The Rational Argumentator

******************************

The two approaches falling within this class considered thus far are (a) computational models that model the biophysical (e.g., electromagnetic, chemical, and kinetic) operation of the neurons—i.e., the physical processes instantiating their emergent functionality, whether at the scale of tissues, molecules and/or atoms, and anything in between—and (b) abstracted models, a term which designates anything that computationally models the neuron using the (sub-neuron but super-protein-complex) components themselves as the chosen model-scale (whereas the latter uses for its chosen model-scale the scale at which physical processes emergently instantiating those higher-level neuronal components exist, such as the membrane and individual proteins forming the transmembrane protein-complexes), regardless of whether each component is abstracted as a normative-electrical-component analogue (i.e., using circuit diagrams in place of biological schematics, like equating the lipid bilayer membrane with a capacitor connected to a variable battery) or mathematical models in which a relevant component or aspect of the neuron becomes a term (e.g., a variable or constant) in an equation.

It was during the process of trying to formulate different ways of mathematically (and otherwise computationally) modeling neurons or sub-neuron regions that I laid the conceptual embryo of the first new possible basis for subjective-continuity: the notion of operational isomorphism.

A New Approach to Subjective-Continuity Through Substrate Replacement

There are two other approaches to increasing the likelihood of subjective-continuity, each based on the presumption of two possible physical bases for discontinuity, that I explored during this period. Note that these approaches are unrelated to graduality, which has been the main determining factor impacting the likelihood of subjective-continuity considered thus far. The new approaches consist of designing the NRUs so as to retain the respective postulated physical bases for subjective-continuity that exist in the biological brain. Thus they are unrelated to increasing the efficacy of the gradual-replacement procedure itself, instead being related to the design requirements of functional-equivalents used to gradually replace the neurons that maintain immediate subjective-continuity.

Operational Isomorphism

Whereas functionality deals only with the emergent effects or end-product of a given entity or process, operationality deals with the procedural operations performed so as to give rise to those emergent effects. A mathematical model of a neuron might be highly functionally equivalent while failing to be operationally equivalent in most respects. Isomorphism can be considered a measure of “sameness”, but technically means a 1-to-1 correspondence between the elements of two sets (which would correspond with operational isomorphism) or between the sums or products of the elements of two sets (which would correspond with functional isomorphism, using the definition of functionality employed above). Thus, operational isomorphism is the degree with which the sub-components (be they material as in entities or procedural as in processes) of the two larger-scale components, or the operational modalities possessed by each respective collection of sub-components, are equivalent.

To what extent does the brain possess operational isomorphism? It seems to depend on the scale being considered. At the highest scale, different areas of the nervous system are classed as systems (as in functional taxonomies) or regions (as in anatomical taxonomies). At this level the separate regions (i.e., components of a shared scale) differ widely from one another in terms of operational-modality; they process information very differently from the way other components on the same scale process information. If this scale was chosen as the model-scale of our replication-approach and the preceding premise (that the physical basis for subjective-continuity is the degree of operational isomorphism between components at a given scale) is accepted, then we would in such a case have a high probability of replicating functionality, but a low probability of retaining subjective-continuity through gradual replacement. This would be true even if we used the degree of operational isomorphism between separate components as the only determining factor for subjective-continuity, and ignored concerns of graduality (e.g., the scale or rate—or scale-to-rate ratio—at which gradual substrate replacement occurs).

Contrast this to the molecular scale, where the operational modality of each component (being a given molecule) and the procedural rules determining the state-changes of components at this scale are highly isomorphic. The state-changes of a given molecule are determined by molecular and atomic forces. Thus if we use an informational-functionalist approach, choose a molecular scale for our model, and accept the same premises as the first example, we would have a high probability of both replicating functionality and retaining subjective-continuity through gradual replacement because the components (molecules) have a high degree of operational isomorphism.

Note that this is only a requirement for the sub-components instantiating the high-level neural regions/systems that embody our personalities and higher cognitive faculties such as the neocortex — i.e., we wouldn’t have to choose a molecular scale as our model scale (if it proved necessary for the reasons described above) for the whole brain, which would be very computationally intensive.

So at the atomic and molecular scale the brain possesses a high degree of operational isomorphism. On the scale of the individual protein complexes, which collectively form a given sub-neuronal component (e.g., ion channel), components still appear to possess a high degree of operational isomorphism because all state-changes are determined by the rules governing macroscale proteins and protein-complexes (i.e., biochemistry and particularly protein-protein interactions); by virtue of being of the same general constituents (amino acids), the factors determining state-changes at this level are shared by all components at this scale. The scale of individual neuronal components, however, seems to possess a comparatively lesser degree of operational isomorphism. Some ion channels are ligand-gated while others are voltage-gated. Thus, different aspects of physicality (i.e., molecular shape and voltage respectively) form the procedural-rules determining state-changes at this scale. Since there are now two different determining factors at this scale, its degree of operational isomorphism is comparatively less than the protein and protein-complex scale and the molecular scale, both of which appear to have only one governing procedural-rule set. The scale of individual neurons by contrast appears to possess a greater degree of operational isomorphism; every neuron fires according to its threshold value, and sums analog action-potential values into a binary output (i.e., neuron either fires or does not). All individual neurons operate in a highly isomorphic manner. Even though individual neurons of a given type are more operationally isomorphic in relation to each other than with a neuron of another type, all neurons regardless of type still act in a highly isomorphic manner. However, the scale of neuron-clusters and neural-networks, which operate and communicate according to spatiotemporal sequences of firing patterns (action-potential patterns), appears to possess a lesser degree of operational isomorphism compared to individual neurons, because different sequences of firing patterns will mean a different thing to two respective neural clusters or networks. Also note that at this scale the degree of functional isomorphism between components appears to be less than their degree of operational isomorphism—that is, the way each cluster or network operates is more similar in relation to each other than is their actual function (i.e., what they effectively do). And lastly, at the scale of high-level neural regions/systems, components (i.e., neural regions) differ significantly in morphology, in operationality, and in functionality; thus they appear to constitute the scale that possesses the least operational isomorphism.

