SPACE OF KNOWLEDGE

Physics deals with real things. It is based and focussed on experience. Which means that physics has to measure itself again and again with reality. Even the most coherent conclusions from the most beautiful theories still do not matter if not verified by real experiences.

On the other hand, physics is, of course, about theories. It is about information about reality; or about images of it. About mathematical equations describing nature in their own way. So there is always some kind of transformation: into the realm of theory, of mental things.

Or, more concrete, into the actual medium of representation.

Physics is a fairly complex system. Single physical statements cannot be understood but with a certain acquaintance, with prior knowledge. So we may say that physics constitutes its own knowledge space.

Sometimes, however, it is possible (and necessary) to distinguish different subareas, relatively self-contained disciplines or approaches defining their own spaces of knowledge. These may penetrate and superpose one another; different theories and models may mesh and complement each other.

Still, in the end, physics makes sense only because there also overlap quite another kind of spaces that are no integral parts of science as such, but of the “real” world, so to speak. Only this enables physics to take effect upon material things, as well as to be affected by them and thus to reflect physical reality.

Physics looks at the world through the eyeglasses of physics. It cannot do more — although sometimes it seems to want more. Which, no doubt, is its right, even its duty. Because ultimately it does not matter what theory says, but only what really happens. Nevertheless, to reason from this that there were something like the one objective reality beyond any such visual aid, would mean to overshoot the mark. And, above all, sometime precisely this idea may mislead to give up — if not to forbid — the struggle for objectivity and reality or truth.*(1)

After all, there is nothing to be said against the assumption that every reality is a certain view of reality. Reality is always a reflected, a known. Something else cannot be ascertained, not with the best will in the world.*(2)

At bottom, all reality is knowledge. This implies that knowing is not the subjective and more or less coincidental adaptation of the independent reality. Instead, knowledge is in the heart of every objective reality — and knowing is itself something objective.

This concept is not so new at all. Logic, for example, is long accepted to be objective, although it is rather some part of the realm of knowledge than of material reality.*(3) However, not only would any kind of scientific investigation of material reality be impossible without logic, but, above all, logic must manifest itself somehow right in the middle of the things, making them operate according to its rules.

Viewed in this light, we do here nothing but simply enhancing this concept, superseding usual logic by X-Logic. Which is not restricted to truth-value operations, but rather explores the fundamental laws of knowing.

Although matter itself is subject to the laws of knowing, thus to logic, this does not mean that real-world events could be deduced merely from logic, not at all, not even theoretically. The theory of X-Logic does neither know absolutely elementary building blocks nor absolutely all-embracing plans. The unique system for everything does not exist, nor do closed partial systems.

Exactly this knowledge can help us develop more robust and more practicable systems. Because it may prevent us from relying on the fancied security of absolute reasons and getting lost in endless chains of them.

So then, does the world need human observers in order to exist? — Well, apart from the fact that we definitely do not know our world without us, this question actually does not have to arise just because we recognize knowledge in the heart of matter. Rather, in defining knowledge, we render it independent of subjective notions, it gets an objective appearance. As such we can let it act in the physical and do not have to stress the subjective human perspective*(4). In this sense, knowledge is not less objective than any atom or so.

But objectivity does not remain unaffected by this addition (of knowledge), of course. Ultimately it gets a human component. What is, after all, perhaps not so bad.

But now, how does knowledge come into the middle of the things?

In order to be deemed physically real, a thing must show a certain constancy in its appearances. This is a criterion that, though naturally used, did never become part of physical theory. Because it is much too fundamental. It is rather logical. That is where it belongs, in the sphere of logic, of mental things, of knowing.

Actually, we have made out this steadiness as being essential for knowledge; indeed, we have used it to define knowledge. Which, of course, makes sense only if complemented by the counterpart, the change, that defines activity.

Not only is knowledge the firm ground we can rely on, resting in sameness like a rock in the rough sea of change and activity; it also manifests itself in characteristic activity. It is a bridged and grasped difference. It is captured activity, calmed down, but always potentially present.

And that is exactly how we have to imagine a material thing, as full of and driven by activity. An activity, however, that is somehow tamed, manifesting itself in continual appearances of the thing. But then, on closer examination, these appearances turn out to be interactions with other things. In the context of physics they may determine the things’ mass and energy, for example, two terms that correspond, in the main, to knowledge and activity, although the latter are meant to be much more general, principal, marking a logical conception.

