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There is no principle of nature that has been the subject of so much bias
as the principle that an isolated system tends toward a homogeneous
distribution of energy, especially when the universe itself is looked upon
as such a system. There are several 'scientific' formulations of this
principle, all of them taking a more or less derogatory tone of voice
rather than a purely descriptive one. It is called "the principle of
degradation of energy" or, worse, "a law [sic] of
thermodynamics" stating that 'the quality of energy is degraded
irreversibly'.
An expert 1 in the field may not
hesitate to tell us that on the basis of this principle potential,
organized energy is degraded to heat, a disorganized form of energy
described as inferior, less noble and lower-quality.
Often, the end-state of homogeneity is not just called "disorganized" but
a state of maximum disorder, even chaos.
When this end-state is described with the term entropy
there is, as it should be, no negative (or positive) connotation, since
entropy is taken from entrope, the Greek word for change or
turning. However, this terminology is not less quasiscientific, because the
connection between change and entropy is not closer than between change and
gravity or change and electricity. For maximum entropy the connection is
even absent, because the system-internal outcome of maximum entropy is a
standstill in which each particle movement is statistically neutralized by
an opposite particle movement. The language of the entropy domain of
discourse could hardly be more chaotic indeed!
By stipulative definition one may, of course, define chair as a
table and table as a chair, but it will not help us to gain any
further insight into
nonpropositional reality.
Similarly, one may define (maximum) entropy as complete disorder or
chaos, but also this will not help us to gain any further insight into
reality. On the contrary, it merely confuses matters.
Chaos is a state in which things are subject to no
principle at all, that is, no principle which applies to the things of
the type considered. Normally tables and chairs are put on a floor with
their legs down and the chairs next to or half under the tables. Only in
such an arrangement can these artifacts be used in the way they have been
designed and are intended to be used for. Should we find these tables and
chairs in every which way --a part of the chairs and tables
upside down, and some chairs on top of the tables, for
instance-- we would say that the room in question is in
disorder or complete disorder. We would not call it "disorder" because the
pieces of furniture would be more evenly spread out over the room, but
because their positions would not comply with any principle for the
arrangement of furniture, regardless of their distribution being
heterogeneous or homogeneous. Normally tables and chairs are arranged in an
orderly way, but order is only order on the basis of a certain ordering
principle, and if there is complete disorder in a room (with nothing else
than tables and chairs), it is because that room is not governed by a
'principle of furniture'. But such a principle is an instrumental principle
for artifacts and has nothing to do with a natural principle such as the
principle of maximum entropy whatsoever.
Maximum entropy is a state of complete order. It is a state of complete
order on the basis of the distribution of bodies or mass and energy over a
system, which is entirely homogeneous in that the density in each and every
region of the system equals the average density of the whole system. It is
everything but chaotic. Chaotic is, perhaps, the force of gravity which
makes apples fall off trees and tables. That is, until it is explained that
the apple and the Earth attract each other, and that the planet of the two
is the heavier and therefore the stronger of the two. But such an
explanation is only a physical explanation valid in the physical
domain of discourse, and in that domain apples and trees do not exist as
apples and trees, for they are biological entities, and in that domain
tables do not exist as tables, for they are artifacts. From the point of
view of the occupant of a room who has dropped a fruit-bowl all the apples
and other fruits on the floor may be a true instance of chaos, but this is
no justification either to claim that the principle of gravitation causes
chaos in the universe. People who use such terms to describe phycical
principles and states of being mix up different domains of discourse and
practise
ideology, not science.
Their terminology is as abominable as the word law, when employed
for a principle of nature or, worse, a hypothesis of physics.
The tendency toward maximum entropy in an isolated system is, perhaps, not
a proven fact at all. It is, then, rather a hypothesis on which, in
thermodynamics, the label Law is stuck to make it appear God-given
or suchlike. Is it not odd that a system would show a tendency
toward a completely equal distribution of its elements over itself,
especially when entirely isolated systems do not seem to exist in reality?
(Except, perhaps, the universe, if it may be called "a system", that is.)
If anything, one would expect the elements or bodies inside the
system to show a tendency toward something.
Take, for example, a system with only electropositive or only
electronegative particles. Such a system would reach maximum entropy
immediately without there being any need to assume that the system as
a whole aims at something, altho*, of course, the assumption that particles
with like electric charges repel each other would still have to be adhered
to. Systems with either electropositive or electronegative particles
exclusively would reach maximum entropy but only as some kind of
by-product. Moreover, as closed systems they are definitely nonexistent.
Obviously, nothing happens to neutral bodies on the basis of
electromagnetic repulsion. At most neutral bodies attract each other not
as electroneutral objects but as material objects. Apples falling off
trees, tables and fruit-bowls are but one example.
