Multiply the unadjusted probability of the series of events by nCr, or
divide its reciprocal the unadjusted improbability by nCr, in order to
obtain an adjusted measure which allows for the other elements of the set.
These elements, consisting solely of events which meet the positive
correlation of truth-value qualifications, would include events not
conceived of and others that failed to occur.
The error introduced by this approximation exaggerates the dilution of
improbability with increasing n, which biases in favour of the BLIARS theory
by reducing its improbability. For example, allowing the combinations 00A,
0A0 and A00 ("A" being any outcome from 0 to 9) suggests 3 x 10 = 30 from
1,000, but this incorrectly counts 000 three times, The accurate but more
complex method above (with the algorithm outlined two paragraphs below)
shows the r=2, n=3 case comprising 00N, 0N0, N00 and 000 which is really 28
from 1,000 combinations. However, the error reduces as the number base B of
our thought experiment random generator increases. If we concentrate on a
few improbable events with probabilities of less than 1 in 10,000, each
digit of the random number has over 10,000 possibilities.
Provided the number base B remains high, the nCr approximation remains
considerably more accurate than our estimate of the probability of each
event or the size n of the set. This holds for larger values of r, the
number of selected improbable events. For example, suppose we have four
events assumed to be of equal probability, and the product of their
probabilities is 1 / (3.2 * 10 ^ 25). We set B equal to the fourth root of
3.2 * 10 ^ 25, and find that the approximation is exaggerating the
improbability dilution by only some 0.0000336% for every element in the set
in excess of four. (0.0000336% being about 80% of the reciprocal of the
fourth root of 3.2 * 10 ^ 25,)
The more precise calculation is obtained from a series with descending
powers of B. In fact, we needn't expand (B - 1). Input the variables B, n
and r, and the number of combinations is totalled by summing the number of
combinations of each power of (B - 1). Start with (B - 1) ^ (n - r)
multiplied by nCr for the actual values of n and r. Then for each
subsequent iteration r is incremented by one until r = n. The accumulated
total of all iterations yields the total number of combinations. This total
is then multiplied by B ^ (r - n) which compensates for the larger sample
space, to obtain the actual factor for division of improbability or
multiplication of probability.
Input B
Input n
Input r
Set grossimprob to B ^ r
Set combinations to zero
For iteration is r to n
a is n
Call factorialcalculator
nfact is factorial
a is iteration
Call factorialcalculator
rfact is factorial
a is n - iteration
Call factorialcalculator
nmrfact is factorial
nCr is nfact / (rfact * nmrfact)
combinations is combinations + (B - 1) ^ (n - iteration) * nCr
Endfor
Set truedilutionfactor to combinations * B ^ (r - n)
Print "True dilution factor ="; truedilutionfactor
Print "True probability = 1 in"; grossimprob / truedilutionfactor
Run
factorialcalculator
factorial is 1
For integer is 1 TO a
factorial is factorial * integer
Endfor
Return
We shall make use of another approximation which allows us to apply either
of the above formulae to the complete set of events, eliminating the need
to split events of various probability into alternative sections and apply
the formulae to each section in turn: Let the product of the individual
probabilities of the selected improbable events be P, and the number of
selected improbable events be r. Then the probability of each improbable
event is assumed to be the rth root of P, and denoted by B.
This approximation also biases in favour of BLIARS. Consider an example of
two 1 in 100 events and two 1 in 10000 events in a set of ten. If we do the
calculation for four 1 in 1000 events in a set of ten, the nCr approximation
indicates an improbability dilution of 210, since if n = 10, r = 4, then
nCr = 210. The unadjusted probability of 1 in 10 ^ 12 is increased to
1 in 4.7619 * 10 ^ 9. Using the exact algorithm, it is actually
1 in 4.7848 * 10 ^ 9, with the nCr approximation exaggerating the
improbability dilution. Now compare with the actual case of two 1 in 100
events in a set of five along with two 1 in 10000 events in another set of
five. For the two 1 in 100 events the improbability dilution is 9.801496 by
the exact method, and for the two 1 in 10000 events it is 9.99800015. So
the additional six elements has raised the probability from 1 in 10 ^ 12 by
a factor of nearly 100, with the corrected probability at
1 in 1.020456495 * 10 ^ 10. The nCr approximation indicates a factor of 10
for each set of five, i.e. 100 in all and a corrected probability of
1 in 10 ^ 10. So the equal probabilities (EP) approximation has raised the
corrected probability by a factor of more than two, the nCr approximation
raised it by a little over 2%, and applying both exaggerated the dilution of
improbability by a little more than application of the EP alone.
To summarise why the EP approximation exaggerates dilution of improbability,
in the above paragraph 210 is greater than 10 squared. For some given
values of n and r, a doubling of both will result in nCr increasing to
rather more than its square.
