In [[William Rowan Hamilton]]'s influential paper "[[@THEORYCONJUGATEFUNCTIONS|Algebra as the Science of Pure Time]]," the term "**Pure Time**" carries a specific and multifaceted meaning. It's not just about everyday, linear time as we experience it, but rather a deeper, abstract concept with several layers: **1. A priori intuition:** Hamilton was heavily influenced by the philosopher Kant, who believed that space and time were not merely external realities, but inherent "a priori intuitions" structuring our experience. For Hamilton, "Pure Time" represented this fundamental intuition of time, independent of any specific objects or events. It was a pure flow of "being," not something measured by clocks or calendars. **2. Source of algebraic operations:** Building on this Kantian foundation, Hamilton argued that the basic operations of algebra (addition, subtraction, multiplication, etc.) could be derived directly from our intuitive understanding of [[Pure Time]]. He envisioned each algebraic quantity as representing a "step" or movement within this pure flow. Adding two numbers would then be like taking two steps forward in time while multiplying them would be like taking steps of a different size or direction. This direction of reasoning directly related to [[David Jaz Myers]]'s idea on [[Hub/Theory/Category Theory/dynamical system]]. **3. Dynamism and order:** Hamilton saw Pure Time not as a static container, but as an active principle of change and order. The flow of time itself generates relationships and structures that correspond to algebraic operations. This dynamism is what allows algebra to be not just a tool for calculations, but a language for describing the unfolding of reality itself. **4. Basis for a "Science of Time":** Ultimately, Hamilton's goal was to establish "Pure Time" as the foundation for a new scientific discipline, independent of geometry and space. He envisioned this "Science of Time" as a way to understand not just physical phenomena, but also the very nature of consciousness and thought. It's important to remember that Hamilton's ideas were quite radical for his time. While his "Science of Time" never fully materialized, the concept of Pure Time had a profound influence on mathematicians and philosophers, inspiring new ways of thinking about time, consciousness, and the relationship between mathematics and reality. # The modern interpretation of Pure Time Given the modern data manipulation technologies, algebraic operations can be automatically conducted by a network of autonomous machines, particularly a system known as [[Software-Defined Data Center]], as discussed in the video: [[@EBPFRoadInvisible2022|A road to invisible network]]. This formulation of a globally distributed, [[Zero-trust network access]] to a network of inter-locking events, could provide a new kind of accounting infrastructure to study the notion of [[Pure Time]]. Although, [[William Rowan Hamilton|Hamilton]] did not explicitly refer to his [[Algebra as the Science of Pure Time]] with [[Double Entry Bookkeeping]], the explicit content regarding [[Conjugate functions]] already showed that his approach is very similar to the way Double Entry Bookkeeping work with data, therefore, a journaling system. # References ```dataview Table title as Title, authors as Authors where contains(subject, "Pure Time") or contains(title, "Pure Time") or contains(subject, "Conjugation") ```