Today, once again, I’m going to turn my blog over to my husband, Arkadiusz Jadczyk who is going to comment on the recent media splash made by Keith Seffen of Cambridge who claims that the collapse of the World Trade Centers is easily explainable according to his "model." I wrote about this myself at the time, and the interested reader might wish to review that post. Having said that, without further ado, Ark takes the floor!

The other day, discussing the subject of modern day scientific research which is most often controlled by politics, I wrote: “The peer-review system has serious flaws. Sometimes completely nonsensical and disinformation papers are published. And quite often good papers are being rejected, because referees have their prejudices and personal interests.” Let me give an example from real life, a sort of “diary of a referee.”

At the end of August, the editors of a professional specialized journal Markov Processes and Related Fields asked me to serve as a referee of a certain paper. One of the authors was an American mathematician, whom I met a few years ago at a conference, the second one, French, from Laboratoire de Recherche en Informatique et ses Applications, whom I did not know. I had a look at the paper, and put it in a drawer – for later. Usually the editors give a couple of months for a review… But then I suffered a hard drive failure, I had to finish my own paper (still waiting to be finished … ) and also there was the work on publishing of the proceedings of a conference that was held a couple of years ago which Springer publisher is waiting for ….

So I forgot about Markov processes and related fields. But when two weeks ago I received from the Chief Editor of the journal a kind and polite reminder, I dug out the paper to be reviewed and started to study it.

As it happens the paper is based on a previous paper by one of the authors, so I had to read it first. It deals with “random walks on hypercubes”. A hypercube, you know, is like an ordinary cube, but in four (or more) dimensions. The four dimensional hypercube is also known as the tesseract. Sacred geometry folks even think that contemplating tesseracts and similar creatures takes us into a higher reality. I don’t know. For me geometry is neither sacred nor scary – mathematics can effectively deal with hyperdimensional constructions without much mystery!

Looking through the cited bibliography in the paper to be reviewed I noticed that my own paper about quantum fractals on hyperspheres is being quoted, so I started to feel sympathy towards the authors. Who of us does not like to be quoted, right? So I started reading the paper with a positive attitude.

At the beginning the reading was easy. A little error here, a small correction there. Every referee likes these small errors because pointing them out does not take much time and, on the other hand, serves as a proof that the referee has indeed read the paper. Some smart authors, those who are aware of referees’ psychology, are making such small errors on purpose – to make the referee happy and to encourage him/her not to look in the paper any deeper!

I was thinking a little bit about what can be the use of random walks on hypercubes, but the authors remarked that it can be used in studies of error propagation. Other well established authors studied similar mathematical problems before, so the subject matter of the paper has been sanctioned this way; doesn’t mean it is true.

As I said above, the start was easy, yet pretty soon I found something that caused me to frown. There was a formula that should not be there, since it was taken from another paper and this other paper dealt with an essentially different case, based on a different set of assumptions. So I highlighted the formula in red and continued reading. Is this formula important for the final results of the paper? It often happens that we are getting right results using wrong methods. Perhaps this is the case here? But then, on page 9, I noticed that this suspicious formula is indeed being used. Here is this page:

and the suspicious term is the last term in the first equation from the top. The full page in pdf format is here.

Scary, isn’t it? Scares me, too, and I’m a mathematician! To check the calculations would take me a full month. What to do?

First, I thought, I will do a computer simulation using a random number generator. If my simulations will give the results that are evidently contradictory to the final results of the authors, then I will return the paper for corrections. If, on the other hand, my simulations will be in agreement with the results of the paper, then I will conclude that the authors, even if they are sinners, know what they are doing and so their sins can be forgiven.

Yet, after some thinking, I realized that to do the simulations would take me probably two weeks. “Why should I do it?”, I was thinking. And then I remembered this phrase from the Bible “Unto a stranger thou mayest lend upon usury” (Deut. 23.20). Eureka! I will suggest, instead, that the authors should do the simulations, which should not be too difficult for them as I knew that they did similar simulations before. And, with this insight, I wrote my referee report. After listing of all the little errors and inexactitude that I noticed I added the following final suggestion:

Now comes my doubt. The formula 1.6 introduces the inner product on the Clifford algebra. This inner product is the same as in the previous paper Ref. [18]. Yet the case now is different - we are dealing with signatures (p,q). This inner product is not a natural inner product for these signatures (it is, in particular, basis dependent). The basis independent inner product is given by slightly different formula - see for instance Proposition 2, (iii), Ref. 10.

I was not able to check all the computations in order to see whether using of such an artificial, in Clifford algebra environment, product affects the results or not. Therefore I am suggesting that the authors make sure, by numerical simulations, in the simplest case of mixed signature, that their results, those that depend on the use of this inner product, do not suffer from using their artificial construction.

