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WTC Towers: The Case For Controlled Demolition
By Herman Schoenfeld In this article we show that "top-down" controlled demolition accurately accounts for the collapse times of the World Trade Center towers. A top-down controlled demolition can be simply characterized as a "pancake collapse" of a building missing its support columns. This demolition profile requires that the support columns holding a floor be destroyed just before that floor is collided with by the upper falling masses. The net effect is a pancake-style collapse at near free fall speed. This model predicts a WTC 1 collapse time of 11.38 seconds, and a WTC 2 collapse time of 9.48 seconds. Those times accurately match the seismographic data of those events.1 Refer to equations (1.9) and (1.10) for details. It should be noted that this model differs massively from a "natural pancake collapse" in that the geometrical composition of the structure is not considered (as it is physically destroyed). A natural pancake collapse features a diminishing velocity rapidly approaching rest due to the resistance offered by the columns and surrounding "steel mesh". DEMOLITION MODEL A top-down controlled demolition of a building is considered as follows 1. An initial block of j floors commences to free fall. 2. The floor below the collapsing block has its support structures disabled just prior the collision with the block. 3. The collapsing block merges with the momentarily levitating floor, increases in mass, decreases in velocity (but preserves momentum), and continues to free fall. 4. If not at ground floor, goto step 2. Let j be the number of floors in the initial set of collapsing floors. Let N be the number of remaining floors to collapse. Let h be the average floor height. Let g be the gravitational field strength at ground-level. Let T be the total collapse time. Using the elementary motion equation distance = (initial velocity) * time + 1/2 * acceleration * time^2 We solve for the time taken by the k'th floor to free fall the height of one floor [1.1] t_k=(-u_k+(u_k^2+2gh))/g where u_k is the initial velocity of the k'th collapsing floor. The total collapse time is the sum of the N individual free fall times [1.2] T = sum(k=0)^N (-u_k+(u_k^2+2gh))/g Now the mass of the k'th floor at the point of collapse is the mass of itself (m) plus the mass of all the floors collapsed before it (k-1)m plus the mass on the initial collapsing block jm. [1.3] m_k=m+(k-1)m+jm =(j+k)m If we let u_k denote the initial velocity of the k'th collapsing floor, the final velocity reached by that floor prior to collision with its below floor is [1.4] v_k=SQRT(u_k^2+2gh) which follows from the elementary equation of motion (final velocity)^2 = (initial velocity)^2 + 2 * (acceleration) * (distance) Conservation of momentum demands that the initial momentum of the k'th floor equal the final momemtum of the (k-1)'th floor. [1.5] m_k u_k = m_(k-1) v_(k-1) Substituting (1.3) and (1.4) into (1.5) [1.6] (j + k)m u_k= (j + k - 1)m SQRT(u_(k-1)^2+ 2gh) Solving for the initial velocity u_k [1.7] u_k=(j + k - 1)/(j + k) SQRT(u_(k-1)^2+2gh) Which is a recurrence equation with base value [1.8] u_0=0 The WTC towers were 417 meters tall and had 110 floors. Tower 1 began collapsing on the 93rd floor. Making substitutions N=93, j=17 , g=9.8 into (1.2) and (1.7) gives [1.9] WTC 1 Collapse Time = sum(k=0)^93 (-u_k+(u_k^2+74.28))/9.8 = 11.38 sec where u_k=(16+ k)/(17+ k ) SQRT(u_(k-1)^2+74.28) ;/ u_0=0 Tower 2 began collapsing on the 77th floor. Making substitutions N=77, j=33 , g=9.8 into (1.2) and (1.7) gives [1.10] WTC 2 Collapse Time =sum(k=0)^77 (-u_k+(u_k^2+74.28))/9.8 = 9.48 sec Where u_k=(32+k)/(33+k) SQRT(u_(k-1)^2+74.28) ;/ u_0=0 REFERENCES "Seismic Waves Generated By Aircraft Impacts and Building Collapses at World Trade Center ", http://www.ldeo.columbia.edu/LCSN/Eq...C_LDEO_KIM.pdf APPENDIX A: HASKELL SIMULATION PROGRAM This function returns the gravitational field strength in SI units. g :: Double g = 9.8 This function calculates the total time for a top-down demolition. Parameters: _H - the total height of building _N - the number of floors in building _J - the floor number which initiated the top-down cascade (the 0'th floor being the ground floor) cascadeTime :: Double - Double - Double - Double cascadeTime _H _N _J = sum [ (- (u k) + sqrt( (u k)^2 + 2*g*h))/g | k-[0..n]] where j = _N - _J n = _N - j h = _H/_N u 0 = 0 u k = (j + k - 1)/(j + k) * sqrt( (u (k-1))^2 + 2*g*h ) Simulates a top-down demolition of WTC 1 in SI units. wtc1 :: Double wtc1 = cascadeTime 417 110 93 Simulates a top-down demolition of WTC 2 in SI units. wtc2 :: Double wtc2 = cascadeTime 417 110 77 |
#2
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This posting doesn't rhyme.
