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Mandelbrot Relativity

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Posted by Alan on December 19, 2001 05:42:09 UTC

Returning to the issue: a collection of undefined events (or
objects); and the inherent logical patterns that occur as you
progressively encounter, or acquire knowledge of, these events
(or objects).

Just as Stephen Hawking talks of the "wave function of the
universe", looking at all possible universes; let us look at all
possible journeys through this field of undefined events (will
use term "events").

To simplify, I am considering just a field containing a small
number of events; with these encountered just once each, in some
arbitrary order. Of all possible pathways through the event field
(probability wave function of event field); take say one actual
path that happens to start with event 'I'.

Suppose there are 26 events, labelled with the letters of the
alphabet. Your starting "yardstick" for measuring the event field
may be called "prior knowledge" (whatever you knew before
encountering the event field).

As soon as you start with 'I', the yardstick (you)(for measuring
the field) obtains knowledge of 'I'. This knowledge comes from
the "prior-knowledge yardstick" comparing 'I' to that prior
knowledge. Thus a self-referent yardstick.

Now the yardstick becomes a "Prior-knowledge that has compared I"
yardstick.

The events field has been subdivided into: known: I; and not-
known: ABCDEFGH JKLMNOPQRSTUVWXYZ.
Now say you encounter J. The events field divides into known: I,
J; unknown: ABCDEFGH KLMNOPQRSTUVWXYZ. Your yardstick becomes a
"Prior-Knowledge-compares-I, compares J" yardstick.

Suppose you now encounter K. The events field has subdivided into
known: I, J, K; unknown: ABCDEFGH LMNOPQRSTUVWXYZ.

Your yardstick is now a "(((Prior knowledge compares I)compares
J)compares K) yardstick.

Suppose you now encounter L. The events field is thus divided
into known: I, J, K, L; unknown: ABCDEFGH MNOPQRSTUVWXYZ.

The yardstick becomes a "((((Prior knowledge compares I)compares
J)compares K)compares L) yardstick.

As you can see from the nesting of brackets, this yardstick is
growing in a fractal dimension manner, with each event encounter.

The yardstick is self-referential, and each event encounter adds
to the data-base of pattern-comparison within the yardstick.

The events field is being divided into "known" and "unknown"
categories. The events in the "known" group are automatically
labelled by the fact of having each been met by a slightly more
knowledgeable yardstick. Each event is getting individually
tagged in this way, by the different knowledge state of the
yardstick for each encounter.

Note that the events field, from the perspective of the
yardstick, divides from "26 unknown": into "1 known", "25
unknown"; then the "25 unknown" splits into: "1 known", "24
unknown"; (also still have the retained "1 known" from before);
and so on.

If you didn't know how many events were in the field; the initial
"26 unknown" may be regarded as just "1 unknown". As you
encounter events, your number of "knowns" increases; and the
remaining "1 unknown" that you are left with could contain any
number of undiscovered events. But the original total "1 unknown"
must contain at least the number of events you have found so far
after part-exploring the field, plus (if you haven't reached the
end) at least one remaining unknown.

The further you progress through the events field; the further
you will have a necessary constraint on what patterns may occur.

The possible order in which remaining events may appear is
constrained by the non-availability of events that have had their
one-allowed encounter.

As the yardstick grows in a particular order; the future-
knowledge-aquisition of the yardstick is limited to knowledge not
yet obtained. The very nature of encountering events in a
sequence; and of comparing those events to a self-referentially
growing data-base of knowledge; appears to give a fractal,
Mandelbrot-set like structure to the data-base.

Even if many events could be encountered simultaneously; and
events were re-encountered many times and in many different
orders; a multiple fractal network of pattern-matching would seem
to be the structure.

If this structure is the minimum logical necessary structure of
data in humans; all physics and mathematics must flow from this
structure in so far as being mappable by this structure. The
structure may be dynamic, with the possibility of jumping from
one place to another within it. Thus one may construct new
patterns from it.

Another possible structure would be direct awareness of what
exists through Existence; (and the fractal networks may be sub-
structures of that).

Once you have travelled through the event field and tagged every
event once, by your different-state-of-knowledge when
encountering each event; you could re-travel your model of the
event field in any order.

You could acquire models of many event fields; and then jump
between them in any order to construct a new field. You could use
the knowledge of all the event fields encountered; to measure
new events by jumping throughout your data-base of pattern-
comparisons, and constructing the preferred explanation of the
new events with reference to past experience. Or may jump to
conclusions about new events, based on hypothesising about them.

One may wander through one event field in many different orders;
and each path gives one a yardstick with a fractal pattern of
finer and finer levels of pattern-comparison for each event
encountered. If all you knew to start with was the first event;
if you WERE the first event; by the time you reached the end of
the field you could be comparing the last event with you. you and
all the others, or you and some of the others.

Although you could re-model the other events in a new order at
the next event-measuring; a simple possibility is that the other
events will have been accumulated as fractal comparisons with
you. (This would start thus: Compare event 1 (me) with event 2;
then compare (me+2) with event 3; then compare ((me+2)+3) with
event 4; etc.).

Suppose you compared the fractal pattern of how your yardstick
looks after travelling a particular order through the event
field; with the fractal pattern of how your yardstick would look
after travelling a DIFFERENT order through the event field.

Perhaps one might call the relativity bewteen these two different
fractal representations of the event field, a "Mandelbrot
relativity", given that they are two different Mandelbrot-set
like representations of one event field.

If Richard Stafford has a partial differential equation that
describes in general how the event field may be differentiated
from the perspective of any one event; maybe that equation also
describes the relativity between two fractal-pattern-structures
that both describe that event field. These two pattern-comparison
structures may be built of fractals, using different starting
events as "you", the initial yardstick to which fractal layers of
pattern comparison is added.

Consider a coastline of an island; giving a longer and longer
total length as you measure it with smaller and smaller
yardsticks (that wander over more detailed ins and outs of the
coastline). When you are the first event measuring an event field
by self-reference; you are effectively the coastline. It is you
that seems to grow, as smaller and smaller events (smaller in
that they are increasingly smaller proportions of your total
experience) measure YOU! As you measure, so you are measured?

You grow at an increasingly slower rate in terms of your
yardstick of experience, it seems. You may have rich new
experiences, but are they not built on reference to early-laid
foundations? In real life this seems to happen: as you get older,
the days, weeks, years seem shorter? There is less encountered
that is entirely new? Maybe this is not just the effect of your
physical height growing? (which makes a large park or tall
building from childhood seem smaller when older and bigger).

Could it be that the bulk of your pattern-comparison yardstick of
the world is built when you are very young?

Do sub-atomic particles have a good measure of their neighbours
soon after the big bang; with particle exchanges since then
mainly utilising information acquired back then?

Actually since you may re-juggle your accumulation of events at
any time; and re-design your yardstick and the relations among
events; your collection of event-encounters might seem more like
an undefined event field itself than a mandelbrot set of pattern-
comparisons. Not quite undefined: defined by you!

Consider a dictionary. Consider all the possible combinations
using any two or three letters that can be found in that
dictionary.

In the dictionary; the greater the mass of words you collect, the
larger a proportion you will have of all the possible
combinations using any two or three letters found in that
dictionary.

The greater the combined masses of two such collections of words,
the more the two masses of words share common combinations of two
or three letters. Maybe gravity is similarly an attraction to
common ground. Maybe the common ground of comparing the Earth
mass to the Universe and the moon-mass to the Universe is what
attracts the Earth to the moon?

-dolphin

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