These observations allow one to formalize the definition of reflection: a reflection is an involutive isometry of an Euclidean space whose set of fixed points is an affine subspace of codimension 1.
Through surveys researchers first determined that subjects perceive future events as being closer than past events, even if the events are equidistant.
A music file or podcast data isn't an analog waveform like this, but rather it's just a long set of points equally spaced apart with their associated values.
According to Descartes, this is just as certain as it is inherent in the idea of a circle that all points of the circle are equidistant from the center.
If we play some transformation and follow where all three of these vectors go, the property that greed lines remain parallel and evenly spaced has a really important consequence.