Inside Science Sept 2025: Pole Vault Physics, Brain Navigation, and Knot Theory Breakthroughs

Episode Snapshot

The latest Inside Science program tackles how physics and engineering enable world-class athletics, the brain’s internal odometer for navigation, and surprising math discoveries influencing biology and geometry. From Armand Duplantis’ pole vault records and the role of sprint speed, pole stiffness, and energy transfer to a brain-mapping study showing a tick-like distance signal in rats and humans, the show links moment-to-moment movement to larger science questions. It also features discussions of two pure-math breakthroughs—a new shape that breaks Rupert’s conjecture and a knot theory finding that changing how two knots combine can reduce the effort to unknot them—as well as a memorable polar exploration narrative tied to climate and biology.

Overview

This Inside Science episode gathers insights from sports engineering, neuroscience, and pure mathematics to illustrate how fundamental principles shape real-world outcomes, from athletic performance to navigation and molecular biology. The discussion weaves together expert analysis, experimental design, and compelling field stories to show how physics, math, and biology illuminate human potential and the natural world.

“the energy that Duplantis puts into the pole isn't used, so that anything you bend is efficient to maybe 80%” - Steve Hake, Professor of Sports Engineering

“it's regular, like a milometer in the brain” - James Ainge, University of Saint Andrews

“The plover eggs became a symbol to me representing both the fragility and resilience of life at the poles” - Neil Shubin, palaeontologist

“the first non Rupert shape, the noperhedron, doesn't have that property” - Katie Steckel

“the pattern of spots on the side of the Jaguar is unique to each animal” - narrator

Pole Vault Physics and Engineering

The show opens with Swedish pole vaulter Armand Mondo Duplantis breaking the world record for the 14th time, prompting a science-based look at what sets a pole vaulter apart. Steve Hake explains that the athlete’s sprint speed, anatomy, and the ability to bend the pole efficiently are crucial. The pole design has evolved from rigid wooden poles to bamboo and finally flexible glow-in-the-dark carbon composites, enabling the energy transfer that turns run speed into height. A simple energy model is used: kinetic energy at plant converts into pole spring energy, which then becomes gravitational potential energy. The pole’s bending efficiency, around 80%, is a key limiter and area for optimization. The discussion also touches on specialized footwear that maximizes sprint energy transfer, with caveats about traction and safety at takeoff and weave through the air. A neat takeaway is that, by modeling speed, bend, and energy, one can estimate the theoretical maximum height for a given athlete.

Katie Steckel adds mathematical nuance, noting that propulsion speed, rather than mass, is central to maximizing kinetic energy, and she highlights that during a jump the athlete’s center of mass can rise higher than the pole tip, thanks to clever geometry of the system. The segment ends with a nod to modeling assumptions that keep the math tractable, even if real-world effects like air resistance are nonzero but small enough to ignore in first-order estimates.

Brain Navigation: The Mileage Clock

Next, the program delves into neuroscience with a study from the University of Saint Andrews on the brain’s internal mileage clock. James Ainge describes an experiment in rats where they must run a defined distance, turn, and return to a start point, while researchers record activity from individual neurons and track the rat’s position. The bursts of neural activity occur at regular intervals roughly every 20–30 centimeters of movement, resembling a ticking odometer that maps distance through space. The same paradigm translates to humans in a large, bar-area arena, strengthening the link between spatial navigation and neural coding. The discussion connects this work to early cognitive deficits in Alzheimer’s disease, suggesting that understanding spatial memory circuits could inform diagnostics or interventions. The segment includes an audible demonstration of a single neuron’s firing pattern during a trial, illustrating the rhythmic coding that underpins navigation.

“a ticking, like a milometer in the brain” - James Ainge

Ends of the Earth: Climate, Poles, and Storytelling

Neil Shubin provides a long-form book excerpt from The Ends of the Earth, read by Nick Mohammed, exploring polar science through vivid field-recollection. The piece emphasizes data drawn from ice, oceans, and fossils to illustrate how polar regions influence global climate and civilization. The narrative interweaves expedition memories with reflections on the fragility and resilience of life at the poles, highlighting how warming temperatures, resource pressures, and shifting shipping routes reshape policy and science. The host and guest discuss the moral and practical implications of preserving polar systems while advancing knowledge through climate research and exploration. A central theme is collaboration, humility, and the humility required to work with extreme environments that have long shaped human history.

“The plover eggs became a symbol to me representing both the fragility and resilience of life at the poles” - Neil Shubin

Pure Mathematics: Rupert’s Problem Revisited

Katie Steckel introduces a striking recent shape that disqualifies Rupert’s Problem for convex bodies. The shape, dubbed the noperhedron, is a golf-ball-like convex body with one end stretched and the other cut, which does not admit passing through a copy of itself in any orientation. This discovery disproves a broad conjecture about convex shapes and “Can you push one through another copy of the same shape?” The finding challenges assumptions in 3D geometry and topology, while serving as a testbed for understanding how rigidity, symmetry, and geometry govern spatial transformations.

“the first non Rupert shape, the noperhedron, doesn't have that property” - Katie Steckel

Knot Theory: How Knots Behave When United

The knot theory discussion highlights how the unknotting number quantifies how many crossing changes are needed to untie a knot. The usual expectation is that the unknotting number of a sum of two knots equals the sum of the unknotting numbers. Recently, researchers found a counterexample: a pair of knots, each requiring three crossing changes to unknot, whose connected sum can be untied with only five changes, fewer than the straightforward sum. This is the first known instance of such a phenomenon, with implications for chemistry and biology, where knotting and untying processes relate to DNA and protein folding and enzyme action.

“the simplest way is to unknot each of the two things separately, and the number of switches would be at least the sum”

Wildlife and Mathematics: Jaguar Swimming

The episode closes with a record-setting jaguar swim that, if proven to be a direct long-distance crossing, would surpass prior distances. The pattern on the jaguar’s flank serves as a biometric identifier, enabling researchers to confirm that the same animal was observed at a bank and an island. The segment emphasizes how mathematical methods, including differential equations, help explain animal coat patterns and contribute to wildlife tracking. This narrative underscores the broader theme of how math and science illuminate both human endeavors and the natural world.

“the pattern of spots on the side of the Jaguar is unique to each animal”

Conclusion and Next Week

The program wraps with thanks to guests and a teaser for next week’s focus on a bird described as a miracle eagle, signaling the ongoing curiosity that threads through science broadcasting, mathematics, neuroscience, and field exploration.