Life 8, Sydney, December 2002
Dorin & Jon McCormack
Centre for Electronic
School of Computer Science & Software Engineering
Monash University, Melbourne, Australia
- Previous work
- The model
- The synthesis of virtual, multi-levelled, dynamical hierarchies exhibiting
emergent properties at each level is an open problem in Artificial Life research.
- In this context, there is no consensus on the meaning of the terms:
- Debate continues about the possibility of building such systems and the
conditions under which it might (not) be possible.
- THIS PAPER...
- Presents a trivial, virtual, infinitely-levelled dynamical
system with emergent properties occurring at each level, with base units
of fixed complexity.
- Demonstrates one way in which more rigour in measuring hierarchical
organization may be introduced.
- Highlights the problems when discussing emergent properties
- A discretized space, tessellated with triangles (or squares).
- Elements which move randomly through the space.
- Bonds which may form and break between neighbouring elements to assemble
A screen grab is
available from software which runs this model (using squares).
Some sample structures
- What is a hierarchical object? (E.g. Baas '94)
- This hierarchy may self-assemble in the above system.
- No additional information needs to be added to the base units for the assembly
of this trivial but nevertheless, infinitely-levelled hierarchy.
A different hierarchy
(Differently shaped at each level)
As well as this hierarchy seen earlier,
This is also a hierarchy,
- How can we measure the difference between them?
Measuring & Comparing Hierarchies
- In the digital realm we can easily measure the redundancy in the specification
of a structure.
Consider a structure X of order n, written Xn.
- Composed of 4^(n-1) X1 primary elements.
- If each primary element X1 requires p bits to specify
position and orientation,
Xn requires p*4^(n-1) bits to specify as an aggregate
- if Xn can be described in terms of the position and
orientation of the 4 lower level elements Xn-1 that
Xn requires p*4 bits to specify in terms of Xn-1.
So, for n levels, Xn can be specified hierarchically in: p*4*(n-1) bits.
- p*4*(n-1) < p*4^(n-1), if n > 2
The hierarchical description is measurably more efficient than the non-hierarchical
Properties are observed by people.
- We do not recognize/observe everything.
- We overlook, ignore, are fascinated and captivated.
In a simulation, properties may be distinguished where the machine
has states to represent them.
- Observers may assign meanings to these states.
- Changes between machine states (and their meanings) are governed by logical
rules, not by chemistry or physics.
Trivial Properties in the Model
- A single element has the property "I may move as an aggregate of 1
- A pair of elements has the property "I may move as an aggregate of
Each level in the hierarchy has a property not found at lower levels.
This sounds like Bedau's "Nominal Emergence".
Not So Trivial Properties in the Model
- Higher levels possess internal-bonding possibilities not present
at lower levels.
Higher levels possess external-bonding possibilities
not present at lower levels.
If a glider in The Game of Life is emergent, surely so
are the structures in this model.
This sounds like Bedau's "Weak Emergence" (Nominal
Emergence + complex derivation).
"How complex is a complex derivation?" (Now emergence
is subjective once again)
We have built an infinitely-levelled
dynamical hierarchy which exhibits emergent properties at each level and has
base units of fixed complexity!
So why are we not excited?
The Artificial Life mantra:
"We seek interesting behaviour"
Multiple-levels of trivial behaviour may produce a level of interesting
- Is the interaction of atoms as "interesting" as the interaction
- Is the interaction of molecules as "interesting" as the interaction
Perhaps the stuff of our simulations is just too boring to ever produce
- What do we mean by dynamical hierarchies and emergent properties?
(Does it matter and why?)
- When is something "interesting"?
- How subjective/objective can we be about this problem?
Is this model what we are looking for?
I doubt it.
What is missing from this model?
It isn't interesting.
Can we measure hierarchical structure in simulations?
Can we measure properties in simulations?
- Can we tell when a property is emergent?
It seems so... but it might be completely subjective... I'll know it when
I see it!
The issue hinges on the Artificial Life