9/11 and Probability Theory Frank M Legge (BSc, PhD) 10 June 2008 …

9/11 and Probability Theory
Frank M Legge (BSc, PhD)
10 June 2008

Introduction
There have been a number of authors who have drawn attention to the improbability of
certain reported events that led up to the disaster that has become known as 9/11, in which
three major buildings at the World Trade Centre collapsed with heavy loss of life. Both
Boolean algebra and probability theory have been invoked as a means of estimating the
likelihood that the official explanation of the event as a whole can be relied upon.1

The official explanation for the building collapses may be distilled from the reports of the
investigations carried out by three government bodies: FEMA,2 NIST 3 and the 9/11
Commission.4

Although these three substantial investigations have taken place there is still uncertainty
about how the attack came about and what took place that day. The co-chairs of the 9/11
Commission themselves have contributed to this uncertainty with their disturbing book,
which cites difficulties that they encountered.5 There are now many scientific papers
disputing the reports and pointing out critical inconsistencies within the reports. A good
source of such papers is the Journal of 9/11 Studies.6 The present paper will not address the
probability of events said to have led up to the attack but will focus on the manner of
collapse of the twin towers. Some reference to building 7 will be included.

Discussion
The NIST report contains no calculations to explain how the towers collapsed. Improbable
though it may seem their lengthy and detailed simulation stops short at the moment when
the buildings were said to be "poised for collapse". For the collapse itself the authors rely
almost entirely on the paper by Bazant and Zhou.7 This paper provides a hint of
improbability right from the start in that it was presented just two days after 9/11, an
extraordinary feat for a complex scientific work. We will extract the stages of the collapse
from their paper:


1
 911 Review: http://911review.com/means/index.html; Global Research:
http://www.globalresearch.ca/articles/DAV504A.html
2
    Federal Emergency Management Authority Report: http://www.fema.gov/rebuild/mat/wtcstudy.shtm
3
    National Institute of Standards and Technology Report: http://wtc.nist.gov/
4
 This is an abbreviated title for the National Commission on Terrorist Attacks upon the United States:
http://govinfo.library.unt.edu/911/report/index.htm
5
  The co-chairs of the 9/11 Commission, Keane and Hamilton, have written a book in which they state that
they were denied access to essential information and given information which was incorrect. "We were set up
to fail": http://www.nyc911initiative.org/faqs.htm#top
6
    Journal of 9/11 Studies: http://journalof911studies.com/
7
    Bazant, ZP and Y Zhou: http://www.civil.northwestern.edu/people/bazant/PDFs/Papers/405.pdf
1.      The plane impact damages some columns and dislodges fireproofing material.

2.      The burning jet fuel and office material heats the columns to 800oC.

3.      The columns, weakened by heat, buckle and rapidly lose strength for a height of at
        least one storey.

4.      The top of the building above the damaged region falls freely toward the region below
        as a solid block.

5.      The impact of the falling block immediately initiates disconnection of the floor trusses
        from the columns, which permits further buckling of the columns below.

6.      The falling block, now heavier and falling more rapidly, collides with the structure
        below, repeating the damage, "and the series of impacts and failures then proceeds all
        the way down".

The only significant difference between this list and that in the NIST report is that the latter
includes, at point 3 above, the assertion that the collapse is initiated by the sagging of floor
trusses which pull the exterior columns out of alignment along part of one wall. This is not
very convincing however as their tests of floor trusses in furnaces did not result in
significant sagging. An "Application for Correction" has been submitted to NIST over this
and many other apparent errors,8 but the reply was unsatisfactory. An "Appeal" was then
lodged but no reply has been received, though it is long overdue.9 An attempt has also been
made to engage NIST in debate about the inconsistencies in their report but so far without
success. An account of this is given in a civil engineering journal.10

Alternative theory
The alternative theory, that the towers collapsed due to controlled demolition using
explosives, has been presented by numerous scientists and engineers. They list the
following evidence and conclusions:

1.      The steel in the towers never did achieve temperatures sufficient to begin collapsing.
        NIST reports that very few samples of steel showed evidence of having been at
        temperatures higher than 250oC. 3 For collapse to become a possibility the steel would
        have to be over 650oC and at that temperature it would be red-hot,11 yet no red-hot
        steel was observed prior to collapse. The NIST simulation provides charts which show
        that the steel at the time of collapse was too cool to allow collapse to occur, 3, 12 a




8
    http://journalof911studies.com/volume/200704/RFCtoNISTbyMcIlvaineDoyleJonesRyanGageSTJ.pdf
9
    http://journalof911studies.com/volume/2007/AppealLetterToNISTGourleyEtAl.pdf
10
     http://www.bentham-open.org/pages/content.php?TOCIEJ/2008/00000002/00000001/35TOCIEJ.SGM
11
   http://kovarna.webzdarma.cz/stranky/zakladni_postupy/tabulky_teplot.htm
http://hypertextbook.com/physics/waves/color/
12
     http://journalof911studies.com/articles/Article_6_Pancake_theory_false_by_NIST_WorldTradeCenter.pdf

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        conclusion which is supported by a photograph of a woman standing in the gap where
        the plane entered the north tower.13

2.      The inherent strength of the tower columns, with substantial design safety factors,
        would be too great to permit the impact of the falling top block to dislodge the storey
        below. The energy in the falling block would be all consumed in elastic and plastic
        compression of the columns before sufficient stress had been created to initiate
        buckling.14

3.      If the heated and damaged storey did start to collapse, the initial descent would not be
        rapid so there could be little impact. It is a property of steel that it becomes stronger as
        it distorts. To overcome this property, commonly known as "work hardening", the
        steel would have to become hotter.15 That would take time.

