sometimes
work against correlations between that same thing and the other member
of the pair.
| Level 1 pair | Level 2 pair |
| coordinate\frequency | \ |
| position\momentum | |
| time\energy | |
| locate\propagate | \ |
| particle\wave | |
| structure\function | |
| inventory\flow | |
| code\excitation | \ |
| genotype\phenotype | |
| idea\organism |
In practice, too much focus on only one member of these pairs is often at the expense of harmony with the other member. The notion is hardly new. For example, ethologists now routinely consider the perspective of the gene as well as that of the organism in their study of behavior. Diffractionists look for peak broadening as useful evidence of shrinking crystal size. Privacy rights protect against excess "reduction" of organisms to replicable code. Auto mechanics warn against running a good thing into the ground (i.e. overdoing function at the expense of structure), and financial advisers recommend against keeping all of your assets in liquid form in part because they make inventory more volatile. Quantum mechanics now respect measuring-instrument induced perturbations, even as they try to figure ways around them. Some other examples are mentioned in passing here.
In theory, phenomenological complementarity associated with the second and third idea-pairs in this list is linked to non-commuting operators* in the dual vector space of quantum observations. Complementarity for the first triplet of idea-pairs (at least in certain cases) also flows from the reciprocal relation between feature size/separation in coordinate and frequency spaces that relate by Fourier transform. As far as I can tell, complementarity for the remaining idea-pairs in the list (including particles and waves) is rarely put into quantitative form.
Qualitative connections exist, however. For example, particles are typically characterized by coordinates in spacetime augmented by a set of physical dimensions, while waves are characterized by spatial/temporal frequencies augmented by a set of coherence widths. Replicable codes survive by remaining fixed and hence marking time, while steady-state excitations abide via control of energy as available work. Similarly, structure and inventory describe "what's located where" as does position, while function and flow describe a system's behavior as does momentum. All of the above concept-pairs thus map loosely with concept-pairs whose complementarity has more quantitative roots, even if some of them are quite impossible quantify.
| Level 1 pair | Level 2 pair |
| inward\outward | \ |
| yin\yang | |
| nurture\explore | |
| cooperation\competition** | |
| internal\external | \ |
| molecular sequence\reaction | |
| cellular metabolism\antibody | |
| bodily organ\hormone | |
| metazoan health\pair-bond | |
| mammalian family\hierarchy | |
| human culture\profession |
The last set lists perspectives that point inward and outward with respect to physical boundaries on different levels in living systems. These boundaries are in sequence: (i) molecule surfaces, (ii) biological cell walls, (iii) organ surfaces, (iv) metazoan skins, (v) gene-pool edges, and (vi) meme-pool boundaries. Recognizing complementarity here therefore translates into respect for such multi-level structures, as well as for the ideas used to help nurture them.
* For a discussion (and some more general references) about issues and mathematics associated with the energy-time uncertainty relation, check this note by John Baez.
** For more on cooperation/competition complementarity, see the discussion provided by Y. Bar-Yam in Making Things Work (Knowledge Press, 2004).