Crash course in entropy

One way to think of entropy gain in a building collapse is thermodynamically, whereby the maximum Boltzmann entropy is reached when one cannot easily distinguish the rubble from the environment. In terms of Shannon entropy, the maximum is reached when one cannot distinguish the signal, or the information consistent with building structure, from the noise, or the ambient information of the environment. The entropy gain means that application of information is required if the building is to be restored.

But we can apply Shannon information somewhat differently to the issue of building collapse, specifically the fire-driven collapse of steel structures. The National Institutes of Standards and Technology concedes that the collapse of a steel-frame building with fire as the main cause is an exceptionally rare event. In fact --excluding the case of the twin towers -- the only one known instance is the collapse of World Trade Center Building 7 at 5:20 p.m. on 9/11.

So we could review records of steel building damage by fire and ask these questions: what percentage of the building was destroyed?; what was the highest point remaining in the post-fire structure?; what degree of symmetry was evident in the collapse? This last question would match the collapse against some symmetrical grid and assign values. We should be able to come up with a method that works satisfactorily for a number of cases.

We then compile our cases, using the statistics gathered, and generate one (or several, if we like) normal curves. Now we know that the highest information is under the outliers and the least within the central 68 percent of the curve. Entropy increase here implies that, statistically, we will tend to move from outlier events to central events.

Here a high-information outlier isn't a building unscathed by its fire, but a building with either near-total collapse or with near-symmetrical collapse (the two cases intersect).


Now the NIST might respond that the information gain reflects a unique building design for Building 7, which proved to be an Achilles heel once fire broke out. The building used an outlier design, in other words.


However, the twin towers also collapsed that day. The NIST deftly suggested that a combination of jet impact and fire led to the collapses. A close reading of the agency's reports, however, shows that its simulations put the blame largely on fire. And, the agency brought up the unique design used in the twin towers. This unique design was the Achilles heel that supposedly permitted the utter collapses. So, in the NIST scenario, the design of the towers would represent another outlier.


The design "flaws" and hence the Achilles heels were completely different in the cases of Building 7 and the twin towers.


The existence of two strikingly different Achilles heels side by side in New York of course represents something highly anomolous. Either the killers were magically aided by one of the most bizarre flukes in history or the gain in information represents a non-random influence.