Please rephrase so it rhymes. |
#3
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In article ,
wrote: WTC Towers: The Case For Controlled Demolition By Herman Schoenfeld In this article we show that "top-down" controlled demolition accurately accounts for the collapse times of the World Trade Center towers. A top-down controlled demolition can be simply characterized as a "pancake collapse" of a building missing its support columns. This demolition profile requires that the support columns holding a floor be destroyed just before that floor is collided with by the upper falling masses. The net effect is a pancake-style collapse at near free fall speed. This model predicts a WTC 1 collapse time of 11.38 seconds, and a WTC 2 collapse time of 9.48 seconds. Those times accurately match the seismographic data of those events.1 Refer to equations (1.9) and (1.10) for details. Right! It *was* a man-made, top-down demolition. It started from the top and a Islamist pilot of a hijacked 757/767 caused it. In this video, Jowenko, a demolition expert, eplains wht WTC1 and 2 WERE NOT caused by demolition explosives: http://www.youtube.com/watch?v=EkZMQ...elated&search= http://jowenko.nl/ -- Meet the Creators of "Loose Change" http://youtube.com/watch?v=Zs5jWvu4tR8 Meet the Scholars for 9/11 Truth http://youtube.com/watch?v=T6fe9YlHQwA Ground Zero 911 Conspiracy Wars by Ray Rivera http://rayrivera.net http://video.google.com/videoplay?do...15283354424113 The Ground Zeros by Mark Roberts http://video.google.com/videoplay?do...37229146&hl=en WTC Ground Zero 9/11/2007 Sad. http://www.youtube.com/watch?v=Qr2LeCXXIjo Les Jamieson and others of NY911Truth.org disparages the FDNY http://wtc7lies.googlepages.com/ny91...ragethefdnyatg How famous Truth Movement people repond to unfortunate truths that show them for what they are http://wtc7lies.googlepages.com/semi...antasizeaboutt The Naudet Film about 9/11 at WTC http://video.google.com/videoplay?do...12957&q=Naudet Marks's collapse video http://video.google.com/videoplay?do...95848233&hl=en "The 9 - 11 Conspiracies - Fact or Fiction" http://www.torrentbox.com/torrent_details?id=125450 Anyone that hasn't seen WTC's Ground Zero in NYC and the "Truth Movement" kooks that hang out there should look at the first three videos. The others should be required viewing by anyone that has an opinion about 9/11 and WTC or has never been to NYC. Here's an interview in which Jowenko says that WTTC7 could only fallen as it did with massive preperation http://www.youtube.com/watch?v=QajDx...elated&search= This video shows demolitions and preperation. http://www.youtube.com/watch?v=hnqHLoa-ml8 Jowenko WTC7 Demolition Interviews, 1 of 3 7 minutes http://www.youtube.com/watch?v=k3DRh...eature=related Jowenko WTC7 Demolition Interviews, 2 of 3 (7 minutes) http://www.youtube.com/watch?v=sep-H...eature=related Jowenko WTC7 Demolition Interviews, 3 of 3 (8 minutes) http://video.google.com/videoplay?do...31148229700505 -- Al Dykes News is something someone wants to suppress, everything else is advertising. - Lord Northcliffe, publisher of the Daily Mail |
#4
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![]() Controlled Demolition? - Rubbish . . . http://www.popularmechanics.com/tech...w/1227842.html http://www.sciencedaily.com/releases...0612152114.htm http://www.time.com/time/magazine/ar...531304,00.html |
#5
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![]() A Huge, Invisible Monster , moving north to south., and detouring into New York harbor caused the Towers to collapse; - But first, he threw two airplanes , one into each tower.. Look at the images of NY harbor after the attack; You can see his footprints.. & The Math I've done supports this theory . . http://www.youtube.com/watch?v=gH02Eh44yUg On Mar 13, 10:06 am, barnegatdx wrote: Controlled Demolition? - Rubbish . . . http://www.popularmechanics.com/tech...w/1227842.html http://www.sciencedaily.com/releases...0612152114.htm http://www.time.com/time/magazine/ar...531304,00.html |
#7
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Godzilla wouldn't do anything like that.Three of my little doggys half a
dozen or so, rubber squeaky doggy toys are Godzilla toys, I buy them at the pet store.Godzilla is harmless. cuhulin |
#8
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barnegatdx wrote:
A Huge, Invisible Monster , moving north to south., and detouring into New York harbor caused the Towers to collapse; - But first, he threw two airplanes , one into each tower.. Look at the images of NY harbor after the attack; You can see his footprints.. & The Math I've done supports this theory . . http://www.youtube.com/watch?v=gH02Eh44yUg Thank God....someone finally speaking truth. |
