THE THERMODYNAMICS OF PSYCHOTHERAPEUTIC COMMUNICATION Anthony F. Badalamenti, Ph.D. and
Robert J. Langs, M.D. The Nathan mine Institute for Psychiatric Research, Building #37 Orangeburg, New York 10962 Given five quantified measures of emotional communication within a psychotherapy session and definitions of work, force and temperature drawn from classical physics, this paper presents calculations of patient and therapist entropy using both the traditional, caloric definition and Shannon’s definition, grounded in the work of Boltzmann. Our results depend on the assumption that the patientJtherapist system is closed and non-dissipative. We present models for reversible heat absorption and frictional heat dissipation-within t h e system-which have meaning i n emotional communication and psychotherapy. Both calculations of entropy produced a lawful dependence on ln(1 + t), where t is time into the session in seconds. The two calculations are essentially the same, verifying in the behavioral domain a law of physics held to be true of material nature. We also verify empirically that the limiting form of the caloric entropy for a purely silent therapist replicates the Shannon entropy for a n individual in a monologue. The force field that moves the representations of patient and therapist in 5-dimensionalspace defines an irreversible process. Thus there are moments of disequilibrium change with respect to the measured variables of emotional communication and at least one moment of disequilibrium between every return to a prior state. This moment may be creative or traumatic. The force field is non-conservative, implying the existence of modalities of heat absorption f o r patient and therapist which may relate to individual characteristics and reflect human psychological variety. The force field constrains motion t o an ellipsoidal shell whose geometry explains the logarithmic growth of Shannon entropy and the finding that the system’s absolute temperature grows linearly with respect to time. The finding that the models and methods of physics reveal a degree of lawfulness in the mentaycommunicativedomain as compared to the material speaks strongly for the isomorphic qualities of divergent levels of nature.
KEYWORDS: entropy, thermodynamics, psychotherapy TYPE OF ARTICLE: mathematical model DIMENSIONS AND UNITS:degrees
INTRODUCTION HISPAPER Is GUIDED by the
T
conviction t h a t human and mental behavior, however immaterial they may be, are p a r t s of n a t u r e a n d therefore not exempt from those laws that describe material processes*. The present work
*This research was supported in part by a grant from the Blumenthal Foundation.
is a continuation of prior efforts t o mathematically explore the nature of communication psychotherapy in four domains: time, frequency, information or complexity, and work and force-the focus here. In the time domain, the Box-Jenkins method (Box & Jenkins, 1976; Kendall, 1976) w a s used t o identify time series’ progression of speaker duration data that in addition were to reflect a Poisson process (Cox & 157
Behavioral Science,Volume 37,1992
Miller, 1965; Gregson, 1983). Also in t h e time domain, cross correlation functions were used to measure lagged linear (and nonlinear) influence between patient (P) and therapist (T) using the 5 dimensions to be discussed in this paper (Badalamenti & Langs, 1989a, 1989b, 1990; Langs & Badalamenti, 1990a, 1990b). In the frequency domain we used power spectra (Jenkins & Watts, 1968) t o locate repetition a n d we calculated coherency t o m e a s u r e harmonic influence and rhythm. I n t h e information domain, we calculated Shannon entropy and found that it grew as ln(1 + t), where t is time in seconds into the session (Badalamenti & Langs, 199Ob). In the work/force domain we found that the force field resultant from the PI" interaction performs work on both P and T information particle (IP; this is the representation of P and T state in 5dimensional space) as a linear function of t i m e (Badalamenti, Langs & Ferguson, 1990). This implies that the force field must be non-conservative (i.e., returns to prior states involve a lapse of time during which work done is positive). An application of Stokes' Theorem, which relates work along a boundary path to rotation within that boundary, then led t o the conclusion t h a t t h e I P m u s t be in a s t a t e of rotation. We returned to the data and verified that communications from both P and T do indeed rotate, in the sense of r e t u r n i n g t o prior s t a t e s while progressing t o new ones (Badalamenti, Langs & Kessler, 1990). This in turn led t o r e s u l t s on t h e geometry of psychotherapy-that the data lives in a 5-dimensional ellipsoidal shell whose shape accounts for the linearity of work and the logarithmic growth of Shannon entropy. Our calculations implied an unusual
