Rousseau's law

[Jonathan Furner]

Dear Ronald and SIGMETRICS:

Thank you, Ronald, for the precise reference to the Contrat Social,
and thanks also for the extracts from your book. (I still wish I
could find a copy of that book!)

I had to refer to an English translation (Cranston's, Penguin, 1968)
of J. J. Rousseau's work, and, after doing so, I'm afraid my
questions still remain. Here's why.

As Ronald says, in Book III, Chapter I, of the Social Contract, J. J.
develops his tripartite distinction between the state (the people as
subjects), the government (the executive), and the sovereign (the
people as the legislature). He is concerned to demonstrate that, if
order is to be maintained, the power of the government should equal
the power of the people (who are the state in one sense and the
sovereign in another). Thus, as the power of the state increases
(e.g., as the number of subjects increases), the power of the
government to control the state should increase correspondingly --
as, indeed, should the power of the sovereign to control the
government. In Cranston's translation (p. 104): "... for the
government to be good, its strength must be increased to the extent
that the people is more numerous."

The only passage in this chapter in which J. J. explicitly considers
the size (as opposed to the power) of the government, and the only
passage in which he uses the term "racine carrée," is translated as
follows (p. 105):

"If anyone, wishing to ridicule this system, suggested that in order
to find the geometrical mean and construct the body of the government
one need only on my view take the square root of the number of the
people, I should reply that I am here using that number only as an
example; and the ratios of which I speak are not measured merely by
the number of men but more generally by the amount of activity, which
results from the occurrence of innumerable causes; I should add that
although I have borrowed momentarily for the sake of expressing
myself in fewer words, the language of geometry, I am still well
aware that geometrical precision has no place in moral calculations."

Here, J. J. seems to be saying (i) that any attempt to derive, from
his broad assertions about balancing the powers of people and
government, a formula for determining the size of the government
would be to "ridicule" his position; (ii) that, in general, neither
the power of the people nor the power of the government may be
measured simply by counting individuals; and (iii) that to use the
square root of the number of people in such a formula would be on the
advice of another, not J. J.

In short, I would submit that, on this account, the current answer to
my second question -- What evidence is there for believing that
Rousseau was indeed responsible for expressing Rousseau's law? -- is
"None." That question still stands, then; and my first question might
be clarified as follows:

Who (before Zipf, 1949) was responsible for the first expression of
Rousseau's law (as that law is understood in the modern literature of
bibliometrics) as "Rousseau's law" -- i.e., who (before Zipf, 1949)
was responsible for the first imputation of Rousseau's law to
Rousseau?

I would, in fact, be interested in *any* pointers to evidence
supporting the various claims made since 1949 to the effect that
Rousseau's law is "so frequently imputed to J. J. Rousseau," has
"long been known in the social sciences," etc.

All the best,
Jonathan


>Dear Jonathan,
>
>In his Contrat Social J.J. Rousseau gives, as an example, the number of people
>that should form 'a government'. He does that by taking the square
>root (racine
>carrée in French)of the number of people that form the state (l'état). So,
>indeed, according to this example, in a population of size n the
>number of high-
>visibility members stands as the square root of n.
>
>See  http://un2sg4.unige.ch/athena/rousseau/jjr_cont.rtf
>
>Book III, chapter 1.
>
>Rousseau
>
>********************************************************
>>  Dear SIGMETRICS list members:
>>
>>  I wonder if one of you might be able to help me out with a small
>>  bibliographical question, about "Rousseau's law."
>>
>>  In his article "American Philosophy Today" (Review of Metaphysics 46,
>>  no. 4, June 1993), Rescher mentions in a footnote "the principle
>>  known in the social sciences as Rousseau's Law, which maintains that
>>  in a population of size n the number of high-visibility members
>>  stands as [the square root of n]." Rescher cites another work of his
>>  own, Scientific Progress (1978), which is also cited by Diodato in
>>  his Dictionary of Bibliometrics (1994): "[The formula stating that]
>>  the volume of really 'important' production stands as the square root
>>  of the total production ... is in fact a rather well known formula in
>>  the study of elites ... Such a relationship was initially mooted by
>>  Jean Jacques Rousseau ..." Diodato also cites Zipf's Human Behavior
>>  and the Principle of Least Effort (1949): "This statement that is so
>>  frequently imputed to J. J. Rousseau seems to evade specific
>>  reference although its sense is apparent in his Contrat Social."
>>
>>  Of course, the relationship between the size of a population and its
>>  square root is remarked upon by Price in Little Science, Big Science
>>  (1963). Price does not mention Rousseau; yet, in an article in IP&M,
>>  Nicholls (1988) notes that Price's law has its roots in Rousseau's
>>  law, which had "long been known in the social sciences."
>>
>>  My (two-part) question is: Who was responsible for the first
>  > imputation of Rousseau's law to Rousseau? What evidence is there for
>>  believing that Rousseau was indeed responsible for expressing
>  > Rousseau's law?
>>
>>  Thanks,
>>  Jonathan
>>
>
>
>
>Ronald Rousseau
>dr. mathematics, dr. information science
>KHBO - Industrial Sciences and Technology
>Zeedijk 101    B-8400  Oostende   Belgium
>Honorary Professor Henan Normal University (Xinxiang, China)
>E-mail: ronald.rousseau at kh.khbo.be
>web page:  users.pandora.be/ronald.rousseau