Mark Waser wrote:
Hi Richard,
Yes, your explanation was crystal clear.
I would rephrase our current state as saying that instead of having a
non-standard definition of complex, you actually have a seriously
non-standard definition of explain . . . .
I would strongly suggest that you consider switching to and using the
word predict (or something similar) rather than the word explain. It is
really unhelpful that your definition below parses to something that
provably incorrect according to what I believe is the majority
definition of
explain.
Richard > First, the strict definition of a complex system is that it has
some observable behavior that can only be explained by a theory that is too
large for us to discover
How about something like the strict definition of a complex system is
that it has some observable behavior that cannot be easily derived from
theory.
Well, yes and no.
I certainly don't accept that the confusion is all the result of my use
of the word 'explain'. I have seen many examples of people saying that
*if* the best thing you can do to understand a system is only to build a
simulation of the system and show that the simulation does what the real
thing does, then you have not really "explained" anything at all.
To take a clearer example than the gravity one, go back to Game of Life,
or any other cellular automaton. If someone said that they wanted an
"explanation" of where the regularities came from (the actual zoo of
creatures observed in GoL), would it be acceptible to put the rules in
front of them, then switch on the simulation, then say "The rules plus
the simulation are your 'explanation'!"? I think that in this case,
someone would protest that this was not an explanation at all. In the
gravity case, though, if someone slapped down the rules of gravity, then
showed you a simulation that exhibited ring-braiding, this would count
as an explanation of sorts.
It is in the context of that Game of Life situation (which is by far the
most common case of an explanation-request, in the space of all complex
systems that have been talked about), that I used the word 'explanation'
as if pushing the start button on a simulation would not, in an
important sense, count as an 'explanation'.
Could I have been clearer? Yes, and from now on I will take into
account this possible confusion. What I will have to do is to develop
some more structure in the explanation of what explanation is! No rest
for the wicked.
= = = = = = =
So, let me jump to the case of the braiding effects in Saturn's rings.
The last I heard (and I hope I am not out of date on this), people
could only 'explain' these by doing computer simulations in which
there were particles and planets and little moons. When you have this
combination, you observe (in the simulations) something like
braiding. So the braiding is a high-level regularity, and the
explanation is .... well, the only explanation is that a simulation
does the same kind of thing. Nobody did an analysis of the basic
Newtonian equation and said "I predict that braiding effects will
occur when there are rings and little moons". As far as I know, we do
not expect such an analysis to be possible.
The fundamental problem with your using explain and explanation this way
is that what you're arguing is really merely "not-explain" (which is not
restrictive), not a positive definition (which would be much more useful).
= = = = = = =
My belief is that you actually brought the whole complexity argument
down on yourself because of a bad definition of complexity because of a bad
definition of explain.
My whole argument with you (F-14 and all) was because I didn't grok your
version of complexity -- which turned out to be identical to what most
people use. I'm really surprised that you didn't say anything when I said
to someone else the following:
<start quote>
Richard's definition of complexity is *NOT* the standard Santa Fe Institute
type sense.
Richard: A system is deemed "complex" if the smallest size of a theory that
will explain that system is so large that, for today's human minds, the
discovery of that theory is simply not practical. Notice that this
definition does not imply that there any such systems in the real world, it
just says that *if* the theory size were ever to go off the scale *then*
the
system would (by definition) be complex.
Santa Fe is quite sure that there are complex systems out there and by
their
examples, since there is no one acknowledged definition, I would say that
intelligence is necessarily complex in their sense.
<end quote>
Oh, that was just an accident. I ran out of time before I could get to
that.
I am running out of time again now, so all I have time for is to say
that I was trying to tighten up he Santa Fe concept of a complex system,
not contradict it.
My wording may have made it look like weird, but there was a missing
next step (which I am now not sure was in that passage you quoted).
The next step was: even though we can never know whether a real system
is going to satisfy this definition of complexity (because we are not
gods, so cannot measure absolute size of theory/prediction/explanation),
we can come up with many example systems that *seem* for a variety of
reasons, to have regularities that we cannot predict or explain. We
call those 'complex systems' even though what we are really doing is
making a bet about how difficult it would be to predict/explain their
regularities with anything except a simulation.
The nature of this 'bet' is what is interesting and important. It turns
out that there are two species of 'local rules' that govern the
interactions between components of systems. One species leads quite
often to behavior that we can both predict and explain. This is the
stuff of natural science.
But the other species of local rules are so hideously tangled that, in
practice, we have noticed that they almost always lead to systems that
are either random or complex.
In between there are grey areas, but we are not interested in those (at
least, I am not). The extreme cases, where the local rules are
seriously tangled, make us feel so sure that the overall system will be
random-or-complex, that we can move right ahead.
Intelligent systems, unlike gravitational systems, have so a
superabundance of nastiness and tangledness in their mechanisms that it
would be the most astonishing event in the universe if they turned out,
after all, to have no complexity in their overall behavior.
There you go. Quick summary. I don't know if I said that before or
not, but that was the full context of my definition of complexity above.
Gotta go for the day.
Richard Loosemore
-------------------------------------------
agi
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