After taking the above into account I have no further objections for the publication of the paper.

End. Now I can return to my own paper, to make 100% sure that I will not make an error in my own work. But …. no. When I was putting back the paper into my file cabinet, I noticed that there is another paper there that is also waiting to be reviewed, for another journal, on another subject.

This time two of the authors were from India and one from China. The subject was also more exotic. It involved octonions (which for mathematicians are much like octopuses), spinning masses, magnetic monopoles, gravi-magnetism and more of such really scary things. A whole zoo. This time I really got scared as the authors were referring to at least six other previous papers published in some obscure journals that I had never heard of. What to do?

So I wrote to the editor of the journal asking him to kindly ask the authors to provide me with copies of their previous works. They did. Looking them over, it was clear that the subject matter happened to be in my domain of expertise (which is probably why I was asked to be a referee). So I skipped the exotic octonion part and moved to the real meat – the EQUATIONS. Well, there was nothing new in the equations; I knew them. What was new was the lousy way they were presented and described in the paper! To make a long story short, I will just include below my sweet and short final report:

After studying the paper, as well as other papers on which this paper is based, I suggest not to accept this paper for publication in (journal name omitted). The reason is two-fold.

1) The paper does not conform to the standards required for publication in mathematical physics

2) There is nothing new in the paper except the reformulation, and if there is something new, this novelty has not been highlighted or studied in detail.

Specific comments:

Eqs. (40) describe the GDM. The following formula tells us that (blah-blah - I’m leaving out the math) as well as that (blah-blah - more math). This is evidently a nonsense. Probably (blah-blah) should be (blah-blah) as in Eq. (40) and probably (blah-blah) should be replaced by (blah-blah) yet such mistakes prove that the authors do not pay attention to what they put in print.

Next, on p. 11 we have a table, where, for instance, (blah-blah) is defined as (blah-blah) Yet neither (blah-blah) nor (blah-blah) were defined before. There are many more similar errors that make it impossible to follow the authors’ reasoning and that disqualify the paper as belonging to the domain of mathematical physics.

After sending this out I thought NOW I can return to my own paper. But no. Not so easy. Now my wife asks me to take a look at a paper by a fellow named Keith Seffen, an engineer at Cambridge who, apparently, wrote “An analysis of the World Trade Center collapse”. She asks me to do things like that now and again and, since she is my wife, I always put her requests at the top of the "to do" list. (We have a very happy marriage!)

Okay, let me have a look at it… I’ll be back in a few minutes…

Okay, I’ve read the paper. If I was a referee for this paper, I would write even less than I wrote about the last paper discussed above. This paper is, as Wolfgang Pauli once said, "not even wrong." (An apparently scientific argument is said to be not even wrong if it is based on assumptions that are known to be incorrect, or alternatively theories which cannot possibly be falsified or used to predict anything. ) That’s probably what I would say in a referee report. But my wife wants me to tell you, the reader, why I say this.

The first thing that comes to my mind is that there is a a very instructive book written by Joel Best, professor and Chair of Sociology and Criminal Justice at the University of Delaware: DAMNED LIES AND STATISTICS. Untangling Numbers from the Media, Politicians, and Activists, (University of California press, Berkeley Los Angeles London, 2001). In the Introduction the author writes:

“This is a book about bad statistics, where they come from, and why they won’t go away. Some statistics are born bad—they aren’t much good from the start, because they are based on nothing more than guesses or dubious data. Other statistics mutate; they become bad after being mangled (as in the case of the Author’s creative rewording). Either way, bad statistics are potentially important: they can be used to stir up public outrage or fear; they can distort our understanding of our world; and they can lead us to make poor policy choices.”

Now, while the online Progressive Collapse of the World Trade Centre: a Simple Analysis by K. A. Seffen from the Department of Engineering, University of Cambridge, does not deal with statistics, it deals with mathematics, a more general domain of science, yet the end result is the same: one can lie with mathematics and by doing so, such lies distort our understanding of our world.

Before going into details let me take a note of another interesting paper, with the title How to Accuse the Other Guy of Lying with Statistics by Charles Murray (Statist. Sci. Volume 20, Number 3 (2005), 239-241). There we read:

“We’ve known how to lie with statistics for 50 years now. What we really need are theory and praxis for accusing someone else of lying with statistics.“

So, accusing someone of lying with math needs, as a rule, someone else who is math literate. That’s me. Yet in the case of “Progressive collapse” this is not even needed (and it would be time-consuming and incomprehensible to the average reader). It is sufficient for you, the reader, to just be able to read and not be scared by pseudo-scientific jargon used in the article. The jargon is being used there for a clear purpose – to hide behind it the zero scientific value of the paper. I know that there is no scientific value to this paper because I read and referee scientific papers all the time and have been doing so for years. When you are not scared by the jargon, you, too, can easily see that the author gives himself away rather easily.

