Love and Relativity

From time to time, I’ve had occa­sion to won­der whether it is pos­si­ble to numer­i­cal­ly quan­ti­fy our feel­ings; that is, their inten­si­ty, mag­ni­tude, depth. I per­son­al­ly think the answer is a resound­ing “no,”  but if we were to assume that such a thing were pos­si­ble, the impli­ca­tions would be both fas­ci­nat­ing and far-reach­ing — in par­tic­u­lar, might it allow us as humans to mea­sure our roman­tic rela­tion­ships such that we could make explic­it com­par­isons between them, and then ren­der sup­pos­ed­ly ratio­nal deci­sions accordingly?

I find the above a heavy ques­tion if for no oth­er rea­son than it jux­ta­pos­es con­cepts some­times thought to be anti­thet­i­cal to each oth­er; name­ly, love and ratio­nal­i­ty, think­ing and feel­ing, emo­tion and log­ic. Of course none of the afore­men­tioned pair­ings are actu­al­ly inher­ent­ly incom­pat­i­ble — indeed, expe­ri­ence has led me per­son­al­ly to believe that love and ratio­nal­i­ty, and think­ing and feel­ing, and emo­tion and log­ic, can and often do go hand in hand — but soci­ety tends to present them as being at odds with each oth­er (if only because doing so makes for good media entertainment). 

Feelings, Past and Present

Recent­ly, I learned that a friend of mine — let’s call him Andrew, for the sake of con­ve­nience — was get­ting mar­ried. I was delight­ed for him, but was sur­prised when he told me that while he loved his fiancée, he believed that he had loved a pre­vi­ous part­ner more, dur­ing the time that he and the pre­vi­ous part­ner were togeth­er. To clar­i­fy Andrew’s posi­tion, he was­n’t stat­ing that he still loved his pre­vi­ous part­ner (let’s call her Bel­la); indeed, he was very clear that he only loved his fiancée (let’s call her Car­o­line). Rather, his point seemed to be more that his feel­ings for Bel­la, through­out the dura­tion of their roman­tic rela­tion­ship, were per­haps of a greater inten­si­ty than his cur­rent feel­ings for Caroline.

I have nei­ther inten­tion nor desire to pass judg­ment on the nature of Andrew’s rela­tion­ship in it of itself, but I do think that it rais­es fas­ci­nat­ing ques­tions in the abstract. Andrew’s sit­u­a­tion, and his views con­cern­ing it, intrigue me because — based on my under­stand­ing — he is essen­tial­ly say­ing (at least implic­it­ly) that he loves Car­o­line enough to mar­ry her and want to spend the rest of his life with her; but also, he does not love her as pas­sion­ate­ly, deeply, mad­ly, what have you, as he knows that he, in the­o­ry, has the capac­i­ty to. This is, of course, my own inter­pre­ta­tion of Andrew’s posi­tion, and it may well be that he would dis­agree with the char­ac­ter­i­za­tion. Whether or not it is an accu­rate assess­ment, I think my inter­pre­ta­tion rais­es an inter­est­ing question:

Is it log­i­cal to con­tin­ue see­ing some­one that makes you hap­pi­er than you are by your­self, but not as hap­py as you know you have the the­o­ret­i­cal capac­i­ty to be?

An Illustration

To bet­ter describe the above quandary, I find that the use of an illus­tra­tive hypo­thet­i­cal is very help­ful. How­ev­er, some famil­iar­i­ty with the eco­nom­ic the­o­ry of util­i­ty is nec­es­sary in order to ful­ly under­stand the hypo­thet­i­cal, so I (attempt to) give a brief expla­na­tion of it below.

Now, I feel the need to issue a dis­claimer with respect to both the illus­tra­tion and my rather slap­dash expla­na­tion of util­i­ty the­o­ry below — kind­ly note that num­bers are not my forte; and that I have only a rather dat­ed bach­e­lor’s degree in eco­nom­ics that, even in its the­o­ret­i­cal prime, was large­ly unused. That said, any­one more math­e­mat­i­cal­ly inclined, please do let me know of any mis­takes I’ve made!