I will now illustrate the concept of operational isomorphism using the physical-functionalist and the informational-functionalist NRU approaches, respectively, as examples. In terms of the physical-functionalist (i.e., prosthetic neuron) approach, both the passive (i.e., “direct”) and CPU-controlled sub-classes, respectively, are operationally isomorphic. An example of a physical-functionalist NRU that would not possess operational isomorphism is one that uses a passive-physicalist approach for the one type of component (e.g., voltage-gated ion channel) and a CPU-controlled/cyber-physicalist approach [see Part 4 of this series] for another type of component (e.g., ligand-gated ion channel)—on that scale the components act according to different technological and methodological infrastructures, exhibit different operational modalities, and thus appear to possess a low degree of operational isomorphism. Note that the concern is not the degree of operational isomorphism between the functional-replication units and their biological counterparts, but rather with the degree of operational isomorphism between the functional-replication units and other units on the same scale.

Another possibly relevant type of operational isomorphism is the degree of isomorphism between the individual sub-components or procedural-operations (i.e., “steps”) composing a given component, designated here as intra-operational isomorphism. While very similar to the degree of isomorphism for the scale immediately below, this differs from (i.e., is not equivalent to) such a designation in that the sub-components of a given larger component could be functionally isomorphic in relation to each other without being operationally isomorphic in relation to all other components on that scale. The passive sub-approach of the physical-functionalist approach would possess a greater degree of intra-operational isomorphism than would the CPU-controlled/cyber-physicalist sub-approach, because presumably each component would interact with the others (via physically embodied feedback) according to the same technological and methodological infrastructure—be it mechanical, electrical, chemical, or otherwise. The CPU-controlled sub-approach by contrast would possess a lesser degree of intra-operational-isomorphism, because the sensors, CPU, and the electric or electromechanical systems, respectively (the three main sub-components for each singular neuronal component—e.g., an artificial ion channel), operate according to different technological and methodological infrastructures and thus exhibit alternate operational modalities in relation to eachother.

In regard to the informational-functionalist approach, an NRU model that would be operationally isomorphic is one wherein, regardless of the scale used, the type of approach used to model a given component on that scale is as isomorphic with the ones used to model other components on the same scale as is possible. For example, if one uses a mathematical model to simulate spiking regions of the dendritic spine, then one shouldn’t use a non-mathematical (e.g., strict computational-logic) approach to model non-spiking regions of the dendritic spine. Since the number of variations to the informational-functionalist approach is greater than could exist for the physical-functionalist approach, there are more gradations to the degree of operational isomorphism. Using the exact same branches of mathematics to mathematically model the two respective components would incur a greater degree of operational isomorphism than if we used alternate mathematical techniques from different disciplines to model them. Likewise, if we used different computational approaches to model the respective components, then we would have a lesser degree of operational isomorphism. If we emulated some components while merely simulating others, we would have a lesser degree of operational isomorphism than if both were either strictly simulatory or strictly emulatory.

If this premise proves true, it suggests that when picking the scale of our replication-approach (be it physical-functionalist or informational-functionalist), we choose a scale that exhibits operational isomorphism—for example, the molecular scale rather than the scale of high-level neural-regions, and that we don’t use widely dissimilar types of modeling techniques to model one component (e.g., a molecular system) than we do for another component on the same scale.

Note that unlike operational-continuity, the degree of operational isomorphism was not an explicit concept or potential physical basis for subjective-continuity at the time of my working on immortality (i.e., this concept wasn’t yet fully fleshed out in 2010), but rather was formulated in response to going over my notes from this period so as to distill the broad developmental gestalt of my project; though it appears to be somewhat inherent (i.e., appears to be hinted at), it hasn’t been explicitized until relatively recently.

The next chapter describes the rest of my work on technological approaches to techno-immortality in 2010, focusing on a second new approach to subjective-continuity through a gradual-substrate-replacement procedure, and concluding with an overview of the ways my project differs from the other techno-immortalist projects.

Franco Cortese is an editor for Transhumanity.net, as well as one of its most frequent contributors.  He has also published articles and essays on Immortal Life and The Rational Argumentator. He contributed 4 essays and 7 debate responses to the digital anthology Human Destiny is to Eliminate Death: Essays, Rants and Arguments About Immortality.