Narrative strength
This page is a short exert from my book on acculturation. In it I develop a theoretical model of narritive strength and prediction using some of the mathematics of neural networks and complexity theory. Fun stuff!
Keywords: Message absorption, narrative ontology, themes, neural wave propagation
In this section I leave behind the limitations of Chomsky–Schützenberger and the induction of the semantic property. Instead I discuss some elementary neural processes, presenting a trivial model of biological systems which can incorporate multicellular architectures. These are similar to the basic AI devices previously discussed, but with the added property of allowing for recursion.
Generally we can say that neural settling or large net acculturation is based primarily upon the strategies enumerated below, where M is a message, S is a message source, and t is the time at which a given message occurs:
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Accept incoming message M,St, OR
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Accept and modify M,St to be more in line with previous message(s) (narrative, ontology, etc.), OR
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Spontaneously create new message(s) M,tr where r is t0k + n to reduce conflict (neural wave extremum etc.), OR
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Reject message M,St
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Go to 1
In other words, messages as compared to the content of previous messages already merged into the nacent ontological pattern. Of course some messages are absorbed into an internal pattern more easily than others. This is in part due to the nature and number of previous iterations (i.e. strength or weights (w) in the model I present below). For example, certain foundation messages may be assumed to be implicit, such as those dictated at base by neural network design, mRNA bandwidth, or DNA mapping. Or we can look higher in the chain such as at delay time in crossing synaptic junctions, information per unit time vs. simple data rate, and so on. All constrained of course by capacity considerations. But importantly, not by message content.
A reminder from the previous section:
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Process are comprised of message source, messages, filters (eg. number of message receptors available per unit time), and finally weights (w) which represent the strength of relation to previous narratives, and current narrative(s).
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Messages are accepted, rejected, created, or modified in order to reduce conflict
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Processes at least for now, are considered to be autopoietic.
Finally, let us hypothesize that the biological acculturation system being discussed is an adaptive linear processes whose behaviour may be formulated by stochastic approximation techniques. And that meaning making occurs as the message moves from source S to narrative N with the simple transfer equation:
Hence to relate multiple sources S to a particular message, where N indicates narrative strength, we can write:
N = ∑nk = 0, j = 0Sk(Mkwj)
This allows recursion can be described as:
Mj, k + 1 = Mjk + Rk(Nk − 1 − Nk)jk
This simplistic model characterizes messages as dependent upon feedback from current and previous messages and current and previous narratives, the sum total of which by definition, compriss the current acculturation or senttling ontology. Or said more simply, the settling process can be described as the process of catagorization analyzed by the interaction of messages arising from a plethora of sources, filters, transductions, and the like. All of which produce a strengthened or weakened message (though not necessarily physical) interconnectivity.
Now while this this model obviously works well with value (that is to say, with message content), it also suggests that the primary task of this neural process is to find a weight vector w such that the resulting settling (or settling strength, depending upon context) may be derived. We can write this process as:
for all S connected or influencing a destination network, where u=(1,2,3..n). Or for a specific iteration step:
N = stepN)∑nk = 0, j = 0wjSk
I would now like to define this value N as settling strength. Settling strength for purposes of this simple model, shall represent for the time being, neural acculturation. Settling strength is the result of differential weightings in connections or influence from source to destination (the neurological constructs for destination are discussed in much more detail later).
Of course there are various strategies for adjusting weights which can be formally addressed without reference to message content. For example, one such strategy is likely to be simple minimizing of the square error function with respect to the weight vector w:
Another strategy that appears sensible here is gradient following. That is, altering vector w to coincide with a gradient of expected conflict minimization without the necessity to calculate the exact location or strength of the gradient.
Yet another could be stochastic approximation to some mean N. And so on - there are many potential strategies the enumeration of which serves little purposehere. Rather what is of importance now, is to see that for these classes of strategies, recourse to message content is not necessary. My model allows the vectors to be randomized or statistically probabilized such that each iteration moves toward convergence upon a sufficiently low level of conflict between internal and external neural systems. That is to say, between already formed acculturation and settling (internal), or stablized (external) networks.
