"Some are Pretty on the Inside"

Mr. Rogers was this Minister on TV in the late Sixties and for couple decades thereafter who talked to little kids ... and chances are pretty good to their "stoned" parents ... about similarities and differences ... about life and death .... about kindnesses and solicitudes .... and especially about sharing. I'm pretty confident in the likelihood that "The Toddling" (Steven King's missing masterpiece) were, indeed, busy hearing about cardigan sweaters and "the Land of Makebelieve" which you arrived at by Trolley, the Moms were busy sharing intoxicants and the Dads were being Dads ... mesmerized by the beautiful young assistant .... maybe her name was Lady Elaine?

Ah, but Fractals. Fractals emphasize the Similarities. In Sierpinski's Triangle, you see, each of the Little Right-side Up Triangles is identical to the whole ... isomorphic to it, as one of the founders of 20th C. Topology would say. I only met, by the by, Warclaw Sierpinski once ... musta been 1968. He, Kazimierz Kuratowski and another guy -- I think his name was Janischiewsky -- decided that, if Lil' PostWar Poland was to make a name for itself Mathematically, they would have to specialize in some area ... and they chose Topology. I know about this due to a barter. When I was a kid, I worked out a deal with Kuratowski when he was on a speaking tour of the USA. I would drive him in my Volvo and on the way to these talks, he would teach me about the History of the Polish Akademie of Sciences ... Poland's MIT. Fractals? I don't think were discussed until some years later.

For any geeky enough to be interested, I think Sierpinski's interest was in a curiosity that such a triangle might posess. For you see, while the above Triangle covers a bunch of ground, when you take into account all the pieces that have been removed, it's area appears to be "zero" .... Ah! But Get ye Curious Geeks to a book on Measure Theory and all will be explained

OK, OK ... paraphrasing what one Vice Presidential Candidate said to another:

                              Howard! You're no Kazimierz Kuratowski!

Yeah, yeah! But in some sense, I've taken on his-KK's age when I remember him, borrowed his nerdy style of dress and arrived at his inability to drive,  as well. Ask M! Ask'er about what it's like to sit in a car at a Green Light with some Last Quarter type while he waits for it to turn Red! (shhhh! I haven't had the heart to tell M that she's Fourth Quarter, too .... .... Don't tell!)

But back to my point. I think it was Jack Paar who would motion his finger in waves from shoulder to shoulder and asked his guest.

                                               OK! What's that?


The guest's 'I dunno' would be responded to with:

                                 Well, I dunno either but here it comes, again.

So, here I am ... no longer the youngster chauffeuring an old man on a trip to give talks on his lifetime of work ... reflecting on "how I didn't but might've known" about this unbroken circle hat Ecclesiastes fascinated about 3000 years ago, still writing a little and munching on rice crackers slathered with Nutella that rightly belongs to M and my houseguest, sleeping upstairs with likely no clue of how such Fractals just keep comin' .... again .... and again!