Chapter 1: The Concept of Distance Through Time

The notion of distance has undergone significant transformation over the centuries, influenced by cultural, scientific, and philosophical developments. Recently, I encountered an announcement for a conference focused on distance. The call for papers outlined the theme:

The long eighteenth century was marked by an exploration of cultural distance through overseas ventures, empires, travel, and commerce. These varied interactions prompted comparisons among different states, communities, languages, and traditions. In light of the physical and social distancing experienced in 2020, this virtual conference encourages participants to reflect on how current experiences can foster a renewed understanding of the role distance played in the communities and cultures of the eighteenth century.

This perspective piqued my interest and inspired me to contribute my thoughts on the subject.

George Berkeley, a notable philosopher of the 18th century, extensively addressed distance in his work, AN ESSAY TOWARDS A NEW THEORY OF VISION (1709). He introduces the concept of distance right from the beginning, underscoring its significance in his analysis. Intriguingly, Berkeley's interpretation of distance may appear unconventional from a contemporary standpoint.

Here are two key points from Berkeley's essay:

1. My aim is to elucidate how we perceive distance, size, and position of objects through sight. I will also explore the differences between the ideas formed by sight and touch, and whether there exists a common idea shared by both senses.
2. It seems generally accepted that distance cannot be directly perceived. As distance is a line directed towards the eye, it only projects a single point onto the retina, which remains constant regardless of the object's distance.

This suggests that the very notion of distance was still evolving. Berkeley’s assertion raises questions about whether distance could be viewed as an inherent quality of the objects we observe. His viewpoint indicates a significant shift in the understanding of perception and distance, asserting that it is logical to claim that distance itself is not visible—a notion that appears self-evident to us today.

The etymology of the term "distance" reveals an interesting history; its definition as “remoteness of space, extent of space between two objects or places” originated in the late 14th century. Earlier meanings included “a dispute or controversy, civil strife, rebellion,” stretching back to the early 14th century.

In my further investigation, I found that Berkeley’s second point challenges Descartes’ perspective. Descartes proposed, aligning more closely with modern interpretations, that distance could be inferred from visual cues—the smaller an object appears, the further away it is. Berkeley, however, dismissed this idea, arguing that you cannot see distance because the same visual information reaches the eye, irrespective of the object’s proximity. While it seems that Berkeley misinterpreted Descartes’ argument—possibly deliberately—this difference in understanding highlights how our contemporary views are shaped by the legacy of Descartes, who, despite being further away in time, feels closer to us than Berkeley.

This exploration of historical thought reveals how early scientists, in their inquiries, grappled with concepts that challenge our current assumptions—assumptions that had yet to be established. For instance, even after Antoine Lavoisier published his Traité élémentaire de chimie (1789), which marked a pivotal moment in modern chemistry, he still considered heat to be a material substance (refer to p. 245 of The Age of Wonder (2008) by Richard Holmes).

Thus, the gap between our understanding and that of earlier thinkers highlights the underlying assumptions we hold. Engaging with these historical texts allows us to experience a profound sense of cultural divergence, transforming it into a journey of discovery.

Chapter 2: Insights from GMAT Math and Speed-Distance-Time

In the context of distance, mathematical concepts can also provide clarity. The following video discusses types of distance questions typically encountered in GMAT Math:

This video titled "GMAT Math | Types of Distance Questions" offers valuable insights into the various ways distance is represented in mathematics.

Moreover, understanding speed, distance, and time is crucial for grasping these concepts. The next video focuses on solving speed-distance-time questions in mathematics:

Titled "How To Work Out Speed Distance Time Questions in Maths," this video further elucidates the interrelation between these fundamental concepts.