The Modeler's Known Unknowns and Unknown Knowns

In Satyajit Das's Blog entitled "Fear & Loathing in Financial Products" one can read the following entry entitled WMD or what are derivatives 

....During the Iraqi conflict, Donald Rumsfeld, the US Defense Secretary, inadvertently stated a framework for understanding the modern world (12 February 2002 Department of Defense News Briefing). The framework perfectly fits the derivatives business. There were “known knowns” – these were things that you knew you knew. There were “known unknowns” – these were things that you knew you did not know. Then, there were “unknown knowns” – things that you did not know you knew. Finally, there were “unknown unknowns” – things that you did not know you did not know...

Then Satyajit goes on to clarify this term a little further:

....In most businesses, the nature of the product is a known known. We do not spend a lot of time debating the use of or our need for a pair of shoes. We also understand our choices – lace up or slip-on, black or brown. I speak, of course, of men’s shoes here. Women’s shoes, well, they are closer to derivatives. Derivatives are more complex. You may not know that you need the product until you saw it – an unknown known. You probably haven’t got the faintest idea of what a double knockout currency option with rebate is or does – a known unknown. What should you pay for this particular item? Definitely, unknown unknown. Derivatives are similar to a Manolo Blahnik or Jimmy Choo pair of women’s shoes....

There is also a word for the last one: Unk-Unk 

n. especially in engineering, something, such as a problem, that has not been and could not have been imagined or anticipated; an unknown unknown.

but I am not sure it fits with the previous definition. Looking up wikipedia, we have:

In epistemology and decision theory, the term unknown unknown refers to circumstances or outcomes that were not conceived of by an observer at a given point in time. The meaning of the term becomes more clear when it is contrasted with the known unknown, which refers to circumstances or outcomes that are known to be possible, but it is unknown whether or not they will be realized. The term is used in project planning and decision analysis to explain that any model of the future can only be informed by information that is currently available to the observer and, as such, faces substantial limitations and unknown risk.

How are these notions applicable to Robust Mathematical Modeling ?  John Cook reminded me recently of the Titanic effect presented initially in Jerry Weinberg's  Secrets of Consulting: A Guide to Giving and Getting Advice Successfully 

The thought that disaster is impossible often leads to an unthinkable disaster.

When modeling a complex  reality, we always strive to make the problem simple and then expect to build a more complex and realistic idealization of that problem. But in the end, even the most complex model is still an idealization of sorts. So every time I get to read about a disaster, grounded in some engineering mistake, I always wonder which part was the known unknown, the unknown known and the unknown unknown.

One of these moment that left me thinking happened back in February 2003 during last flight of the Space Shuttle Columbia. As you know, the spacecraft disintegrated over Texas. It did so because a piece of foam had hit one of its wings fifteen days earlier at launch. That explanation relied on a footage of the launch showing a piece of foam slowly falling from the main booster onto the edge of the wing of the Orbiter. Fifteen days later, when the Orbiter came back to land in Florida, it had a large hole that enabled air at a speed of Mach 17 to enter the inside of the wing, damaging it and thereby destroying the spacecraft. The remains of our experiment showed the temperature had reached well over 600C for a long period of time.

I was in the room next to the MCC during STS-107 as we were flying an instrument on top of the orbiter. We watched the take-off, we listened to all the conversations in the com loop between MCC and the astronauts during the fifteen days it flew (we asked some of the astronauts to manipulate our instrument at one point). At no time was there a hint of a possible mishap. We learned afterwards that even engineers, in the room next door and who had doubts, had requested  imagery from spy sats (but management canceled that request). However what was the most revealing after the tragedy was that I specifically recall that nobody around me could conceive the foam could have been making that much damage. None of us thought the speed differential between the foam and the spacecraft at launch could be that large. According to a simple computation based on the video of the launch, a half pound piece of foam hit the leading edge of the Orbiter's wing at an estimated speed of  924 fps or 1060 km/hr. It's always the square of the velocity that kills you.

More photos of the test performed in San Antonio on July 7, 2003 to recreate what happened can be found here.

As one can see from the small movie above, all previous tests had been performed with small pieces of foam. Further, attention had always been focused on the tiles underneath the Orbiter - never on the leading edge of the wings-. The video of the test performed in San Antonio, several months later, had everyone gasping in horror when the piece of foam opened a large hole in the leading edge of the wing. The most aggravating part of the story is that the Columbia flew for fifteen days with very little care about this issue while the Shuttle program had already seen take-offs with several near dangerous hits in the past.

On an unrelated issue, Ed Tufte also pointed out very clearly how the communication style using Powerpoint was a point of failure in the decision making process of deciding whether the foam strike  was a problem or not.. 

Of note, the communication to managment did not clearly delineate that there was absolutely no experience with such a large chunk of foam (experiments had been performed with 3 inch cube "bullets" vs an actual impactor with a volume of more than 1920 inch cube).

What were the known unknowns, the unknown knowns and the unknown unknowns in this instance ? First let me reframe all the categories of knowns/unknowns:for a modeler of reality or the engineers: With the help of wikipedia, let me summarize them as follows: To a modeler

• the known known refers to circumstances or outcomes that are known to be possible, it is known that they will be realized with some probability (based on adequate experiments/data)
• the known unknown refers to circumstances or outcomes that are known to be possible, but it is unknown whether or not they will be realized (no data or very low probability/extreme events).
• the unknown unknown refers to circumstances or outcomes that were not conceived of by a modeler at a given point in time.
• the unknown known refers to circumstances or outcome a modeler intentionally refuse to acknowledge that he/she knows

Looking back at the Columbia mishap, how can we categorize the different mistakes made:

• the foam hitting the RCC was a unknown known to the modelers. People had done their homework and knew that:
• falling pieces were hitting the orbiter at every launch
• some launches had bad tile destruction because of falling pieces
The engineers went through a series of tests that they eventually put in a database. Most past foam hits fell in the known knowns, as pieces of foam were clearly fitting dimensions used in the database. They knew foam could fall on the RCC instead of the tile yet did not do tests or felt the tests were necessary. At issue is really the fact that there was an assumption that the RCC was tougher than tiles. It actually is more brittle but then a lot of things are brittle when hit with a large chunk of something at 1000 km/hr.
•  The speed of the foam was also a known known to the modelers. It could be computed right after the launch and was within the range listed in the database mentioned above.
• A known unknown to the modeler was the impact effect of a very large piece of foam on the leading edge of the wing. This is reflected in the size fragments used in the database. There was simply no data.
• An unknown unknown to the manager and the rest of the world was the eventual demise of the whole spacecraft fifteen days later due to this impact. To the modeler, I believe the demise of the spacecraft was rather a unknown known.

Unknown unknowns are clearly outside of most modeling for a multitude of reasons. Robust mathematical modeling ought to provide some warning about known unknowns and most importantly provide a framework for not allowing unknown knowns to go unnoticed by either the engineers or their management.

[1] Beautiful Evidence, Edward Tufte.