Measuring Entropy

The following is a standard equation used for finding a change of entropy in an open system:

Change in Entropy = Internal Created Entropy + Entropy Exchanged with Environment

This is the standard equation for Prigogine’s entropy S of an open system. For the ego, dS/dt$0 during all four states. However, dSe/dt is positive during the waking state and negative during the dream state. The ego builds up entropy when awake and dissipates entropy during dreams, and therefore dreams are, in a very real sense, the primary high entropy waste products of the psyche.

Another way to calculate entropy changes is to look for deviations from equilibrium conditions:

where )S is called a Lyapounov function because it is a measure of system stability.

For the ego, )S$0 in all four states. A positive Lyapounov function generally indicates the presence of a chaotic attractor. Thus the ego experiences chaotic attractors in all four states, and all four states are important for the individuation process.

The entropy of a dynamic system can often be determined from one of the system’s ordering parameters. For the ego we can write

where the assimilation factor 8 is a state parameter that can cause the ego to be unstable. A typical plot of entropy versus assimilation, as shown in Figure 33 which assumes K=1, shows a bell-shaped curved where both ends approach zero entropy. A value of 80 suggests the inability of the ego to assimilate experience (such as infants or psychotics) whereas 81 suggests the ability to assimilate almost any experience (equivalent to a high psychic maturity). Neither condition produces very much entropy. Maximum entropy is produced when 8.5, the average condition. The bell-shaped curve here is similar to that of the idealized ego trajectory through phase space.

where S is the entropy of a system in state Q at time t and P(Q) is the probability of being in state Q. In this equation, the entropy S is equivalent to the probability of a system being in state Q at time t. Figure 34 shows the entropy curve for any system on a 24-hour cycle using the above equation.

The ego has many minor system states, but only four major states: waking, dreaming (REM and SREM), sleep (NREM), and transpersonal of which only the first three are generally considered “normal” states. Children sleep about 10 hours per day, and are awake for about 14 hours. Children also spend approximately equal time in REM and NREM states. Adults, on the other hand sleep for about 8 hours and have approximately 2 hours of REM and 6 hours of NREM. According to van de Castle (1994), “there is no period during sleep in which our mind is “blank”; some kind of mental activity is always occurring” (p. 267). Using the above equation together with Figure 34, values for probability P and entropy S are given in the table below.

	Waking	Dreaming	Sleeping
Children, P	14/24	5/24	5/24
Children, S	.314	.326	.326
Adults, P	16/24	2/24	6/24
Adults, S	.27	.21	.35

Although the table above is a gross oversimplification, it does show that the entropy accumulated during the waking state is approximately equal to the average entropy dissipated during the dream and sleep states. For children, the entropy associated with all three normal states is approximately equal with the average dissipated during dream and sleep (.326) approximately equal to that accumulated during the waking state (.314). Adults don’t spend as much time in the dream state, but the average (the average of .21 and .35 is .28) dissipated is approximately equal to the amount accumulated in the waking state (.27).

It can be concluded that at all ages of maturity, the ego gains entropy during the waking state and then loses that amount in dream and sleep so that the length of time spent sleeping at night depends on the amount of entropy accumulated during the day.

Sometimes entropy is defined as remaining ignorance plus algorithmic randomness or E = RI + AR where AR addresses the randomness that exists in the available data. An IGUS (information gathering and using system) is an observer who makes measurements, and whose efficiency can be defined as the ability to assimilate information into a worldview or a self-image. Thus we have

where RI is remaining ignorance, AR is algorithmic randomness, wv is worldview and si is self-image. Then efficiency, E_ff, can be defined in terms of probabilities as

We can also define RI as the smallest number of bit of information needed to fully define the worldview, and AR the smallest number of bits of information needed to fully define the self-image. We must also remember that AR is impossible to measure exactly due to what is sometimes called Godel’s undecidability. Using entropy this way is tricky, however, because while observations decrease ignorance and thus reduce entropy, they simultaneously increase memory which increases entropy.