Behavioral Science, Volume 37,1992
relation which motivated the present paper: h a l f t h e work done by t h e r e s u l t a n t force field always a c t s t o change the IPS kinetic energy. What then became of t h e other half of the work? We appealed t o t h e laws of thermodynamics for explanation and set out to calculate t h e caloric entropy, based on the assumption t h a t the Pi" system i s closed. We were trying t o u n d e r s t a n d t h e relation of work t o entropy in light of the finding that half the work done results in kinetic energy changes. T h e equivalence of t h e BoItzmann (probabilistic) entropy, upon which Shannon's definitions i s based, a n d caloric entropy (for material processes), is still an open question (Lee, Sears & Turncotte, 1973; Zemansky, 1968). As far as we have been able to determine, t h e equivalence h a s only been established i n a small n u m b e r of experiments, mostly a t low temperatures. Prior studies led us t o postulate that t h e laws of thermodynamics would elucidate the energy issue within the PIT system if we could assign temperature values t o the system. In addition, we were concerned with the irreversibility of the process because thermodynamics maintains that all natural processes are irreversible. If Shannon entropy were equivalent t o caloric entropy, then the logarithmic growth of entropy as a function of time would definitively imply irreversibility (see below). The present study depends on formal definitions for work, force, and a 5dimensional I P (information particle). Using both definitions of entropy, we will investigate the entropic vicissitudes of t h e IP i n t h e course of six psych other a py consul t a t ions session s carried o u t by six well known, experienced psychoanalysts with two
1
THERMODYNAMICS OF P~YCHCYIXEWEUTIC COMMUNICATION women patients. Our goal is to develop a rigorous and repeatable methodology for psychotherapy research which will, in the present paper, reveal that the laws of thermodynamics also elucidate human behavior. Since we appeal to thermodynamics, the definitions of force, work and power are exactly those of physics (Courant & Hilbert, 1953; Goldstein, 1965; Lin & Segel, 1974; Zemansky, 1968). We advance in a spirit similar to t h a t of efforts i n chaos theory, attractorsstrange or otherwise-and information theory where concepts from physics are being fruitfully applied t o diverse phenomenology and systems (Prigogine & Courbage, 1979; Ruelle, 1987; Shannon, 1948; Shannon & Weaver, 1949).
159
i n t e r - r a t e r reliability was achieved (p
Robert J. Langs, M.D. The Nathan mine Institute for Psychiatric Research, Building #37 Orangeburg, New York 10962 Given five quantified measures of emotional communication within a psychotherapy session and definitions of work, force and temperature drawn from classical physics, this paper presents calculations of patient and therapist entropy using both the traditional, caloric definition and Shannon’s definition, grounded in the work of Boltzmann. Our results depend on the assumption that the patientJtherapist system is closed and non-dissipative. We present models for reversible heat absorption and frictional heat dissipation-within t h e system-which have meaning i n emotional communication and psychotherapy. Both calculations of entropy produced a lawful dependence on ln(1 + t), where t is time into the session in seconds. The two calculations are essentially the same, verifying in the behavioral domain a law of physics held to be true of material nature. We also verify empirically that the limiting form of the caloric entropy for a purely silent therapist replicates the Shannon entropy for a n individual in a monologue. The force field that moves the representations of patient and therapist in 5-dimensionalspace defines an irreversible process. Thus there are moments of disequilibrium change with respect to the measured variables of emotional communication and at least one moment of disequilibrium between every return to a prior state. This moment may be creative or traumatic. The force field is non-conservative, implying the existence of modalities of heat absorption f o r patient and therapist which may relate to individual characteristics and reflect human psychological variety. The force field constrains motion t o an ellipsoidal shell whose geometry explains the logarithmic growth of Shannon entropy and the finding that the system’s absolute temperature grows linearly with respect to time. The finding that the models and methods of physics reveal a degree of lawfulness in the mentaycommunicativedomain as compared to the material speaks strongly for the isomorphic qualities of divergent levels of nature.
