Re: PCP course exercise

Jack Adams-Webber (
Mon, 30 Jan 95 14:24:06 -0500

>Dear Jack:
>What did Bateson (Gregory) have to say about the golden section?
>While I am on the topic, I might add that I have a hunch that the golden
>section may be the "bedrock" of the concepts of "illusory optimism" aka
>"depressive realism," as advanced by Peter Lewinsohn, Seligman, Lauren Alloy,
>Lyn Abramson (sp?) and others. That is, people in a state (not trait) or
>episode of depression simply lose their golden ratio. Assuming this is a
>viable construction, I then have the question of whether the work of the golden
>ratio might actually have preceded the work of these other colleagues and went
>unnoticed. Historically, I think that the article by Peter Lewinsohn, Walt
>Mischel et al. was actually the first on their work. Any thoughts or
>historical documentation on this?
>Rue L. Cromwell

Rue (and any other interested parties):

Let me get back to you re: Gregory Bateson (as I hate to bear false
witness, I'll have to dig out that reference.)

More to the specific point that you have raised, there are precious few
references to the GS ratio in the psychology literature between Fechner
(1876) and McCulloch (1965).

Warren McCulloch (1965; Embodiments of Mind) concluded that there is ample
evidence that the golden section represents an invariant proportionality in
the exercise of human judgment, but that it is probably a product of
intuition ("insight") rather than computation because "the golden section
is a ratio that cannot be computed by any Turing machine without an
infinite tape or in less than an infinite time...nor does it arise from any
set of probabilities."

As Harvey ("Failsafe") Wheeler (The Structure of Human Reflexion, 1990, p.
89) put it, the "golden section hypothesis states that people employ
homologous evaluative protocols tending towards golden section ratios for
the appropriateness of judgments about persons, places, things and action."
In sharp contrast to McCulloch, Vladimir Lefebvre (J. Math. Psychol.,1985;
p. 291) recently argues that this hypothesis can be derived mathematically
from his own algebraic model of ethical cognition according to which each
individual relies on a "special computer" to evaluate events, and "the
constant 0.62 is a characteristic of this computer." He infers that "under
very broad conditions its value is 0.625, and other more constrained
conditions it is equal to the golden section exactly" (see Lefebvre,J.
Math. Psychol., 1992).

Wheeler (1990; p. 80) speculates that "saliency (the negative pole of the
golden section distribution of judgments) may be an index of the
environmental adaptation mechanism of our species."Adams-Webber (Advances
in PCP,1990) suggests that a 'cognitive protocol' for encoding information
about the world that serves to mark unusual events in such a way that they
stand out as maximally salient could be useful in adapting to an
environment in which 'deviant' events are more likely to pose a threat to
us than are 'normal' events. This assumption is consistent with Rigdon and
Epting's (J. Pers. Soc. Psychol.,1982) finding that, the more useful a
subject judges a particular bipolar dimension for understanding people, the
more closely the distribution of her/his positive and negative judgments of
other persons on that dimension approximates 62/38 respectively. They argue
that "people who view most of the events in their life (approximately 62%)
as positive will more effectively discriminate between positive and
negative events in their life and be prepared to cope with negative events
(Rigdon & Epting, 1982, p. 1086)".

Following "Zajonc's (1980) more general argument that affective reactions
as a whole must be very rapidly available, perhaps in the form of an
automatic bias", Tuohy (Br. J. Psychol. 1987, p. 44; Tuohy & Cooke, 1992;
Tuohy & Stradling, 1987, 1992) posits that "the informational bias
identified by Benjafield and Adams-Webber (1976) may constitute an
operating characteristic of a relatively independent affective mediator (p.
41)". Tuohy (1987, p. 49) also sees "maximal differentiation of negative
evaluation as a basic operating characteristic of the affective mediator".
For example, Stradling, Tuohy and Harper (Appl. Cog, Psychol., 1990, p.
409) report that, when 522 police officers and probationer constables rated
40 sets of circumstances as to how far each would influence them to
prosecute or not prosecute a motorist stopped for speeding, "the
distribution of responses about the ipsative means exhibited an asymmetry,
consistent with the maximum salience bias towards a negative proportion of
1/e" (i.e., approximately 37%).

>From a clinical perspective, Schwartz and Garamoni (1986) reanalyzed data
from 27 clinical assessment studies "in which functional and dysfunctional
groups were compared on measures of positive and negative cognitions",
including internal dialogue, self-referent memory, free association,
thought listing, free recall, and talking aloud. The results indicated that
"subjects independently assessed as normal on clinically relevant indices
of psychological functioning were characterized by a balance of positive
and negative cognitions that approximated the golden section", whereas
"subjects classified as dysfunctional on independent measures of anxiety,
depression, nonassertiveness, low self-esteem and impaired coping had a
mean cognitive balance that was significantly lower than the golden section
(Schwartz, Int. J. PCP, 1992, p. 132)."

Hope that these references are of some use to you.



Jack Adams-Webber Tel: 905 (688) 5544 [x 3714]
Department of Psychology Fax: 905 (688) 6922
Brock University E-mail:
St. Catharines, Ontario