**Title: Grasping the Endless Journeys of Numbers: An Overview of Benjamin Wardhaugh’s *Counting: Humans, History, and the Infinite Lives of Numbers***
In 2020, I first encountered Benjamin Wardhaugh’s work through an exceptionally favorable review of his thought-provoking book, *The Book of Wonder*: *The Many Lives of Euclid’s Elements*. This led me to delve deeper into his editorial achievement, *Reading Mathematics in Early Modern Europe*, which I also reviewed with enthusiasm. Both publications are products of the captivating research endeavor, *Reading Euclid*. Recently, I had the pleasure of receiving Wardhaugh’s newest release, *Counting: Humans, History, and the Infinite Lives of Numbers*. As someone fascinated by numerical history, I eagerly immersed myself in this latest venture through the annals of mathematics.
Wardhaugh’s latest volume invites readers on an anthropological journey through counting, scrutinizing its development from the Stone Age to the modern digital landscape. It challenges traditional linear historical narratives, instead weaving a complex tapestry of diverse cultural customs. As Wardhaugh proposes, counting encapsulates a vast spectrum of varied cultural practices that often resist a singular interpretation. Drawing from the philosopher Gottfried Leibniz, he describes counting as ‘repeated attention’ – an enchanting perspective revealing simplicity hidden within complexity.
The book is artfully organized as a tree with roots, various branches, and numerous twigs, each symbolizing the progression of counting across different cultures and epochs. Wardhaugh underscores that the narrative of counting is not a uniform story, but a compilation of interwoven trajectories representing humanity’s varied practices.
The initial section, *Roots*, delves into the pre-counting phase – our intrinsic capacity to estimate quantities, a trait shared with animals, alongside prehistoric artifacts that suggest early counting methods. The subsequent section, *Counting before Writing*, investigates conjectures about the emergence of counting terminology and artifacts from prehistoric Africa seen as proto-counting implements.
After establishing the foundational roots, Wardhaugh guides us through branches reflecting various cultural advancements in counting. The *Counting with Words and Symbols in the Fertile Crescent* section explores ancient Mesopotamian counting systems, enriched with personal narratives from historical contexts. He employs vivid stories, such as Egypt’s Teianti and her transaction, highlighting the profound integration of counting into daily existence.
The branch titled *Counters* examines ancient Greek and Roman counting practices, investigating intriguing devices such as counting boards still utilized up to the thirteenth century. The third branch discusses the crucial emergence of numeric symbols from India and their transmission through Islamic cultures to Europe, illustrated with accounts of historical figures like Bhaskara II and Ibn Mun’im.
Wardhaugh’s narrative takes a turn towards Eastern Asia, introducing *Machines that Count*. This branch investigates abacus systems in China, Japan, and Korea, and extends to nineteenth-century innovations like Ichitaro’s and Hollerith’s tabulating machines. It concludes with an examination of contemporary counting in the digital space, particularly focusing on social media metrics.
In a novel viewpoint, he unveils the realm of *Counting Words and More in the Pacific World*, presenting intriguing practices from Australian indigenous cultures to the complexities of Tongan counting. The final branch delves into counting across the Americas, exploring versatile systems from Alaskan tally sticks and Pomo currency beads to the sophisticated Mayan calendars.
Wardhaugh’s conclusion succinctly encapsulates the diverse trajectories of counting, highlighting its cultural and historical richness and limitless variety. Despite the absence of conventional footnotes, the book offers a well-researched bibliography and index, adding to its academic rigor.
*Counting: Humans, History, and the Infinite Lives of Numbers* functions not merely as a historical evaluation but as a contemplation on counting’s integral role in everyday life. From tallying blessings and calories to votes and days, the book provides an enriched understanding for all readers, not limited to mathematicians or historians, of the everyday act of counting. Wardhaugh’s work stands as a tribute to the lasting intricacies, cultural importance, and historical depth of a practice that frequently goes unnoticed in its straightforwardness yet forms the backbone of human civilization.