........some find the subject
a little hard going
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(occasionally I add to this and other pages without checking
older stuff for quality) 3/00 ph
Nature can be interpreted as globally deterministic because sufficiently
narrow circumstances seem to completely determine every effect.
There are also important gaps in this finding.
Deterministic rules allow exceedingly small differences to sometimes be
multiplied and have large effects,
It is readily observable that nature is locally, not remotely, organized.
For nature to be globally deterministic and local organized at the same
time may seem incompatible, but it's only our minds that are lacking.
The way it works it that first things need to get organized and then they
can be controlled. If controlling one part determines the behavior
of all the others, it is because they are organized that way.
Without the organization, there's no special influence to be had.
The old tools and concepts were (and are still) good at uncovering how
things are organized and how we can take advantage of it, but tell us very
little about how things get organized in the first place. It's
a separate problem. To some degree, it means learning how to
be interested in, and to watch things, that are a little out of control,
and then to identify the locally opportunistic mechanisms that develop
to bring about some order. Once those have taken place things can
then potentially be predicted and controlled.
Scientific writing makes difficult reading. It's not just that science
involves special terminology and complicated methods, its also that scientists
have highly enriched sets of images that originate from direct observation
of their physical subjects, things no one else may observe as closely,
so it's can be hard to know what's being talked about.
One of the keys to good science is a scientist's personal immersion in
the details of the physical subject. That's the intuitive basis of science.
Scientists have extensive collections of images in their minds that they
are referring to, that they didn't get from just reading.
The physical subject here is the pattern of little accelerations of change
found at the beginning and end of most events. That includes the way a
muscle tenses and relaxes, in a microscopically seamless way, or how a
storm develops and subsides, or how current flow in a spark grows and decays
as seen on an oscilloscope. Any regular measure of virtually any natural
event shows leading and following trails, with a peak of some shape in
the middle, as if following a continuous path. Looked at closely, of course,
one always finds that these smooth transitions to coming and going are
not really continuous. Nothing in nature is. All nature can be broken down
into a cascade of ever smaller inner workings.
What this is about, instead of looking for how things can be taken apart,
is the opposite, looking for the telltale patterns of change that show
local organizational processes, and how the inner workings become to be
connected. You may have never thought of that before. The attempt
here is to make that inquiry into a disciplined and useful scientific tool.
Finding continuous patterns of change over time is the main subject, and
this means drawing curves. One of the most curious features of nature is
that all apparent curves, when looked at closely, are made of 'dots', the
ink on the page as well as the data and the physical subject it refers
to, presenting a total discontinuity! Yet there is continuity, but not
seamless like in mathematics, and whether there are connections in nature
or not, only the connections between the dots, that we make,
allow us to see it.
This connected and disjointed character of nature and information can be
genuinely confusing. It would appear that the full appreciation of this
fact is not even quite dawning on the scientific community, still uncomfortable,
after a hundred years, about the failure of classical determinism. We still
rely on it heavily, and find it difficult if not impossible to emulate
the order in events that nature so amply demonstrates using random variables
in nonlinear mathematical models. The position taken here is that continuity
is not violated by discontinuity, that nature is not math. It's different.
This is a little like the confusion physicists have about the wave-particle
nature of light. It doesn't seem to make any sense, and part of the fun
is that the concept encourages you to think 'forbidden' thoughts, like
that the connections exist only when you make them. (Homework: figure
that out...). Its a tricky subject and there's much to pay attention to....
What one can always go back to for reassurance is some subject for which
you can see both sides, the evident continuity, composed of separate events
(the dots). This work is based on reading patterns of dots that display
sequential proportional change.
'Connecting the dots', to find useful patterns, is a subject of literally
every task and discipline. In science it is conventionally done with mathematics,
substituting equations for data and building a larger theory of interconnected
equations. Here it is done with a kind of constructed near-mathematics
which does not have specific equations. It's a form of imaging with mathematical
rules. Good images, though, make for good questions, and that is the object.
Speaking about a complicated scientific subject, to a broad interdisciplinary
scientific audience, requires speaking quite precisely, but with fewer
specialized terms than usual. On many of the subjects I address I don't
know many of the technical terms myself, and would not help anyone by creating
a number of my own to make the reading more difficult. Some parts of this
subject would still benefit from developing specialized terminology but
that is largely avoided in favor of using generalized terms and references
to physical subjects. A simple glossary is perhaps becoming needed.
