One of the reasons for continuing conceptual development of the physical-functionalist NRU (neuron-replication-unit) approach, despite the perceived advantages of the informational-functionalist approach, was in the event that computational emulation would either fail to successfully replicate a given physical process (thus a functional-modality concern) or fail to successfully maintain subjective-continuity (thus an operational-modality concern), most likely due to a difference in the physical operation of possible computational substrates compared to the physical operation of the brain (see Chapter 2). In regard to functionality, we might fail to computationally replicate (whether in simulation or emulation) a relevant physical process for reasons other than vitalism. We could fail to understand the underlying principles governing it, or we might understand its underlying principles so as to predictively model it yet still fail to understand how it affects the other processes occurring in the neuron—for instance if we used different modeling techniques or general model types to model each component, effectively being able to predictively model each individually while being unable to model how they affect eachother due to model untranslatability. Neither of these cases precludes the aspect in question from being completely material, and thus completely potentially explicable using the normative techniques we use to predictively model the universe. The physical-functionalist approach attempted to solve these potential problems through several NRU sub-classes, some of which kept certain biological features and functionally replaced certain others, and others that kept alternate biological features and likewise functionally replicated alternate biological features. These can be considered as varieties of biological-nonbiological NRU hybrids that functionally integrate those biological features into their own, predominantly non-biological operation, as they exist in the biological nervous system, which we failed to functionally or operationally replicate successfully.
The subjective-continuity problem, however, is not concerned with whether something can be functionally replicated but with whether it can be functionally replicated while still retaining subjective-continuity throughout the procedure.
This category of possible basis for subjective-continuity has stark similarities to the possible problematic aspects (i.e., operational discontinuity) of current computational paradigms and substrates discussed in Chapter 2. In that case it was postulated that discontinuity occurred as a result of taking something normally operationally continuous and making it discontinuous: namely, (a) the fact that current computational paradigms are serial (whereas the brain has massive parallelism), which may cause components to only be instantiated one at a time, and (b) the fact that the resting membrane potential of biological neurons makes them procedurally continuous—that is, when in a resting or inoperative state they are still both on and undergoing minor fluctuations—whereas normative logic gates both do not produce a steady voltage when in an inoperative state (thus being procedurally discontinuous) and do not undergo minor fluctuations within such a steady-state voltage (or, more generally, a continuous signal) while in an inoperative state. I had a similar fear in regard to some mathematical and computational models as I understood them in 2009: what if we were taking what was a continuous process in its biological environment, and—by using multiple elements or procedural (e.g., computational, algorithmic) steps to replicate what would have been one element or procedural step in the original—effectively making it discontinuous by introducing additional intermediate steps? Or would we simply be introducing a number of continuous steps—that is, if each element or procedural step were operationally continuous in the same way that the components of a neuron are, would it then preserve operational continuity nonetheless?
This led to my attempting to develop a modeling approach aiming to retain the same operational continuity as exists in biological neurons, which I will call the relationally isomorphic mathematical model. The biophysical processes comprising an existing neuron are what implements computation; by using biophysical-mathematical models as our modeling approach, we might be introducing an element of discontinuity by mathematically modeling the physical processes giving rise to a computation/calculation, rather than modeling the computation/calculation directly. It might be the difference between modeling a given program, and the physical processes comprising the logic elements giving rise to the program. Thus, my novel approach during this period was to explore ways to model this directly.
Rather than using a host of mathematical operations to model the physical components that themselves give rise to a different type of mathematics, we instead use a modeling approach that maintains a 1-to-1 element or procedural-step correspondence with the level-of-scale that embodies the salient (i.e., aimed-for) computation. My attempts at developing this produced the following approach, though I lack the pure mathematical and computer-science background to judge its true accuracy or utility. The components, their properties, and the inputs used for a given model (at whatever scale) are substituted by numerical values, the magnitude of which preserves the relationships (e.g., ratio relationships) between components/properties and inputs, and by mathematical operations which preserve the relationships exhibited by their interaction. For instance: if the interaction between a given component/property and a given input produces an emergent inhibitory effect biologically, then one would combine them to get their difference or their factors, respectively, depending on whether they exemplify a linear or nonlinear relationship. If the component/property and the input combine to produce emergently excitatory effects biologically, one would combine them to get their sum or products, respectively, depending on whether they increased excitation in a linear or nonlinear manner.
