Circles rolling on circles (2014)
&gt; Each of the above explanations describes the circle&#x27;s movement as a decomposition into rotation and revolution, but in reality no such decomposition is taking place.<p>Comments:<p>1. This is a specific instance of a widely taught principle from Buddhism: “Concepts are not real things; a conceptualized world is a dead world. Living actualities lose their life when put into concepts.” ― Gyomay M. Kubose, Everyday Suchness: Buddhist Essays on Everyday Living<p>2. For a broader audience, I&#x27;d probably rephrase the above as: &quot;Concepts are human representations; they are <i>different</i> than the actual phenomena.&quot;<p>3. The above decomposition is represented in many of our brains. In that sense it is &quot;real&quot; as any other form of physical matter. Why? The concept is (somehow) encoded in the structure and relationships of neurons (as I understand it).<p>4. I&#x27;m torn: saying that &quot;decomposition&quot; isn&#x27;t &quot;taking place&quot; is simultaneously insightful and obvious. In any case, as phrased, for a modern audience, it risks missing the point; namely, a decomposition is a useful way of understanding the world. For example, the idea of decomposing motion into {rotation and translation} is similar to decomposing the position of a point by referring to its {position in a coordinate system}, whether it be Cartesian, polar, barycentric, or otherwise. Doing so helps us bring analytic methods to bear.