[xtm-wg] Structural constraints are extensions of equality

[Andrius Kulikauskas <ms@ms.lt>]

I wrote earlier about the work by the Minciu Sodas Laboratory to develop
an import/export standard (as simple as a spreadsheet) for tools for
organizing thoughts (such as TheBrain, www.thebrain.com, and
MindManager, www.mindmanager.com) with emphasis on the kinds of
structural constraints used.  We may describe this as a simplification
(popularization?) of TopicMaps.  I share new ideas and appreciate your
help in adding to the kinds of structures that I describe.  
Andrius Kulikauskas
********************************

I have a new idea for how we can identify and define, for practical
purposes, the basic kinds of structural constraints that we rely on to
organize our thoughts.  The idea is that each structural constraint
works by defining, in its own way, what it means for thoughts to be
"similar" or "different".  These structural constraints are crucial for
doing meaningful transfers of aggregates of thoughts from one software
tool to another. 

I should first put this in context of what we've done so far.  I started
with the idea of Kestas Augutis (which also Roy Roebuck had) that our
minds rely on three different structures for organizing thoughts:
sequences, hierarchies, networks.  Computers allow us to use these three
structures in a balanced way, so that we can choose these different ways
of organizing our thoughts so as to promote different kinds of
thinking.  In September 1999, I wrote a paper "Developing Import/Export
Standards for Aggregates of Notes" summarizing work at the Minciu Sodas
laboratory on how to define these three structures from a human point of
view.  An important result was that visualizations involve restructuring
one of these three structures (S, H, N) with another, yielding six
visualization types: chronicle (S to H), evolution (H to S), catalog (H
to N), atlas (N to H), canon (S to N), tour (N to S).  This paper is at:

http://www.ms.lt/ms/projects/formatkinds/990917shn.html

In order to come up with a usable import/export format as soon as
possible, in response to the pragmatic perspective of Saulius
Maskeliunas, we then started an investigation, "Linking Locally is
Thinking Globally", sponsored by TheBrain, to see what kinds of
structural links are used by existing software and standards.  A cursory
view has suggested structures such as: Ordered Hierarchy, Unordered
Hierarchy, Radial Hierarchy, and Directed Network and Nondirected
Network.  However, we need to make a more concerted effort to find more
structural link types.  Also, some of these structural constraints
actually require pairs of links, for example, to code an ordered
hierarchy we need to know, given a branch, not only who its parent
branch is, but also which sibling does it come after in the ordering. 
We need to have a way of reasoning, whether an ordered hierarchy is just
one link type (ordered hierarchy), or two link types (ordered sequence)
and (hierarchy).

So I am glad to have come up with a new way of thinking about these
structural link types.  The idea is that the purpose of the structure is
to give us a way of thinking about the sense in which two thoughts are
the same.  An example is the method by which I put together results for
our Thoughtful Wishing usage matrix
http://www.ms.lt/thoughtfulwishing.html of tools wished for by people
who enjoy thinking.  I had two or three dozen categories that I wanted
to relate, collapse, refine.  So I placed them on a sheet (using
Microsoft Paint) and worked to arrange them so that related ideas were
next to each other.  This gave me a diagram that I could think about how
to structure and purify.  What was I doing here?  Was the
two-dimensional constraint relevant?  Not really, not at this point. 
Most relevant was the concept that categories adjacent to each other
were very closely related, whereas categories far away from each other
were related only by way of intermediary categories.  In other words, a
nondirected network (a network with bidirectional links, which TheBrain
calls "jumps") is what I was really using, even though I did not draw
them.  Thinking about this, I concluded that, in general, this is
arguably the whole purpose of nondirected networks, that thoughts are
equal to the degree that they are adjacent. So thoughts are equal to
themselves, thoughts that are adjacent are almost equal, and the more
thoughts in between, the less they are equal.  A strange, but I think,
very useful way of looking at "equality" - that structural link types
extend the meaning of equality in very different ways.  In other words,
equality is a structural concept, not a semantic concept, and perhaps
the only structural concepts are extensions of equality.

With this in mind, I give a preliminary list of structural constraints
that I know from practice.  This can serve as a "style guide" for using
TheBrain and other tools for thinking.  I invite your critique and,
especially, additions.


