Computational causality

One way to keep computational causalities time-invariant as proposed in [8] is to use sinks of invariant causality in conjunction with a modulated transformer MTF b t) that switches off and on degrees of freedom. 

The standard Sequential Causality Assignment Procedure (SCAP) can be applied without any modification resulting in time-invariant computational causalities. 

In this book, a bond graph representation of hybrid system models is chosen as basis for bond graph model-based EDI in Chap. 4. The representation is system mode independent with regard to computational causalities and allows for deriving a set of... 

Fig. B.4 Computational causality indicating the direction of effort and flow...

Ngwompo and his co-authors [24] state that a LTI SISO system is structurally invertible if there is at least one causal path in the causal direct bond graph between the input variable and the output variable ([24, Proposition 1, p. 162]). Furthermore, they show how the state equations of the inverse system can be directly determined from a causal direct bond graph model or from a bicausal bond graph. (In order to support tasks such as bond graph-based system inversion, Gawthrop extended the concept of computational causality by introducing the notion of bicausality [19, 25].) Clearly, the state equations of the inverse model of a SISO system can be converted into a transfer function. 

All variables involved in a relation are divided into two classes, namely antecedents and consequences. For any equation x = f (y,z), where /( ) is a function, the variable(s) on the left side, e.g., x, is (are) consequence(s) whereas the variables on the right side, e.g., y and z, are antecedents. Construction of antecedents and consequences follows directly from the computational causalities imposed on the bond graph model. Note that parameters always appear in the antecedents. 

We now apply these results to compute 1 v(2>) the Fourier transform of Kuv(x), in terms of its imaginary part Im OL p). Causality asserts that J uv(p) is an analytic function of p0 in Imp0 > 0, and hence that there exists a dispersion relation relating the real and imaginary parts of... 

Causality requires that the filter response at time n be computed on the basis of present and past information and not require knowledge of either the future input or output. Thus, the computation of zm (n) involves only present and past (values of the) inputs and only past outputs. 

Computational methods have been applied to determine the connections in systems that are not well-defined by canonical pathways. This is either done by semi-automated and/or curated literature causal modeling [1] or by statistical methods based on large-scale data from expression or proteomic studies (a mostly theoretical approach is given by reference [2] and a more applied approach is in reference [3]). Many methods, including clustering, Bayesian analysis and principal component analysis have been used to find relationships and "fingerprints" in gene expression data [4]. 

The important point in the present context is that these cognitive abilities do not come for free. It is clear that high levels of intensionality are extremely difficult to cope with in computational terms. Kinderman et al. (in press), for example, tested normal adults with a series of tests similar to those used in standard ToM tests but which allowed for up to fifth order intensionality (as opposed to the conventional second order of standard ToM false belief tests). At the same time, subjects were also given tests of environmental causal relationships that required only memory of a sequence of events. Memory tests involved causal relationships of up to sixth orders of embeddness ( A caused B which caused C which. caused F ). Error rates on memory tasks varied fairly uniformly between 5-15% across the six levels of embeddness with no significant trends in contrast, error rates on the ToM tasks increased exponentially with order of embeddness (i.e. intensionality). 

All sorts of causal paradoxes can arise with more than one dimension of time. However, 1 do not think this precludes life, even if the behavior or the universe would be quite disturbing to us. Also, electrons, protons, and photons could still be stable if their energies were sufficiently low—creatures could still exit in cold regions of universes with greater than one time dimension. However, without well-defined cause and effect in these universes, it might be difficult for brains (or even computers) to evolve and function. 

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