[Network Evolution Rules] - A New Kind of Science: The NKS Forum

A New Kind of Science: The NKS Forum

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Network Evolution Rules

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Posted by: steinhoff

Let's find the "theory of everything" and
solve the puzzle already! I'm hoping for
some thoughtful answers for the main
question below, especially from people who
don't usually post but have thought about
this before...thanks!

------------------------------------------

I'm a big believer in Wolfram's "Space as
a Network" idea and even wrote a program
to quickly evolve a given starting network
via given "find-and-replace rules". This
all follows the NKS Ch 9 Sec 7/12
proposal, but is somewhat more general by
allowing directed connections (i.e.,
connections with arrows) and by allowing
more than three connections. This seems
so much more elegant and powerful to me
than the "fixed-grid" cellular automata
approach which most people here, including
Wolfram, seem more interested in (perhaps
I'm missing some generalization here which
makes the CA grid more flexible?).

In the end, these "find-and-replace rules"
destroy and create sub-networks, and some
set of starting networks should represent,
for a simple but useful example, the set
of electron-electron scattering states.
So, can somebody propose both rules and
starting networks with potential for this?

The challenge here is in the details, so
I'd like full specifics...please test any
ideas on paper for dynamic "life". I've
been brainstorming ideas for months and
seem to always get rules that quickly lead
to a dull/dead dynamic. I am, of course,
biased by a belief that the rules should
be simple to express in our language
(though I have convinced myself that there
probably are at least two simultaneous
rules, one creating points, one destroying
points). By the way, I have looked at a
few specific examples in these forums but
have arguments against them.

Sleepless in Dallas,
steinhoff


Posted by: Tony Smith

steinhoff, I won't have time for a detailed response to your post for a few days, so I figured I should first ask whether I was intentionally excluded by your "people who don't usually post" clause and whether you are across my Tick Tock experiment?

The lack of response to Tick Tock has confirmed my view that the focus remains on cellular automata because they are preceptually a lot easier to deal with than evolving networks.

Hopefully your post will garner useful responses from others.


Posted by: steinhoff

Tony -

You're definitely not excluded. I had
looked at Tick Tock and do like how one
simple rule can cause elaborate inflating
and deflating.

My main difficulty is that this rule must
be applied globally and synchronously for
a general network. I'd prefer rules that
operate locally (with no dependence on the
applied order when more than one network
transformation can be made, as Wolfram
describes in NKS Ch 9 Sec 12). This only
happens in Tick Tock when the triangle
clusters themselves are localized, but
these clusters then immediately separate
from the background network, killing any
chance for global interaction.

I'd prefer local rules/disturbances to
have global impact. Can you simulate
anything resembling propagation? ...I
have hope that a slight rule modification
(to keep triangle clusters attached to
some background network) could represent
the scattering electrons example.


Posted by: Tony Smith

steinhoff, I agree entirely that "synchronous" is a problem that it would be nice to be able to get away from, but I haven't been clever enough to think of an escape route. However the Tick Tock rule really is as local as it is possible to get. Any global effects are just a consequence.

I was also very deliberate in avoiding any kind of "background network" because I was aiming to test Wolfram, Smolin, et al's conjecture that a graph-theoretic network is the most likely candidate for the bottom level network.

I have no expectation of anything like an electron emerging directly from the lowest level rule. If I was betting it would be that we would find at least a couple of intermediate levels of emergent functionality between that most primitive level and the smallest physical phenomena that are directly accessible by experiment, with maybe the lower level roughly corresponding to Smolin's loop quantum gravity and the upper level corresponding with (super)string/M theory.

Certainly we do need "propagation" to emerge very early, but we likewise need forms of conservation to emerge at the same time. I have half a draft of a paper on "bottom up reality" in progress. Just hope it doesn't take half as long to get back to as my long promised and still unfinished paper comparing Prigogine and Margulis mechanisms for emergence.


Posted by: Philip Ronald Dutton

steinhoff said:
"...(though I have convinced myself that there probably are at least two simultaneous rules, one creating points, one destroying points)..."



EVERY 1D CA's output can be viewed as "something is creating and destroying points." More specifically, "something is turning on cells and turning off cells."

What I just said is of course very obvious. I Just wanted to mention the CAs in light of this thread's previous discussion.




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