Physics, said Anderson, is almost the study of symmetry
Everyday talk of symmetry means pleasing balance. Mathematicians mean something sharper: a shape that stays itself under a move such as a flip, a turn, a slide, or a resize. Physicist P. W. Anderson went further in 1972, nearly equating physics itself with the hunt for those invariances.
Reflectional symmetry splits an object along a line—or a plane in three dimensions—into matching mirror halves. Rotational symmetry lets you spin around a fixed point or axis and still recognise the whole. Translational symmetry survives a uniform slide; helical symmetry mixes a slide with a twist along a screw axis. Scale symmetry keeps the outline when you enlarge or shrink; fractals show a related pattern of self-similar parts. Glide reflections and rotoreflections combine flips with slides or turns.
The same idea travels far beyond shapes. A relation is symmetric when Rab implies Rba—Paul and Mary being the same age works both ways. In logic, connectives such as and, or, and if-and-only-if behave symmetrically, while plain if does not. Operations that leave a property untouched form a group, so even and odd functions, symmetric matrices, and Galois groups each carry their own flavour of invariance. Noether’s theorem links continuous symmetries to conserved quantities such as energy or momentum; Wigner’s classification ties the symmetries of physical law to the particles nature allows.
Biology wears the pattern on its sleeve. Bilateral animals, including people, are roughly mirrored across the sagittal plane that divides left from right; movers need a head and a tail, so left–right pairing of muscles and bones follows, even when organs stay asymmetric. Sessile creatures such as sea anemones often favour radial or rotational layouts; echinoderms—starfish, sea urchins, sea lilies—display fivefold symmetry. Chemists classify molecules with rotation axes Cn (a C3 axis means a 120° turn restores the look), mirror planes σ, and inversion centres i, all returning to the identity E after enough repetitions.
Human vision is biased too. Ernst Mach noted in 1897 that a vertical mirror axis, like a face, stands out more than other regularities. Later work finds reflectional symmetry spotted in roughly 100 to 150 milliseconds, with fMRI studies by Sasaki and colleagues lighting up extrastriate occipital areas such as V3A, V4, V7, and the lateral occipital complex rather than primary visual cortex.
Source: Symmetry
