The Basics

of knowledge spaces can here, as a start, only be outlined, of course. Because although in principle things are quite simple, new questions will surely arise time and again asking for new answers. So that all threatens to grow more complicated. Not every information inevitably elucidates; if appearing out of place or out of time, many things rather obscure.

Which finds us, though hardly realizing it, right in the middle. For the above statement is no superficial platitude at all, but indeed a basic law of knowledge. A logical principle, so to speak.

It may be called principle of simplicity. Knowledge must be simple. Simplification is a vital element of every gain of knowledge. Knowing must find simple forms. Only these can be grasped and effectively used.*(1)

Which brings us to the next basic principle, that of application. Knowledge could hardly be denoted as knowledge if it were never employed. But to be capable of being used it must be reproducible. Its usage reproduces it. Thus knowledge multiplies.

These two principles describe two opposite motions that sometimes may appear as contraction and expansion, for example. The former leads to formation of simple things, the latter to their propagation and distribution in space.

Thus we have found two fundamental forces or activities as constituent features of knowledge cooperating to generate and structure space.

Not bad for a start.


Once we have discovered a certain regularity, we try to recover this pattern elsewhere, everywhere. So our view on things changes, we see them with new eyes, in a new light. Thus many things may suddenly become clearer, finally making sense.

Yet it is just a matter of course that this cannot go on the same way forever. Time will come when we realize the boundedness of even the new view. Which then has become just this: one (no longer that new) view, just another way to look at things. Glasses that definitely should be taken off from time to time.

In principle knowledge is infinitely usable. It does not dissipate through its application. So its space is basically boundless. — On the other hand, knowledge cannot be used but in some already existing space. Application is interaction with this context. And of course not all environments do fit equally well. The same knowledge does not apply everywhere. So in this sense knowledge spaces surely have bounds.

But these bounds do not arise from the space itself. A certain way of seeing cannot see things unseeable to it. A limited knowledge does not know its limits. Knowing them is due to a new act of knowing.*(2)

From The Frontier

Knowledge is always whole and all-embracing. As soon as new things are discovered, they are already integrated.

But on the other hand, in particular the fact that there remains always something new to discover indicates that all knowledge is sort of limited.

Traditionally we resolve this contradiction in holding that knowledge advances. The limit of knowledge is a frontier being pushed farther and farther towards the unknown. Thus knowledge grows continuously.

This approach is somewhat aggressively expansive. Resistances must be overcome, the fight never ends, the enemy is everywhere. Not only does he crop up out there in the not yet known, but he is also lurking around in here where his name is oblivion. How easily the hard-won fortune may vanish into nothingness! Finally experience teaches that this cannot really be inhibited. Still we are far from accepting it. It’s just a weakness. And every weakness can and must be overwhelmed.*(3)

Not least this mental attitude drove us to accumulate more and more knowledge, while permanently enhancing the corresponding methods. Even the loss of knowledge, the forgetting, was pushed further and further back. By means of the new media, for instance, which allow us to represent knowledge in new forms and store them persistently.

But when we make ample use of them we probably become aware of a quite different face of knowledge. It turns out that knowledge has many faces. Which do not look all together in the same direction. And this is exactly what makes knowledge! The diversity, the different angles and perspectives. Together they draw an image which no single image can ever display.

True knowledge comprehends everything, it is the whole — and precisely for this reason there is no single all-embracing knowledge, but rather a basic substantial pluralism. With contradictions not to be wiped off.

Differences are essential for knowledge.

Knowledge Particles

Sometimes we mean by “knowledge” the whole, the totality of all known data, models, theories, laws, and so on. At other times, however, speaking of “knowledge” refers to single elements, even tiny little facts, measured values, the length of a rod, for example.

In analogy to physical concepts we may talk here of bodies of knowledge in the space of knowledge.

The abstract physical space can be defined by generalizing the concept of extent, a characteristic feature of the concretely perceptible physical objects. But the objects of knowledge? Do they also have kind of length or anything comparable, being abstractable to some corresponding space?

