Symmetry

Big Frank has been thinking about symmetry lately. Not being a symmetrician or a bifurcationologist he admittedly is coming at this subject with less than, a whole lot less than, any expertise. Nonetheless, this is something that merits some thought. Take a look at yourself – go ahead, look down at your body. What do you see? OK, there are two legs, two arms, and if you look in the mirror a couple of eyes and a left side that pretty much matches the right side (we are not getting into small differences here – granted it’s not an exact match). Still if you split yourself down the middle (God forbid) you would have two pretty equal pieces. This is true right across the spectrum of the rest of your mammal, your animal, and your plant relatives - OK, the plants are pretty distant. Even when you look at the constituent parts – cells, molecules, atoms etc. And if we move up to a larger dimension we find it true there also – planets, stars, and galaxies. So why is this and what does it mean? Big Frank is not sure, but he’s on it.

Big Frank is not going to go into the mathematical symmetry (he pretty much stopped after algebra); however, in physics it has been generalized to mean invariance—that is, lack of any visible change—under any kind of transformation. In fact this has become a powerful tool in theoretical physics. Not surprisingly, one could state that practically all laws of nature originate in symmetries. In fact, this role inspired the Nobel laureate P.W. Anderson to write in his widely-read 1972 article More is Different that "it is only slightly overstating the case to say that physics is the study of symmetry."

And so, one might ask – certainly Big Frank does: what about in social interactions? Well, it turns out in fact people in healthy relationships do observe symmetry in their interaction, in a variety of contexts. You can find this is assessments of reciprocity, empathy, apology, dialog, respect, and justice. Symmetrical interactions send the message "we are all the same" while asymmetrical interactions send the message "I am special; better than you". Peer relationships are based on symmetry, power relationships are based on asymmetry. So, one might say to the extent that one prefers asymmetrical interactions, one sets up an imbalance. And we all know what happens when things are out of balance, don't we?