Category Archives: mathematical analogies

Existential Wave Functions: A Proposed Model of the Self

I recently spent a week at my parents, staying in the bedroom where I had slept throughout high school and much of college. The room is essentially unchanged, except for my cork board and posters that are long gone. The home itself is comfortably similar, although my parents have added a back deck, and my dad is frequently, though usually unsuccesful, modifying the basement shower. Sitting outside on the deck or the concrete steps of the front porch, I’m struck by how much smaller scale everything seems. As the owners of the old Eggertson place tear down their car port, I notice how close the Holdners’ house is. I fancy I could throw a baseball from my aprents front yard and have Lyle catch it in his driveway. Even though I could always see the Wasatach peaks towering over the valley miles away, I realize my world was very small. But persistent. It has been ages since I’ve seen any of my old neighborhood peers, yet their parents are still here, and the facades of the houses where I played and deviated are still unchanged.  I’m tempted to walk over to the corner of my parents’ yard, climb up on the cinderblock wall, and walk over to David’s house to see if our shack still stood behind his garage. But I can’t imagine my knees enjoying the climb, nor the new neighbors tolertating my intrustion into their space. It isn’t all exactly the same.
On Thursday Susan Hunt picked me up for lunch. Over the ten years I’ve lived in Pittsburgh we get together for lunch or dinner whenever I’m in town for work or to visit my parents. We decided to eat at Ruth’s Diner, someplace we have never eaten together over the 25 years we’ve known each other, despite frequently driving up Emigration Canyon together. I ordered a pork loin sandwich; Susan had chicken enchiladas. We both drank water with lemon.
We talked mostly about her faithlessness draging her bishopric-first-counselor husband down, and about my potential move from Pittsburgh to San Diego or Palo Alto.
Eventually, inevitably, our conversation turned to our “Tribe” reunion eight months previous. The “Tribe,” a term coined, I believe, by Christina but never used by me, consisted of friends from high school. Everyone that I would have consider part of the “Tribe” attended except for Julie, who was apparently persona non grata, and Becky, who was living in Texas. David, a friend more of Nate and Curtis than a member of the group, came along also. The reunion consisted of a flurry of group e-mails planning the event, a Friday afternoon hike to Cecret Lake in Albion Basin and a Saturday evening dinner generously hosted by Nate at his house in West Jordan.
I couldn’t say, really, what had caused the “Tribe” to congeal in the first place. The girls had, I believe, attended the same LDS ward, and the guys had all gone to elementary school together. The first social interactions between the guys and girls had to have been initiated by the girls’ preference dances where Christina had asked John to one and me to another. I had fallen in love with Cindy, had my favorite high school date with Lara, became best friends with Susan, and become complexly intertwined with Christina. Amazingly, we had all mostly stayed friends through high school, the beginnings of college, missions and marriage. I had kept in touch with almost everyone reasonably well, at least until I moved to Pittsburgh ten years ago, when Susan became my only regular contact.  For our many years of separation and the variety of courses our lives have taken, we, for the most part, all got a long remarkably well, assuming our standard roles. And when we didn’t get along, it was also just as it was 25 years earlier.
As Susan and I talked over our lunch, a comment of her’s caught my attention: “I always think I’m a completely different person now. But after spending the evening with everyone, I realized: we’re all just the same.”
For the sameness of others, there was a lot of evidence. Lara pretty and quiet, sitting removed from the drama generated by Christina and me at Cecret Lake. Nate flittering among all the pretty women. Curtis making humorous, irreverent quips.  Me trying to be philosophical about it all.  And one friend—despite her frequent, almost violent, assertions that the girl we knew in high school was long dead—had mannerisms and assumptions that were so consistent with her former self, talking with her had the feel of a time-travel short story. Considering all the frustration we had experienced 25 years earlier with her, it wasn’t surprising that another friend  later commented “I wanted to grab her husband and ask ‘How do you cope? Do you lock yourself in the basement and scream?'”
Yet by any reasonable measure we, were not the same people. We were all married, several of us for over 18 years; Nate was working on his third marriage. We were all parents. We had mortgages. Over the 18 years of my marriage,  I knew I had changed a lot. Friends in Pittsburgh point out the tangible differences in me over just the past five years. I was a better parent to Jeremiah than I was to Alec, eight years older. I had experienced  professional, social, religious, and personal triumphs and failures. I had lived in Madison, Wisconsin and Pittsburgh, Pennsylvania, exposing me to a far greater cultural, racial, meteorological, and economic diversity than I had ever experienced growing up in Utah. Six years of cognitive therapy had surely changed something in me. I had to conclude that Nate’s divorces, John’s bouts of unemployment, Cindy’s living in Atlanta, Susan’s years of prosecuting sex crimes, Lara coping with her husband’s cancer had, among the multitude of other life events, had similarly changed them.
We were obviously different. We were undeniably the same.