Well, whatever that may be, normally we do not seem to really need it. Facts, at least, should better be exact, measured values should be as precise as possible, truth must not be possibly wrong. Such kinds of extents would be rather distracting.*(4)

On the other hand, however, it is just the in-between that matters. The pure facts are poor facts, actually no facts at all. Standing isolated for themselves they do not make any sense. They must form a body. This body never comes from the facts alone. It is knowledge. Widespread though widely unprovable knowledge. This is the real substance of every body. It makes its volume, it is spatial, extended.

So after all every thing is extended, even the seemingly most infinitesimal tiny little fact. Because it is knowledge.


Even the smallest point still allows to be spread open, unfolds into a whole world.

And, the other way round, from the proper perspective the whole wide space with all the trimmings shrink to a single point — if anything of that is still to be seen at all.

Whole Parts

Space is all-embracing and contains all things. It also comprises all potential views of itself, from all possible perspectives. So each view realizes merely part of space.

The current view itself, however, cannot see its own partiality. It therefore must perceive itself as complete, comprehending the whole — although, for sure, it eventually turns out to be partial.

A logical consequence to be drawn here is that there exists no principal distinction between any partial space and the whole one. Uncompleteness cannot be seen but from the outside, so to speak, from another perspective — which again can offer nothing but a particular view of reality.


The all comprising infinite space becomes finite if observed from outside, so to speak. Hence it solidifies into a thing with cognizable properties distinguishing it from other things. With these it shares the common all-embracing unique space.

Since this process repeats again and again, the idea of nested spaces may arise, each one bigger than its predecessor. So that a successive, though probably never perfect, approximation to the one and only true space might take place. The conception of a hierarchy of spaces (or things), which is widely used, in one way or another, may be due to this.

However, this idea tacitly implies the existence of an order relation applying to all possible spaces — here denoted by “bigger than its predecessor”. But in being recognized, which, as said above, means observed from the “outside”, such a relation looses its absolute questionless universality, because in that moment spaces become thinkable that do not possess this property. The spaces with such an order thus become part of a still more universal space which does not possess it in the same manner. And which therefore cannot be called “bigger”.


In being recognized, the characteristics of space crystallize into a thing. This process is definitely invertible: a thing may widen into infinite space. Its inner structure becomes the stucture of space — so completely that it cannot be perceived anymore. How huge an impact it has on perception and consciousness becomes clear not until the glasses are taken off. But each time this happens, in truth just one pair of glasses is replaced by another.

Every thing can serve as eyeglasses through which the world is perceived and in a certain way filtered. And every perception passes through such glasses, through a thing; perception is reflection at a thing, projection upon a thing. Only through this process anything can be perceived and known. Through transmission onto and into another medium.


A space known to have a particular structure becomes a particular and thus somehow distinct space — and therefore some thing in space. That way there may be defined and segregated almost any number of sub-spaces, which, viewed from the other side, unite all together in the one space of knowledge. Thereby they penetrate one another, loosing any sharp distinction between them.

Every thing in space can be regarded as an objectified (sub)space. And every (sub)space is an illimited thing. Space and thing are different aspects of one and the same. Every thing corresponds to a specific space, and vice versa.

So every interaction between things can be considered a penetration or superposition of their spaces. And every appearance of a thing is due to such an interaction. The thing mirrors itself in another thing and so comes into appearance. Which can also be understood as penetration and inducement of its space by another one.

From another angle the same process may be viewed quite the other way round, as an appearance of the other thing. Instead of different “angles of view” we may alternatively speak of different “knowledge spaces” where the respective things appear. Then a thing marks the passage from one space to the other, so to speak, precisely because it can be seen like this and like that. Every thing is a crystallization of several interpenetrating spaces.

Too Other

All that is seemingly not present — though somehow active — does not exist as distinct things. It is somewhere in between, between the things. It is the space between, its substance. It is that what makes up space.

As such it is ungraspable — unless it does become something, a thing. So many things may emerge out of space. At last, space is totally made of things, nothing else. They just cannot be seen — in the moment. Maybe they are too small, too big, too far away, too close, too well-known, too strange, too many …

Still, somehow they are there, and they have some influence on those things that can be seen. So we give them a name, as a whole. Here, in this context, we call it “space”.*(5)

Integrated Bounds

Every thing has its own space — although there is only one space, space, for it is endless. Everything that exists is part of it, a thing in it.

