Symmetry

Symmetry in Mathematics

• Geometric shapes can be symmetric through reflectional, rotational, translational, or helical symmetry.
• Symmetry in logic refers to the property of a relation being the same in both directions.
• Symmetric logical connectives include 'and', 'or', and 'if and only if'.
• Symmetry exists in various mathematical structures, such as even and odd functions, symmetric groups, symmetric matrices, and Galois groups.
• Symmetry is seen in symmetric probability distributions and as skewness in statistics.

Symmetry in Science and Nature

• Symmetry in physics refers to invariance or lack of change under any transformation.
• Many laws of nature originate from symmetries.
• Noether's theorem states that for every continuous mathematical symmetry, there is a corresponding conserved quantity.
• Wigner's classification states that the symmetries of the laws of physics determine the properties of particles.
• Symmetry is observed in continuous and discrete symmetries of spacetime, internal symmetries of particles, and supersymmetry.

Symmetry in Biology and Chemistry

• Bilateral animals exhibit symmetry with respect to the sagittal plane.
• Plants and sessile animals often have radial or rotational symmetry.
• Symmetry changes in biology correspond to the appearance of new parts and dynamics.
• Symmetry is important in chemistry for understanding interactions between molecules and quantum chemistry.

Symmetry in Psychology and Neuroscience

• Humans and animals have special sensitivity to reflection symmetry.
• Bilateral symmetry is a key factor in perceptual grouping.
• Symmetry detection is fast, efficient, and robust to perturbations.

Symmetry in Social Interactions, Arts, and Architecture

• Symmetrical interactions include reciprocity, empathy, dialogue, and respect.
• Asymmetrical interactions may convey superiority or specialness.
• Symmetry is used in various art forms and architecture, such as visual arts, ceramics, textiles, and building design.

Symmetry Data Sources