The mathematical theory of categories calls morphism a function, which is able to preserve an object that belongs to certain categories. We take catjects to act as morphisms of this kind. They produce objects and subjects, entangled into some circular structure, which defines their codependency. They produce themselves, providing for a heterarchy of values, which gives space to oscillation, memory, and subversion, and to proemial relationships, which define order and exchange. Their way of reproduction is to act as an attractor state, or *eigen*-value, of recursive functions, which allow for perturbation.

Of course, this is more of a list of ideas giving way to a research program than already the demonstration of the usefulness of the notion of a catject. Our idea is that catjects are to be considered as comprising of a particular set of distinctions, an "arrangement", as Spencer-Brown would have it, which produces a network synthesis consisting of variables whose values again are codependent. Our four societies, distinguished with respect to their respectively dominating dissemination medium, are cases in point. Oral or tribal, literal or ancient, printing press or modern, and computer or next society are, any one of them in its own right, catjects, which define how values must network, i.e., prejudice their choice, in order to lend determination to the indeterminate. The overall society, which we pictured by spelling out the network synthesis of social action as such, comprising the values of the variables action, talk, group, grid, society, and the unmarked state, is another case in point of a catject.

But catjects, as I think of them, are self-similar *eigen*-values which are to be found on the most different levels of the social. They may be thought of as resembling those steady states, or plateaus, which fascinate evolutionary theory and social philosophy alike. Indeed, to allow for variation, to secure selection, and to at any instant provide for some re-entry of the selections among the variations may eventually be said to indicate what they are all about.

Yet, the reason why we are interested in the concept of catjects is not only that it may provide a shortcut to an analytically robust reintegration of all these concepts just mentioned. More importantly, it seems to me, the concept of catjects possibly offers a translation of some old puzzles of the cybernetics into the contemporary interest in search algorithms, semantic webs, and social software, which all three of them conveniently are labeled by the name, or, rather, "call to action," of the Web 2.0 (Tim O'Reilly).

Three puzzles, says Warren McCulloch, the early cyberneticians, who are Norbert Wiener, John von Neumann, and himself, were not able to solve, the puzzle of the statistical, the puzzle of the coupling of nonlinear oscillators, and the puzzle of continuous nonlinear prediction. The puzzle of the statistical consists in the lack of the long runs of data under essentially constant conditions which would enable cybernetics to spell out the mechanisms and formalisms of the organization of complex phenomena such as a society social philosophers like Margaret Mead and Gregory Bateson asked for at that time.

The puzzle of the coupling of nonlinear oscillators relates to the question of the design of filtering devices able to provide for a mechanism of adaptive learning. W. Ross Ashby deals with this puzzle in terms of a system consisting of an organism and an environment, which are coupled by feedbacks which are able to distinguish between goals and their states, on one hand, and disturbances, on the other, a kind of cybernetic reformulation of the aristotelean *telos*.

And the puzzle of continuous nonlinear prediction consists in decoupling a system from any physical ways to determine its states, going instead for the operational closure of information to describe its self-organization and self-determination, and then in again recoupling the system on its own terms to the physical environment. To explain how a system may be able to predict its own states, and how an observer may discover the impossibility to do likewise, given the complexity of the system, means to consider information in terms of operational closure, which comes easy enough if one thinks of neurophysiology and the mathematical theory of communication, but is hard to swallow both inside and outside academia nevertheless since it so much contradicts a common sense, which is supported by the brain's perceptions making sure that all possible impressions, save dreams, get attributed externally, if not certain indications of disturbance do suggest otherwise.

Catjects tell us that we must look not for objects guaranteed to be possibly true, nor for subjects considered able to empirically back up themselves to transcendental reason, but for arrangements of distinctions able to reproduce such that they generate their own statistics, i.e. a data set of experiences and expectations, such that they are capable of dealing with variations always coming as a kind of surprise, and such that they develop some means of foresight, the most important of which is the acknowledgment of the future being unknown not only to them but to any observer. It may indeed be helpful to look for sociology in getting some ideas on how the three puzzles of cybernetics may be dealt with.

If the web 2.0 is indeed about the organization of metadata in addition to the production and storing of data (Tom Fürstner, this journal), then this organization may well prove to be another example of catjects in that the search, the linking, and the socially distributed use of the data will only be sustainable if there is some self-reference informing the links, some reference becoming reliable, and some accounting for the network becoming visible, which make the data trustworthy. Metadata will have to be informed by knowledge, that is, they will both be drawn from, and producing, a kind of knowledge, which is no longer considered to be consisting of definite data stored away in some memory, but will emerge and disappear along with natural and artificial users producing it while surfing the data surface of the natural, social, and artificial world.

Metadata will come with catjects, which are able to capture, number, order, and re-enter social data which are in a way, and with respect to a first approach, indistinctly oral, textual, visual, acoustic, and iconic. Our model of social action tells us that catjects able to do so must provide for action overflow, ambiguous talk, cohesive group, grid address, and some knowing of the society and the unmarked state coming with it, by the latter lending social, including emotional, fascination, and relevance of matter to the data.

Again referring to Charles Sanders Peirce we may say that catjects are able to organize data with reference to metadata if they provide for terms, i.e., for means to interlink sensibly, for propositions about objects of some kind, and for arguments, which both relate to interpretation and reveal it. The most difficult piece of it may turn out to be the provision of terms. Terms indeed map catjects back to themselves, thus lending them an inner depth and void which hitherto was experienced only by human souls (Blaise Pascal). But it may turn out to be exactly that inner depth and void which enables catjects to rely, with their operation and recursion, not on certainties of reference, but on addresses of networks.

But then, propositions and interpretations abound, which is why we just have to watch ourselves dealing with their overflow if we want to collect some metadata of how we deal with data, and of how we look for more, and other, data in order to be able to double-check on our metadata. I leave it at that, having given nothing more but the roughest sketch of some theoretical ideas coming to a mind watching the next society emerging. The prove of all this will lie in the use of some or other idea of this survey of possible sociological thinking for the construction of further examples of what we may mean in text, picture, music, or code.