TREE = UNORDERED HIERARCHY
Sometimes I want to accumulate my thoughts over time regarding a topic
(an idea, category, problem...), so that I could later go over those
thoughts and see how they relate, and what kinds of issues come up, and
sort those thoughts into these issues, making for new subtopics, and so
on.  Here thoughts are different to the extent that they do or may
belong to different topics.

Comment: 
Here and elsewhere, what is important is our global "intent" as authors,
not the actual structure, which may end up clashing with our intent.  So
our intent to structure our thoughts into a tree will naturally lead as
well to "forests", and possibly to "multiple hierarchies", or even
network type structures where a topic may be the subtopic of several
different topics.  What matters here is whether (or not) the author
intends the links to form a tree.

Comment:
There is no structural constraint "ordered hierarchy" or "radial
hierarchy".  A radial hierarchy (such as the branches extending from the
root of the tree in MindManager, www.mindmanager.com) involves two very
different kinds of relationships.  One is that thoughts are organized in
a tree, as described above.  Another is that we can think of the
branches as being adjacent to each other, or even to branches within
other branches, depending on how the tree is layed out.  This adjacency
has the same purpose as the nondirected network described above.  So
arranging the thoughts with respect to these two different bases (by
topic, and by adjacency-relatedness) makes for a creative tension, part
of what the MindManager website refers to as using both the "left-brain"
(by topic) and the "right-brain" (by relatedness).  Similarly, I think
that when we have an ordered hierarchy, then we are using both a
hierarchy and a sequence, as described below.

OPEN SEQUENCE
I think there are at least two kinds of sequences.
One I call an open sequence, which is used for listing priorities.  I
call it open because priorities can be reshuffled, and new priorities
can be inserted, and we can still think of it as the same sequence.  
Maybe more important is that there is no concept of the end of the
sequence.  Each priority can be thought of as a filter, so that we have
a stack of filters.  We may think of the first priority as a null
filter, which says that we do not have to do anything.  Subsequent
priorities are interesting only to the extent that they are different
from all of the preceding priorities, for otherwise they do not have any
effect, do not require any response.  Thoughts are equal to the extent
that they extend the preceding thoughts in the same way.

CLOSED SEQUENCE
I call a closed sequence of thoughts one which has a definite beginning
and a definite end.  This is used for documenting reasoning, where each
thought follows from the preceding thoughts.  Presumably there must be a
single chain of thoughts connecting the beginning and the end, because
otherwise we would have to keep a separate record of what they are. 
This means that there can be no "gaps" between thoughts.  Instead,
thoughts can be refined, over time, into subsequences of thoughts.  As
this happens, the tree structure can be used to identify the
subsequences of narrower thoughts with the broader thoughts that they
broke down.  (This gives rise to a chronicle: a sequence restructured
with a hierarchy).  I imagine that here subsequences of thoughts are
equal to the extent that they are interchangeable.

NONDIRECTED NETWORK
As described above, in a non-directional network (where the links are
bi-directional), thoughts are different to the degree that they are not
adjacent.

Comment:
The nondirected network should, I imagine, be implemented with pairs of
directed links.  There may be - unintended - cases where the link ends
up one-directional.

DIRECTED NETWORK, NO CYCLES ALLOWED
Sometimes thoughts are organized so that there is a link from A to B
whenever B depends on A (or B requires A).  This lets us see which
concepts are more fundamental, for example, the concept of "divorce"
requires the concept of "marriage", but not the other way around, so
"marriage" is more fundamental.  Or more complex molecules require
simpler ones.  Or, as in architect Christopher Alexander's theory of
patterns, certain patterns are layed down first, and they are required
by other patterns that refine them.  We have a lattice in which cycles
are not allowed, or at least, not intended to be allowed.  This
structure is for evolving complexity, and cycles would disrupt the
evolution of this complexity.  We use this structure to figure out the
underlying vocabulary of concepts or words or patterns, from which
"sentences" are generated.  Thoughts are equal to the extent that the
thoughts they require are the same.

