Thanks for sending the picture... a thousand words? nay, a thousand times a thousand words, to wax Bard-ian about it.
I think that anyone who's made any kind of concerted legitimate statistical effort, even a simple one such as the one you're guiding me through, has got to conclude that Stephen Wolfram is wrong: the world is not made in the image of a cellular automaton or group thereof, but rather in the image of a statistical automaton, or group thereof.
That is, statistics are the "Ding an sich", to use the Kantian term, not a mere description of the "Ding an Sich".
I wish that my Chomskyan traing as an undergrad taking grad courses had not predisposed me against the behaviorism rampant in the pysch departments during the late 60's. Perhaps I would have appreciated statistics sooner rather than later.