Replying to LO25576 --
Replying to Fred Nickols in LO25576
Dear Fred, dear LO'ers,
My suggestion to include in some way also the environment or surroundings
when trying to get an answer on the question of the subject, brought you
to the following words:
> In any event, my point here is to agree with Leo regarding the importance
> of boundaries but to also point out that they don't really exist. We set
> them, we establish them, we impose them. When I trace a production
> process at a company, it always goes forward into interactions with
> "customers" and backward into interactions with "suppliers." These labels
> don't really identify distinct entities (except legally), but they do
> identify boundaries that we establish, set and impose. Where we draw the
> lines is a choice we make, not a "reality" that we discover or uncover.
Fred, I fully agree with you. It are our definitions that set the
It reminds me of some examples that come from the science of fractals.
We probably could remember that our grandma was knitting with two needles
and a clew of wool. If we observe this clew of wool from, say a kilometre
distance, it is just a spot - zero dimension. If we come somewhat closer,
this spot appears to be a circular disk, as the full moon - 2 dimensions.
Still closer, we will see that this disk actually is a ball - 3
dimensions. If we come so close to this ball that we could see the wool
threads this 3D becomes even clearer. But then, still minimising our
observing distance, we will see only one single thread - 1 dimensional. We
could still go further, entering this thread, and so on, until we may see
the individual molecules or atoms. Every now and then, the dimension
'flips' from number to number: 0 - 2 - 3 - 1 etc.
So here we already could imagine the point that Fred made. As a matter of
fact, maybe I should have used the word 'scale' in stead of 'dimension' in
my former post.
Another famous example is the length of the coastline of Great Brittain.
The coastline as the boundary between land-structure and water-structure.
We could measure this length, using a topographic map from the atlas. The
length will be a certain quantity of miles or kilometres. But, surprise,
this length of the coastline depends logarithmically with the scale of
the used map. A more detailed map, will give a greater length of the
coastline. If we try to measure the coast by walking with a measuring
stick of -say 5 metres - along the entire coast, its length will become
larger again. If the measuring stick is shorter, the length of the
measured coastline will still increase. There appears to be the same
relationship between length of coast and scale of measurement.
But when walking along the coast, what is actually land and where does the
water starts? There are tides, there are marshes and swamps, where does
the river ends, or where does the sea begins. There seems to be an area
where there is both, land AND water.
A brick wall of a building from a distance looks like a plane surface - 2
dimensional. If we come closer, we may discern the individual bricks and
the somewhat deeper lying grooves of cement in between the bricks. The
wall becomes 'a little bit' 3-dimensional.
The interesting thing is that in these days the roughness of a surface is
expressed by this 'a little bit 3D' with a number that is in between 2 and
3. Thus the roughness of the brickwaal could be something like
The same as the brickwall could be done with the coastline. It is not a
sharp 1-dimensional line, but this coast is 'somewhat' 2D, hence the
dimension is between 1 and 2.
The same with the clew of wool. Dimensions do not flip from one number to
the other, but there are transitional trajectories between these numbers,
depending on the scale of observation, or measurement.
In all these examples it is clear that defining boudaries is a special
science on itself. And the very boundary is in itself a particular
structure. The boudary depends on the definition, scale of
And what counts for the boundary, counts for the structure within its
boundary too. This is one of the themes of the reply that At has written
dr. Leo D. Minnigh
Library Technical University Delft
PO BOX 98, 2600 MG Delft, The Netherlands
Tel.: 31 15 2782226
Let your thoughts meander towards a sea of ideas.
Leo Minnigh <email@example.com>
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