DIRECTED NETWORK, CYCLES ALLOWED
Allowing for cycles makes for a qualitatively different kind of
structure, which by which we follow the movement of our attention.  For
example, we may have a network of questions (and possibly answers), each
question leading to other questions, possibly resulting in cycles. 
Hyperlinks are another example where our attention moves from thought
(or document) to thought.  We can think of each link as a
transformation, and a cycle as consisting of "energy-conserving"
transformations.  Thoughts are equal to the extent that they occur on
the same cycles, that is, they can be readily transformed into each
other.

Comment:
Given the structure defined above, I doubt that there is any need for a
separate structure for cycles - which are quite rare for organizing
thoughts, and many cases where they do appear (like the water cycle -
"clouds-rivers-ocean", or Socratic questioning) are in the spirit of the
structure above.

THOUGHTS & FINITE STRUCTURAL TEMPLATES
Aside from the structures above, which can grow (like crystals), there
are many finite structures that one can impose on thoughts.  Or we may
simply have isolated thoughts.  In these cases the thoughts are all
different, but equal to the extent that they participate within the
template.

*************************************************
SUMMARY OF WAYS OF EXTENDING EQUALITY
I appreciate your help in identifying more types of structure that you
use to organize your thoughts.  This line of thinking has yielded the
following (which I associate with earlier work on visualizations from
the paper I mentioned):

CLOSED SEQUENCE
for: reasoning
Thoughts are equal to the extent that:
they belong to subsequences that are interchangeable.
visualization: chronicle (sequence restructured with hierarchy)

OPEN SEQUENCE
for: priorities
Thoughts are equal to the extent that:
they extend the preceding thoughts in the same way.
visualization: canon (sequence restructured with network)

TREE, HIERARCHY
for: relevance
Thoughts are equal to the extent that:
they belong to the same, but not different topics.
visualization: catalog (hierarchy restructured with network)

DIRECTED NETWORK, NO CYCLES ALLOWED
for: requirements
Thoughts are equal to the extent that:
the thoughts they require are the same.
visualization: evolution (hierarchy restructured with sequence)

DIRECTED NETWORK, CYCLES ALLOWED
for: attention
Thoughts are equal to the extent that:
they occur on the same cycles.
visualization: tour (network restructured with sequence)

NONDIRECTED NETWORK
for: adjacency, relatedness
Thoughts are equal to the extent that:
they are adjacent to each other.
visualization: atlas (network restructured with hierarchy)
*************************************************

CONCLUSIONS
One conclusion is that the notion of "extending equality" is helpful to
distinguish between what aspects are structural (formal, syntactic...)
and what are semantic.  The idea suggested is that equality (and the
extension of equality to various kinds of similarity) is a purely
structural concept (and the only structural concept).

Another conclusion is that a tool for thinking is successful (as an aid
for thinking) to the extent that it allows us to switch back and forth
between different kinds of structures.  For example, MindManager,
www.mindmanager.com, lets us switch back and forth between thinking
about the TREE structure, and thinking about the NONDIRECTED NETWORK
given by the layout of the branches, which is adjacent to which. 
Likewise, TheBrain, www.thebrain.com, is - I believe - helpful as an aid
for thinking, to the extent that we switch back and forth between
thinking about the DIRECTED NETWORK (WITH CYCLES) given by the
parent-child relationship, and the NONDIRECTED NETWORK given by the jump
relationship.  

I should temper the above statement to say that both tools can actually
be used to think the other structure as well.  For example, branches in
MindManager can be ordered by priority (OPEN SEQUENCE), or the
parent-child relationship in TheBrain may be thought of as a TREE. 
This, however, just emphasizes the point that in doing import/export
between tools, the person performing the transformation should be aware
of the structure that the author of the thoughts had in mind.  Such
transformations are, first of all, a problem of modeling, and only then,
converting.

The associations with the visualizations suggest to me that we will not
find more than the six kinds of structures above.  So I very much
welcome your evidence to show me wrong, or ideas to point me right, both
large and small.  This will make for an elegant and useful modeling
standard for the import/export of aggregates of thoughts between tools
for organizing thoughts.

Andrius Kulikauskas
Director
Minciu Sodas Laboratory
http://www.ms.lt/importexport.html
ms@ms.lt


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