Notice a paucity of pk posts recently?
It's because I've been painting. Oh, no; not as in art (my art is here!); as in painting the house. It was the landlord who finally convinced me that it needed painting. (Hell, the last paint job was only thirty years old.) But once I noticed that it needed painting (you mean there really is a world(!) that we live in?), I started noticing more and more: which prompted me to try to explain Mandelbrot math and chaos physics to my landlord (who fled after a minimum of polite listening).
Mandelbrot asked the generic question How long is a coastline? His answer is that It depends entirely on the length of the ruler you're measuring with. If you walk the coast of Maine you'll take a different number of baby steps from giant steps. The telescope does not see the same universe as does the microscope. I've painted the house. Now I'll go back over it with an artists brush. I doubt that I'll then don a jewelers glass, but I'll be tempted.
Of course I already knew this principle: from when I'd occasionally wash the mildew from the aluminum siding. First I'd see one patch that needed a little stress and discouragement. That clean, I'll notice another. By the time I'd be done, the last patch, the one originally least noticed, would look to me the worst in the whole history.
Once we notice that Hitler himself had a Jewish taint, and needed cleansing, where will we stop?
But that's not all. A decade ago I got a nice email from my late seventeenth-century English teacher's widow. At the beginning of April I heard from her again. Then two weeks went into developing a nice cross-continental friendship. She mentioned an old friend of hers who painted. So another week went into initiating an exploratory friendship there.
But of course lots and lots of little things still got done at all pk domains. A bunch more of Shakespeare's sonnets, for example, got posted (more than 2/3 as of 2005/04 27).
2011 07 26 I've thinking about Mandelbrot and coastlines recently, while playing the form of solitaire I call 49. The cards, all but three, are dealt out in 7 files. Twelve, all in the first three files, are face down. Cards promote, Ace up, as in other solitairs; but cards reorganize in the files by succession within suit, not by succession of opposite color. Only the deuce of spades can promote onto the ace of spades, only the jack of spades can move under the queen of spades: and brings any extra tail with it.
I see the array as a coastline. I see the probabilities of there being a card to move next in relation to the jaggedness of "coastline" of the random arrangement of the 49 cards: which changes propabilities with each move.
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