connecting dots perpendicular to the page
Posted by Phil Henshaw-2 on Oct 07, 2006; 2:49am
URL: http://friam.383.s1.nabble.com/Fw-Re-Unstrung-tp522691p522719.html
When one has a series of measurements of something, a bunch of dots,
there are two basic choices. You can look at them as an equation to be
described, connecting them in the plane of the page. You can also look
at them as physical processes to be found, not directly connecting the
dots to each other, but indirectly connecting them through other things.
That links the dots through loops perpendicular to the page.
Math is parallel to the page, processes perpendicular. Together they
provide useful independent dimensions of understanding made possible by
measurement.
There's a very useful corollary of the conservation laws, following from
their implication that rates of change and their derivatives can not be
infinite. For things to begin or end there must be periods during which
all rates of change are of the same sign, and fall between upper and
lower bound exponential curves. That's a reasoning that could equally
lead to the conclusion that there had to be an inflationary period in
the big bang.
I'm not certain the principles used are the same, but there's a
similarity. What's new for the scientific method in this, though, is
that you can see the same phenomenon in most any sort of beginning or
ending too. It provides a very useful standard hypothesis for probing
the clues of how events that begin and end occur.
Math and process reasoning can be used together, or you can ignore one
or the other. Each deals with the same world in a different way. For
just one example, building an equation that has the same structure from
beginning to end to represent any natural process of change, will not
help much for picking out what actually happening. Carefully filtering
data to reveal its independent shapes and their start and end points, on
the other hand, can coax clues from the data about many new kinds of
events. The main reason that's useful, of course, is there's lots there
to see, frequently evolving systems.
Phil Henshaw ????.?? ? `?.????
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