#9
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"barnegatdx" wrote in message
... snip On Mar 13, 10:06 am, barnegatdx wrote: Controlled Demolition? - Rubbish . . . http://www.popularmechanics.com/tech...w/1227842.html That propaganda shill rag Popular Mechanics actually bowed out of a discussion that they couldn't win when, in a live interview, they got caught in a completely absurd fabrication. Listen to this interview: http://www.youtube.com/watch?v=WULRQCgvsdE ---------------------------- SIMPLE PHYSICS EXPOSES THE BIG 9/11 LIE - GOVERNMENT BUILDING COLLAPSE EXPLANATION FAILS REALITY CHECK On September 11, 2001, the world watched in horror as the World Trade Center (WTC) Twin Towers collapsed, killing thousands of innocent people. Videos of the collapses were replayed ad nauseam on TV for days. About 5 hours after the towers fell, WTC building 7 also collapsed suddenly, completely, and straight down at near free-fall speed. This steel-framed building was not touched by the planes that struck the towers, and had sustained relatively minor debris damage and small fires. Nearby buildings far more heavily damaged remained standing. In June 2005, in an apparent response to an article by Morgan Reynolds, former CIA Director and current Secretary of Defense Robert Gates stated, "The American people know what they saw with their own eyes on September 11, 2001. To suggest any kind of government conspiracy in the events of that day goes beyond the pale." We will prove here, with scientific rigor, that it's the government's tale that's "beyond the pale"! Did most of the American people really understand the unprecedented phenomena they had witnessed? Could a lack of knowledge of physics, and the emotional shock of this mass-murderous "terrorist attack" have stymied objective thinking and led to the blind acceptance of authoritarian assertions? The government and the media TOLD US what we saw. The government told us that we had witnessed a "gravitational" collapse; what is now referred to as a "pancake collapse". According to the government claims, the plane crashes and subsequent kerosene (like lamp oil - jet fuel is NOT exotic) fires heated the UL-certified structural steel to the point where it was significantly weakened, which is very difficult to believe, never mind repeat in an experiment. Even with massive fires that incinerate everything else, the steel frames of such buildings generally remain standing. According to the "pancake theory", this purported (all physical evidence was quickly and illegally destroyed) weakening supposedly caused part of the tower to collapse downward onto the rest of the tower, which, we've been repeatedly told, somehow resulted in a chain reaction of the lower floors sequentially, one at a time, yielding to the weight falling from above. There are some problems with that theory - it does not fit the observed facts: * It cannot account for the total failure of the immense vertical steel core columns - as if they were there one moment and gone the next. * The collapse times were near free-fall, far too rapid to be due to gravity alone. This article focuses on the latter of these two discrepancies. Those that concocted the "pancake theory" made a fatal error - they didn't check their story against the inviolate laws of physics! This is easy to do, even without any physical evidence to examine. We can test that incredible pancake tale using basic high-school physics. Let's do that - use a simple, unassailable, incontrovertible conservation-of-energy analysis to perform a reality check that establishes once and for all that the government, and such government story backers as PBS, Popular Mechanics, and Scientific American have falsified the true nature of the 9/11 disaster. How Gravity Acts: Sir Isaac Newton noticed that apples fell from trees. Others had also noticed this, but none had ever devised a theory of gravity from the observation. Over the years, mankind has learned that the force of gravity at and near Earth's surface produces an acceleration of known constant magnitude. That doesn't mean we know HOW it works, or WHY, but we have become able to predict its effects with a high degree of precision and certainty - gravity has always had the same, predictable, effect. Galileo Galilei used the leaning tower of Pisa to demonstrate that a large ball and a small one (of lesser mass) fell (accelerated downward) at the same rate. Prior to Galileo, people had just assumed that heavier objects fall faster, much the way they had assumed the Earth was flat. So while an object of greater mass will exert more force (its weight) upon anything supporting it against gravity's pull, it does not