The concept of thing has to be called “logical” because it is simply indispensable. Whenever we think, perceive, measure (or whatever) something, it is about something. This something we call “thing”. And it does not matter whether this means a verbal expression, for example, or a mental image, a notion, an idea, a law, or maybe a material thing. Purely logically that makes no difference.

Of course, however, this does not mean that mental and physical things are equal in all respects, or that we know much about the things “a priori”, so to speak. It is always up to the physics (among others) to find out and to decide whether something does really (physically) exist or not — with experience playing an important role.*(5)

In the context of our explorations the notion of space plays an important role — which may differ quite a lot from that normally appearing in physics. This is probably confusing, at first. But hopefully our approach will turn out to be a well founded enhancement that makes sense in the framework of physics, too.

Especially the theory of relativity makes clear how problematic the conception of absolute space can be. For in order to assign to space physical reality, based on experience, it has to be defined starting with physically real objects. Taken strictly, this implies that whenever we speak of “space” we always mean the “space belonging to a body A”. Exactly this approach is fundamental for the concept developed here, where every thing of whatever kind has a corresponding space of its own.

Science is not only theory but also practice; and as such it always stays close to reality and experiences. Its theoretical part, however, is permanently in danger of losing contact.

So, for example, if trying to realize the idea of one single all-embracing system constructed from few simple building blocks: sooner or later its complexity must get out of hand. Endless chains of deduction lead to no concrete results. The truth, that should be granted by them, gets lost on the way to realization. For it cannot enter the scene but from the other side, from reality, through experience.

Existence need not be justified. It appears. Beyond any reasoning and description.*(6)

At latest since the discoveries of mechanics, it is generally accepted in physics (and other sciences) that everything happens because of internal forces. The observable things embody all that causes whichever effects.

More modern developments, as for example the theory(s) of relativity, may be interpreted in a way that they abandon this view, putting the focus much more on so-called “fields” and the like. This may go so far as to consider physical objects to be nothing but special states of a kind of space.

Logically, however, this makes no principal difference to us. For whatever replaces the traditional physical things: it has to be, in the sense of X-Logic, things, no matter whether we call them “spaces”, “fields”, or likewise. Even if all material interpretations are set aside and only mathematical objects, such as “tensors”, are considered. Yes, even the physical laws themselves are things of this type — with their related spaces.

In the context of the Theory of Relativity, the “space belonging to a body A” was originally named “space of reference”. Today the term “frame of reference” is more usual. But here the cited approach shall be broadend to a general concept of space. For that purpose we pick up the idea that the so-called “body of reference” remains, by definition, always at rest.

This conception is now generalized, so that for every thing it can be said that in its space it is never subject to any alteration and thus remains always the same.

Seen in this light, the thing is effectively not present in its space; it is perfectly passive, unable to come into appearance, and thus cannot be observed. Though all other things can, in a way that may be called “objective”, insofar as the central thing is the unmovable, so to speak “neutral”, observer. All things are determined in reference to it, while the space is the reflection of these relations, representing the properties of all the other things — in reference to the focussed thing.

The existence of a physical object manifests itself in the object’s meetings — or, as it is frequently said, its interactions — with others. Through them it comes into appearance. From its effects on them, their changes induced by it, its own properties — and hence its existence — are deducible.

Some of these encounters may alterate the thing to such a degree that it does not stay the same thing. Maybe it splits into several others; or it fuses with another to form a new one; or it is absorbed by the other; maybe it even disappears completely, dissipating into some radiation or so (though this can be understood as consisting of kind of — somewhat curious — objects, too).

But normally contacts with other things do not change an object too seriously; so it does not only stay the same afterwards, but also between these contacts.*(7)

Most of the meetings with other objects do not seem to touch and affect a physical body in any way. Photons, as the assumed particles of light are called, and other quantum objects are meant to bomb it all through its lifetime — without any noticeable impact. That is one reason why observation is possible: it shows the things how they are, leaving them untouched.

In this sense, observation effectively does not take place, it is not existent, so to speak. And so, because it carries no weight, it can take place all the time.