The idea of a system with electropositive or electronegative bodies
exclusively is imaginary or even nonsensical in itself, but could we use it
for an analogy? Could we say that the elements in an isolated system show a
tendency toward something that makes the whole system end up in a state of
maximum entropy on the basis of an entropy-specific mutual
repulsion? It would, then, not be gravitational repulsion (which does not
exist) and it would not be electromagnetic repulsion (which has no
explanatory power here) but some kind of distributional repulsion between
the elements of a system. The answer is Yes and no. The answer is
Yes for regions of the system with an energy density greater than
the density of the whole system and the answer is No for regions of
the system with an energy density smaller than the density of the whole
system. For the latter regions we will have to hypothesize not repulsion but
attraction. With both an entropy-specific repulsion and an entropy-specific
attraction the analogy does not hold water anymore. Moreover, the cause of
the repulsion and attraction does not lie in a property of the particle
itself, as in the case of electropositive and electronegative particles,
but in a relation which that particle or body has with one or more
other bodies or in a property of the (sub)system it belongs to. One might
reason that in a system with a full internal exchange of information two
bodies attract each other if their distance is greater than the average
distance and repel each other if their distance is smaller than the average
distance between the bodies of that system. Also on this approach it does
not have to be claimed that the system shows a tendency toward
something.
The tendency is postulated on the level of the elements of the system.
When we confine ourselves to gravity, electricity and entropy, we are now
faced with three 'forces' in a loose sense of the word. First, there is
a gravitational force which drives all bodies towards each other. Second,
there is an electrical force which drives bodies with opposite charges
towards each other and bodies with like charges (but possibly different
magnitudes of charge) away from each other. And third, there is a
distributional force which drives bodies in thin fields towards each other
but bodies in thick fields away from each other until complete homogeneity
is reached in the system to which they belong. On the basis of these
descriptions gravity is the odd one out here with only attraction as a
manifestation of it. But even the similarity between the electrical and the
distributional force does not go further than that these two forces can
manifest themselves both in repulsion and in attraction. By speaking in the
terms we have spoken in until now we have not found and will not find a
common denominator for these two forces, let alone for all three of them.
And without such a common denominator we may be able to do all our
calculations, but we will always be haunted by their arbitrariness. Is the
universe that chaotic that it is full of forces of attraction and forces of
repulsion between which no other connection exists than that sometimes two
of these forces are each other's opposites?
I will now explain why and how, in my opinion, the physical attractions
and repulsions between bodies in electromagnetic, gravitational and
distributional fields can be subsumed under one common denominator.
First of all, the electrical force which causes the distance between a
positive and a negative particle to decrease and the distance between two
particles of like charge to increase favors electroneutrality in both the
cases of repulsion and the cases of attraction. (Other things being equal;
that is, given that there are no effects of other forces, of course.) An
opposite,
extremity-directed force would
favor the accumulation of an exclusively positive or an exclusively
negative electrical charge at one place and in one body. So neither
repulsion nor attraction are of explanatory significance in themselves.
What counts is
neutrality-directedness: the
promotion of electroneutrality in bodies and/or places.
Gravity only knows attraction, and altho it would have been possible to
claim of two objects in a universe with only two objects that the one
happens to be 'positive' and the other 'negative', such a construction will
not do for the almost infinite number of objects in the universe which all
attract one another to a smaller or larger degree. Is there any other way
in which the gravitational force, like the electrical force, might be
interpreted as neutral(ity)-directed as well then?
In the language of today neutral has different meanings and
neutrality may be considered too vague a notion to be of any
scientific or systematic-philosophical use. Yet, neutral is
used among others in chemistry for neither acid nor alkaline and
neutrality is used among others in physics for the state
between electronegativity and electropositivity. So neutrality
may be used in science, provided an exact definition is given. Such
a definition will always require that neutrality is something between
negativity on the one side and positivity on the other. This kind of
neutrality is
catenical 2
neutrality, for it presupposes a
catena of one or more negative
predicates, one neutral predicate and one or more positive predicates.
By predicate i* then mean a property or relation, and by negative
predicate a predicate which corresponds with a negative catena value,
and so on. Now, this will do away with concepts of neutral and forms
of 'neutrality' which are not catenical at all. It will still raise many
questions, such as the question whether any property or relation of a
predicate catena other than the one on the extreme (negative?) left and the
one on the extreme (positive?) right may be considered 'neutral'. Or the
question whether an object which has a property or relation which is
neutral with respect to one catena does not at the same time have a
logically related property or relation which is not neutral with respect to
another catena. Such matters are matters of catenical theory and analysis
i cannot deal with here. But i will have to draw upon a few catenical
notions where it is necessary for my present purpose.
