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.

Colliderscope

Gail Collins mixes some sci-fi with politics in her New York Times column today. Even though jokingly, she makes sure to refute my suspicion that black holes in the Large Hadron Collider had made the Times' squelch list.

Check the post below and her column at http://nytimes.com

It must be a wormhole. That explains how we journalists are bypassing the embargoes.

Paint it black

So suppose Hawking is right that the Large Hadron Collider will have a one in a hundred chance of producing mini-black holes? His theory, buttressed by many physicists, is that such entities would vaporize so fast they could do no harm.

But I'd like to know, are they sure these little buggers aren't quantum entities subject to the Heisenberg uncertainty principle? Because if they are quantum entities, wouldn't that imply that every once in a great while something improbable happens? The hole violates energy conservation just long enough to translate from virtual to real, in which case it I presume could then gobble the planet in short order.

The fact that statistically energy conservation can't be violated does no good if one little beastie acts wildly but in accord with quantum rules. Remember, all solid state circuits are based on this improbable energy violation, whereby a "particle" slips through an energy barrier or potential well. So occasional energy violation would be expected if the mini-holes are quantum particles.

If hundreds of thousands of such particles are produced, is there a signficant chance that one will balloon into a doomsday particle within the next, say, 20 years?

Anybody have an answer for me?

Aug. 4, 2009--Today's New York Times had a feature on the CERN collider saying that the engineers were having a tough time getting the machine to crank up the highest energies. They're still tinkering with it. Scientists would be happy even if it doesn't go at full tilt since the energy levels would still be far higher than those the Fermilab's Tevatron can produce.

Nowhere in Dennis Overbye's otherwise respectable story were black holes mentioned. So I suppose we must infer that we shouldn't worry because the collider won't reach black hole energy levels anytime soon. Funny how many things are on the uncool-to-discuss list. Now even the scientific topic of black holes has made the list, it seems.