In fact, physical events, the motions of a physical body, for example, are treated as being wholly observed. That means, as having at every distinct time at a precisely distinct place a distinct velocity (and so on). Every state of that object is completely defined — may this conception be practically realizable or not. The object is the sum of its defined states or appearances, which are thought to be infinitesimal (that is: of infinitely small extent). They make up its existence.

Continual reappearing is necessarily accompanied by continual disappearing. Between a thing’s occurances, even infinitesimal, there have to be gaps. Though these gaps are traditionally no theme in physics, they are actually of crucial importance. They allow outer forces to interact and so to change the otherwise uniform linear motion of a body. Only because this motion is everywhere interrupted, it can flexibly react on everything, conform to everything.

However, if the motion is interrupted again and again — how does it manage to stay normally the same all the time? And where does the body intermittently disappear to? — Well, both questions have in principle the same answer: the thing dissolves into its space, but this is a very special one, with a specific structure that makes the same thing reappear constantly.

The space is the program, so to speak. And the structure is, maybe, a certain short routine being continually initialized and producing always the same output, the same thing. But in between the program permanently resumes control, in order to listen for new user input, for instance, that may affect the routine.

The output — is it caused by the program? Or by the user input? Or by the computer? Or by the electric current?

Each of these things — if not quite another one — may be referred to as the relevant cause, depending on context.

In physics it has become common practice to take the laws of nature as fundamental causes. If we describe an event in a way that clearly shows the effective laws of nature, then we explicate it physically.

So we say, in the framework of mechanics, that a body principally moves linearly uniformly, as long as no forces act upon it. Nobody reasonably involved in that matter still asks “why?“.

But here, in the framework of these investigations, we take the next — maybe just small — step. We declare the moving body to be a special case of a thing, saying that every thing multiplies.

This is a law — and cause of all kinds of events.

The (reference-) space of a measurement device may be called “measurement space” or “property space”. There all other objects are specified relative to the measurement device, mostly in form of measured values of a characteristic property of that device.

At each point of this space the measuring instrument takes a specific form when interacting with the object to be measured; normally it displays a certain value.

By that value, by that form, this point of this space is defined. The entirety of all these points make up the space of that measuring instrument, the corresponding measurement- or property-space.

In this sense, our common three-dimensional space is a special measurement space. The associated measurement device is traditionally a measuring rod, a ruler or so.

Every thing has more than one property. It is specified in multiple ways, interacting with many other things.

In the sciences this multitude is often considered disturbing. It makes the things incalculable, unpredictable in their behavior.

Scientific theory always covers only a — partial — aspect of the real things. These therefore appear as idealized things in theory, reduced to what is essential — in that context.

But also on their practical side, sciences normally need to preclude disturbing influences. This is done by spaces which are closed exactly in this sense, thus providing a context that fits the theory.

The idealizations, so essential for physics and other sciences, are often seen as reflecting the original conditions, before any pollution, so to speak: the things how they really are.

But actually these things do show their supposed “true colors” not before they appear in a very special environment. In a space often laboriously arranged in advance. Only there they can multiply and so come into appearance.

But then, in this environment, under these arranged (laboratory) conditions, only those phenomena can flourish and be observed that fit into it.

Anything else is then regarded as scientifically not verifiable.

The ideal of mechanics is the empty space where few objects interact whose behavior is determined only by their masses. Pretty close to that ideal comes the space between the large heavenly bodies of our solar system. And in fact, the laws of gravitation and inertia and so on were first derived from observations of the stars, especially of the planets’ motions.

On earth it was essential that situations could be found or arranged, where disturbing factors, such as friction, did not carry too much weight and thus could be ignored. (Billiard) balls rolling on slick surfaces or hanging on strings while colliding are suitable here, as well as free falling bodies. Comparisions of their movements with those of the celestial bodies gave rise to the discoveries of impressively universal new laws.

How much our world is formed by this ideal of mechanics is reflected not only by the slick surfaces to be found everywhere, for example, but above all by our brains, our deep mental (mis)concepts: True reality must be hard and slick and as hostile as the empty outer space.

The overwhelming success of mechanics during the past centuries left no real choice: the whole world was to be seen as a unique stubborn machanism — and consequentially has been adapted better and better to that ideal.