This may appear counter-intuitive when contrasted to the more common approach in so much of the neurological and psychological literature, wherein it is typical to theorize by means of ascribing meaning or value to hypothesized internal mechanisms. I detailed some of the ideas previously. But I am suggesting that this is not necessary. At least for this simple model. For the simple mathematics of weight adjustment as the model iterates can be sufficient (as the AI literature certainly indicates) for useful process exclusive of message content. Particularly because as I show later when discussing complexity theory, the model in extension allows for strange attractors as point around which the stability of neural acculturation can formA.
But first, let us now expand the simple model above:
Zhuangzi whom I quoted at the beginning of this section, knew that small systems are seldom aware of the larger systems which subsume them. In this he was in congruence with certain aspects of cybernetic theory. For example, there is Gall’s doctrineB [Ch.2, pp. 207, V.] that in studying any complex system, fundamental rules are unlikely to be detected without first considering the meta-system.
Recall from the previous section that feedback mechanisms may be relevant to the process of habituation. For example, I indicated that acculturation systems were cybernetic in nature, and embodied full autopoieticity. They were thereby fully interactive with their environment.
This can now be more formerly stated. In doing so I have expanded work of TurchinC and his co-workers [3, 4, 5] as described below.
To begin, consider a system ’Y’. Y is a self-replicating system. The replications need not be identical. Communication, trade, information interchange, and other forms of contact between Y1, Y2, ... Yn allow us to consider a further system Y’. Y’ is a network since its nodes interconnect and carry information. By definition Y’ contains all systems of type Y as subsystems within itself.
Hence Y’ is a meta-system for all Y, but not the only meta-system possible.
Suppose there is a mechanism T which controls the behaviour, production, or erasure of any or all Y-subsystems. Hence T’(Y’) is the overall control mechanism governing the behaviour of Y’. T’(Y’) subsumes Tn(Y0..k). That is to say, T’(Y’) is composed of many T each of which may have between 0 and n dependent and/or contributing systems.
You can see therefore, that T is neural theme. (Recall from the previous section that a theme is the field fuction upon which individual messages exist.) Furthermore, Y can be interpreted and constrained as being any system neural, artifical, AI, societal or otherwise which effects or is effected by inherent settling.
Stated more succinctly, I propose that a stabilizing (ie. acculturating) system N may be defined as:
were Wk is defined as the weight applied to Tk for the systems it controls under narrative Nk. (Note that this definition is therefore an expansion of the earlier definition of weight vector w I discussed in Chapter Four, i.e. similar to weighting in a trivial neural net). W is a directional vector since it is a signed value (+ or -) depending on whether the values it modifies are pushed or pulled from a particular direction.
We can now define the overall stabilizing system as:
Nm = |∑nk = 0, j = 1(wkTk(∑nj = 1Yj))|
or more succinctly as
where N’ is the overall settling due to network history. Or from the previous discussion, overall acculturation narrative. N’ is composed of the systems and subsystems described earlier in this work, each of which is constrained by the themes and the strength of habituation (w) into a given meta-system. Because of the freedom from content, the meta-system can be anything from a group of synaptic junctions to something far more complex.
Finally, it is important to note that by definition, both Y and T are constants. Hence they contribute to Nm by quantity. That is to say, the number of systems involved in a meta-narrative is directly related to narrative strength. The same argument applies to T. The more themes controlling the inculcation of a narrative, the greater the strength of said narrative. Albeit constrained in force by vectors W.
A trivial example at the macro level of human interaction will help clarify this:
Suppose there exist two systems: Y1 is a pub or tavern, and Y2 is a book club. Suppose further, that we wish to conduct a public relations campaign to convince the members of both systems to support a particular brand of beer. It may be taken as a given that a dominant theme of any pub is alcoholism.
Let us call this theme, T1. T1 is less likely to be the dominant theme of a book club, which we may suppose to be an orientation toward reading and the ideas stemming therefrom. Let us call the conceptual discussion theme, T2. Vector W1 may be defined as the amount of alcoholism, and vector W2 as the predilection to idea discussion resulting from reading.
