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 irreversibly to an inferior, less noble, lower-quality form heat, a phenomenon described as disorganized energy. 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.

60.NEY-61.SEL