Let me first point out that in order to model reality, whatever the reality in question is, one first has to choose a model. Whatever a given scientist may have in mind at the beginning, he can always choose a model that will confirm his preconceptions. If he then covers his tracks by using incomprehensible (to the average reader) jargon, no one will have the patience to go through the details. Or no one will care. The paper may even be published in a peer-reviewed journal if the referee is incompetent or when the editor of the journal, for some reason, decides to publish the paper with no referee at all. In fact this happened recently, when Myron W. Evans managed to get a nonsensical paper published in a professional physics journal Acta Physica Polonica B. It took three other scientists a full two months of hard work to fully expose its nonsense, even when the harbingers of the nonsense were visible at first sight. (The editor admitted the error).

In the case of Progressive collapse, the harbringers of nonsense are also clearly visible. Let me show them to you:

" …it is clear that the initial loads imposed by both parts falling onto the undamaged buildings beneath were exceptionally high due to the unforeseen preceding events, and that damage was bound to propagate into the floors below: this is the initiation phase. It is also clear that both collapse modes were progressive, as indicated by film footage: there was the sound of each successive impact of floor upon floor and a matching sequence of lateral ejection of debris. Therefore, it is valid to consider the behaviour formally in the proposed terms.”

Yes, indeed, there were sounds of each successive impact. But there were also sounds of explosions and there are other important factors (for instance unusually melted steel, angularly cut beams, insufficient temperature to melt steel, and so on). The author seems to not care about these factors. Why? Because taking them into account would force him to choose a different model and he is either not willing or not able to do so.

Then we have:

“Accordingly, the assumption of progressive collapse enables a continuum viewpoint, which permits a simpler formulation compared to, say, a finite element analysis.”

He clearly tells us that it is his assumption that enables him to choose “a simpler formulation”. And what if he had taken a different assumption? Well, the answer is easy: He could well get a different result such as the building collapse pictured at left!

He continues:

“A frivolous but useful analogue is the inflation of a rubber party balloon”

It is indeed a frivolous analogue. But then, his model of progressive collapse is a frivolous analogue.

Then he gives himself away completely:

“The precise variation does not matter”

And where is the proof that it does not matter? And what if it does matter? This fact would probably be kept “undisclosed”.

“Of course, it can be argued that such dissipation introduces a means for capturing dynamical effects arising from, say, column-upon-column impacts, but it is prescriptive rather than attentive in terms of correct amount, which would be very difficult to estimate. Thus, it is entirely appropriate to move the study forward within the spirit of using Eqn 10 directly…”

In short, he is giving away his secret: it is his intent to "move the study forward" within a particular "spirit." And that "spirit" of obfuscation permeates every word of this pseudo-scientific paper. Finally our author admits:

“The collapse mode is highly idealised: none of the falling mass moves laterally; any impulsive action between successive floor impacts is neglected; and the final stage of collapse after the crush-front reaches the base is discounted. However, the incorporation of these features into a subsequent model would rely on estimations apportioning their relative contributions, which are not straightforward. Such refinements may negate the ability to obtain closed-form solutions, which are essential in ascribing the generic character of behaviour and for distilling key formulae ….”

In short, one cannot include all the elements involved with the collapse of the WTC towers because if you did, you would not be able to obtain the solution that Seffen has obtained by discounting them. Notice this: “ the incorporation of these features into a subsequent model would rely on estimations apportioning their relative contributions, which are not straightforward”. And he then tells us that obtaining "the solution" he has already decided he must obtain – is “essential”.

Now we understand. If he would incorporate some additional “features”, he would not be able to get to the conclusion that he has been instructed to get, or wishes to get in order to “move up” in the academic world controlled by politics!

So what does this paper prove? It proves only one thing: that is so easy to distort our understanding of the world. But, as it happens often with bad, but politically charged, science, the mass media will certainly carry his message all around the world.

Now, where was I? Oh yes, there is a German engineer who thinks that he has discovered mysteries of gravity and electromagnetism that were overlooked by Maxwell, Einstein and their followers. Perhaps he indeed discovered them? So, I should help him to put his work in a form that will be understood by others. But this time I am not in a hurry, so I wrote to my German correspondent that I will not be able to devote to his problem more than an hour per day. Well, perhaps more …..

And after two hours spent on trying to understand what he is really doing I realized that he is making a fundamental error neglecting reality completely and is deaf to any criticism. Why? Because, as he admitted to me, he wants to be famous. An educated guess may be that the real reason for Progressive Collapse may be the same – the author - Keith Seffen, photo at left - wants to be famous.

Progressive collapse indeed – of Science.