Field Notes: Crowd Dynamics, Mosh Pits, and Randomness in Dice Design | The Rest Is Science

Overview

In this Field Notes episode from The Rest Is Science, hosts Michael and Hannah explore how language shapes mathematics, then dive into crowd dynamics using moshing as a physics case, and finish with a playful tour of dice design and randomness. They discuss how people in crowds can behave like particles in a fluid, the emergence of patterns such as gas-like states and vortices, and how safety design, like bollards, can improve crowd flow. The show then pivots to dice design, explaining how different polyhedra are made fair, the idea of a D1 coin die, and the notion of using physical randomness with books and pi digits to generate randomness. Listeners are invited to contribute ideas for Field Notes.

Note, sponsorship mentions are part of the episode but not central to the core ideas discussed here.

Introduction and framing

The episode opens with Field Notes, a segment of The Rest Is Science where Michael and Hannah bring in objects or questions to discuss. The conversation begins with a linguistic detour about math versus maths, highlighting differences in British and American usage and the broader role of language in science communication. The hosts acknowledge the sometimes opaque way science is presented and set up the field notes format as a lighter, object‑driven exploration of ideas that sit at the boundary between everyday life and scientific modeling.

Language and mathematics

The discussion then turns to language itself, with a light examination of why people say math or maths, and how terminology can shape our thinking about mathematics as a unified discipline or a set of subfields like geometry, trigonometry, and algebra. The hosts emphasize that both usages are acceptable and that linguistic variety reflects culture and context, not a right or wrong approach. This segment frames how science communication can bridge different audiences through careful language choices.

Mosh pits as a physics problem

Max Sebastian asks about mosh pits and fluid dynamics and how these relate to crowd safety at large concerts. The hosts connect the question to a landmark 2010s paper, Collective Motions of Humans in Mosh Pits and Circle Pits at Heavy Metal Concerts, written by mathematicians and physicists. The paper describes a mood influenced by loud sound, fast rhythms, strobe lights, and often intoxication, and then reframes the problem by treating concertgoers as particles in a fluid or granular medium. The discussion highlights two crowd tendencies: flocking, where individuals copy their neighbors, and random movement, where personal choices create variability. These behaviors yield emergent collective states that resemble gas-like disordered motion and, with higher density, vortex-like circular motion. The hosts stress that even though people act with individual will, large-scale patterns can emerge from local interactions.

Emergent states and safety implications

The conversation explains how crowd behavior can transition from flowing to congested as density increases, a phenomenon described as granular flow. They note a density threshold around 5 to 6 people per square meter, beyond which flow becomes harder to control and the risk of dangerous crushes rises. The discussion moves to counterintuitive design strategies, such as placing a bollard in front of a doorway to prevent immediate clogging directly above the exit. This barrier encourages the formation of lanes around the opening, enabling smoother flow by reducing local jamming. The speakers draw a parallel with granular media like sand and explain that such designs are now incorporated into modern stadiums and public spaces to optimize safety. They acknowledge that implementing bollards in real exits would feel risky, but emphasize the safety benefits when thoughtfully designed with curved approaches and offset barriers.

From field to classroom: objects, models, and safety design

Field Notes then transitions back to the overarching theme of using simple physical models to gain insights about complex social systems. The hosts discuss how fluid dynamics and statistical physics can yield counterintuitive results about crowd movement and safety planning, underscoring the value of interdisciplinary thinking in public safety design. The segment ends with the promise of future Field Notes exploring further bizarre behaviors and emergent phenomena in other systems.

Show and tell: dice, randomness, and tools for decision making

Returning from the break, the hosts pivot to a classic Field Notes topic: dice and randomness. Michael introduces a two-sided coin die, then a range of dice from a D1 used for a single decision to D10 for a 1–10 outcome. They explain how a D1 is conceptually a die that only has one stable outcome due to how it balances, effectively functioning like a single-choice decision tool. They then describe four and five-sided dice, including a four-sided tetrahedron and a five-sided die designed as a thick triangular prism so it can land on any face with equal probability, a solution to the long-standing puzzle of fair five-faced dice. They discuss the challenges of achieving true fairness and the heavy mathematical work behind the scenes, including 3D printing prototypes and working with injection-molded parts to ensure equal likelihood of each outcome.

Strategic design and playful skepticism

The conversation delves into the debate about standard dice versus more eccentric shapes. They debate the redundancy in a standard cube die and consider optimized dice with minimal symmetry to achieve fairness. The hosts introduce the idea of wonky dice that skew neither fairness nor balance but offer a more engaging user experience. They discuss a pentagonal prism for the seven, a thickness-calibrated prism for the nine, and the general design principles that make such dice fair in practice. The discussion also touches on real-world applications beyond gaming, such as using dice for making decisions at day-to-day crossroads or at larger social events, highlighting the ubiquity and practicality of randomness in everyday life.

Random numbers and mathematical curiosities

Beyond physical dice, the hosts showcase a suite of randomness resources. They compare physical randomness to pseudo random number generators used in computer models and share a favorite humorous prop, a small book of random numbers. They explain the historical importance of genuine randomness for large calculations in the 1950s and beyond, including uses in space program planning and secure routing. The book relies on natural phenomena like radioactive decay or lava lamps to produce truly random numbers. They discuss how humans struggle to generate randomness without using a physical process and why such randomness matters for robust modeling.

Pi digits and the mile of pi

The conversation veers into a memorable aside about pi digits, referencing Brady Heron and Matt Parker and their famous act of printing a mile-long roll of pi digits by hand. They recount the logistics and the social dynamic of sharing or auctioning such a display, turning a mathematical joke into a thought-provoking demonstration of patience and scale. The segment closes with a lighthearted note about a mile of pi annotated by a friend and the potential for such artifacts to spark curiosity and conversation about mathematics in everyday life.

Closing and call for contributions

Field Notes ends with a closing invitation for listeners to contribute objects, questions, or confessional anecdotes. The hosts reiterate the show is about exploring ideas at the edge of science in an accessible, joyful way, and they invite audience participation to fuel future episodes.