030728 – The simplest incomplete grammar

030728 – The simplest incomplete grammar

If grammars are inherently incomplete, what is the simplest incomplete grammar?  Actually the question should be given an example based on say English of the simplest incomplete grammar.

Even if grammars are not inherently incomplete, one may argue that individuals acquire aspects of a grammar over time.  I vaguely recall that certain grammatical structures are in fact acquired at different ages as children learn languages.  Moreover, there are some built-in conflicts in the grammar of English (and probably just about any other language).  For example:

It’s me.  (Arguably based on the Norman French equivalent of modern French C’est moi).

It is I.  (Based on the rule that the verb to be takes the nominative case on both sides).

We’re truly unaccustomed to thinking about massively parallel computing.  Our approach to computing has been to create very fast single threaded processors; and as an afterthought, ordinarily to take advantage of idle time, we have introduced multi programming.  I think it is fair to say that our excursions into the realm of massively parallel computing are still in their infancy.  Without having done a careful survey of the literature, it would seem that the challenge of massively parallel computing  (at least that which would be patterned after neural structures in the mammalian brain) is to be able to handle the large number of interconnections found in the brain as well as the large number of projections from place to place.  [However, it is emphatically not the case that in the brain everything is connected directly to everything else.  It would be impractical, and it’s hard to see what it would accomplish beyond confusion.]

To hazard a gross oversimplification of the computational architecture of the brain, the brain is composed of layers of neurons, whose layers are identified by their common synaptic distance from some source of input.  Layers are stacked like layers in a cake (giving rise to “columns”, identified by their association with predecessor and postdecessor synapses.  To the extent the word “column” suggests a cylinder of roughly constant diameter, or even constant cross-section, it may be a bad choice of metaphor.  I imagine the diameter of a “column” to increase initially (as inputs pass deeper into the processor) and then to decrease (as signals that are to become outputs pass towards the effectors).  At various stages in the processing, intermediate outputs are transmitted to other areas (projections, via fiber bundles).  Depending on the stage of processing, a layer may receive synchronic input (that is, all inputs represent some class of inputs that originated at essentially the same moment in time, e.g., visual input from the retina) or, it may receive diachronic input (that is, a set of samples over time that originated at essentially the same location).  Indeed, some layers may receive both synchronic and diachronic inputs.

We don’t know much about how to think about the functions computed (computable) by such a system.  Not to mention that I don’t know much of anything about synaptic transmission.  Yeah, yeah, neurotransmitters pour into the synaptic gap.  Some of them are taken up by receptors on the axon and if enough of them arrive, the axon fires into the neuron.  But there are lots of different neurotransmitters.  Why?  How do the stellate glia affect the speed and nature of the pulses and slow potentials?  Do concentrations of neurotransmitters change globally?  Locally?

Somebody pointed out (Damasio?) that “homeostasis” is not really a good metaphor because the “set point” (my term) of the system changes depending on things.  In some cases, it’s clear what goes on: Too much water in the system?  Excrete water?  But the other side of that: Too much salt in the system?  Conserve water?  Well, yes, but what needs to happen is the triggering of an appetitive state that leads to locating a source of water (in some form, e.g., a water tap, a pond, a peach) and taking the appropriate steps to make that water internally available (e.g., get a glass, open the tap, fill the glass, drink the water; stick face in water, slurp it up; eat the peach).

At its core, this is a sort of low-level optimizer.  Based on the readings of a set of enteroceptors (sensors), create an internal state that either modifies the internal environment directly or that “motivates” (“activates”) behaviors that will indirectly modify the internal state.

It’s all very well to say that if one drips hypersaline solution into the CSF by the hypothalamus, the goat “gets thirsty and drinks lots of water,” but an awful lot has to happen on the way.

And it’s not very safe for the optimizer (governor?) to call for specific external behavior.  It can specify the goal state and monitor whether the organism is getting closer to or farther away from the goal state, but it’s not clear (with respect to thirst, say) how the information about getting closer to the goal can get to the optimizer at any time before an appropriate change in the internal environment is detected, e.g., the organism begins to ingest something that triggers the “incoming water” detectors.  Prior to that, it’s all promises.  Presumably, it goes something like this: behaviors “associated” with triggering the “incoming water” detectors are “primed”.  How?  Maybe by presentation of the feeling of thirst.  Priming of those behaviors triggers back-chained behaviors associated with the initiation of the “directly” primed behaviors.  And so on, like ripples in a pond.  The ever-widening circles of primed behaviors are looking for triggers that can be found in the current environment (more correctly, that can be found in the current internal environment as it represents the current external environment).

[Back-chaining seems related to abduction, the process of concocting hypotheses to account for observed circumstances.]

I keep coming around to this pattern matching paradigm as an explanation of all behavior.  It’s really a variation of innate releasing mechanisms and fixed action patterns.

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