|
Many thanks.
Much as people rightly admire John Nash for his
recovery, without drugs, from a long standing psychotic illness, I have to say
that the comments below could also fit. ie the disorder could be seen as an
_expression_ in turn of psychosocial factors on the individual. Even that there is
an interaction, a synergy, between the ideology of the society and the ideology
of the individual in this case.
I have just checked "Madness Explained" by Richard
Bentall (2003) which among other things sums up a generation of
experimental studies in the UK by psychologists. The core of his model of
paranoia is based on studies of attribution theory. Just as the depressive
person tends to over attrribute the causes of their misfortunes to internatl
personal failings, the person with a tendency to paranoia tends to make external
attibutions in excess of probably the reality and the psychological
norm.
This could fit with formulations below that it was
important for this proud, attractive and talented man, in a highly competitive
environment, to have a sense of integrity of his own identity and to regard
interaction from outside as potentially threatening.
If there is some truth in this connection, Nash
cured himself by gradually mellowing psychologically, perhaps helped by the care
of his estranged wife.
But I am writing in because I think the
observations below are not in fact disrespectful of his courage and other
qualities, and to provide a contribution for thinking further about the
psychological values of mid-late capitalist ideology.
Regards
Chris Burford
----- Original Message -----
Sent: Wednesday, May 19, 2004 8:54
PM
Subject: [PEN-L] Mirowski on Nash's
"brilliant insight"
From the section (pp. 335-49) in Philip Mirowski's *Machine
Dreams* on "what has come in retrospect to be regarded the signal mathematical
development in game theory in the 1950s, the event most consequential for the
subsequent history of *economics*, the invention of the 'Nash equilibrium'
concept." p. 331
"The Nash equilibrium is the embodiment of the idea
that the economic agents are rational; that they simultaneously act to
maximize their utility; Nash equilibrium embodies the most important and
fundamental idea in economics" (Robert Aumann, quoted by Mirowski on p.
343)
"by the mid-1950s things started going seriously wrong. In his
[Nash's] own words:
'the staff at my university, the Massachusetts
Institute of Technology, and later all of Boston were behaving strangely
towards me. ... I started to see crypto-communists everywhere. ... I started
to think I was a man of great religious importance, and to hear voices all the
time. I began to hear something like telephone calls in my head, from people
opposed to my ideas. ... The delirium was like a dream from which I never
seemed to awake.' "In the spring of 1959 Nash was committed to McLean Hospital
in Belmont, Massachusetts, diagnosed as a paranoid schizophrenic." p. 338
"what Nash himself was aiming at [was] a definition of rationality in
game play so transparent and unassailable that everyone would voluntarily
acknowledge its salience and conform to its dictates, entirely independent of
any external interpersonal considerations. We shall dissect the Nash
equilibrium in detail, but, for starters, it will suffice to define 'Nash
equilibrium' as the personal best strategic reply to an opponent (i.e., a
constrained maximum) who is himself trying to discern your best strategic
option and deploy his own best response, where the two desiderata coincide. It
is clearly an attempt to extend constrained optimization of something which
behaves very much like expected utility to contexts of interdependent payoffs.
Nash himself described it as 'an n-tuple such that each player's mixed
strategy maximizes his payoff if the strategies of the others are held fixed.
Thus each player's strategy is optimal against those of the others' (1996, p.
23). It all sounds so simple, except when you pick up diverse game theory
texts and find they rarely tender the same explanation of the meaning of this
'rationality' from one instance to the next.
"In this volume, we shall
treat the Nash equilibrium as the next logical extension of the Walrasian
general equilibrium tradition into the Cold War context." pp.
339-40
"the notion of rationality encapsulated in the Nash formalism
... [is] omniscient and all encompassing of all possible worlds" p.
340
"Nash agents are inflicted with terminal paranoia" p.
340
"It would be a dire mistake to let the mathematics obscure the very
real emotional content of the Nash solution concept, for that would leave us
bereft of an appreciation for the nature of its appeal in the postwar
era.
"Although it far outstrips our capacity, or even interest, to engage
in psychological theorizing, a very stimulating comparison can be found
between paranoia and the cognitive style of the masculine scientist in the
work of Evelyn Fox Keller (1985). We quote some of her analysis, not so much
to endorse it as to evoke some parallels with the Nash solution
concept.
