Chapter 1: Understanding Ancient Geometry

As someone passionate about both geometry and history, I am excited to delve into a recent investigation surrounding limestone spheroids from the Early Acheulean site at ‘Ubeidiya, Israel, which dates back approximately 1.4 million years.

The research, spearheaded by Antoine Muller from the Hebrew University of Jerusalem, involved an international team that meticulously examined 150 spheroids through cutting-edge 3D scanning and geometric analysis techniques. These spheroids, often referred to as stone balls, polyhedrons, or bolas, rank among the earliest known types of lithic tools, originating during the Oldowan period and persisting into the Middle Paleolithic era.

However, the exact purpose and crafting methods of these spheroids have long been subjects of speculation. Previous research faced limitations due to small sample sizes and subjective classification methods.

To address these challenges, the team employed innovative quantitative approaches, including edge angle measurement, center of mass calculations, surface curvature assessments, and notably, spherical harmonics analysis.

Spherical harmonics offered a groundbreaking way to reconstruct 3D shapes based on their spherical coefficients, allowing for a more accurate quantification of complex artifact geometries and comparisons to an ideal sphere.

The findings indicated that as the spheroids were refined, they became increasingly spherical, necessitating skilled knapping to eliminate high-angled flakes from a spherical platform. This deliberate imposition of spherical geometry points to advanced cognitive abilities among these early hominids.

“While surface smoothness can occur naturally, achieving spherical form—where an object closely resembles a true sphere—is exceptionally rare in nature,” the researchers noted. “For instance, river cobbles may become smoother over time in flowing water, but they seldom reach a perfectly spherical shape.”

The study posits that these spheroids reflect an early instance of hominins intentionally shaping stone tools to achieve form and symmetry, akin to the well-known Acheulean handaxes.

Through the most comprehensive quantitative analysis of spheroids to date, the research reveals patterns suggesting these artifacts were purposefully crafted with the goal of achieving a spherical morphology rather than being mere byproducts of other activities.

This video titled "A 300,000-Year History of Human Evolution" provides further context on the cognitive abilities of early humans, illustrating how such skills might have developed over time.

Section 1.1: Symbolic Cognition in Hominins

The revelation that the spheroids from ‘Ubeidiya were intentionally shaped carries significant implications. They represent some of the earliest evidence for symbolic cognition among hominins outside of Africa.

Their widespread presence across various regions and their longevity imply that these spheroids played an essential role in Paleolithic cultures over extensive periods and distances.

Spheroids, crafted by hand, demonstrate a high level of skill. Credit: Royal Society Open Science, Antoine Muller et al.

This research underscores the cognitive sophistication of early Acheulean hominins, as they intentionally imposed three-dimensional geometry onto basic raw materials.

Subsection 1.1.1: The Role of Digital Technologies

The enigmatic nature of these artifacts is gradually being clarified through the application of digital technologies in archaeology.

Moreover, the researchers discovered that each spheroid featured a distinct “primary surface” from which most of the flaking occurred. This pattern was neither random nor incidental; it revealed a purposeful reduction strategy, countering theories that suggested these spheroids were merely the result of hasty flaking or percussive activities.

Chapter 2: The Cognitive Legacy of Hominins

In the TEDx talk "Mathematics is the sense you never knew you had," Eddie Woo explores how mathematical understanding can inform us about the capabilities of our ancestors, offering another perspective on the cognitive skills that enabled early hominins to craft sophisticated tools.