“Uncertainty Principle” by Hermin Abramovitch
Jan 3, 2015
“Our choicest plans have fallen through, our airiest castles tumbled over, because of lines we neatly drew and later neatly stumbled over.”
— Piet Hein GROOKS
I was checking out the dynamics describing the orbit of SOHO, the sun-watching satellite oscillating around a mathematical point in empty space, when I stumbled over a few of Piet Hein’s neatly drawn lines. In order to solve the equations of motion, a few simplifying assumptions had to be made:
1. The Earth’s orbit was made circular.
2. SOHO was made massless.
3. The coordinate system was put into rotation.
These assumptions were stated, but others weren’t: The Moon (and all the other planets) were ignored. The Earth and Sun were made dimensionless points. Those are the kind of “of course” assumptions that are easily recalled. But there are more subtle-and more pernicious-ones: That the underlying theory is a law that’s universal and ahistorical. That there are no consequences to our unawareness of the vast ignorance we have of the complex real world frolicking just beyond the circle of our assumptions’ illumination.
An apt symbol of this stumbling over neatly drawn lines is Einstein’s assertion that time is an illusion. The simplified equations are solved; the simplifying assumptions are forgotten; and people begin to believe nature is as simple as the math. Because the idealized deductions work “close enough” in certain carefully-selected situations, they’re believed to be more real than reality. They break out of their domains of validity and hold us hostage to their degraded logic.
Those simple, universal, time-symmetric laws have no place for chance, no place for choice, no place for the emergent, higher levels of order and intelligibility we see filling the real world. Outside its domain of validity, that simplified and reduced world of ideal equations has turned out to be a prison of determinism, an exile of impoverishment. We have become captives of our own simplifying assumptions.
Ilya Prigogine and his associates have worked out a reformulation of the laws of physics that accounts for irreversible time (see his The End of Certainty). They incorporate insights from instability physics, resonant systems, and non-equilibrium states. In this reformulation, probability and uncertainty become essential, rather than begrudged concessions to ignorance. The old, deterministic physics becomes a special case within the new, more general formulation: When conditions of stability and equilibrium actually occur (usually in “dead” systems), the simplification of probabilities and the reduction to certainties describes the real. In all other cases–the majority of real conditions–probability and uncertainty lead to complex hierarchies of self-organizing systems.
The simplifying assumptions can be put back in their properly-limited places. We can break free from their tyranny. “We are observing the birth of a science that is no longer limited to idealized and simplified situations but reflects the complexity of the real world, a science that views us and our creativity as part of a fundamental trend present at all levels of nature.”
— Ilya Prigogine, The End of Certainty, p. 7.
Mel Acheson