4.      If the impact had destroyed the storey below, and started a chain reaction, as in
        Bazant's theory, the collapse would have taken longer than observed. This is proved
        by application of the law of conservation of momentum.16

5.      No mechanism is presented by Bazant to explain why the impact of the falling block
        should destroy the lower portion of the building rather than the block itself. Indeed the
        assertion that the steel in the block has been heated by fires to the point of collapse, 3
        if true, would have ensured the collapse of the block.

6.      If one looks at the videos of the collapse of the north tower it is obvious that the top
        block does disintegrate first. The rigid falling block which Bazant and NIST rely upon
        to rapidly destroy the undamaged, unheated lower portion of the building ceased to
        exist, or at least was greatly reduced, before it could function as a hammer.17 This is
        however not proof that the block was very hot as other explanations are possible.

7.      The buildings came down too straight. For random unsymmetrical fires to heat the
        columns so uniformly that a building would collapse straight down is highly
        improbable. For such a thing to happen three times in one day is improbable in the
        extreme. In the case of building 7, in which the fire had virtually burned out or was
        confined to one side of the building, a straight down collapse was not merely
        improbable but impossible.18

8.      It was observed that localized heating to temperatures far higher than can be achieved
        by the burning of jet fuel and office materials occurred in the south tower. Incendiary
        materials are implicated.3, 8


13
   http://www.whatreallyhappened.com/wtc1_woman.html,
http://journalof911studies.com/volume/2007/LeggeConspiracy&Myth7b.pdf
14
     Gordon Ross: http://journalof911studies.com/articles/Journal_5_PTransferRoss.pdf
15
   Szamboti, T and F Legge:
http://journalof911studies.com/volume/200703/Sudden_collapse_initiation_impossible.pdf
16
     Kuttler, K: http://journalof911studies.com/letters/ProfKuttlerWTC1CollapseTimeCalculations.pdf
17
     http://911research.wtc7.net/wtc/evidence/videos/nt_ne.html
18
     http://journalof911studies.com/volume/2007/LeggeVerticalCollapseWTC7_6.pdf

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9.      The discovery of small iron-rich spheres in the dust provides startling evidence. The
        fact that these are spherical proves that the material was once molten, and their small
        size shows that something very violent scattered the material into the air, where it
        cooled and solidified. To be molten is further evidence for temperatures far higher
        than ordinary fires can produce. Analysis of these spheres shows that they contain
        aluminium and other elements characteristic of thermite and derivatives of thermite.
        These materials are either explosive or incendiary.19

10. The recent discovery of small particles of unreacted thermite in the dust appears to seal
    the case. This material was found in samples taken from four locations for analysis. It
    is hard to think of any innocent way in which substantial quantities of thermite and
    thermite residues could be so uniformly present in the dust.20

Comparison and Conclusion
If we compare these two explanations for the collapse of the towers it is immediately
apparent that they are different in a particularly significant way: the fire based official
explanation is a series of events,21 like links in a chain, while the explosive based
explanation is a parallel set of scientific studies of evidence. When challenged they behave
in very different ways:

If an explanation is in the form of a chain it is only necessary to prove one link wrong to
destroy the case. In contrast, with a parallel set of explanations it is only necessary to prove
one explanation correct to establish the case. What do we find?

It has already been pointed out that links 2 to 6 of the official explanation are incorrect and
link 1, about the fireproofing, has been strongly disputed.22

In the case of the alternative explanation we have a list of 10 studies which show that
certain observations can only be explained if explosives were involved. Just one of these is
enough to make the case. There are now hundreds of scientists, including architects,
engineers, demolition experts, physicists and other specialists, who are arguing that the case
for explosive demolition has been more than adequately made and who are calling for a
truly independent investigation.23

Given the devastation in the Middle East24 which flowed from this tragedy, should we not
all be calling for a new investigation? If we do not, does the evidence not suggest that we
will be at risk of being called complicit in the development of a ruthless regime by future
generations?


19
     http://journalof911studies.com/articles/WTCHighTemp2.pdf
20
     http://www.911blogger.com/node/13090?page=1
21
  Although these links in the chain are here referred to as "events" they would more properly be described as
suppositions as they are not derived from observations. No evidence is presented that the steel reached
800oC, or that a sudden gap in the structure developed.
22
     Ryan, K: http://www.journalof911studies.com/letters/b/MackeyLetter.pdf
23
   Architects and Engineers: http://www.ae911truth.org/; Scholars for 9/11 Truth and Justice:
http://www.stj911.org/index.html; Pilots for 9/11 Truth: http://www.pilotsfor911truth.org/
24
     http://onlinejournal.com/artman/publish/article_2958.shtml
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