"The complex plane is just the 90° rotation plane-the rotation plane with the structure imposed by the 90° Rotation metaphor added to it. Multiplication by i is "just" rotation by 90°. This is not arbitrary; it makes sense. Multiplication by -1 is rotation by 180°. A rotation of 180° is the result of two 90° rotations. Since i times i is -1, it makes sense that multiplication by i should be a rotation by 90°, since two of them yield a rotation by 180°, which is multiplication by -1." (George Lakoff & Rafael E Nuñez, "Where Mathematics Come From: How the Embodied Mind Brings Mathematics into Being", 2000)
"All pendulums exhibit such rotation, but for most pendulums this behavior is masked by other more prominent effects. For an ideal Foucault pendulum, the plane of oscillation would be seen as fixed by an observer positioned in the stars. (In this discussion we ignore the rotation of the earth around the sun, and the rotation of the sun around the center of the galaxy, and so forth.) Therefore the earthbound observer sees a slow rotation of the plane of oscillation and it is this remarkable feature of the Foucault pendulum which demonstrates, on a large scale, the rotation of the earth." (Gregory L Baker & Jammes A Blackburn, "The Pendulum: A Case Study in Physics", 2005)
"But like every profound mathematical idea, the concept of a group reveals something about the nature of the world that lies beyond the mathematician’s symbols. […] There is […] a royal road between group theory and the most fundamental processes in nature. Some groups represent - they are reflections of - continuous rotations, things that whiz around and around smoothly." (David Berlinski, "Infinite Ascent: A short history of mathematics", 2005)
"In theory, any earth-based pendulum is a Foucault pendulum. However, a realistic Foucault pendulum is a one that is specially constructed to highlight the rotation of its plane of oscillation due to the earth’s rotation relative to a frame of reference fixed in the stars. That is, the plane of the pendulum’s oscillation is fixed relative to the stars while the earth rotates underneath it." (Gregory L Baker & Jammes A Blackburn, "The Pendulum: A Case Study in Physics", 2005)
"[...] one of the fundamental intellectual breakthroughs in the historical understanding of just what i = √-1 means, physically, came with the insight that multiplication by a complex number is associated with a rotation in the complex plane. That is, multiplying the vector of a complex number by the complex exponential e^iθ rotates that vector counterclockwise through angle θ." (Paul J Nahin, "Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills", 2006)
"Geometric algebra provides the most powerful artefact for dealing with rotations and dilations. It generalizes the role of complex numbers in two dimensions, and quaternions in three dimensions, to a wider scheme for dealing with rotations in arbitrary dimensions in a simple and comprehensive manner." (Venzo de Sabbata & Bidyut K Datta, "Geometric Algebra and Applications to Physics", 2007)
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