The act of knowing always takes place in a non-empty space. Every search for knowledge tries to discover a stable pattern — in examining a pre-existing structure. Even the pattern itself is in a sense already existing.
Nevertheless something is created: exposing the new means changing the existent. The pattern becomes a thing that has not been so before. It solidifies, becomes concrete, graspable. So that something new arises being more than simply a new arrangement. The crux is its creation which does not happen once and for all, but ever anew, whenever the new thing appears. The fact that this happens habitually or automatically does not mean that no activity is needed.
The elements of knowledge structures mentioned before are exactly that what we have elsewhere called the objects or bodies or particles of knowledge. Nowadays we may primarily think of data, but every other representation of some knowledge (or information, as one might sometimes say) is also implied; it merely must be reproducible and somehow uniformly applicable so that it has kind of constant meaning. Like a mathematical formula, for example. Or a description of a plant. That means that these elements or objects or things may have quite different forms, some of them very complex. Still, in a way each of them is one thing. “One” just means that it may be duplicated as a whole, One is the base of every plurality. And seen in this light every such thing is — in spite of all possible complexity — simple. This is no magic, but sheer logic.
The act of knowing (as described before) is central and fundamental and has impacts on everything based upon it. It affects the structure of knowledge, making it fundamentally dynamic.
So, what does this mean? Is there no stable structure at all?
Well, initially it says that the elements of every structure emerge from activity and actually are activity, in their deepest inside, as one might say.
Yet, we have found out some more, namely that there is also always a spatial structural component, such as a net of relations and a field of tension. Thus we can redescribe the act of knowing so that a spatial structure concentrates and reduces to one thing.
This thing is a thing only because it represents a repeatedly observable regularity, that is, because it muliplies. So it constitutes a particular structure of its own, established by its appearances. Seen in this light, the central act of knowledge is the passing from one structure to another.
Hence activity is not only enclosed in the elements that form the structures of knowledge, but the deformations and reorganisations of the structures themselves are in effect the same activity.
The very essential parts of knowledge-structures, their true elements, are their alterations!
Knowledge puts various things together — and makes them be one thing.
Knowledge determines how the things act and interact. That they behave according to certain rules, expressing constant relationship. It is this regular behavior, recurring always in the same manner, that constitutes the new certain thing of knowledge, the fact. Thus crystallized it becomes graspable and handy, making it a gain in knowledge.
So we have just described the key process of knowledge. We should replay it frequently before our mind’s eye, recapitulate it, internalize it. Only so we can really understand it.
In particular it is most important to realize this to be actually a process; something is happening, a change. Activity takes place. Without that there were no realization, no understanding, no knowledge. For it is this activity that brings together what formerly seemed to be totally unrelated. A transition takes place. And only when this transition becomes an unalterable habit the represented relation is firmly established. From now on it automatically replicates itself. Now it is clearly evident, without a doubt, that those things belong that way together — in this sense being one thing.
Conventional logic and thereupon based scientific systems largely lack the ability to express dynamic contents adequately. They are too rigid, building on never changing conditions. New things are just added, not created by conversing the old. Fundamental changes would destroy the foundations of the whole system.
To avoid this, the basics were more and more abstracted and miniaturized, down to smallest building blocks and most general rules. Of these all sorts of things may be constructed. Meanwhile, however, the road from the most elementary preconditions to the real outcome has become unmanageably long and complex.
In practice nobody goes the whole way. For single purposes specific models are in use. Although these should principally be reducible to those generally accepted foundations, this is actually not practicable at all. What ultimately counts is to find and to establish the methods fitting for a particular purpose.
The problem is that this common – and, besides, the only realistic – practice misses well-founded theoretical reasons. So there is no common ground for communicating about it. There exists no certain plan covering larger areas.
By no means is it ready, time and time again something new is added. Normaly things are first published in the blog Prospects, where they may also be commented and discussed. Then most of these posts are inserted in the appropriate chapters, while their contents as well as the classification and almost every other stuff can permanently be developed and modified.
The revised versions are accessible by corresponding links in the footers of the original posts. For backwards reference the headlines of the paragraphs should be clicked.
The space of knowledge affords and demands a new logic, a logic of knowing; whereas traditional logic deals with truth, particularly with truth values, that means in general with true and false. These necessarily exclude one another: what is true cannot be false, and vice versa.
To knowledge, however, this does not apply in the same manner. Its potential embodiments, spanning a much broader spectrum, can exist side by side, even if they partially contradict one another. This coexistence is crucial, it constitutes a field of tension, a network of relations that are indispensible for all kinds of knowing. So knowledge in all its possible formings is extended and full of inner tension. While each of these appearances again combines with others to form always new figures of knowledge.
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, normaly 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.
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.
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.
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.
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.
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 just 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.
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. Knowledge does not apply everywhere. So in this sense knowledge spaces very well 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.
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?
of knowledge spaces can here, as a start, only be outlined, of course. For although in principle things are quite simple, yet for sure new questions will arise time and again asking for new answers. So that all threatens to grow more complicated. Not every information inevitably elucidates; 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, as to speak.
It may be called 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.
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.
About spaces of knowledge. This term is understood here in a sense that lets almost every representation of knowledge fall under it. Thus knowledge always forms kind of a space, it can always be regarded and described as such.
So, what is to say of these knowledge spaces in general? Are there any recurring patterns, overall structures, binding rules, or even fundamental laws, actually?
That is our starting point. And the reason why our investigations should make sense.
Naturally, everything that may be expounded here cannot really be new. It must have been there all the time. And, for sure, many have long noticed this or that here and there. But perhaps not yet quite as a whole. That such a kind of view is very well needed – and realizable too – remains to be seen.