experience any greater acceleration when gravity's pull is not opposed - when it is falling. Earth's gravity at and near the surface of the planet can only accelerate objects downward at one known, constant rate: 32 feet per second for each second of free fall. As Galileo demonstrated centuries ago, heavier objects are not accelerated any quicker than are lighter objects. So Earth's gravity produces a downward acceleration of 32 feet per second per second. This means that an object, after falling one second, will be falling at a speed of 32 ft/sec. After the 2nd second, it will be falling at 64 ft/sec. After the 3rd second, it will be falling at 96 ft/sec., and so on. Further, since gravity's acceleration is constant, and an object is falling at 32 ft/sec after one second has elapsed, we know that it has averaged 16 ft/sec for the entire distance. Thus after one second, the object has fallen 16 feet. Scientists have derived simple free-fall equations that can be used to harness this knowledge mathematically. These equations can be found in any high-school physics book: * Falling velocity = acceleration of gravity x time. (V = G x T) And * Distance fallen = 1/2 x acceleration of gravity x time squared. (D = 1/2 x G x T x T) So if we want to know how far an object has free-fallen after 3 seconds: Distance = 1/2 x 32 x 9 = 144 feet So after 3 seconds in Earth's gravity, an object will have fallen 144 feet and will be falling at 96 ft/sec. Checking Our Work: We've just solved a simple physics problem. Now let's check our work, using conservation of energy. We know that energy can neither be created nor destroyed - it merely changes form. If we take the potential (in this case chemical, molecular) energy in a barrel of oil and burn it, it changes to heat energy. When we burn gasoline in our car's engine, we get kinetic (motional) energy, plus some heat, as an engine is not 100% efficient. When we use our car's brakes to bleed off some of that kinetic energy (slow down), that energy is converted into heat (the brakes get hot). Explosives convert potential energy [molecular or atomic] to kinetic energy (explosive force) quickly enough to shatter or even pulverize concrete. In the case of the free-falling object, the two kinds of energy we are concerned with are kinetic energy and potential energy. Examples of potential (gravitational) energy are the energy available from water stored up high in a water tower, or a boulder perched atop a hill. If whatever is holding it up there is removed, it will fall under the influence of gravity's pull. As it accelerates downward, the potential energy is converted to the kinetic energy of the object's motion. So, as an object falls, it changes its potential energy into kinetic energy. The equation for potential energy is: * Potential Energy = Mass (or weight) x Gravity x Height. (PE = M x G x H) The equation for kinetic energy is: * Kinetic Energy = 1/2 x Mass x Velocity squared. (KE = 1/2 x M x V x V) So let's just say, for the sake of simplicity, that our falling object has a mass of 1. (Remember, the object's mass will affect its energy, and its momentum, but not its rate of free-fall.) The potential energy given up by falling 3 seconds (144 ft) is: 1 x 32 x 144 = 4608 The kinetic energy gained after falling 3 secs is 1/2 x 1 x 96 squared = 1/2 x 9216 = 4608 So, the available potential energy was converted into kinetic energy. Seeing that energy was, in fact, conserved is how we know that the answer in the simple case above was correct. We've checked our work, using an independent analysis, based upon the sound physical principle of conservation of energy. Now, and only now, we can be certain that our answer was correct. One Little Complication - the effect of air resistance: The free-fall equations above reflect a perfect, frictionless world. They perfectly predict the behavior of falling bodies in a vacuum. In fact, you may have seen a science class demonstration in which the air is pumped out of a tube and then a feather will fall, in that vacuum, just as fast as will a solid metal ball. That's how parachutes work: much of the falling object's potential energy gets expended doing the work of pushing a lot of air out of the way in order for the object to fall. As a result, not all of the gravitational potential energy can go towards accelerating the object downward at gravity's rate of 32 ft/sec/sec. In other words, only when there is zero frictional resistance can any falling object's potential energy be completely converted into kinetic energy. Anything that resists a falling object's downward velocity reduces its acceleration from the maximum gravitational acceleration of 32 feet per second per second, as some