Things may sometimes be regarded as the opposite of space — since space is open and boundless, while the things are rather bounded and closed. As such they separate a region of space. And that is exactly how, after all, space is somehow bounded: by the things. Through them it can be left — and another one can be entered.

It is the space of the thing, that is entered in this way. But, once entered, the space that initially appears to be the closed interior of the thing turns out to be space itself, the endless one, the universe. Because from inside no bounds are to be recognized.

So, where do they go? — Well, quite simply: again they are incorporated in the things of (this) space; and so they are perfectly integrated, yes, they are the ultimate substance of space.

Wider Space

Things emerge from space. Although somehow invisible, they have been there all the time. This shall be true even if a thing appears for the first time, newly created.

Yet, for this purpose, the notion of space has to be taken much wider than usual. And that is exactly what we do; this is our conception.

That way our ordinary three-dimensional space becomes a simple sub-space, one part of the whole. A hugh bunch of such partial spaces may be distinguished, as there are a special space of physics, for example, or that of mathematics, as well as a social space, psychological, biological, ecological spaces, and so on.

Each of these spaces relates to a specific point of view, often a scientific one, and may be called “knowledge space”.

The whole, however, the unification of all spaces, we usually refer to as the “space of knowledge” or simply “space”.


Every (partial) space is associated with a corresponding thing. However, there is probably an inifnite number of ways to define a thing’s space. Extremely different pictures may be used, no single one can display every aspect of this relation — because in the end every possible explanation has to stay in its own space, which is necessarily partial.

It is actually this plentitude of different views, together with their apparent inconsistency, that are able to give a vivid impression of what matters. It is a kind of movement, a certain activity, that transforms the thing into its space (and vice versa). While occuring in various environments, it takes various respective forms.

The Space Of A Thing

Things appear in their spaces. A thing is made of its appearances, it exists in them.

A thing’s appearances may be different instances of one and the same thing; or they are supposed to be different states of one single thing; sometimes different parts of a thing may be regarded as its appearances; or just different views, showing the thing’s different sides, for example.

All these are possible appearances of a thing. They all constitute – on their own specific way – somthing we can call the space of the thing.

Measurement Space

The 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.


Conventional logic views the things from outside, so to speak. Hence they appear limited and closed. They become objects.

So this logic corresponds to the conventional ideal of science, the objectivity, always intended, but in the end remaining an idealization. For even science is persistently forced to immerse itself, to get into the thick of it, to be touched by the other, to take part, without a distance.

Actually, it is no problem to accept our own entanglement in reality as an essential condition for knowing. We merely have to factor the step towards objectivity into our computations by giving room for the spaces. They just belong to the things. The space stands for all that the thing cannot do without it. In particular the interactions, the outside contacts. It is space what mingles with others, what penetrates them and is penetrated by them.

In this way, by means of the space, the thing is able to leave itself behind it, to become another. While also remaining entirely itself, since only in permanent renewal it is. Seen in this light, its being is made exactly of this distancing from itself, of viewing itself through another’s eyes.

That is the core of every existence. And activity. It is what we sometimes call time. But before any standardization, without the artificial monotony of clocks. Lacking any coldness. It is life. And this life is knowledge. Reflection is elementary.

Distinct Spaces

Things that move change their location, while the space that comprises all possible locations remains unchanged. Any seemingly changed space has actually become a different one, there is a plurality of distinct spaces.

So (each) space can stay the same forever and represent unchangeable knowledge we can rely on.

Motion In Space

A space is the entirety of a thing’s potential places or states. Every such point is reachable by motion. So, in this sense, it represents the corresponding motion. While the space represents the entirety of potential motions. Motion, after all, is the activity bound to a particular space, the activity characteristic of it.


Every space is, in a certain manner, connected with sort of a program determining the possible motions characteristic of that space. In the case of traditional three-dimensional space, for example, the laws of mechanics might be regarded as such a program.

Viewed in this light, all of physical science is ultimately nothing else than an attempt to decipher the program of physical space.