The critic might consider that if we are going to split into sections for
different probabilities, then maybe the higher probability events (being
more commonplace) should take up more than half of the total set, and
perhaps this would favour the BLIARS theory and show that the EP
approximation is not kind to the BLIARS theory after all. It's a sound
approach. Let's suppose we have two 1 in 100 events from a set of six and
two 1 in 10000 events from a set of four. Firstly, for the two 1 in 100
events from a set of six, the exact algorithm shows that the actual dilution
factor is 14.60447605. Then, for the two 1 in 10000 events from a set of
four, the exact method shows the dilution factor is 5.99920003. The product
of the two is only 87.61517316 compared to 97.99535848 or greater before.
An unequal split lowers dilution and probability and raises improbability.
Hence, it does not help the BLIARS theory, the equal split EP does instead!
So we imagine a random number generator with the number base B being the
reciprocal of the rth root of P. A '0' is required to denote the occurrence
of an improbable event. Since each digit has over 10,000 variations, 'A'
(any outcome) is very nearly equal to 'N' (any outcome but '0'), and the
dilution of improbability is obtained fairly accurately from the approximate
formula below:
The corrected probability for the series of improbable events, after
allowing for the extra elements in the set, is given by
P * n!
Pdiluted = -------------
r! * (n - r)!
where P is the product of the individual probabilities of unlikely events
n is the number of elements or events in the set
r is the number of selected improbable events within the set.
or
Pdiluted = P * nCr
with many calculators carrying the nCr function.
To conclude, our approach will analyse a few very low probability events
rather than a large quantity of fairly low probability events. The latter
would require the more complex algorithm to compute improbability dilution
to sufficient precision, identification of additional anomalous events, and
in any case would establish guilt to a lower degree of certainty. Given
that we assume that the total number n of elements in the set is more than
twice the number r of selected improbable events (which we do), it follows
that for a given product of probabilities P, any increase in r will increase
the dilution of improbability. Also, increasing r to include higher
probability events with a lower correlation with the test theory's
truth-value implies that we should assume a greater value for n, which would
further dilute the improbability.
Identification of large numbers of anomalies has already been achieved on
numerous websites to provide interesting qualitative analyses. Our approach
can identify the guilty parties with a confidence factor approaching
certainty, whilst using a readily available algorithm provided in many
scientific calculators.
The official BLIARS version of events
Several years after the event, websites continue to flourish and papers
continue to emerge. Some sites detail well over 100 problems with the
BLIARS version of events. Fortunately, we need not estimate improbabilities
for every aspect of the story.
According to BLIARS, on the morning of September 11, 2001, 19 Arab hijackers
took over four planes and in three cases successfully navigated and steered
the planes into their targets. Three New York skyscrapers collapsed as a
result of fires after planes hit two of them, a third plane damaged the
Pentagon, and a fourth crashed into the ground at Shanksville, Pennsylvania
following a revolt by passengers. The hijackers were armed with box cutters
and plastic knives which they had smuggled on board. They had also managed
to bring a gun and a bomb on Flight 93, and gas canisters and possibly a gun
on Flight 11. According to some reports, they had also smuggled electronic
navigation units on board.
In all cases, the hijackers managed to take control of the plane without the
pilot or co-pilot being able to type in the four-digit piracy distress code
to warn ground control of a hijacking, the hijackers managed to switch off
the plane's transponder, they managed to avoid being photographed by any
airport CCTVs when embarking at Boston, Dulles or Newark, they managed to
avoid being listed in any of the passenger manifests, and they managed to
evade any defensive response by the mighty US Air Force. (July 2004 update
below, regarding "Dulles hijackers video".)
The operation was masterminded by Osama Bin Laden, a wealthy, brilliant but
evil Muslim terrorist whose ambition appears to be world domination and the
elimination of "freedom". Alternative accounts hold that Saddam Hussein was
a key conspirator.
The authorities said that they "didn't see this one coming", it was
"something we had never even thought of", and "there were no warning signs".
Nonetheless, within hours, the valiant vigilant FBI knew who did it. Cell
phone calls from the doomed aircraft passengers, including Barbara Olson the
US solicitor general's wife, provided some of the first hard evidence
pointing to Muslim terrorism. By 9 p.m. on the day of the hijackings,
police and FBI agents towed a white Mitsubishi Mirage, rented by Mohamed
Atta and used by five of the hijackers, which had been found at Boston's
Logan Airport containing incriminating evidence such as an Arabic language
flight manual. At 11 p.m. that day, a blue Nissan Altima also rented by
Atta was found at Portland International Airport, Maine, and towed away four
hours later. (ABC News of September 12.) Within a day of the hijackings,
the slightly charred passport of hijacker Satam Al Suqami was found in the
World Trade Centre rubble. FBI press releases of September 14th and 27th
each included the same list of 19 hijackers' names.