From extensive behavioural study, the public relations company concludes that the tavern is themed (+10W1)T1 and (-10W2)T2; the book club on the other hand appears to be best described as (-5W1)T1 and (+10W2)T2. And so we can write:
Nm = |∑nk = 0, j = 1(wkTk(∑nj = 1Yj))| = |∑2k = 0, j = 1wkTk(∑2j = 1Yj))|
N1 = (( + 10T1 + ( − 5T1)))2 = − 20
N2 = ( − 10T2 + ( + 10T2))2 = 2
Therefore the overt narrative strength of alcoholism out-ways that of enjoyment of fine literature within the study populations. The PR firm therefore reports to its beer-making clients, that they should concentrate on extolling beer rather than bother with using literary references during an advertising campaign.
Note that the overall narrative strength of the two combined (Nm) can be compared with other campaigns and other narratives. The total of all Nm equates to the underlying ontological stability - i.e. acculturation, hidden narrative, common belief, underlying structure, etc. - of all social systems under study.
You may have noticed that no reference was made in this trivial example to the size of the study populations. That is because this simple model is scalable. While designed for activity in wetware as well as AI networks, it deals with any system regardless of size. And a system need not necessarily consist of individual neural nets, but rather of many in aggregate. Of course if network population size contributes to acculturation strength, it is accounted for by the size of the vector W.
This definition can also apply to the more traditional ideas of narrative strength. Albeit in a rather different manner from that of postmodern expression or the legions of writers proposing their own narrative definitions. For example, Macht mech Recht and Vae, Victis are certainly strong narratives in North American culture. Yet they are but two of many possible candidates for a for underlying ontological acculturation. N’ however, while not as poetic a statement as Vae Victus, allows for any number of narrative statements to be included with reference or need for their content. They can also be vectored (w).
Recall that a theme is a control (modifying) principle upon a system. Hence what is usually called a basic or fundamental stability can be seen in the definition of N’ to be simply a theme. In human terms Vae Victis is an example of a theme which effects a system with vector w and strength T. This seems to me to be more intellectually satisfying that postmodern or other philosphic analyses which after all, are tied to specific cases rather than giving a universal abstraction. My little theory or stability and acculturation here (which I later prove to be far too simplistic and inaccurate, but very useful in developing the full theory of acculturation begun in the next section), allows for a more inclusive doxalD description than is possible by the usual slew of catch phrases, however poetic they may be.
N’ allows for the clear delineation of the subjacent acculturation strength in any network, neuralogical, AI, or societal.
The next section takes this simple view of N’ and adds two modifications - negative time and randomness. I will show that with these two additions N’ moves away from simplistic autopoiety, becoming instead a wavefront migrating through the phase space of a chaotic dynamical system. The neural topology involved centres around the magic of strange attractors.
Notes:
A: A quick note about mathematical models in this context: I am more interested herein in systems from the point of view of stochastic, continuous, floating viewpoint. Deterministic linear systems are very interesting of course, but as I stated in the previous chapter, they do not to me seem appropriate to the process of neural processing. Later on when looking at complexity models (in Chapter Six), I discuss some of the findings from neuroimaging which seem to me to back up this point.
B: It is unfortunate that Gall’s brilliant contributions are not better known. I am particularly enamoured of his insights into communication theory, particularly Dunn’s Indeterminacy from which Gall was able to deduce [Gall, Ch.19, pp. 100] that communication is always present in any networked system. And moreover, the axiom that the meaning therefrom is not necessarily the meaning of the communication, but rather of the resultant system behavior - a point which R. Bandler has also elucidated.
C: His meta-systems transition theory makes for a very enjoyable read. Highly recommended.
D: By doxal here I am refering to Bourdieu’s definition in his “Outline of a Theory of Practice”. There he narrowed the more general meaning of “common belief” to something which is “taken for granted” and therefore often invisible to the system.