'The cognitive style of the paranoid ... [is] grounded in the
fear of being controlled by others rather than in apprehension about lack of
self-control, in the fear of giving in to others rather than one's own
unwelcome impulses, the attention of the paranoid is rigid, but it is not
narrowly focused. Rather than ignore what does not fit, he or she must be
alert to every possible clue. Nothing - no detail, however minor - eludes
scrutiny. Everything *must* fit. The paranoid delusion suffers not from a lack
of logic but from unreality. Indeed, its distortion derives, at least in part,
from the very effort to make all the clues fit into a single interpretation.
... For the paranoid, interpretation is determined primarily by subjective
need - in particular, by the need to defend against the pervasive sense of
threat to one's own autonomy. ... the very fact of such vigilance - even while
it sharpens some forms of perception and may be extremely useful for many
kinds of scientific work - also works against all those affective and
cognitive experiences that require receptivity, reciprocity, or simply a
relaxed state of mind. The world of objects that emerges is a world that may
be defined with extraordinary accuracy in many respects, but is one whose
parameters are determined principally by the needs of the observer. (pp.
121-22)’
"This mortal fear of abject capitulation to others is the
moral center of gravity of the Nash equilibrium, and its implacable commitment
to the solitary self-sufficiency of the ego is the marginal supplement that
renders the otherwise quite confused and contradictory textbook justifications
of the Nash equilibria comprehensible. It is also the key to linking the Nash
equilibrium to the Cold War. The Nash equilibrium stands as the mathematical
_expression_ of the very essence of the closed-world mentality of impervious
rationality: 'paranoids exhibit remarkable consistent and coherence in their
belief systems. However, it is extremely difficult to convince such people
that they have made errors in reasoning' (Einhorn in Cohen, 1981)." pp.
341-2
"the Nash solution is best glossed as the rationality of the
paranoid. Nash appropriated the notion of a strategy as an algorithmic program
and pushed it to the nth degree. In the grips of paranoia, the only way to
elude the control of others is unwavering eternal vigilance and hyperactive
simulation of the thought processes of the Other (Pierides, 1998). Not only
must one monitor the relative 'dominance' of one's own strategies, but
vigilance demands the complete and total reconstruction of the thought
processes of the Other - *without* communication, *without* interaction,
*without* cooperation - so that one could internally reproduce (or *simulate*)
the very intentionality of the opponent as a precondition for choosing the
best response. An equilibrium point is attained when the solitary thinker has
convinced himself that the infinite regress of simulation, dissimulation, and
countersimulation has reached a fixed point, a situation where his simulation
of the response of the Other coincides with the other's own understanding of
his optimal choice. Everything must fit into a single interpretation, come
hell or high water.
"There may be multiplicity of such possible
interpretations, but that is no cause for undue alarm; all that really counts
is that one such comprehensive account exists, that it can be demonstrated to
the player's satisfaction that it is *consistent*. (When others resist the
paranoid's construction of events, usually it only serves to reinforce his
paranoia.) Patently, the fact that this happens within the confines of a
single isolated consciousness suspends the maximization calculation outside
the conventional bounds of time and space: instead it occurs within the closed
world of closely scripted apocalyptic conflicts. Equilibration is not a
process, isn't learned, and it is most assuredly asocial. The fact that the
mere choice of strategies could itself be construed as an act of
'communication' is irrelevant in this context; all play is unremittingly
virtual. Appeals to learning or signalling or shared 'common knowledge' would
be most emphatically beside the point, because the other has been rendered
irrelevant." pp. 343-4
"Nash invented a distinction ... between
cooperative and noncooperative games. Questions of the actual numbers of
opponents (they're everywhere!) and the extent of their hostility (as
expressed in conservation principles of joint valuation) are not matters of
import for the paranoid mind-set. Rather, in Nash's scheme, von Neumann's
minimax-cum-imputation values were to be relegated to the narrow cooperative
category, as a prelude to being swallowed up by the 'more general'
noncooperative approach. This mantra became the hallmark of the Nash program:
'One proceeds by constructing a model of the pre-play negotiation so that the
steps of the negotiation become moves in a larger non-cooperative game [which
will have an infinity of pure strategies] describing the total situation'
(Nash, 1996, p. 31). The 'game' would therefore need to expand exponentially
to encompass everything that would potentially bear any possible relevance to
strategic play in any conceivable scenario; it would be hard to discern where
the game stopped and life took up the slack. But paranoia is marked by the
belief that one can defend oneself against *every possible contingency*." p.
346
"For Nash ... the act of axiomatization was the paradigm of making
everything 'fit' the scheme of rationality (1996, p. 42); consistency would
invariably trump tractability and practicality. Here, of course, resides the
paranoid core of the Cold War fascination with formal axiomatics that so
pervaded the social sciences in the postwar period." p. 347
|