In an example from my notes, I tried to formulate how a chemical synapse could be modeled in this way. Neurotransmitters are given analog values such as positive or negative numbers, the sign of which (i.e., positive or negative) depends on whether it is excitatory or inhibitory and the magnitude of which depends on how much more excitatory/inhibitory it is than other neurotransmitters, all in reference to a baseline value (perhaps 0 if neutral or neither excitatory nor inhibitory; however, we may need to make this a negative value, considering that the neuron’s resting membrane-potential is electrically negative, and not electrochemically neutral). If they are neurotransmitter clusters, then one value would represent the neurotransmitter and another value its quantity, the sum or product of which represents the cluster. If the neurotransmitter clusters consist of multiple neurotransmitters, then two values (i.e., type and quantity) would be used for each, and the product of all values represents the cluster. Each summative-product value is given a second vector value separate from its state-value, representing its direction and speed in the 3D space of the synaptic junction. Thus by summing the products of all, the numerical value should contain the relational operations each value corresponds to, and the interactions and relationships represented by the first- and second-order products. The key lies in determining whether the relationship between two elements (e.g., two neurotransmitters) is linear (in which case they are summed), or nonlinear (in which case they are combined to produce a product), and whether it is a positive or negative relationship—in which case their factor, rather than their difference, or their product, rather than their sum, would be used. Combining the vector products would take into account how each cluster’s speed and position affects the end result, thus effectively emulating the process of diffusion across the synaptic junction. The model’s past states (which might need to be included in such a modeling methodology to account for synaptic plasticity—e.g., long-term potentiation and long-term modulation) would hypothetically be incorporated into the model via a temporal-vector value, wherein a third value (position along a temporal or “functional”/”operational” axis) is used when combining the values into a final summative product. This is similar to such modeling techniques as phase-space, which is a quantitative technique for modeling a given system’s “system-vector-states” or the functional/operational states it has the potential to possess.
How excitatory or inhibitory a given neurotransmitter is may depend upon other neurotransmitters already present in the synaptic junction; thus if the relationship between one neurotransmitter and another is not the same as that first neurotransmitter and an arbitrary third, then one cannot use static numerical values for them because the sequence in which they were released would affect how cumulatively excitatory or inhibitory a given synaptic transmission is.
A hypothetically possible case of this would be if one type of neurotransmitter can bond or react with two or more types of neurotransmitter. Let’s say that it’s more likely to bond or react with one than with the other. If the chemically less attractive (or reactive) one were released first, it would bond anyways due to the absence of the comparatively more chemically attractive one, such that if the more attractive one were released thereafter, then it wouldn’t bond because the original one would have already bonded with the chemically less attractive one.
If a given neurotransmitter’s numerical value or weighting is determined by its relation to other neurotransmitters (i.e., if one is excitatory, and another is twice as excitatory, then if the first was 1.5, the second would be 3—assuming a linear relationship), and a given neurotransmitter does prove to have a different relationship to one neurotransmitter than it does another, then we cannot use a single value for it. Thus we might not be able to configure it such that the normative mathematical operations follow naturally from each other; instead, we may have to computationally model (via the [hypothetically] subjectively discontinuous method that incurs additional procedural steps) which mathematical operations to perform, and then perform them continuously without having to stop and compute what comes next, so as to preserve subjective-continuity.
We could also run the subjectively discontinuous model at a faster speed to account for its higher quantity of steps/operations and the need to keep up with the relationally isomorphic mathematical model, which possesses comparatively fewer procedural steps. Thus subjective-continuity could hypothetically be achieved (given the validity of the present postulated basis for subjective-continuity—operational continuity) via this method of intermittent external intervention, even if we need extra computational steps to replicate the single informational transformations and signal-combinations of the relationally isomorphic mathematical model.
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.