Today, in the era of computers, one might say: the whole universe is following one program. Which seems to be even worse. Perfection taken to the next level, even more alien to our nature, more inscrutable.

Upon a closer look, however, it becomes obvious that groundbreaking changes are happening. Programs are no mechanical apparatuses.

Programs are different, they have quite another quality than mechanical objects, a further dimension, so to speak. The dimension of knowledge. They embody knowledge. They are bodies of knowledge.

Furthermore, they are much more obviously related to activity; they do not appear but in operation. So they can also be regarded as bodies of activity. Both bodies go far beyond the scope of any familiar notion of thing, pointing up the spatial nature of everything existing. And maybe giving an idea of how spaces communicate.

Physical formulas and models represent spaces of knowledge. These are structured in a way that allows them to link the relevant data closely together. The distances between the data thus become very short and are done almost automatically. That way, corresponding events can be predicted fast and easily, while in reality, they procede crucially slower, taking much more effort.

In the natural sciences we are used to structure the spaces of knowledge mathematically. We search for mathematical formulas showing us how things belong together.

This practice has developed in the course of time. Mathematics was reckoned to be the optimum way to express absolutely reliable knowledge. It is made of simple graphical symbols. Combined into rows, drawn on a flat surface, these are in line with the standard lay-out of texts, which are probably the most widespread means to store and convey knowledge.

Mathematics lines up there, even though it often blocks the normal text flow. In general, mathematical terms are separated from verbal expressions, if possible, and gathered into their own systems of equations and the like. Their meaning is grasped, with few additional words, if ever, by insiders, who have learned to handle those formulas the right way.

Mathematics is learned by learning the correct use of the mathematical terms. In this sense, these are and have always been coded instructions, programs.

Physics’ universality is due to extreme generalizations. It searches for the basis of all physical bodies of whatever kind. Such a radical abstraction is always in danger of irrelevance: meant to be good for everything and everyone may eventually mean to be good for nothing and nobody. Reality is squeezed into a fearful one-size-fits-all corset that takes the breath and crushes the life out of the body.

Originally, the physical body is the measure of the physical reality. Physically real is what we can see, hear, feel. That makes physics actually so interesting, that its subject is quite concrete, perceivable, material. In trying to get a grip on this matter, however, we have killed it. Until finally the completely lifeless body, the dead matter, became the measure of all things.

In reality, matter is not dead at all.

Since the beginning of mechanics there has been an inherent principle of elementary reproduction. It is implied in the use of differential calculus. Every motion — and even the non-motion, the state of rest — is a series of temporal states; time is devided into infinitesimal moments. So, in order to exist physically, a thing has to reproduce itself — or it has to be reproduced — every moment anew.

In mechanics, the principle of reproduction is often called “inertia”. Today we might instead speak of a “program” that lets a physical body recur again and again in the same manner. This behavior can be modified by forces, which, as a rule, are due to other objects — the execution of the program can be modified by inputs, ultimately by other programs.

Here we generally make use of still another terminology saying that it is the thing’s “space” that lets the thing reproduce itself, maybe influenced — or superposed — by other spaces, spaces of other things.

The notion of thing, as used here, does not necessarily refer to a physical object. Actually, it is rather a concept of logic than of physics. Is is absolutely indispensable for our orientation in the world. That is why we find it always and everywhere — the world must consist of things.

This truth is in no way limited to the physical world. Rather, in associating this notion with logic, we point out that even the things that we recognize as physical objects still have quite another dimension, that they are incorporated in a system of fundamental — namely logical — relations forming an essential part of their nature.

A thing multiplies as a whole. So it can be treated as one. That makes it simple — although, on the other hand, it is complex, comprising other things. Exactly for that reason we need it. We get a grip on what otherwise could neither be handled nor be understood.

Generalized in this way, things occur everywhere in physics, naturally, not only in form of physical objects, but also as universal constants, for instance. Even mathematical equations expressing the laws of physics are things in this sense.

So we have various types of things in different fields of physics on different levels*(8) and it is often extremely important not to mix them up. Though, to become aware of how easily this may happen, it ought to be understood that logically all these different things are equal*(9).

