Feb12

# Mathematics of the mosh pit

Maths of mosh

Rock music fans are aware of the phenomenon of the mosh pit at concerts — a riotous area, usually close to the stage, where concert-goers, in lieu of learning complicated dance steps, slam violently into each other (and hence an alternative name for moshing is slam dancing).

Until now the fascinating mathematics of this emergent property of crowds has been unjustly ignored. However, this has changed with the advance publication on the arXiv Collective Motion of Moshers at Heavy Metal Concerts by Silverberg, Bierbaum, Sterna and Cohen.

The abstract states

Human collective behavior can vary from calm to panicked depending on social context. Using videos publicly available online, we study the highly energized collective motion of attendees at heavy metal concerts. We find these extreme social gatherings generate similarly extreme behaviors: a disordered gas-like state called a mosh pit and an ordered vortex-like state called a circle pit. Both phenomena are reproduced in flocking simulations demonstrating that human collective behavior is consistent with the predictions of simplified models.

The authors model the behaviour of the mosh pit (and circle pit), provide source code and Java script interactive moshpit

The conclusions will be surprising to many:

If we increase the self-propulsion coefficient $\mu$ (decrease $\tau _{prop}$), we find the motion, though random, is no longer fit by a Maxwell-Boltzmann distribution. Instead, collisions between active and passive MASHers [Mobile Active Simulated Humanoid] on the boundary of the simulated mosh pit removes energy faster than collisions among active MASHers can rethermalize the system. Consequently, measurements in silico show a radial temperature gradient is established with a higher effective temperature at the core of the simulated mosh pit and a lower effective temperature at the edge

A valuable and timely addition to the literature. Ok, let’s rock.