From: Osher Doctorow [log in to unmask], Sat. Sept. 29, 2001 4:29PM
My interests are mathematical physics, mathematical logic (including fuzzy
multivalued logics), mathematical probability/statistics, geometry/topology,
and mathematical models in general. Abstracts of 62 of my papers in a fair
amount of detail are at http://www.logic.univie.ac.at (Institute for Logic
of the University of Vienna - select ABSTRACT SERVER, then BY AUTHOR, then
my name in that exact order).
Feedback is of considerable interest in the human thermoregulatory system
among others, and in terms of the kidneys there is somewhat of a balance
between the amount of fluid ingested and the amount of fluid excreted with
some effects on solid matter also. In general, there is considered to be an
optimal level of fluid to be ingested per day, e.g., 6-8 glasses of water.
A sizeable fraction of this is ordinarily excreted in the form of urine or
fecal matter.
With aging, some curious *hole effects* occur. There is often increase in
the permeability of membranes in the intestines and colon, ulcers of various
size in the stomach and intestines, and even operable or inoperable holes in
the colon. Also, control of sphincter muscles may tend to diminish, with
uncomfortable side effects and even negative social and psychological
effects.
These hole effects are often ignored in considering renal and excretory
system feedback, but they may not be ignored psychologically by the aging
patient. One of the most likely responses is decrease in ingestion of
liquids, since aging patients may well reason that with less liquid there
will be less *spillage* and other negative side effects. Using the
symbol --> to indicate the direction of causation or probable influence, we
may write roughly and with the appropriate conditions:
1) hole with age --> psychological stress --> decrease in fluid ingestion
Of course, less food may be required with age as activity levels diminsh,
but there is something more going on here beyond that - (1) suggests a way
in which holes interrupt the usual digestive and thermoregulatory/renal and
excretory systems.
Can one make (1) more explicit in terms of holes, and why? I will merely
point out here that holes are extremely interesting to mathematicians
because the branch of mathematical topology, often abbreviated to topology,
is largely devoted to study of them, and they have been found to be related
to geometry and to physics and so on. Since the ingestion of fluids
involves another hole, this time the mouth at least, let hi refer to
internal hole in the stomach or intestines or colon and let he refer to the
*mouth as a hole*. We then write (1) as:
2) hi with age --> psychological stress --> he ingestion decrease
This is obviously a *double hole* process, a hole in input and in output
which is disorienting (in a sense) the usual renal and digestive and
excretory feedback mechanisms.
What does topology say about double holes? Topology has discovered that in
many respects, objects with different numbers of holes are in *different
worlds*. The number of holes is one of the main determinants of
topological type or class. Curiously, the search for holes in space is one
of the most interesting endeavors in physics and astrophysics and astronomy
today. Black holes are not merely figurative holes in space - there really
is a hole there, although it seems to eventually become so narrow that no
material object can move through, and the tidal forces crush material
objects. We are not sure what happens *at the other end*, or even where
the *other end* is if anywhere. It would be especially interesting if the
*other end* were another hole of larger size somewhere else in the universe.
Wormholes in space or spacetime are somewhat different - theoretically they
are supposed to be wider than black holes and according to Professor Kip
Thorne of Caltech and others they may be kept large enough for someone to
pass through with reinforcement by *exotic matter*, if certain conditions
are met (and they might not be).
Holes in the sense of black holes and wormholes are related to
*singularities* - extremely unusual behavior which is the rough physical
equivalent of *almost but not quite impossible*. The Big Bang at the birth
of the universe is generally regarded as a singularity.
I hope that I have provided enough ideas for thought in a new direction in
relation to evidence-based-health, although most of my examples have been
based on more or less accepted or known facts but ones that are seldom
considered together.
Osher Doctorow Ph.D.
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