ONE WAY DOOR
(C)1997 Alan M. Schwartz
Is the universe more complex than its contents, the human brain
plus electronic prosthetics, can accurately model? Is the
structure of reality a one way door wherein the sum of all
observations cannot recreate the originating pattern? One might
fancy that the principle of microscopic reversibility obtains:
For any path from here to there, each infinitesimal increment
along the path is arbitrarily reversible in time. One could
therefore wander backwards, terminus to point of departure, in
mirrored increments along the branching path.
Trapdoor functions used in public encryption algorithms hint
there is more to it than that. The wide and narrow ends of a
funnel are distinct. Stroke a cat tail to head for a bloody
tutorial on asymmetric pathways.
It is much worse than that at primitive levels. Consider two
crossed lines, a hyperbola, a parabola, an ellipse, a circle, and
a point. All are trivially obtained by slicing the surface of a
double cone - a cone reflected perpendicular to its axis at its
apex - with a plane. Run the plane in the axis get two crossed
lines. Displace it parallel to its foregoing slice to get the
hyperbola. Tilt the plane to only intersect one cone to cut out
the parabola. Tilt it more so that it cuts a closed loop,
approaching perpendicular to the cone's axis, to get the ellipse.
When the plane is perpendicular to the cone's axis you cut a
circle. If that plane is now parallel displaced to where the
double cone's apices coincide, that is a point.
Going from cone to conic sections is a high school exercise. How
would you go from two crossed lines, a hyperbola, a parabola, an
ellipse, a circle, and a point to regenerate the parent double
cone and plane? You have tremendous aggregates of information
within the pieces, yet there is some insubstantial knowledge
ratchet which only goes one way, and with a vengeance. A flurry
of discrete analysis might fail where a single Gestalt heuristic
validated by observation would swallow it whole.
Scientific method is incremental validation by empirical testing
of a large and growing body of knowledge. Those who would manage
science with spreadsheets, PERT and GANT charts, discounted
cashflow/return on investment calculations, and other shibboleths
of good business practice are eternally stunned (not that they
personally care much - it is not their investment) that the most
tightly managed research is minutely documented perpetual
progress going nowhere. Officially despicable individuals, often
in garages, routinely outperform billion dollar corporations and
their polished teams to wrest discovery from the void.
The War on Drugs, Haz-Mat, the Occupational Health and Safety
Administration, and the Environmental Protection Agency have
emplaced jackbooted state terror to cultivate extermination of
the home inventor. A dribble of cutting oil will precipitate
confiscation of everything you own, a six figure environmental
remediation charge, and maybe State prosecution in the indefinite
future. Why prosecute when the punishment precedes the trial?
Japan is infamous for seizing nascent invention and squeezing the
juice out of it. State/corporate/banking integration (MITI) will
dedicate a whole building of professional fanatics, a huge
budget, and remarkable patience until there is nothing left to
optimize or exploit. Japan is equally distinguished for its
inability to foster creativity. Like the Romans who drew a line
from here to there on a map and built the road straight no matter
what the intervening obstacles, the Japanese have forsaken
serendipity for rigor. Keuffel & Esser was a $500 million/year
slide rule empire which followed rigor all the way to rigor
mortis. The HP-35 calculator was their undertaker less than six
months after its introduction. A good new idea can be that good.
Western civilization - desperately clutching the ears of
technology's tiger - built its edifice upon simple numbers
inserted into increasingly complex mathematics and therefrom-
derived increasingly complex recursive manipulation (lathes
building better lathes). String theory and octonoions - 8-fold
fields of numbers manipulated as single entities - seem to be
encroaching upon a working (empirically verified prediction)
Theory of Everything. We are looking at how we look rather than
only looking at what we see. There will be a payoff.
I expect humanity will again pull a turn of the century rabbit
out of its hat as the 1900s saw relativity and quantum mechanics
emerge to reshape the world. The hallmark of a bullseye is
obvious: It will be stranger than we can imagine (at first), but
not stranger than we can use. We will pursue it in wonder,
assiduously ignoring Luddites calling it sin.