Dual scale histograms

David Dirlam (ddirlam who-is-at weber.ucsd.edu)
Thu, 20 Nov 1997 09:04:11 -0800 (PST)

On Wed, 19 Nov 1997, Jay Lemke wrote:

>
> The dimensional view captures nicely one aspect of the issues, but we need
> more.
>
> Fortunately I am postmodern enough not to need to insist that there be a
> single consistent picture for the whole problem; as long as my bag of
> tricks always has a tool to the purpose, and my ways of using the toolkit
> can be learned by others (or improved on), I am perfectly happy to
> juxtapose philosophically or mathematically inconsistent notions.

Well put, Jay. Dual-scale histograms are merely one more tool for
our kit.
But I think your cautionary point about *missing occasions when an
event on one scale influences those on another* might be mistaken. To see
this, I first generalized it as follows: When using a dual-scale
histogram, one needs to look for sensitive dependence in larger scales on
small changes in one of the other scales. Actually, it seems that these
dependencies would be EASIER to see with the dual-scale histograms than
with almost any other figure I can imagine -- they would spread out like a
wave in a blanket.
Oh, oh, Bill Barowy -- there's your Fourier analysis, just when I
was thinking it wouldn't apply.
I see another problem in the dual-scale conception, though.
There's no distinction between individual and collective. Any ideas of how
to add this?

David