Contextuality From Quantum Physics to Psychology by Dzhafarov Ehtibar N

Author:Dzhafarov, Ehtibar N.
Language: eng
Format: epub
ISBN: 9789814730624
Publisher: World Scientific Publishing Company
Published: 2016-04-30T04:00:00+00:00

2.Symmetry

Most of us have a good idea of what the term symmetry means, typically defining symmetry as meaning some type of correspondence in the shape or configuration of an image or object. Accordingly, people often refer to the bilateral or mirror symmetry of the human face or body when defining the term. Others often refer to numerous geometric shapes, such as a circle, star, or octagon as having symmetry, stating how these shapes look exactly the same when rotated or reflected in certain ways. Although this commonplace understanding of symmetry is fundamentally correct, the principle of symmetry is one that applies to much more than the shapes or patterns of objects and images. Indeed, the principle of symmetry is a much more abstract concept that can be applied to understanding the regularity or order of anything, from mathematical functions, to chemical compounds and crystals, to quantum mechanics and the fundamental conservation laws of physics.

To understand this more general notion of symmetry, we can define the term symmetry as simply referring to an equivalence or invariance of some kind, given some form of transformation. The vagueness of this definition is deliberate, in that ‘some kind’ of equivalence or invariance and ‘some form’ of transformation could stand for almost anything. For example, an equivalence or invariance could refer to the fact that a square looks exactly the same when rotated by 90 degrees or reflected about a midline axis, or that a stack of three tennis balls in a cylindrical tennis ball container would look the same if one permutes the order in which the tennis balls are stacked on top of each other (the original and permuted tennis ball arrangements would be indistinguishable from each other), or to use a more large scale example (one fundamental to scientific inquiry), finding that the results of an experiment conducted on Wednesday September 8th 2014 at 9 am at the Psychology Department at the University of Cincinnati in Ohio, USA, replicate the results obtained using the same experimental method on Friday March 12th 2013 at 1 pm at the Psychology Department at University of Auckland in New Zealand, which also replicate the results obtained from the Department of Cognitive and Information Sciences at the University of California Merced, on Monday November 21st, 2012 at 5:30 pm.

As is the case in each of the previous examples, the central aspect of what makes something symmetric, is whether the specific phenomena or observable in question is indistinguishable with respect to a specific type or set of transformations. With this more abstract definition of symmetry in hand, one can also start to see how the symmetry of an object, phenomena, or thing can be quantified, in that some object, phenomena, or thing may have more or less symmetry than some other object, phenomena, or thing. To use a common example, consider the geometric shapes of a circle and an equilateral triangle. There are an infinite number of rotations and midpoint reflections that leave a circle looking the same,

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