Fast recursive filters for simulating nonlinear dynamic systems

A fast and accurate computational scheme for simulating nonlinear dynamic systems is presented. The scheme assumes that the system can be represented by a combination of components of only two different types: first-order low-pass filters and static nonlinearities. The parameters of these filters and nonlinearities may depend on system variables, and the topology of the system may be complex, including feedback. Several examples taken from neuroscience are given: phototransduction, photopigment bleaching, and spike generation according to the Hodgkin-Huxley equations. The scheme uses two slightly different forms of autoregressive filters, with an implicit delay of zero for feedforward control and an implicit delay of half a sample distance for feedback control. On a fairly complex model of the macaque retinal horizontal cell it computes, for a given level of accuracy, 1-2 orders of magnitude faster than 4th-order Runge-Kutta. The computational scheme has minimal memory requirements, and is also suited for computation on a stream processor, such as a GPU (Graphical Processing Unit).Comment: 20 pages, 8 figures, 1 table. A comparison with 4th-order Runge-Kutta integration shows that the new algorithm is 1-2 orders of magnitude faster. The paper is in press now at Neural Computatio

Causal non-locality can arise from constrained replication

The fundamental theories of physics are local theories, depending on local interactions of local variables. It is not clear if and how strictly local theories can produce non-local variables that have causal effectiveness. Yet, non-local effectiveness appears to exist, such as in the form of memory (non-locality through time) and causally effective spatial structures (non-locality through space). Here it is shown, by construction, how such non-locality can be produced from elementary components: non-isolated systems, multiplicative noise, self-replication, and elimination. A theory is derived that explains how causal non-locality can arise from strictly local interactions.Comment: Revision, 5 page

Active causation and the origin of meaning

Purpose and meaning are necessary concepts for understanding mind and culture, but appear to be absent from the physical world and are not part of the explanatory framework of the natural sciences. Understanding how meaning (in the broad sense of the term) could arise from a physical world has proven to be a tough problem. The basic scheme of Darwinian evolution produces adaptations that only represent apparent ("as if") goals and meaning. Here I use evolutionary models to show that a slight, evolvable extension of the basic scheme is sufficient to produce genuine goals. The extension, targeted modulation of mutation rate, is known to be generally present in biological cells, and gives rise to two phenomena that are absent from the non-living world: intrinsic meaning and the ability to initiate goal-directed chains of causation (active causation). The extended scheme accomplishes this by utilizing randomness modulated by a feedback loop that is itself regulated by evolutionary pressure. The mechanism can be extended to behavioural variability as well, and thus shows how freedom of behaviour is possible. A further extension to communication suggests that the active exchange of intrinsic meaning between organisms may be the origin of consciousness, which in combination with active causation can provide a physical basis for the phenomenon of free will.Comment: revised and extende

Solutions to some philosophical problems of consciousness

A recently developed computational and neurobiological theory of phenomenal consciousness is applied to a series of persistent philosophical problems of consciousness (in recent formulations by Tye, Searle, and Chalmers). Each problem has a clear solution according to this theory, as is briefly explained here

Constructing a Naturalistic Theory of Intentionality

A naturalistic theory of intentionality is proposed that differs from previous evolutionary and tracking theories. Full-blown intentionality is constructed through a series of evolvable refinements. A first, minimal version of intentionality originates from a conjectured internal process that estimates an organism’s own fitness and that continually modifies the organism. This process produces the directedness of intentionality. The internal estimator can be parsed into intentional components that point to components of the process that produces fitness. It is argued that such intentional components can point to mistaken or non-existing entities. Different Fregian senses of the same reference correspond to different components that have different roles in the estimator. Intentional components that point to intentional components in other organisms produce directedness towards semi-abstract entities. Finally, adding a general, population-wide means of communication enables intentional components that point to fully abstract entities. Intentionality thus naturalized has all of its expected properties: being directed; potentially making errors; possibly pointing to non-existent, abstract, or rigid entities; capable of pointing many-to-one and one-to-many; distinguishing sense and reference; having perspective and grain; and having determinate content. Several examples, such as ‘swampman’ and ‘brain-in-a-vat’, illustrate how the theory can be applied

A Unifying Theory of Biological Function

A new theory that naturalizes biological function is explained and compared with earlier etiological and causal role theories. Etiological theories explain functions from how they are caused over their evolutionary history. Causal role theories analyze how functional mechanisms serve the current capacities of their containing system. The new proposal unifies the key notions of both kinds of theories, but goes beyond them by explaining how functions in an organism can exist as factors with autonomous causal efficacy. The goal-directedness and normativity of functions exist in this strict sense as well. The theory depends on an internal physiological or neural process that mimics an organism’s fitness, and modulates the organism’s variability accordingly. The structure of the internal process can be subdivided into subprocesses that monitor specific functions in an organism. The theory matches well with each intuition on a previously published list of intuited ideas about biological functions, including intuitions that have posed difficulties for other theories