Util­i­ty the­o­ry in eco­nom­ics harkens back to the ear­li­er ques­tion of whether we can some­how quan­ti­fy our feel­ings, more specif­i­cal­ly, our hap­pi­ness. In eco­nom­ics, util­i­ty loose­ly refers to the degree of plea­sure or sat­is­fac­tion that one derives from some sort of con­sump­tion or eco­nom­ic activ­i­ty. A util­i­ty func­tion is often used to describe a pref­er­ence for one set of goods, X, ver­sus anoth­er set of goods, Y, and may be expressed as some­thing like:

U(X,Y) = X^\alpha Y^\beta.

For our pur­pos­es, how­ev­er, it is suf­fi­cient that the util­i­ty, or “sat­is­fac­tion,” derived from a par­tic­u­lar activ­i­ty is expressed as a sim­ple numer­ic val­ue, for example:

U(eating \space ice \space cream) = 5

Which here essen­tial­ly means that the sat­is­fac­tion I derive from eat­ing ice cream is 5 utils (units of hap­pi­ness, basi­cal­ly), or phrased dif­fer­ent­ly, the act of con­sum­ing ice cream puts me at a util­i­ty lev­el of 5.

I will use three peo­ple — Per­son O, our main char­ac­ter, for all intents and pur­pos­es; Per­son A, a roman­tic inter­est of Per­son O; and Per­son B, anoth­er (sub­se­quent) roman­tic inter­est of Per­son O (belat­ed spoil­er alert, I sup­pose, but alas, Per­son O and Per­son A do not work out) — and eval­u­ate their util­i­ty lev­els based on three dis­tinct sit­u­a­tions, defined as follows:

O: Per­son O is not roman­ti­cal­ly attached

A: Per­son O is roman­ti­cal­ly attached to Per­son A

B: Per­son O is roman­ti­cal­ly attached to Per­son B

The nota­tion here is slop­py on my part — I under­stand that it is in poor form for me to use the same let­ter to rep­re­sent both a sit­u­a­tion and a per­son. But I think that for our very lim­it­ed pur­pos­es, doing so makes the illus­tra­tion less tedious lat­er, as the iden­ti­cal­ly-named sit­u­a­tion and per­son are inex­tri­ca­bly intertwined. 

Sup­pose that when Per­son O is not roman­ti­cal­ly attached — that is, as a sin­gle lady — she enjoys a util­i­ty lev­el of 10:

U(O) = 10

Sup­pose, then, that Per­son O engages in a roman­tic rela­tion­ship with Per­son A, and that being with them brings her to a util­i­ty lev­el of 20. We are assum­ing that being in a rela­tion­ship with Per­son A (or any per­son, for the sake of this exam­ple) only increas­es Per­son O’s util­i­ty lev­el; oth­er­wise, sup­pos­ed­ly, she would sim­ply choose to remain roman­ti­cal­ly unattached:

U(A) = 20

That’s all well and good for Per­son O, but alas, sup­pose she and Per­son A ulti­mate­ly end their roman­tic rela­tion­ship. Per­haps after endur­ing the ini­tial emo­tion­al tur­moil that the stan­dard breakup entails, Per­son O’s util­i­ty lev­el would even­tu­al­ly return to 10:

U(O) = 10

Sup­pose, now, that Per­son O even­tu­al­ly meets and becomes roman­ti­cal­ly attached to Per­son B. Again, let’s assume that being in a rela­tion­ship with Per­son B only rais­es Per­son O’s util­i­ty, in this case to 15 such that:

U(B) = 15

This, I think, is where opin­ions can and will dif­fer as to what Per­son O’s opti­mal course of action is: more specif­i­cal­ly, does it make sense for Per­son O to remain with Per­son B, even though she knows she has the capac­i­ty to be hap­pi­er with some oth­er part­ner (as demon­strat­ed by her past rela­tion­ship with Per­son A)? Or does it make more sense for Per­son O to remain roman­ti­cal­ly unat­tached, pre­sum­ably until she encoun­ters anoth­er part­ner, i.e. some yet undis­cov­ered Per­son C, who can make her at least as hap­py as she was with Per­son A?