of gravity's potential energy is consumed in overcoming frictional resistance. This explains the phenomena of "terminal velocity". The free-fall equations predict that a falling object's velocity will continue to increase without limit. But in air, once a falling object reaches a certain speed, its propensity to fall will be matched by the air's resistance to the fall. At that point the object will continue to fall, but its speed will no longer increase over time. Another way of looking at it is this: gravity's incessant force produces a downward acceleration, but friction with the air creates an upward force and thus an upward acceleration. When falling at terminal velocity, the acceleration downward equals the acceleration upward, they cancel each other out, and a constant downward velocity is maintained. Thus the parachute, with its high air friction resistance, allows the person attached to it to float to earth unharmed. A Quick Recap: Earth's gravity causes objects to fall, and they fall according to precise physical equations. The equations assume no air or other resistance. Any resistance at all will cause the object to fall less rapidly than it would without that resistance. If a falling object is affected by air resistance it falls slower than it would if free-falling, and it will take longer to fall a given distance. Free-fall From WTC Building Heights: The towers were 1350 and 1360 feet tall; average = 1355 feet. Let's start by using our free-fall equation to see how long it should take an object to free-fall from the towers' height. Distance = 1/2 x Gravity x Time squared. (D = 1/2 x G x T x T) With a little basic algebra, we solve the equation for the fall time, T: 2 x Distance = Gravity x Time(squared) (2 x D = G x T x T) Time squared = (2 x Distance) / Gravity (T x T = 2 x D / G) Time squared = 2 x 1355 / 32 = 84.7 (T = square root of (2 x D / G)) Time = 9.2 So our equation tells us that it takes 9.2 seconds to free-fall to the ground from the height of the WTC towers. Using our simpler equation, V = G x T, we can see that at 9.2 seconds, the free-falling object's velocity must be about 295 ft/sec, which is just over 200 mph. But that can only occur IN A VACUUM. Since the WTC was in Earth's atmosphere at sea level, you might be able to imagine how much air resistance that represents. Think about putting your arm out the window of a car moving even half that fast! Most free-falling objects reach their terminal velocity long before they reach 200 mph. For example, the terminal velocity of a free-falling human body is around 120 mph. The terminal velocity of a free-falling cat is around 60 mph. Therefore, it is clear that air resistance alone will make it take longer than 9.2 seconds for anything falling from the towers' height to reach the ground. Observations from 9/11: On page 305 of the 9/11 Commission Report, we are told, in the government's "complete and final report" on 9/11, that the South Tower collapsed in 10 seconds. Here is the exact quote: "At 9:58:59, the South Tower collapsed in ten seconds". That's the government's official number. With all the videos that show it, they could not lie about this. But as we've determined above, the FREE-FALL TIME IN A VACUUM is 9.2 seconds, and 10 seconds is an exceptionally short fall time through the air. This "collapse" was not without far more physical resistance than from the air alone. It proceeded through all the lower stories of the tower. Those undamaged floors below the plane impact zone offered resistance thousands of times greater than that of air. Those lower stories, and the central steel core columns, had successfully supported the mass of the tower for 30 years despite hurricane-force winds and tremors. Air cannot do that. Can anyone possibly imagine undamaged lower floors getting out of the way of the upper floors as gracefully and relatively frictionlessly as air would? Can anyone possibly imagine the lower stories slowing the fall of the upper floors less than would, say, a parachute? It is beyond the scope of the simple but uncontested physics here to tell you how long such a collapse should have taken. Would it have taken a minute? Ten minutes? Hard to say, but certainly it would take far more than 10 seconds! What is certain, beyond any shadow of a doubt, is that the towers could not have collapsed gravitationally, through their intact lower stories, as rapidly as was observed on 9/11. Not even close. This is shown above to be physically impossible! Not only was tremendous energy expended in causing the observed massive high-speed sideways debris ejections, but virtually all the concrete and glass of the tower was pulverized - actually dissociated is a better