Keep Your Hats On: Keith Seffen's "Mathematical Model Of The WTC Collapse" Is Incoherent, Inappropriate, And Almost Meaningless

Dr. Keith Seffen's long-awaited "research paper", "Progressive Collapse of the World Trade Centre: a Simple Analysis", is available for review.

The paper has been the subject of much conjecture, here and elsewhere, since it was cited by the BBC in an article published on September 11, 2007.

According to the BBC, Dr. Seffen had constructed a "mathematical model" of the collapses of the towers. The article quoted Seffen as saying his research showed that once the collapse got started, it was destined to be "rapid and total" and that in "all senses, the collapse sequence was quite ordinary and natural."

Strikingly, the BBC described Dr. Seffen's paper as "published", even though it had not been published at that time. A search of the publisher's archives found no mention of the paper, or its author, and after I pointed this out, the folks at the BBC changed their report, which now says Dr. Seffen's paper is "to be published". (Copies of the original text were preserved here and here).

Articles published elsewhere propagated the error. And it turned out that the confusion stemmed from a press release put out by the University of Cambridge, where Dr. Seffen is a senior lecturer. The opening paragraph of the press release says that Dr. Seffen's paper is "published", but much later it says the paper is "to be published".

On September 14th, I wrote a long and very critical article about the press release, in which I said:

I may be reading too much into this press release. The proof is in the pudding, as they say, and we won't know for sure whether Keith Seffen's paper contains any proof -- or anything approaching proof -- until we see it.

If the paper [...] proves that "in all senses, the collapse sequence was quite ordinary and natural", then I will tip my frozen cap to the paper, and to its author, and I will encourage the world to do the same. But if it doesn't, then the world and I will have no choice but to consider Keith Seffen a willing accomplice, an accessory-after-the-fact in a most despicable case of mass murder.

I've read the paper, and here's my report:

At no point while reading it did I even think about reaching for my cap.

I read Dr. Seffen's paper with two main questions in mind:

First: Is the model coherent? In other words, is it internally consistent? Does it respect the laws of physics? Does it follow the principles of mathematics?

Second: Is the model appropriate? Does Dr. Seffen's mathematical model accurately describe the physical reality it attempts to model?

These two questions were intended to help clarify the third line of questioning that has been rattling around in my brain for two months: What if Seffen were correct? What would that mean?

On a more specific note, if the paper were coherent and appropriate; if it showed logically, physically, mathematically, that the towers could have come down as fast as they did, in the way that they did, without explosives or cutting charges or directed energy beams or anything else other than gravity: Would it really demolish all the conspiracy theories surrounding the attacks of 9/11 (as claimed and/or hinted in the coverage Dr. Seffen's story received two months ago, especially the article in Business Weekly)?

To answer the final question first: NO! There are hundreds of unanswered questions about 9/11. One of them concerns the reason for the collapse of the twin towers. So even if this particular question were answered satisfactorily, it would still leave hundreds of other unanswered questions. In other words, those who claim that Seffen's paper puts an end to the debate are dreaming -- even if he's absolutely correct!

It is also important to note that even if Seffen has it right, his paper does not explain the collapses of the towers. It only covers -- and it only claims to cover -- the continuation of the collapse once it began. Whether the collapses began without assistance is still an open question in my mind, and I am certainly not alone in that.

But even then, even if Seffen is correct, this paper wouldn't prove that gravity-driven collapse was the way it happened; it would only prove that the gravity-driven explanation is theoretically plausible.

In other words, far from confirming the official story on this point, it would merely position the official explanation among several other explanations which a neutral observer might call "worthy of consideration".

None of the articles in the news media (and none of the blogs I know) have presented Seffen's paper in this context. It's been "Zero Grounds For Conspiracy Theory" and "Bad News For Truthers" and so on, but the practical impact of the paper -- even if it were correct -- would actually be fairly insignificant.

You may feel inclined to argue with me on this point, but the argument would be irrelevant, because Dr. Seffen's mathematical model is incoherent.

Dr. Seffen assumes that a constant force, supplied by the suddenly unsupported top of the tower, was pressing down, crushing each story, one after another, all the way down to the ground. An elementary understanding of physics would tell you that this is not possible, unless the top section of the building -- the part doing the crushing -- were made of much denser material than the bottom section -- the material being crushed.

A single brick could crush a huge stack of paper cups and emerge intact. And this is the sort of situation Seffen's paper models. But that's not what happened to the World Trade Center.

