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, 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.
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