word. Never mind what happened to all the supporting steel core columns! The energy requirements to do anything like that, alone, rival the total amount of potential energy that the entire tower had to give. Gravity alone is sufficient to cause some things to fall that far, even through air, in close to the observed 10 second collapse time. But that is without the huge expenditure of energy necessary to pulverize all of that concrete and glass, eject debris, plus cause the steel core columns to effectively disappear. The gravitational potential energy present was certainly not enough to have done all these things at once. Energy can neither be created nor destroyed; it only changes form. So WHERE DID ALL THAT ADDITIONAL DESTRUCTIVE ENERGY COME FROM? Conclusions: In order for the towers to have collapsed "gravitationally" in the observed duration, as we've been told over and over again, one or more of the following zany-sounding conditions must have been met: * The undamaged structure below the impact zone offered zero resistance to the collapse. * The glass and concrete spontaneously disintegrated without any expenditure of energy. * The massive vertical steel core columns simply vanished, as if by magic. * On 9/11 alone, in that location alone, gravity was much stronger than gravity. * On 9/11 alone, in that location alone, energy was not conserved. None of these laws-of-physics-violating, and thus impossible, conditions can be accounted for by the official government theory of 9/11, nor by any of the subsequent analyses and arguments designed to prop up this official myth of 9/11. The Bottom Line: The government explanations for the WTC collapses fail the most basic conservation-of-energy reality check. Therefore the government theory is FALSE; it does not fit the observed facts, and the notion of a "pancake collapse" cannot account for what happened. The "pancake collapse" explanation is impossible, and thus absurd. It is A LIE. It is utterly impossible for a gravitational collapse to proceed so destructively through a path of such great resistance in anywhere near free-fall time. This fact debunks the preposterous contention that the WTC collapses can be blamed solely upon damage resulting from the plane impacts. The unnaturally short durations of the top-down collapses reveal that the towers did not disintegrate because they were coming down, but rather they came down because something else was causing them to disintegrate. So, to the extent that people accept the ridiculous "pancake collapse" story, former CIA Director and current Secretary of Defense Gates' other premise, that people know what they saw, is also false. It is left to you to decide if his conclusion, which was based upon clearly incorrect presumptions, is also flawed. The collapse of WTC building 7, which was NOT hit by any plane, and which also collapsed within a second of free-fall time later that same day, similarly fails the conservation-of-energy analysis. The 9/11 Commission made no attempt to explain it. Just how and why so many highly-accredited and credentialed people all so miserably failed to check the "pancake collapse" theory, by giving it this basic physics reality check, is beyond the scope of this analysis. --------------------------------- FURTHER IRREFUTABLE PROOF BY PHYSICS OF THE 9/11 INSIDE JOB: http://vehme.blogspot.com/2007/12/gl...tter-than.html http://en.wikipedia.org/wiki/Planck's_law_of_black_body_radiation |
#10
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"Jorge" wrote in message
... On Thu, 13 Mar 2008 18:43:13 GMT, "Freedom Fighter" wrote: "barnegatdx" wrote in message ... snip On Mar 13, 10:06 am, barnegatdx wrote: Controlled Demolition? - Rubbish . . . http://www.popularmechanics.com/tech...w/1227842.html That propaganda shill rag Popular Mechanics actually bowed out of a discussion that they couldn't win when, in a live interview, they got caught in a completely absurd fabrication. Listen to this interview: http://www.youtube.com/watch?v=WULRQCgvsdE snip psychotic Trufer rantings It is really hard to put up with such unresonable psychotic ****s that have no concept of reality and factuality. Ad-hominem attack is the refuge of unintelligent and immature people incapable of disproving a valid assertion with facts or logic, so in frustration they resort to childish name-calling. Pathetic! You just get to a point with these folks where the best thing to do is to give up because you just get visions of these ****s getting on one of their mesaanic highs and threatening your family some dark night. Jorge It is those that you blindly defend that you really have the most reason to fear. |
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