July 2004 update: We are addressing the official story as of the first half
of 2004. If the official story changes almost three years after the fact to
include a "surveillance video" that has suddenly emerged, this does not
merit a lengthy response. If CCTV had recorded any hijackers at Boston,
Washington or Newark, there is no doubt that media outlets would have
broadcast images within a matter of days or hours. It took just two to six
months to produce the animation for each episode of the highly acclaimed
series "Walking with Dinosaurs", so allowing three years to fake a security
video is rather like allowing a candidate three years to write in the
answers to a two-hour exam, given unlimited access to computers and the
answer paper. The grainy "Dulles hijackers surveillance video" lacked time
and date stamps, yet the authorities still claimed to know the time of each
section, to the minute.
At the alleged time of the hijackers' security checks, 07:18 on 9/11 which
was half an hour after sunrise at Dulles airport, the solar elevation angle
was only 5.1 degrees. At solar noon, 13:06 local time, the elevation angle
was 55.4 degrees. Thus, at 07:18 an object would have cast a shadow 11.2
times its height (from 1 / tan [5.1 deg.]), and 16.2 times longer than its
13:06 true noon shadow. The natural light intensity at 07:18 was 9.26 times
lower than it was at 13:06 (from sin [5.1 deg.] / sin [55.4 deg.]).
Washington weather records also show that there was some cloud around from
06:51 to 07:51. Judging by the video's brilliance of light streaming in
through the airport entrance and shortness of shadows cast by cabs, the
forgers not only failed to fake the video at the right time of day, they
also produced it close to the summer solstice in late June, which would
concur with its July broadcasting.
October 2004 update: Just four days before the US elections, a video of
"Osama Bin Laden" conveniently appeared on TV. This is a man said to be
living in a cave in mountains near the Pakistan / Afghanistan border, yet
the video's background suggests that the recording was made in a TV studio.
US intelligence services claimed to know exactly where he is; they "just
can't get him". In that case, why not blockade the area and prevent
movement of supplies? "Bin Laden" or the actor playing him admitted
responsibility for 9/11 - why wait for over three years? The forgers should
have shot the video on location, say somewhere like the Rockies or
Appalachian range. Or in a Hollywood studio they could at least have used
cardboard cutouts of a mountainous panorama, as in early westerns or
children's TV.
The BLIARS theory vs Gross Incompetence / Bush Administration Complicity
The BLIARS theory itself implies gross incompetence and a massive cover-up.
Let's consider some of the problems with BLIARS that might be resolved by
substituting an incompetence theory which retains the Muslim kamikaze
kernel.
The nineteen named hijackers: The problem here is that at least eight of
these 19 "suicide hijackers" had turned up alive and well by September 23,
2001, plus a ninth by September 29, having mostly been in Saudi Arabia at
the time of the attacks. It didn't stop the FBI from releasing the same 19
names on September 27 that they had already released on the 14th. They
would not let facts get in the way of a good story.
Authorities had never conceived of planes being used as bombs:
Unfortunately for this claim, the FBI and CIA had been aware since 1995 of
plans to simultaneously hijack several planes with the options of blowing
them up over the Pacific or crashing them into targets in the US such as the
World Trade Centre. In the weeks leading up to 9/11, the US government
received intelligence from Egypt, France, Iran, Israel, Russia and other
sources, warning of an imminent attack. Some of these warnings were
specifically about hijacked airplanes to be used against buildings. And the
National Reconnaissance Office (NRO), based in Chantilly, Virginia and
intrinsically entangled with the CIA and the Department of Defense (DoD),
had scheduled an exercise starting at 9:00 on September 11, 2001, involving
an aircraft hitting one of its buildings.
There were also a number of wargames operating simultaneously, controlled by
Dick Cheney: Vigilant Guardian, Vigilant Warrior, Northern Guardian,
Northern Vigilance, and Tripod II. The first three were all to do with
hijacked airplanes in NE US airspace. Some of these drills were live-fly
exercises with remote-controlled planes, simulating the behaviour of
hijacked airliners and coinciding with the alleged start of the "Arab
hijackings".
US Air Force defences stand down: This has been well documented. The
world's most powerful air force routinely intercepted commercial or civilian
planes that strayed off course as part of its standard operating procedures,
whenever the problem could not be resolved through radio contact. From
September 2000 to June 2001, for example, jet fighters were scrambled 67
times. Major Douglas Martin, a NORAD spokesman, said that an order must be
given by President Bush or Donald Rumsfeld prior to the ultimate response of
shooting down a suspect plane. However, the preliminary measures of
scrambling, intercepting, attracting the errant pilot's attention by rocking
the fighter's wingtips or passing in front of the plane or firing tracer
rounds in its path, would require no such order.