As far as gravity is concerned we do not have to ask ourselves whether
there is a neutral point in three-dimensional space and, if so, where.
If the universe once came into being at one particular place, that
single spot (where the big bang occurred, for instance) might be a given
neutral point for the three spatial dimensions, but such an assumption is
not needed here. It is not needed, because gravity is not a force which
works on this basic level. The force of gravity does not push bodies to
some central point in three-dimensional space; it pushes them towards each
other, regardless of their position in the universe. The three spatial
basic catenas are therefore not interesting in this domain, nor are certain
other catenas which can be logically derived from them in the same system
of catenas. (The picture is quite a different one if we conceive of the
'accessible universe' as the three-dimensional surface of a sphere in a
world with four spatial dimensions. In that case there is a central point
in four-dimensional space, even tho it is not accessible or not
accessible anymore.)
The type of derivative catena which deserves our
attention here above all is the so-called
"bicatenal bivariant difference
catena" 3 . One can think of one for
each spatial dimension. In the context of such a catena a difference in the
values on one spatial dimension is either positive or negative, and having
the same value is neutral. Any force aimed at having the same spatial
position is therefore a neutral-directed force. In catenical terms any
type of equality is difference-catenary neutrality, also spatial equality
for the three or more dimensions concerned. In other words, a
force which promotes for each separate spatial dimension, and for all
spatial dimensions together, equality as distinct from positive or negative
inequality is neutral-directed. (Gravity is not the only one, for also the
nuclear force or 'strong interaction', which holds protons and neutrons
together on the subatomic level, is such a force.) On the face of it, it
looks as if the end-state of gravity (and of the nuclear force as well) is
a state of maximum proximity, but the predicates ranging from maximum to
minimum proximity have positive values only and do therefore not constitute
a catena with a neutral predicate in the middle. It is possible to
construct a 'proximity catena' but such a
modulus-catena 4
does not take precedence over the bicatenal bivariant difference catena
from which it is derived. So, any suggestion that gravity would tend to
extremity is mistaken; it tends to neutrality instead. (See
the Model of Neutral-Inclusivity,
especially section 2.5.1 of
the Book of Instruments,
Basic or original catenas and difference
catenas, and section 3.1.6 of
the Book of Fundamentals,
Spatiotemporal neutrality and
neutral-directedness.)
When considering the tendency toward maximum entropy again, some might also
be tempted here to believe that, if anything, extremity is favored, that
is, either the extremity of a maximum entropy or the extremity of a maximum
distance between particles. To start with the latter: the distributional
force does not favor the greatest distance between bodies possible; it
favors the average distance (while this distance is treated as a
nonnegative quantity). Whether it aims at such an average distance is a
different matter. The thermodynamical principle states that the system
tends to maximum entropy or a completely homogeneous distribution of
particles over the system. Such a state is reached when the energy density
of every region of the system is the same as the energy density in every
other region of the system; not more, not less. Unlike distance, density is
a basic quality which cannot be assigned a negative value. It does not
become a catenical predicate until we assign negative catena values to low
densities or thin fields, the catena value 0 to the average
density 5 and positive catena values
to high densities or thick fields. There is no original catena in the same
system which could take precedence over such a density catena. So, a force
which causes the densities of the regions of an isolated system to change
in the direction of the average density for the whole system is a
neutral-directed force.
It is not right to reason that the end-state is
neutral because the distribution of the particles over the system is an
equal distribution of those particles and because equality is neutrality.
This reasoning is fallacious where an unequal distribution always carries a
positive value (or always carries a negative value). For distributions
which are assigned nonnegative (or nonpositive) values only do not
correspond with catena predicates. And here catena values can only be
assigned to the subsystems of the system. Hence, to be neutral-directed the
force is not exerted on the isolated system itself but from within on its
subsystems.
If the idea of thin and thick subsystems adjusting themselves to the
average density of the total system may seem incomprehensible or even
magical for some, it is no more incomprehensible or magical than the
idea of unconnected bodies attracting each other over great distances in
the name of gravity or attracting each other over smaller distances in the
name of electricity or, alternatively, the idea of bodies repelling each
other in the name of electricity. The role assigned by me to
neutral-directedness is definitely not 'magical' in any sense of the word.