In the case of the WTC, the material being crushed was nearly identical to the material doing the crushing. In fact, the structural steel was thicker at the bottom than the top, in which light Seffen's model appears even less appropriate to the event (not that this makes very much difference in the long run).

The point is: If the top of the building had crushed all the stories below it, then the damage to the top portion would have been significant: we would naturally expect that the amount of damage to the top would be similar to the amount of damage to the bottom. Or, thinking about the thickness of the steel, we might expect the damage to the top to be even greater than the damage to the bottom.

But in Dr. Seffen's model, the top section of the building is not destroyed in the process of crushing the stories below it; instead, its entire mass is still available to crush even the lowest stories.

If post-collapse photos from Ground Zero had showed the top 20 or 30 stories of each tower, virtually intact and sitting on the ground, then Seffen's model could perhaps be considered appropriate. But according to all the video and photographic evidence, it's not even close.

But that only stands to reason. After all, mathematics is abstract; it can model anything. As a modeler, you can always choose to model something that's not possible, but in that case your model will never be an accurate description of reality.

In other words, having failed the first test makes the second question irrelevant. Since the paper is incoherent, it could never be appropriate.

Having failed the first two tests makes further discussion almost irrelevant. In one sense, the paper is meaningless. It shows nothing with respect to the collapse of the towers.

But on the other hand, it's not entirely meaningless. because it shows how implausible the official story really is.

If a Cambridge University whiz kid with a PhD and a list of papers a mile long can't make a better attempt than this ... but no! he couldn't!

Keith Seffen has not bolstered the official explanation of 9/11 in any way; in fact -- and as can be seen by all who read his paper with an open mind -- he has discredited the official story even further.

The paper also shows quite a bit about Dr. Seffen, and it brings great discredit upon him personally, upon his career, and upon the University of Cambridge, which he represents, and under whose auspices this very shady venture was publicized and continues to be protected.

As supporters of Dr. Seffen have pointed out, he is very bright and well educated. He holds a large number of impressive degrees, and he has published an impressive series of papers.

But this makes his transgression all the worse, in my estimation. He is clearly bright enough and well-enough educated to realize that his paper is incoherent. And as clearly pointed out by Arkadiusz Jadczyk, Seffen's attempt to circumvent logic is readily apparent.

Seffen "explains" that certain simplifications in the model were "essential" in order to bring the equations into a "closed form". That's math-speak for "We had to do it this way to get the results we wanted." In this respect, as Jadczyk points out, Seffen's paper is "not even wrong".

It's also a huge red flag for anyone with mathematical modeling experience, because it often requires a complex model to represent processes which seem simple.

But on the other hand it is never possible to explain a complex process by means of a simple model. Anyone with enough skill to design such a model certainly knows this. And with the awesome power of today's computers at our disposal, there's no need for "closed form" models anymore. The elegant equations so beloved by mathematicians throughout history have lost some of their sparkle in the past half-century, as number-crunching has become less and less onerous. So there's almost never any need for "a simple analysis", especially when the process being analyzed is so complex.

In other words, the term "unwitting" does not apply here.

A similar argument could be made, of course, about the BBC. But that's no surprise; we've already seen the BBC's true colours (with their Conspiracy Files hit piece, and of course their precognitive reporting of the collapse of Building 7).

In my opinion we should never be surprised to see this supposedly respectable news organization spinning.

All of which brings me back to my previous statement:

If the paper [...] proves that "in all senses, the collapse sequence was quite ordinary and natural", then I will tip my frozen cap to the paper, and to its author, and I will encourage the world to do the same. But if it doesn't, then the world and I will have no choice but to consider Keith Seffen a willing accomplice, an accessory-after-the-fact in a most despicable case of mass murder.

So ... tell me about the UK: Do they have laws against murder? Do those laws include provisions pertaining to accessories-after-the-fact? How about mass murder? Wouldn't that make it worse?

Where's Scotland Yard when you need them?

They still can't all be weeping over their conviction in the Jean Charles de Menezes murder, can they?

Somebody needs to wake a few of them up or drag them out of the pub and get them moving.

It shouldn't take very much effort to get them headed in the right direction.

After all, the University of Cambridge News Centre says:

Journalists seeking further information about the University can contact the Office of Communications at:

* Telephone: +44 1223 332300
* Fax: +44 1223 330262
* Email: communications@admin.cam.ac.uk