The following essay is an attempt to frame one aspect of human behavior in such a way that it can be made quantitative, once suitable psychometric association of the parameters is made. At this point, it is merely a vague outline, with lots of supposition about the way various parameters are introduced and described. Nevertheless, from my discussion with a few others who have experienced grief, the exponential decay model seems realistic. I would be interested in hearing comments at em@operanut.com .

Decrease of Grief with Time

© Emory Menefee

Grief can be defined as a more or less prolonged mental suffering or distress following the loss or afflction of someone loved, or in some cases the loss of something held dear. While grief is primarily a human phenomenon, it can occur in other animals as well. The extent of grief is difficult to estimate in quantitative terms, since its experience is so nearly internalized. Nevertheless, some general observations can be made. Our own experience tells us that the pain of grief peaks sharply immediately following an unfortunate event, and that it does diminish with time, though perhaps never entirely disappearing. Furthermore, while we cannot easily place a numerical value on the intensity of grief, we can suppose that there may be a scale for each individual, which perhaps could be approached from the crude quantitation method of asking for a "one to ten" estimate of intensity.

Assuming that there can be some quantitative measure of grief, the way that it decays with time suggests that grief may be analogous to a first order kinetic process, in which the rate of decay of some quantity is proportional to the magnitude of the quantity at a given time, measured from the onset of the event at t=0. A convenient analogy to use in expressing the time course of grief may be found in the viscoelastic behavior of a polymer strained at t=0, for which the relaxation of stress follows approximately a first order exponential decay (disregarding any induction period):

G = G₀ exp (- t / τ )

Here G₀ is the maximum level of grief experienced immediately after stressing, and τ is a relaxation time characterizing the exponential decay. The relaxation time is a measure of how fast G will diminish -- the larger its value the more prolonged the decay. The time for G to decay to half its initial value (the half life time) is about 0.69 τ .

In mechanics, the relaxation time is the ratio of a dynamic resistance to recovery (viscosity) to a static stiffness factor (modulus of elasticity). A material with a high modulus will, first of all, not distort as much under stress as a material with low modulus. Further, whatever distortion does occur will be give rise to a higher force to restore it to its original position. The rate of restoration is affected by the viscosity. A high viscosity will lengthen the time of recovery, and vice versa. Thus, a material with high modulus and high viscosity might recover from a distortion in about the same time as one with low modulus and low viscosity. High modulus and low viscosity will produce fast recovery, while low modulus and high viscosity will give rise to slow recovery..

Translating this into our analog of grief, we might associate the modulus with emotional rigidity, or perhaps a measure of obliviousness. This will be called E. Individuals with high E might be expected to be relatively unaffected by a tragic event as compared to those with a low value. In the absence of a retarding effect, however, recovery would be rapid in any case. The grief analog of viscosity would be a measure of retardation of recovery (R), the inverse of rate of forgetting. A person with large R will recover correspondingly slower from a shock than one with small R. These ideas can be combined in the definition of the relaxation time τ, namely τ = R / E , where R represents retardation of recovery and E represents emotional rigidity. As in the mechanical prototype, when τ is small, the grief recovery period will be less than when τ is large.

The interest in such an approach, when fleshed out in more quantitative terms, is its offering of a degree of predictability. Quantitative psychological studies and evaluations are able to provide methodology for estimating individual obliviousness to shock, as well as the rate of forgetting of important events. Framed quantitatively, the relaxation equation should be of interest in predicting and correlating.