Derivative The term 'derivative' is used for the slopes and accelerations
of a curve. This is usually reserved for the very specific meaning it has
in calculus, for curves having mathematical continuity. It is most frequently
used here to refer to the successive differences between points in a sequence,
the slopes and accelerations of a series. Behind its use for that purpose
is also an expanded theoretical meaning. Using special rules a sequence
of points can represent a 'constructible' mathematical continuity, one
that could be made to satisfy the strict rules of mathematical continuity
by iteration. These are wonderfully complex theoretical subjects, that
are not yet fully developed, and will most often be referred to by using
'derivatives' and other terms in their broadest possible sense.
Proportional walk The technical term for finite sequences associated
with such a rule for becoming differentiable is a 'proportional walk'.
Such rules also concern the means of distinguishing and connecting mathematical
continuity and physical continuity. Physical continuity can only be partly
observed, usually indicated by proportional change being displayed in physical
System Innovation in science is often a matter of different people
looking at the same thing in different ways and developing incompatible
terminology for it, to be resolved later. The term 'system', for one, has
a tortuous history, like the blind wise men all trying to describe an elephant
from feeling different parts, it has come to have many incompatible meanings.
A possible unified meaning of the term is that it refers to something (anything)
that 'connects the dots'. Then those who insist that 'a system' is an equation,
and those who insist it is an object and others who insist it is a physical
process, or that it is a set of rules of organization, or a polarity of
environmental interaction, etc. could all be talking about the same thing.
Seems to depart from the scientific method?
Yes, and no. This approach does not seek to impose equations on physical
events to represent them.
The practical necessity of raising this issue comes from the conventional
regimented application of the statistical method to time series, uniformly
treating data as representing equations, particularly containing random
variables. The main trouble with rigidly following that approach is that
an equation is a constant structure, and in imposing one you first have
to assume the subject has a constant structure. It could often be a sampling
of a complex of processes having changing structure. The more fundamental
problem as I see it is that the conventional method takes a 'top-up' approach,
starting from the theoretical and refining toward the theoretical. It has
worked great on a lot of things, but it is inherently flawed when dealing
with complex processes, when any number of layers of continuing and transient
processes could be (and usually are) expressed in the available data.
What is offered here is more of a 'bottom-up' approach, starting from the
data and distilling organic patterns of theoretical interest. When mathematically
suggestive patterns appear, they are much more directly rooted in the phenomena
themselves. What you tend to find also then includes what you would
least expect, and facilitates discovery.
Roughly speaking this approach fits within the scientific method as a precursor
to conventional analysis. It is a tool designed to enhance direct observation
and facilitate the necessary development of informed scientific intuition
before applying conventional techniques.
It may be quite difficult for scientists to imagine what kind of order
is there if you take out the equations, but that's the purpose, and just
what you find out.
Just Sounds fictional?
The central part of this work is a disciplined method of suggesting new
hypotheses, displaying the patterns of nature clearly enough for us to
form better questions about them. As a hypothesis generator the product
is inherently a kind of fiction, something to stimulate the imagination.
Because it is a method of distilling patterns, rather than of testing preconceived
ideas, this tends to expose the fictional character of some of the conclusions
others have reached. Under the conventional method only the theories an
investigator has thought of are tested, and that leaves a lot of room for
Still just sounds nuts?
Then there's the more basic problem of the author's own occasional inconsistencies,
errors in method and interpretation, and sometimes inappropriate characterization.
The author is somewhat, but not fully, conversant in the fields addressed,
and is inevitably prone to misusing some of the terms and glossing over
some of the details to fill in the gaps.
Still the fact remains, and is no illusion, that there are beginning and
ending trails of data for virtually all observable events, and we don't
know what they are there for. What those little wisps of data seem to be
are the tell-tale evidence of the physical mechanism of causation, the
physical steps of building connecting events. It becomes apparent that
these are processes are part of every process. (....And it is just
a little nuts to imagine that this has somehow been just overlooked.)
There is then, more order to be found in data, and complex order in nature,
than much of anyone is able to venture. The intent here is to press the
limits, using the current direction, to make a little more of it clearly
visible for study.
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