At first blush, it seems the answer log­i­cal­ly has to be that Per­son O should con­tin­ue see­ing Per­son B; after all, U(B) > U(O). But reflex­ive­ly — at least for me per­son­al­ly — this does­n’t seem quite right. To wit, a more threshed-out explo­ration of the facts reveals that the issue is both far more nuanced and sub­jec­tive than it first appears, and that there is real­ly no one cor­rect answer.

Finding the Optimal Choice

Recall that the cen­tral issue of our hypo­thet­i­cal is that being with Per­son B makes Per­son O hap­pi­er than she is by her­self, but less hap­py than she was when she was with Per­son A, such that:

U(A)> U(B) > U(O)

It is seem­ing­ly ratio­nal for Per­son O to remain with Per­son B, if only because U(B) > U(O). But my ques­tion is, should it mat­ter that Per­son O was hap­pi­er with Per­son A, such that U(A) > U(B)? Note that for all intents and pur­pos­es, Per­son A is gone, out of the pic­ture, removed entire­ly — there is no hope of rec­on­cil­i­a­tion, so it isn’t as if Per­son O can sim­ply return to Per­son A and by effect that high­er util­i­ty lev­el of 20.

To that end, I think the issue becomes whether the sim­ple knowl­edge that she has the capac­i­ty to be hap­pi­er with a part­ner than she is now, both­ers Per­son O; that is, whether such knowl­edge detracts from Per­son O’s cur­rent util­i­ty. It may, or it may not, or it may both­er Per­son O but not enough to dis­suade her from remain­ing with Per­son B — real­ly, the pos­si­bil­i­ties are end­less. But let’s sup­pose that it does both­er Per­son O, know­ing that there is the­o­ret­i­cal­ly some­one out there, whether Per­son A or some yet undis­cov­ered Per­son C, who can make her hap­pi­er than she is now.

Indeed, we can assign the act of so know­ing a util­i­ty val­ue, but because it makes Per­son O unhap­py, it would be a neg­a­tive val­ue. For our pur­pos­es, we can refer to such neg­a­tive util­i­ty as disu­til­i­ty, which is essen­tial­ly the oppo­site of util­i­ty — where util­i­ty describes the plea­sure or sat­is­fac­tion a per­son derives from a cer­tain activ­i­ty, disu­til­i­ty describes the dis­plea­sure or dis­sat­is­fac­tion a per­son derives from a cer­tain activ­i­ty. Greater disu­til­i­ty (that is, greater dis­plea­sure) is asso­ci­at­ed with a larg­er numer­ic val­ue in absolute terms: for exam­ple, I would say that an activ­i­ty bring­ing me a disu­til­i­ty of -10, is of a greater disu­til­i­ty than an activ­i­ty bring­ing me a disu­til­i­ty of -5, even though this may seem coun­ter­in­tu­itive (since ‑5 > ‑10).

Return­ing to our illus­tra­tion, let’s sup­pose the disu­til­i­ty that Per­son O derives from know­ing she could poten­tial­ly be hap­pi­er is -6 such that:

U(knowing) = ‑6

Recall that when Per­son O was unboth­ered by such knowl­edge, the util­i­ty she derived from being with Per­son B was 15. But now, oper­at­ing under the assump­tion that Per­son O is so both­ered, we can incor­po­rate the rel­e­vant disu­til­i­ty to define a new sit­u­a­tion: B^{\prime}, where­in Per­son O is roman­ti­cal­ly attached to Per­son B, but derives neg­a­tive util­i­ty from know­ing that she could the­o­ret­i­cal­ly be hap­pi­er with some­one else (in com­mon par­lance, from know­ing that she is “set­tling,” so to speak). Recall­ing that U(knowing) = ‑6 and U(B) = 15, I think that U(B^{\prime}) would prob­a­bly rep­re­sent an amal­gam of those cir­cum­stances such that:

U(B^{\prime}) = 9

In such a case, it would indeed make more sense for Per­son O to remain roman­ti­cal­ly unat­tached, rather than to con­tin­ue see­ing Per­son B, since U(O) > U(B^{\prime}). Crit­i­cal­ly, though, if I had assigned the act of know­ing a small­er disu­til­i­ty val­ue (in absolute terms), the out­come could have been very dif­fer­ent. For exam­ple, if I instead set U(knowing) = ‑4, then U(B^{\prime}) = 11, and it would again be log­i­cal for Per­son O to remain with Per­son B.

