Judith wrote: If I was coming to these ideas with skepticism and ran into a situation like that, where the logic in the foundations of some hybrid theory were inconsistent... I'd walk away. Nature is not inconsistent. HP: Certainly Nature is not inconsistent, but some models of Nature certainly are. I agree. My point was that Rosennean Complexity is not inconsistent
within itself nor with nature. There is a difference between "complementary"
views that are not reducible to one another (but are both true and don't negate
one another) and incompatible views that cannot both be true. This is what
bothered Einstein about Quantum Theory and Relativity Theory. They were
incompatible rather than complementary and he felt that meant something was
wrong, somewhere. He was right.
HP: One must be careful here. If we are bothered by incompatibility it is usually because our naive intuition enjoys consistency and because Aristotelean logic has culturally indoctrinated consistency into our logic. But you have already admitted that nature is not inconsistent. I
would argue therefore that it is a natural intuition, with nothing
"naive" about it. And I would further argue that Aristotle was displaying deep
insight into the behavior of the natural world.
It is true that a single formal model of a system must be internally
consistent, but an "adequate explanation" of a system may require two or more
complementary models that are formally inconsistent with each other.
A single formal model of a system must also be consistent in the
mapping of entailments from the inferential entailments of the model to the
causal entailments of the actual system. That's your Hertzian thing, is it not?
In RR terminology: if the two commute, then you have a solid modeling relation,
and consequently; a "good" model.
Rosen often used the example of a gas that can be modeled by reversible
microscopic dynamics and also with irreversible statistical dynamics.
He may have been pointing out the flaws in those modeling
techniques. I would have to see his entire discussion of it in order to tell you
what he was illustrating. If he was showing how those are incompatible models,
rather than complementary ones, that's a different discussion than it would be
if he was showing how those two models are both accurate but radically different
from each other (complementarity). My intuition from this snippet is that
he may have been showing how these are incompatible, and therefore was
making a point that the entire approach is flawed.
What is a "gas", really? I remember the moment in high school when
I realized that the way things are at room temperature is not their full
capability. Water is a very common example: everyone knows that it has a
freezing point and a boiling point... But so do all elements, compounds, etc.
All gasses can be liquids, or solids, depending on how they interact with
various other aspects of the environment. Temperature is one aspect, pressure is
another...
I traveled with my father on one of his trips to Abisko, Sweden, in
the late 1980's. I loved it there-- It was one of my favorites, out of all
the places we've been to. We were there in May, so winter was ending, but they
spoke of a hotel, called "the ice hotel," that is built every year at the town
nearby. It really IS a hotel built using ice as it's building medium. They
build a new one, every year, because of course... it melts when the season
changes. That means it stops being a solid and becomes a liquid, which isn't
appropriate for human hotels... It sounds ridiculously obvious, put that way,
and yet this is a profound concept. I recently saw a documentary on
the ice hotel, on TV and was happy to finally see what they did and how they did
it, after being in Abisko myself. Vaulted ceilings, gothic arches, ice
sculptures... the way they handle lighting is amazing.... Way
cool!
The same is often the case even with informal conceptual models. The continuous wave image of light is not compatible with the discrete particle image of light. It's clear that these modes of representation are both incomplete; so are they incompatible or just complementary? What if light is both and we're just "measuring" different aspects? What if our measurement mode is creating artifactual information that taint the results? Perhaps it's all of the above. What we call "light" is not all that it is. If it's true that matter and energy are different forms of the same thing, sort of like water, steam, and ice... (as a loose analogy), then surely light is capable of being complicated, if not complex? Judith
|