Topic: momentum in the dimension of scale
Member # 1713
posted 16. August 2005 06:47
Here is a new dimension for consideration.
In physics, it can be shown that symmetry is equivalent to conservation, in the sense that:
Symmetry (invariance) of the laws of physics over possible (x,y,z) positions in the universe implies conservation of linear momentum (p); symmetry of laws of physics with respect to angle of the the experiment (theta, phi) corresponds to conservation of angular momentum (L) ; invariance of the laws of physics with respect to starting time (t) of the experiment implies conservation of energy (E).
In fact the pairs of quantities correspond to those involved in uncertainty laws. (ie,
delta-t times delta-E > some constant regardless).
So, my suggestion for exploration is the hypothesis, corresponding to local empirical observations, that the world appears to be somewhat hierarchically ordered (atoms, cells, people, nations/cultures, planets, galaxies,
So, hypothesize that the laws of physics are invariant over SCALE, and see if that works or leads to a contradiction. A very large experimenter, working on a scale of galaxies, and a very small experimenter, working on a scale of meters, should observe identical laws of physics.
Interestingly, of course, this breaks down
on the downward direction, unless life around us on our scale displays quantum mechanical properties we've missed on this scale. Hmm.
The point of the initial discussion however, is that, to the extent that physics is SCALE INVARIANT, then there should be something akin to SCALE-MOMENTUM and a conservation law,
although it could break down at very small and very large values.
SCALE-Momentum might be something like, I don't know, if a large system is organizing itself hiearchically and has organizational "momentum" it's hard to stop it.
Or, maybe, hierarchical organization (versus just entropy type organization) needs an "outside force" to change its value. Nothing
an astronaut in space can do by waving arms will alter his linear or angular momentum. Maybe nothing humans can do by rearranging staff can alter hierarchical momentum.
It's a thought. Maybe someone else can take it somewhere.
I'm suggesting a non-continuous symmetry as one option, that has natural levels and gaps between levels, somewhat like Marsden Bloise's "curiously laminated" structure of Life's hierarchy.
That would make the primitive units for equations not just tensors, but fractals - akin
to pine trees that are intermittently self-similar, not continously self-similar. And these would have dimensionality that could be investigated empirically, and possible constraints we haven't realized. What is the fractal dimension of life-on-earth?
If there IS, even locally, such symmetry, then, once we understand it, we can translate observations at one level rigorously to other levels, leveraginging what we know in science
across scales by a method far stronger than "analogy". We could figure out how to abstract what we can see easily at human scales and translate it to cellular or global corporate scales, and vice versa, rigorously - generating all sorts of new hypotheses to test.
It's the prospect of such power to take what we know in area A and use it to fill in the gaps in area B that makes this idea seem worth a few minutes of consideration.
One last repass at this. Imagine OCTAVES on a piano. The key "C" at each octave is a different key, and yet, in some abstract ways, a very predictable analog of the "C" on each side of it. (Well, a multiple of 2 in this case.)
The New York Times today discusses the efforts to model E-Coli, and an interview with Dr. Michael Ellison at the University of Alberta, trying to model E-Coli upwards from each gene.
The hierarchical-symmetry/octave model would suggest a totally different tack: first find those aspects of "Life" which ARE pretty obviously scale invariant, and get THOSE fitted empirically with the data. Then flesh THAT out.
More of a "top-down" model.
This says not every aspect of life is symmetrical. Cells, people, and the US Government each have issues that are only relevant at that specific level and don't translate. ignore those. Start with the issues that ARE abstractly identical at each level,
and probably even recursively simple, and model those.
For example, at each level of life a major design concern has to be "survival against noise"
("recooling" to bounce off the last post) or an analog of "homeostasis". The entity has to have a self-identity, be tracking itself, and be capable of taking corrective responsive action if that homestasis is at risk of being breeched. In other words, it has to have a feedback-control system, and that system has to have a controller. Control Systems theory is definitely scale invariant, and issues such as a trade-off between stability and responsiveness occur at every level of life.
THAT's where to start modeling, as a skeleton, I'd think, because everything else has to be compatible with that.
And, I would look first for manageable concepts that are, in fact, "recursively simple", and only look for more complex solutions if the easy one's won't suffice.
Here's where religion or wholism has to overcome the artificial barriers set up between, say, biology, psychology, and sociology.
There is only ONE complex entity, a
cell-people-government entity, even though the parts can slide across each other.
So, NOT ONLY does each level have to solve the homeostatic control problem, but they ALL have to solve such problems SIMULTANEOUSLY AND COMPATIBLY. That's a very powerful constraint.
Governments/Nations need people to "belong" compatibly, or we have terrorism or depression; people need cells to "belong" or we have ill health; cells need whatever, I'm sure.
Maybe as in group theory, the new constraint of simultaneous and compatible actually simplifies the solution, because it doesn't leave much space. The solutions have to be compatible, and, as with a piano or harmonic modes, maybe in fact the solutions are actually identically shaped, which guarantees compatibility.
And, to find that shape, we can use data from every level simultaneously, across all the "fields" of "science".
[ 16. August 2005, 07:53: Message edited by: Wade ]
Member # 1377
posted 15. September 2005 03:56
Here’s what I think is the truth of the matter, the complexity we observe developing is only a temporal view of a system that contains a duality, this duality giving the other its contextual meaning.
And if you chose to follow me down this rabbit hole , this search for a design will take on a whole new meaning.
Complexity in its final form, does not exist as a prior form, but as an eternal form. A singularity .
What we observe as time and movement between a simple ordered state and higher ordered state is merely a cognitive movement between the two aspects of time, one of eternity, Were all things are complete whole forms and the temporal state of becoming.
Let me approach this from architectural view point. When building a structure using regular geometry, small mistakes in the initial measurements will be amplified as the construction progresses, until a point is reached were the initial small instability surpasses and overwhelms the stability factors causing a catastrophic collapse, destroying the intended design.
Now catastrophe theory combined with embedded phi-wave dynamics and a dissipative physical component is were this scenario happens in reverse.
The instant all the physical and dynamic elements arrive they cause a catastrophic constructive collapse toward a higher ordered state, in this particular scenario the attractor forms around water waves. Initial instabilities become creative as they are compresses by the horizontal “whirlwind” or phi-waves dynamics. This state of creative instability is referred to as “edge of chaos” Coined by Doyne Farmer.
This state exist between the chaotic regime and the order regime. These attractors self-construct, by generating a circular vortex drawing energy from its environment. Most of these forms are short lived as in actual vortexes of just wind and water.
The reason I compare the vesica attractor to a black hole is because they both form stable attractors, one though gravity, the other though cognition. These two forces seem to be the only way to stabilize a point in the quantum field.
[ 15. September 2005, 04:10: Message edited by: christopher humphrey ]