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Jack Woehr

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Homogeneity of Physical Systems

January 08, 2010

The image “” "Nature has played a joke on the mathematicians. The 19th-century mathematicians may have been lacking in imagination, but Nature was not. The same pathological structures that the mathematicians invented to break loose from 19th-century naturalism turn out to be inherent in familiar objects all around us." - Freeman Dyson, 'Characterizing Irregularity', Science, quoted in Benoit Mandelbrot's The Fractal Geometry of Nature

Perhaps twenty years ago around this season of the year, a younger brother-in-law and I were seated by the holiday board engaged in a discussion heated enough to cook the holiday turkey. The subject was the possibility of life on Mars ...

The BIL, nowadays a noted microbiologist, was at the time a scienterrificist college student. At that bygone holiday dinner, he became incensed at my suggestion that life could indeed exist on Mars. He held that the thermodynamics of the planet's atmosphere as observed by that time ruled out any such discovery.

There was an error in the BIL's reasoning more significant than the wispy tenousness of the long chain of inferences then current regarding Mars, many of which in the succeeding two decades were blasted beyond recovery by further Mars missions. The more significant error was his tacit assumption of homogeneity of physical systems.

For instance, Mars certainly possesses a broad array of microenvironments:

  • surface irregularities ("cracks") where some, not much, water ice is stored
  • low points where atmosphere achieves densities unknown elsewhere on the planet
  • isolated abundances of certain chemical combinations


Homogeneity of physical systems is rare to nonexistent.

When the nominal guardians of order fire tear gas to disperse an angry or befuddled crowd, the gas distributes in flumes, as does pollution in ground water.

Approaching homogeneity in one or another physical system is the difficult goal of various engineering processes. The arduous mixing of the vulcanisation chemicals into raw rubber is one of the most common and least tractable problems of this sort.

We habitually assume homogeneity of physical systems in our daily world, occasionally to our hurt.

The oven thermometer inserted into the back of the holiday turkey announces dinner but the undercooked breast sends Uncle Fred running to the restroom.

We wash our hands and hope that the population of harmful bacteria is sufficiently, though hardly absolutely, reduced to the level that our body's natural defences will be able to handle the sudden infusion with our luch panini.

We dissolve salt or other substances in water and depend in bulk on a sufficiently even ionic distribution for certain well-known taxonomies to be realized.

So any scientific argument based on a homogenous theory of physical phenomena ... say, choosing one at random, the Big Bang theory, now wounded perhaps beyond healing by the incremental telescopic discovery of stuff beyond stuff beyond stuff in space ... is immediately suspect. Much in the way Benoit Mandelbrot elucidated the utter absence of ideal geometrical forms in Nature, there is an analogous lack of homogenity in the physical universe.

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