THE AVERAGE OF MEN'S SOULS
(C)1997 Alan M. Schwartz
A lone ant is an idiot slated for proximate death. 100,000 ants
in a colony roil rapport, reshaping the world and abiding hostile
technological fury of Homo sapiens, each of whose brains is two
orders of magnitude as massive as all the ants totaled. Near-
random performances of so many ants loosely bound by shared data
sum to astonishing operational capabilities. Delphi experiments
tap that gestalten mandate: Numbers of people are individually
polled about topics in which they may or may not wield expertise.
The average response may be returned for successive rounds of
refinement. Does (recursive) summation of idiots' notions yield
good answers? Yes it does, enough so to keep Delphi in vogue.
Niklas Matthies, CS Department of the University Of Saarland,
Germany, (matthies@fsinfo.cs.uni-sb.de) posted a 1997 Usenet
tidbit, in part:
"Participants submit a real number between 0 and 1 inclusive by
e-mail (representations like 1/sqrt(pi) are allowed). The average
(arithmetic mean) of all submitted numbers will be determined.
The submission closest to 2/3 of this average wins the contest.
(Multiple submission from the same person will be disqualified.)"
Two questions abruptly haunt the reader. What is the average
favorite number? How close will the winner be to the (constantly
moving) target? Three decimal places' correspondence is one part
in a thousand random chance. This will be interesting!
There were 151 valid entries, but (sin(10^(10^100)))^2 was tossed
for lack of computability. That was very naughty, Thomas
Fischbacher! The resulting target number, two-thirds of the
arithmetic mean of the remaining 150 entries (0.22222331), was
0.14814887.
Axel Reichert from Dusseldorf, Germany won with his entry of 4/27
= 0.14814814 approximately. Second place was 401/2700 =
0.14851851 (Uwe Jendritzki); third was 0.15 (Paul Merriam). Out
of 150 entries, the winner was accurate to six decimal places -
one chance in a million! This stares down random odds quite
nicely. A single instance is outside statistical prophecy. One
wonders about the runner-up contestant, before and after.
Is 0.22222331 something special? A table of pi to 500,001 places
(a purely random bunch of digits less one exception) gives five
instances of 22222 (on the nosey statistics-wise) and one of
222223 (starting at the 200,081th decimal place). The source,
submissions and names of contest participants hint that abundant
input originated from the math department. Has Mr. Matthies
discovered a subtlety of human thought otherwise forever hidden
beyond the imagination of orthodox psychometricians?
Suppose medical doctors, mothers (married and otherwise),
construction workers, postmen, diplomats, high school students
(gifted, normal, diverse); racial, ethnic, religious groups;
whatever, were given the task: "Choose a number between 0 and 1
inclusive that will be closest to 2/3 the arithmetic average of
all submissions." We have thousands and millions of potential
participants in untold numbers of professional, genotypical,
phenotypical, cognitive, cultural... genres. Will it be the same
number? Will there be a number characteristic of each group?
At face value this may appear to be a silly conjecture, but it is
not. Phenomena from fluid turbulence to population surges of
hares and hawks - processes with feedback that touch critical
points (chaos, in the technical sense) - eerily embrace the
Feigenbaum number, 4.6692016091029906718532038... the limiting
ratio of successive generations of iterations. That number pops
up everywhere (often as a propagating typographic error with an
extra "6" inserted as the eight decimal place) no matter how
disparate the processes.
Alfred Binet and Theodore Simon in 1905 sought to objectively
winnow French pupils early on. Separating the average from the
below-average permitted precious assets to be invested in the
former and amelioration in the latter. In 1916 Lewis Terman at
Stanford University extended the exemplar (armed forces' Alpha
and Beta tests), revising it in 1937 and again in 1960 (with
Lewis Merrill). In the 1920s Terman began study of 1500
California students testing IQ 135 and higher ("Termites"),
publishing his results in 1959 as "Genetic Studies of Genius."
Intelligence does exit, it can be measured, it does make a
difference. (American zero-goal education exercises this
doctrine abetted by massive Federal subsidies and 180 degree
reversal - improved means to deteriorated ends.)
For all furiously accumulated and analyzed intelligence testing
we still cannot predict whether a pubescent child or a 40-year
old adult will be happiest and most adept at pondering eldritch
molecular structures or delivering mail. Perhaps atomistic
attacks upon intelligence are curious and useful but deeply
wrong. Sentient mind is a finely woven manifestation nervously
supported by blatantly insufficient microstructural complexity of
its container, the brain. Does the whole of individual - or at
least allied group - reality corkscrew down to a trifling number
trivially obtained? We would profit from looking at how we look
as well as looking at what we see.