How the Famous Robbers Cave Experiment Defines The Torus and Self Similarity – SDP#33

PODCAST-The simplest nonlinear system is The Torus and it governs our daily lives into expected routines.  It has one loose but stable outcome basin. If you commute to work, the outcome basin is most likely your arrival at work at an approximate time each day. The dynamics of The Torus are marked by self-similarity. Self-similarity, as a concept, firms & entire societies, may be similar day-to-day, year-to-year or generation to generation However, no one embodiment in any given cycle or iteration of the behavior of any given system is precisely like a previous embodiment. While your daily commute might seem routine and typical, it is always different, in fact, probably much more different from what you realize! In addition, routine dynamics inside a factory, an office, a hospital, a school or a prison have the character of a torus.


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Imagine a substantial alteration to your daily commute – perhaps something that changes your trip so drastically that it is now removed from the largely predictable, patterned Torus such as an accident or severe weather. In such situations in which the basin is no longer predictable, chaos ensues.

In the image below, The Torus resembles an inner tube or a doughnut. One can move within the space inside of The Torus during a routine or pattern, again, such as a daily commute.  However, significant changes to a routine can drift outside of the envelope of The Torus. Dr. Perrodin describes these instances as “entering chaos”. Thankfully, things return to some type of torus state as chaos is temporary. Yet, the “returned to” Torus might be different from the pattern previously known by the person. An example might be someone who loses an arm during combat or is transferred to a job in another country.


Even in high-tolerance manufacturing, there are similarities between items & not sameness. This dates back to the work of such quality control experts as W. E. Demming. Statistical variation always exists between items or processes.


When we expect things to be the same, things to follow a predictable sequence, we can easily overlook subtle, but very critical changes that alert us to compromised safety situations. Many people in the Twin Towers stayed at their desks for 4-minutes following the first plane crash. People simply thought that in a few minutes an “All Clear” would be issued or else struggled to accept the magnitude of the attack & continued to believe that their day was still within the parameters of The Torus.  Once people consciously acknowledged that they were operating outside of The Torus (which is person-specific), they depended upon situation leadership and self-preservation skills to cope with contextual and situation contexts.


In the summer of 1954, social psychologist Muzafer Sherif examined what is now known as “Realistic Conflict Theory” which accounts for group conflict, negative prejudices, and stereotypes as being the result of competition between groups for desired resources. Sherif’s field experiment demonstrated devolving The Torus to chaos & involved 2 groups of 12 y.o. boys at Robbers Cave State Park in Oklahoma.


Boys randomly assigned to 2 groups & encouraged to bond with their group. They did not know of the existence of the other group. One group was “The Eagles” & the other “The Rattlers” and such logos / words were on their shirts & flags.


Competition stage where friction between the groups was to occur for the next 4-6 days such as baseball games & tug-of-war.  Winners were heavily awarded & cumulative scores were kept. Prejudice increased from name calling to physical altercations. The Eagles burned the Rattlers flag & then the Rattlers ransacked the Eagle’s cabin & stole private property. The groups became so aggressive that the researchers had to separate them. The study confirmed Sherif’s Realistic Conflict Theory.

However, the theory wasn’t observed in the block-deep lines of people seeking a coveted spot on a boat during the 9/11/01 Lower Manhattan rescue. Why? Dr. Perrodin refers to an earlier podcast addressing the concept of transference as a primary contributor to the orderly rescue in Lower Manhattan.


David will respond to discussion thread comments or questions & also to emails.  The Safety Doc Podcast is hosted & produced by David Perrodin, PhD.