In the 1950s scientists used radioactive traces to estiamte that 98% of our atoms are replaced each year (see NPR story on atom replacement). Materially we are not even close to being the same person. But the organization of that changing matter, from the DNA in our cells to the neural connections in our brains would have been largely similar to what they were in high school.
Searching for a suitable metaphor for personal persistence, I inevitably turned to mathematics to try to find a suitable answer, or at least a metaphor for what we are. Am I a line integral along a particular parameterized path through space-time? Am I a convolution between some my  “self” and the system of the universe? This seemed close but still left me unsatisfied. For example, the assumption of system invariance ignores the important aspect of my modifying this universe-system. I needed a more complex metaphor.
Musing on metaphors of the self, brings to mind a favorite saying from a former mathematics professor of mine:
Heisenberg Uncertainty Principle of the Social Sciences: Your in-laws can never really who you are since their act of observing you changes who you are.
I believe for “in-laws” there are a variety of substitutions that could be made. In fact, can you get together with any group of associates (friends, colleagues, in-laws) and not be modified by their presence? Of course the essence of quantum mechanics is the wave function.
So I ask, Can we think of ourselves as existential wave functions, akin to the quantum mechanic models of Heisenberg, that must match the boundary of conditions of the external world? When we gather around old friends, don’t they exert boundary conditions on us, boundary conditions similar (but not identical) to what they exerted on us in the past, thus eliciting from us present modes of existence similar (but again, not identical) to the modes exhibited by us in response to their presence in the past? When the group of friends becomes larger, are not the boundary conditions even more constrained, and thus evoking from us even more similar (to them) modes of existence?
The modes of a wave depends not only of the external boundary conditions, but also on the medium of the wave. For my analogy, the wave medium is our constituent self: the pattern of our material existence encoded into our DNA, the structure of our actual cells and organs, our history recorded in the neural connections in our brain. So since my medium is continually evolving, I can never exert the identical modes I did previously in response to a given set of boundary conditions.  But our self is not equally moldable throughout our lives. Obviously our bodies mature as teenagers (and then decay), but our minds also become less plastic as we age. Consequently, while we’ve been continually adding to my personality, the weights assigned to these changes decrease as we age, thus, perhaps the twenty-plus years of personal modifications since the “Tribe” was last together are but mere modulations compared to the personality formations while we were students together.
The “self” is not just a passive accumulation of past experience and response to external conditions, however,  but an active agent in the universe that can choose, in part, how much energy to exert into a particular mode, energy  minimization principles seem to fit well both with my wave theory of existence, and the observed continuity of the self I’m struggling to explain. When at the reunion I put my iPhone on Nate’s stereo dock, I set the music to play David Bowie, not Mary Gauthier, even though these days I listen to the former less than the latter. I assumed that none of my friends would know who Mary Gauthier was and this ignorance would require from me the energy of explanation, possibly even justification. Bowie, on the other hand, required neither explanation nor justification for my friends. Couldn’t it be similar to other aspects of our lives? We revert back to our old, familiar modes so as to minimize the energy we must exert? In fact, does not any sub-group of associates make use of a particular sub-language and mythology based on a common history to minimize the energy required to interact? Should we feel bad that we have different faces for different people? This model would suggest not necessarily.
Am I satisfied with my wave function metaphor with its modes of existence? Not really, but I think it is a good start at explaining the constancy we perceive amidst the change we experience. There are some interesting implications of the model. For instance, you cannot have one self that is portrayed in all circumstances, since each circumstance has a unique set of boundary conditions and thus require a different mode of existence.
Do I think that I’m the same person I was twenty-five years ago. Not at all. But I do think I’m similar, and I think that is good. While I am at times frustrated that I wake up each morning the same, less-than-desirable person (think Tillich, “You Are Accepted”), cannot I also be relieved that there is continuity in myself? Isn’t it good that for all the differences in the paths our lives have taken, Susan finds a “sameness” in me that is pleasant?  And more, wouldn’t I find it more frustrating to not have continuity? Without the continuity of my personality, couldn’t I wake up each morning with a different set of desires (books, music, clothing, for example), incompatible with the set I went to sleep with? (I hear an echo of a David Hume argument in my mind). My daily life retains value today because I’m essentially the same today as I was yesterday. But looking back at myself, I’m very glad that my wave function has, I believe, aged well.
I think my next metaphor might resort to cheese.

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