Both neutrality and neutral-directedness play a special role in science and
in everyday life. When the principle of homogeneous distribution concerns
the distribution of thermal energy it is called "the second law of
thermodynamics" in traditional science. This principle is said to govern
the quality of energy, while the principle of conservation of energy
is said to govern its quantity. This latter principle ("the first
law of thermodynamics") states that the quantity of energy in an isolated
system (such as the universe) remains constant, that is, neither decreases
nor increases. Energy or the combination of mass and energy is a
nonnegative quantity and has therefore no neutral value. Even antimatter is
not opposed to matter in that its particles would have an opposite mass. (A
particle of antimatter has an opposite electrical charge or a magnetic
moment in the opposite direction.)
But energy decrease with all its
negative values, energy constancy and energy increase with all its positive
values constitute a catena over which no other catena takes precedence. It
is the neutral predicate of this energy-increase catena which plays a
special role in this first principle, just as it is the neutral predicate
of the density catena which plays a special role in the second principle.
Such is the case in thermodynamics and such is the case in so many other
fields, even when the 'principles' involved are, perhaps, no more than
hypotheses.
When i conclude that the forces at work in the fields of entropy, gravity
and electricity are neutrality-directed forces, it is not the use of the
term force which matters here. What matters is that the scientific
principles formulated in these domains of discourse make an implicit use of
the distinction between neutrality and unneutrality and that they give a
description of the world that unquestioningly favors neutrality. I claim
this not only without doubt but also without worry. The worry is for the
rank and file led and misled by chaos gurus who confuse distributional
neutrality with 'complete disorder' and who fear the destruction of all
organized systems. But such systems, too, are governed by their own
principles with their own form or forms of neutrality and
neutral-directedness. It may be equally worthwhile to put those principles
in a common, neutral perspective, as i have done above for entropy, gravity
and electricity. It is not 'inferior' or 'less noble' to opt for a neutral
perspective. Not at all! Apart from neither implicitly nor explicitly
assuming anything, it is the
noblest 6 thing one can think
of and do.
[MP3, 5.3 MB, 2:17]
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| 1 |
J. de Rosnay at
pespmcl.vub.ac.be/ENTRTHER.html (Principia Cybernetica, 3 July
1998) |
| 2 |
In the theory of catenas attributes
and relations are characterized on the basis of their position in, or
with respect to, a catena or system of catenas. A catena is a whole of
catenated predicates (properties or relations) of which the
extensionality can be divided into a negative, a neutral and a positive
subset. The adjective catenical applies to the theory of catenas
and any product of thought which makes use of its conceptual
framework. (See
The tripartite structure of the
catena and
Subdivisions of the catena's
extensionality.) |
| 3 |
A thing which has a predicate of a
catena is called "a catenal". Of two separate things which are catenal
with respect to an (original) catena the catena value of the one is more
(positive) than, the same as or less (positive) than the catena value of
the other. The catena corresponding with this (positivity) difference is
a 'bicatenal positivity-difference catena'. If neither catena value of
the original catena is fixed or a given constant, the difference catena
concerned is bivariant. |
| 4 |
The original catena value of a
catenal is more neutral (less unneutral) than, equally
(un)neutral as or less neutral (more unneutral) than the
original catena value of another catenal. On this view we can
distinguish a neutrality-difference catena. It is 'bicatenal' if the
catenals in question are wholes in themselves (instead of one of them
being a component part of the other). It is 'monovariant' if one of the
two catena values is fixed. This is the case when an original catena
value is compared with the average value of the total system concerned.
In the theory of catenas the bicatenal monovariant neutrality-difference
catena of an original catena is called "its modulus-catena". The
proximity catena is the modulus-catena of the bicatenal bivariant
positivity-difference catena of a spatial basic catena. The neutral
modulus-catena value 0 is not predetermined in physical terms, for the
physical quantity corresponding with a physical modulus-catena is
nonnegative. It represents concepts such as neither close nor far
and neither thick nor thin with so-called 'fuzzy borders' between
close and far and between thick and thin.
(See
Basic or original catenas and difference
catenas.) |
| 5 |
It may seem a simple matter of choice
to assign the catena value 0 to the average density. But,
firstly, there is no other special physical value, and secondly, there
is a special relationship between neutral and mean values. (An
average is an arithmetic mean.) Those who are not (yet) convinced may
consider it a mere hypothesis. (See
Where neutrality determines the
mean and
Where the mean determines neutrality and
moderateness.) |
| 6 |
I admit this is a rather unscientific
final comment. It was motivated by the at least equally unscientific use
of the word noble referred to in the first paragraph |
| * |
The first-person singular pronoun is
spelled with a small i, as i do not consider myself a Supreme
Being or anything else of that Ilk. (Al)tho is a
more phonetic lexical variant than (al)though. From
a phonemic point of view, however, it would be better to spell this word
(al)thoh. See
The values of linguistic systems
and the
Vocabulary of Alliteration. |
60.ENE-61.ESW
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