Not always is it a mistake to treat different things (from different spaces) as if they were one and the same. Actually, it is often quite natural and inevitable. So, for example, when a physical object is identified by — and with! — its name or symbol. Without such an identity it would be impossible to speak about anything, to comprehend anything, to know anything.

What we do in cases like that is creating — or using — a new thing comprising the others, which by themselves remain what they are: distinct, actually incompatible. But their spaces can penetrate one another. So they can form a new space for the new thing, which is different from the original things, although somehow combining them.

This process is extremely important, it is fundamental for knowledge of any kind. We have called it the central “act of knowing”. It is the process by which we get a mental representation of the physical thing, in combining it with the proper symbol, so to speak.

Such a “mental representation” is thing because it multiplies, which means that it is used again and again. This usage is primarily a kind of habit, a continually repeated activity: the symbol is associated repeatedly with the respective object. Whether or not this habit is represented by a physical manifestation, as a permanent connection in the brain, for example, does not matter. Although it is pretty well possible.

Not every repeated activity manifests itself physically. But every physical thing is a manifestation of repeated activities.*(10)

Every thing is characterized by its activities. These activities, constantly recurring, constitute the thing, they make up its appearances, letting it multiply. The typical effects these activities have on other things indicate the existence of the causing thing.

If there are such characteristic effects, recurring, forming a noticeable pattern, then there is a thing. If the effects are in accordance with certain rules (some of them called “laws of physics”), then the origin of the effects is a physical object.

Many things must come together before we speak of a physical object. But once we are sure that such an object is there, not much is needed. In general, slightest signs suffice to recognize a physical thing. Often it is determined by very few measured values, while all the others are included, so to speak. Frequently, they can be computed, derived from the known laws of physics. These laws form the space providing the material that build up a complete physical object in gathering around the nucleus consisting of maybe not more than one single measurement

A thing is meant to be given at once. It is always the whole thing. As such it appears, each time it appears, at just one moment, marking one point in its space.

On the other hand, every thing is also complex, extensive, distributed. It forms a more or less constant structure in space — which then, however, is another space, not the specific space of that thing.

Every thing leaves its traces (some of them forming characteristic structures) in many spaces. Every aspect of a thing is associated with a specific space. And new aspects can be found virtually endlessly.

As we can analyze a thing into its various aspects, so we can also join diverse aspects together. The thing itself is the fusion of all its aspects, so to speak. Yet, it does not show them directly; additional activity is needed, the respective spaces have to be entered in order to get a grip on these aspects.

A thing comprises various aspects of itself and so constitutes its own space. Every point of this space is a potential appearance of the thing. The thing appears when it is reflected by another thing. In these reflections*(11) the thing exists.

In general, the plentitude of one thing’s potential appearances allow the construction of manifold existences of it.

Every such existence is an appearance of another thing, a reflection in the space of that thing. This space is made of the existences of many things. All these (individual) existences do not exist but inside that space; they are appearances of the respective (common) thing and may be called functions or embodiments of that community.

The physical things exist in the physical space. This, their physical existence, is maintained by all other physical existences, only together they are possible. But no thing as such depends on any other. It is just its physical existence, its appearing in the physical world, which is a function of that world.

Every existence is perfectly woven into its context. Every thing, however, exists totally independently of each of its existences.

Knowledge is selective. That’s crucial. We have to filter out a lot, all that is disguising, all the data that we do not need at this moment. If we see nothing but the relevant phenomena, decision is easy.

Every space is a space of knowledge representing just a certain selection. To enter a particular space means to make a specific selection.

Still, this is generally more than simply applying an absorbing filter. It is principally different from merely selecting ready-made things. It is an active process, the things are to be manufactured.

It is much like applying a program.

We are actively forming and selecting our world, even the physical reality. That means that there are other possibilities, all the time. We decide which one is real.

Physics — as well as other domains of knowledge — enable us to calculate and predict the outcome of selected events and actions. Based on this knowledge we can decide better what to do next.

This is one of the main purposes of knowledge: to provide us with certain pieces of activity, clearly defined processes allowing us to achieve precisely determined results.

Knowledge helps us find the best action in a particular situation. Not always do we know one that applies perfectly. Sometimes experience just tells us not to repeat a certain mistake.