KEYWORDS: entropy, thermodynamics, psychotherapy TYPE OF ARTICLE: mathematical model DIMENSIONS AND UNITS:degrees
INTRODUCTION HISPAPER Is GUIDED by the
T
conviction t h a t human and mental behavior, however immaterial they may be, are p a r t s of n a t u r e a n d therefore not exempt from those laws that describe material processes*. The present work
*This research was supported in part by a grant from the Blumenthal Foundation.
is a continuation of prior efforts t o mathematically explore the nature of communication psychotherapy in four domains: time, frequency, information or complexity, and work and force-the focus here. In the time domain, the Box-Jenkins method (Box & Jenkins, 1976; Kendall, 1976) w a s used t o identify time series’ progression of speaker duration data that in addition were to reflect a Poisson process (Cox & 157
Behavioral Science,Volume 37,1992
Miller, 1965; Gregson, 1983). Also in t h e time domain, cross correlation functions were used to measure lagged linear (and nonlinear) influence between patient (P) and therapist (T) using the 5 dimensions to be discussed in this paper (Badalamenti & Langs, 1989a, 1989b, 1990; Langs & Badalamenti, 1990a, 1990b). In the frequency domain we used power spectra (Jenkins & Watts, 1968) t o locate repetition a n d we calculated coherency t o m e a s u r e harmonic influence and rhythm. I n t h e information domain, we calculated Shannon entropy and found that it grew as ln(1 + t), where t is time in seconds into the session (Badalamenti & Langs, 199Ob). In the work/force domain we found that the force field resultant from the PI" interaction performs work on both P and T information particle (IP; this is the representation of P and T state in 5dimensional space) as a linear function of t i m e (Badalamenti, Langs & Ferguson, 1990). This implies that the force field must be non-conservative (i.e., returns to prior states involve a lapse of time during which work done is positive). An application of Stokes' Theorem, which relates work along a boundary path to rotation within that boundary, then led t o the conclusion t h a t t h e I P m u s t be in a s t a t e of rotation. We returned to the data and verified that communications from both P and T do indeed rotate, in the sense of r e t u r n i n g t o prior s t a t e s while progressing t o new ones (Badalamenti, Langs & Kessler, 1990). This in turn led t o r e s u l t s on t h e geometry of psychotherapy-that the data lives in a 5-dimensional ellipsoidal shell whose shape accounts for the linearity of work and the logarithmic growth of Shannon entropy. Our calculations implied an unusual
Behavioral Science, Volume 37,1992
relation which motivated the present paper: h a l f t h e work done by t h e r e s u l t a n t force field always a c t s t o change the IPS kinetic energy. What then became of t h e other half of the work? We appealed t o t h e laws of thermodynamics for explanation and set out to calculate t h e caloric entropy, based on the assumption t h a t the Pi" system i s closed. We were trying t o u n d e r s t a n d t h e relation of work t o entropy in light of the finding that half the work done results in kinetic energy changes. T h e equivalence of t h e BoItzmann (probabilistic) entropy, upon which Shannon's definitions i s based, a n d caloric entropy (for material processes), is still an open question (Lee, Sears & Turncotte, 1973; Zemansky, 1968). As far as we have been able to determine, t h e equivalence h a s only been established i n a small n u m b e r of experiments, mostly a t low temperatures. Prior studies led us t o postulate that t h e laws of thermodynamics would elucidate the energy issue within the PIT system if we could assign temperature values t o the system. In addition, we were concerned with the irreversibility of the process because thermodynamics maintains that all natural processes are irreversible. If Shannon entropy were equivalent t o caloric entropy, then the logarithmic growth of entropy as a function of time would definitively imply irreversibility (see below). The present study depends on formal definitions for work, force, and a 5dimensional I P (information particle). Using both definitions of entropy, we will investigate the entropic vicissitudes of t h e IP i n t h e course of six psych other a py consul t a t ions session s carried o u t by six well known, experienced psychoanalysts with two
1
THERMODYNAMICS OF P~YCHCYIXEWEUTIC COMMUNICATION women patients. Our goal is to develop a rigorous and repeatable methodology for psychotherapy research which will, in the present paper, reveal that the laws of thermodynamics also elucidate human behavior. Since we appeal to thermodynamics, the definitions of force, work and power are exactly those of physics (Courant & Hilbert, 1953; Goldstein, 1965; Lin & Segel, 1974; Zemansky, 1968). We advance in a spirit similar to t h a t of efforts i n chaos theory, attractorsstrange or otherwise-and information theory where concepts from physics are being fruitfully applied t o diverse phenomenology and systems (Prigogine & Courbage, 1979; Ruelle, 1987; Shannon, 1948; Shannon & Weaver, 1949).
159
i n t e r - r a t e r reliability was achieved (p
