How a system of symbols can reveal hidden physical truths
In short: We often view notation as a mere container for ideas, but it can also be a generative tool. By formalizing complex actions into symbols, we can uncover hidden connections and predict entirely new possibilities that were previously invisible to the human mind.
The relationship between notation and discovery is best illustrated by the development of a juggling notation in the mid-1980s. Before this formal system existed, juggling tricks were often viewed as isolated feats. However, once a precise notation was established, it revealed unexpected connections between existing tricks. This transformation proved that notation is not just a passive record of what we already know; it is an active lens that can expose underlying structures in physical movements.
Beyond simply mapping what is already there, this notation began to reveal emerging patterns. These patterns suggested the existence of new, previously unknown tricks that had never been performed before. By identifying these mathematical or structural possibilities, the notation provided a roadmap for innovation. It fundamentally changed how people thought about, taught, and learned juggling, moving the practice from a series of learned habits to a structured field of exploration where new material could be systematically built upon.
This principle resonates across various disciplines, including mathematics. For instance, Wilson's theorem in number theory provides a way to determine if a number is prime by multiplying all preceding integers and adding one. The theorem highlights how specific logical structures can define the boundaries of prime numbers. While ideas are the ultimate goal, the power of a good notation is indispensable because it allows us to see the 'shape' of an idea, making the invisible visible and the unknown reachable.
Ultimately, the goal of notation is to move from observation to prediction. When we create a language for a complex system—whether it is the physics of juggling balls or the properties of prime numbers—we gain the ability to navigate that system with greater precision. It allows us to move past trial and error toward a more deliberate form of discovery.
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Sources
- Summary by Intellect · source: Notation, Patterns and New Discoveries - Dr Colin Wright
- Also: Notation, Patterns & New Discoveries
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