Every space has a specific structure, which means that its content is arranged in a certain manner. This arrangement may be traced back to some underlying program, or it may be regarded itself as kind of program, a rule, a pattern observable all-around in that space, in all that is happening there.

The structure is all that matters; the program is just a possible description of this phenomenon. A description laying particularly stress on activity. As well as establishing a relationship to knowledge.

“Structure” is often preferable because it does not implicate anything like some foreign creator or so. It says nothing about its origin. But if using this term we should nevertheless keep in mind the other implications of “program”, activity and knowledge. They are essential.

At A Glance

If we comprehend and represent a temporal series of events or stages, a process, as a whole, then these stages come to lie side by side, establishing a spatial dimension, so to speak.

That’s all there is to it. That way we get the whole process at a glance. We know what happens, what did happen and will happen.

Spatial arrangement is the expression of knowledge, space is always a space of knowledge, and knowledge is always spatial. Knowledge is the ultimate dimension (of space).


The three-dimensional space, being so familiar to us, is essentially an extremely complex construction of our mind, conditioned by our manner of perception*(6). Its apparent simplicity is simply an expression of our familiarity with it.

We do not have to construct anything consciously, provided we are generally able to behave normally. The program that is responsible for this construction is elementary in that it is part of our basic mental configuration.

It constitutes not only space, but also everything in space, which means: the whole universe.


The familiar three-dimensionality is one possible structure of space. Many others are possible, too. Although the expression “possible” may be misleading here, since every possible structure is actually existing. No matter whether or not it is presently realized. Like a program, which exists, no matter that it is currently active — or not.

Space embraces all possible structures, as a framework, so to speak, allowing each structure to appear. Nonetheless, space does never appear without any kind of structure.

In our system structures may be placed, roughly speaking, somewhere between space and thing. Unlike those they are flexible and dynamic.


Knowledge comprises different things, it comprehends the similarities between them, the common pattern, makes it fixed, makes something of it, a thing.

For that, the different parts are pushed together. This may, at first, be a laborious action, yet, eventually, it becomes a matter of course, an automatism, a spontaneous coincidence. So that, in the end, the different elements come to lie directly side by side.

Still, for all others, not engaged in this process and thus not gaining this knowledge, nothing changes with the original constellation.

So different spaces (of knowledge) coexist. Without bordering each other.

*(1) In general knowledge is very complex, of course!
Here, however, it shall particularly be pointed out that this is not the whole story. If knowledge never stops growing more complex, then it eventually becomes irreproducible and thus worthless. Then again simple forms must be found, making things comprehensible and usable.
That these again may be used to put up complicated buildings very soon, that’s the other side which still remains to be illuminated. The (following) reproduction of knowledge is intended as a first approach, as the effective principle, the driving force behind it.

*(2) Be that as it may, in general we are much more interested in the new wide perspective and the opening opportunities than in the narrowness of the old one. We hardly remember it, once it is gone.
Although… where did it go? Does it still exist somewhere? And what about all these endless spaces? And the knowledge — left behind — as well as not yet gained…
Who cares?

*(3) This is almost a natural law. That’s how it works. Only the fittest, the strongest, will survive. This applies also — and even particularly — to knowledge. Because real knowledge must be true. There is only one knowledge, the true one. Knowledge cannot be false. What proved to be false was ultimately no knowledge. True knowledge does not accept any other beside it. Everything not according to our consolidated knowledge is merely illusion, even if others suppose to know it. Everything that is true, however, automatically integrates.

*(4) Which, by the way, generally applies to physical objects, too. In mechanics, for instance, we are used to ignore any potential or real extents, treating the bodies as mere point masses. Their motions are transitions between distinct occurances at definite points in space.
So, seen in the light of physical science, the physical objects actually are objects of knowledge. They do not verifiably exist but in their observable, especially measurable, appearances. These are the facts. The rest is interpretation. Of course, we know that they exist in between. Experience proves it. But all that definitely counts are the facts, the data, the knowledge particles.

*(5) But we must not forget that it is what we call “knowledge”, too. And “activity”. And, of course, “thing(s)”.

*(6) especially with the eyes