The Individuality of Experience

As demon­strat­ed above, what the opti­mal course of action is — that is, whether or not to com­mit to a per­son who makes you hap­pi­er than you are on your own, but less hap­py than you demon­stra­bly know you could be — is doomed to be a sub­jec­tive inquiry, one entire­ly depen­dent on the per­son. Some peo­ple will derive sig­nif­i­cant disu­til­i­ty from know­ing that they are not as hap­py as they could be. Oth­ers won’t care, and their opti­mal course of action will dif­fer accordingly.

To that end, I am of the mind that expe­ri­ence, even a pure­ly phys­i­cal expe­ri­ence, is a unique­ly indi­vid­ual phe­nom­e­non. Imag­ine that I pinch you on the cheek; what you might per­ceive as a pin­prick of pain, anoth­er might reg­is­ter as a punch to the face. This is a dra­mat­ic, exag­ger­at­ed exam­ple, of course: it is unlike­ly that there would be such dis­crep­an­cy in how two indi­vid­u­als per­ceive pain — espe­cial­ly if both are what we might call peo­ple of “rea­son­able firm­ness,” a stan­dard used in legal fic­tion — but my point is more that per­cep­tion is a unique­ly indi­vid­ual sen­sa­tion; no two peo­ple will ever share exact­ly the same expe­ri­ence, even in response to the same stim­u­lus. Dif­fer­ences may be triv­ial, but dif­fer­ences they are nonetheless.

Accord­ing­ly, I would posit that we all expe­ri­ence and thus reg­is­ter love dif­fer­ent­ly. Some peo­ple will be more like Andrew — able to implic­it­ly quan­ti­fy the inten­si­ty of their feel­ings, and thus view their rela­tion­ships rel­a­tive to each oth­er. I per­son­al­ly empathize more with a slight­ly more exis­ten­tial approach: that is, feel­ings either are or aren’t, in an almost bina­ry sense, and can­not be mea­sured in a way that lends itself eas­i­ly to comparison. 

The illus­tra­tion involv­ing Per­sons O, A, and B is a gross sim­pli­fi­ca­tion of real-world cir­cum­stances and feel­ings, of course. There are count­less oth­er fac­tors that a real per­son would take into account when decid­ing whether to com­mit to some part­ner that makes them hap­py, but not as hap­py as they know they could be — when I pre­sent­ed this sce­nario to my friends, for exam­ple, near­ly all of them asked, “How old is Per­son O?”,  sug­gest­ing that tim­ing and age are just some of the man­i­fold fac­tors a per­son may con­sid­er in eval­u­at­ing the sit­u­a­tion. Oth­ers asked whether util­i­ty could increase over time; that is, whether feel­ings could change and grow, which is cer­tain­ly pos­si­ble and per­haps even prob­a­ble (for the lim­it­ed pur­pos­es of the above illus­tra­tion, how­ev­er, I oper­at­ed under the assump­tion that they did not).

I think, then, that the only con­clu­sion has to be that there is sim­ply no uni­ver­sal­ly opti­mal choice in mat­ters of the heart. It’s a roman­tic notion — the sug­ges­tion that feel­ings tran­scend quan­tifi­ca­tion, that love can defy log­ic (or per­haps, equiv­a­lent­ly, that log­ic can defy love) — but one that I believe must be true giv­en how indi­vid­u­al­ly tai­lored, how unique to the indi­vid­ual, the phe­nom­e­na of expe­ri­ence and per­cep­tion are.

The con­tent of this post con­sti­tutes an expres­sion pure­ly of my per­son­al opin­ion and con­jec­ture, and accord­ing­ly, is intend­ed only to enter­tain rather than to inform or instruct. If you see any errors, please *****@*******ol.me”>let me know.