The BLIARS version of events evolved in the days immediately following 9/11,
as the Bush Administration floated various cover stories. On September 13
General Richard Myers claimed that fighter jets had not been scrambled until
after the Pentagon was hit. Later revisions held that fighters had in fact
been scrambled from Otis ANG Base, Cape Cod, Massachusetts at 8:52, and from
Langley AF Base at 9:30, seven minutes before the Pentagon was hit. In
these versions, fighter jets were scrambled, but arrived too late because
inexplicably they only flew at some 25% of their maximum speed, and the
Andrews AF Base which is supposed to maintain a ready response force and is
only 10 miles from Washington DC, did not have fighters available.
BLIARS maintains that at 8:20 AA Flight 11's transponder was turned off, and
at 8:25 two flight attendants had alerted American Airlines, and Boston air
traffic control had heard a hijacker saying, "We have some planes. Just
stay quiet and you will be OK." Since it was not until about 9:37 that AA
77 struck the Pentagon and UA 93 did not crash near Shanksville until around
10:06, the authorities had over an hour's warning that hijackings were in
progress. Yet whichever cover story we assume, the response was too little
too late.
Widespread scattering of Flight 93 wreckage: Part of the wreckage including
engine and body parts was found eight miles from the main crash site, with
more debris at a location six miles distant. According to the BLIARS
account, debris might have been blown eight miles by the wind. Yet
windspeed was only around 10mph on the day. A light breeze is hardly likely
to blow engine parts and body parts up out of a crater and over a distance
of eight miles. And if so, there would be a continuous debris field, rather
than debris concentrated at three main sites. Eyewitnesses heard
explosions, saw a fireball and white smoke coming from the plane before the
impact, and saw a second white jet nearby when the Boeing 757 came down.
Thus, the evidence is indicative of the plane having been shot down, and
inconsistent with the story of the "passengers' revolt" - which had shades
of the Jessica Lynch POW "plucky damsel rescued from sadistic Iraqis" myth.
Cell phone calls: These are extremely unreliable at altitudes and
velocities anywhere near to the typical Boeing 757 and 767 cruising altitude
of 35000 feet or cruising speed of 530 mph. At high altitudes the signal is
attenuated such that a successful connection is highly improbable. It is
now claimed that more than 30 phone calls were made from Flight 93, lasting
up to 26 minutes, and mostly through mobile cell phones. Why would
terrorists allow passengers to make calls which might jeopardise the
mission? With four terrorists on UA 93, one (Jarrah) remained in the
cockpit leaving three to subjugate the passengers with the aid of knives,
box cutters, a gun, and a device with wires that was said to be a bomb.
Let's suppose the chance of a successful connection via cell phones is 1 in
20. What is the probability of at least 20 successful connections from 100
attempts? The undiluted probability is 1 in 20 ^ 20 = 1 in 1.05 * 10 ^ 26.
Since the improbability of each event is only 20 and nCr for n = 100, r = 20
is very high at over 10 ^ 20, the nCr approximation grossly exaggerates the
improbability diluting effect of the 80 failed connections.
Using the
nCr approximation, then
Pdiluted = (1 in 1.05 * 10 ^ 26) * (nCr for n = 100, r = 20)
= (1 in 1.05 * 10 ^ 26) * 5.36 * 10 ^ 20 = 1 in 195,630
A calculation using the exact algorithm shows the nCr approximation has
over-corrected in this case by a factor of nearly 50. The actual
probability, after assuming 80 unsuccessful attempts to call, is only around
1 in 9,503,036.
Alternatively, suppose there were only 13 successful cell phone calls from
100 attempts, but the probability of a successful connection is only 1 in
100. The uncorrected probability is 1 in 100 ^ 13 = 1 in 10 ^ 26.
Multiplying this by nCr for n = 100, r = 13, the adjusted probability
becomes 1 in 1.41 * 10 ^ 10. An exact calculation shows this to be within
an order of magnitude, since the actual probability is 1 in 3.16 * 10 ^ 10
after assuming 87 failed connections.
The serendipity of incriminating evidence immediately after 9/11. Luckily
for the authorities, a driver at Boston's Logan airport just happened to
have an argument over a parking space with several Arabic-looking men.
Improbable cell phone calls had provided the first evidence of an Arabic
connection. The non-Arabic driver heard the news and contacted the
authorities, who subsequently found an Arabic flight manual inside the
abandoned white Mitsubishi. It was quickly discovered that the offending
vehicle had been rented by Mohamed Atta.
Atta was the only passenger (of 81 aboard Flight 11) whose luggage didn't
make the flight. One bag contained a leather-bound Koran, a navy suit and a
bottle of cologne. The other contained a videotape and flight manual for a
Boeing 757, an Arab-English dictionary, and a manual slide-rule device known
as a "flight computer".
Continue to Preposterous Passport "Discovery"