The paleological history of the early tetrapods is remarkably complex, unfortunately supported with incomplete fossil records, but the history that is relevant to the Organon Sutra can be summarized from a somewhat less complex perspective of the evolution which shaped the organic central nervous systems of extant species today.
The amniotic organisms which established the earliest tetrapodal beachheads on this new frontier of land, initially diversified into two distinct groups collectively called the Synapsids and the Sauropsids.
The Synapsids developed into the group Therapsida, a group with traits having, among others, limbs extending beneath the body, as opposed to the sprawling posture of reptiles. The Therapsids included the Cynodonts, a group that developed into mammals in the late Triassic period, about 225 million years ago. The Cynodonts were the only group of Therapsids to survive the pronounced Triassic-Jurassic extinction event that occurred about 201 million years ago, a period of major global ecological change which also drastically affected the diversification of the other amniote lineage.
This second branch of amniotic descendants were the Sauropsids, the “lizard faced” taxonomic clade which, throughout the Mesozoic era, produced the largest animals in the ecosphere, and from which descended the dinosaurs, about 240 million years ago. It was the dinosaurs that became the dominant terrestrial vertebrates following the Triassic-Jurassic extinction event, sharing the new ecosphere with the remaining mammals, which at this point in paleological history, were thought to occupy a primarily separate ecological niche, as insectivorous, nocturnal animals.
The neurophysiology which was bequeathed to the co-existing lineages of dinosaurs and mammals developed in a coincident fashion because of a singular biological necessity: the unique characteristics of tetrapodal locomotion demanded that the visual apparatus must now participate in the command loop for motor control. And although the optokinetic visual process which had evolved in the primordial vertebrate, with its developed interfaces between the emotive complex and primordial basal ganglia, would still be serviceable for the survival priority of detecting predators, it could not provide the needed discrimination for terrain imaging. Nature would need the newly evolving second visual process of vergence imaging to accomplish a parameterization of the visual space, providing the feed-forward control for a motive complex which now includes “egocentric” motor intentions in addition to the well-adapted stimulus-bound motoric programs.
This new vergence imaging process, introduced in the last discussion, would provide a second, additional vision “channel”, neuro-physically separate from the structures in the optic tectum that develop the optokinetic image fields, over which will comprise one component of this new “egocentric” motoric control system. As the selective pressures resulting from the survival value of the vergence imaging process evolve tetrapodal cranial structures, bringing the ocular orbits closer together, in a fashion which tended to increase the degree of binocular overlap, those adaptations would multiply the number of retinal receptive elements which could be wired for this vergence state abstraction process, abstracting larger image fields with greater detail.
But this greater detail would not be utilized for any analysis leading to visual cues in a cognitive process. Just like all of the previous iterations of photonic sensation, which primarily evolved to determine the “where” in the visual field of those sensations over the “what” that comprised their possible cognition, the newest form of vergence imaging would be developed to determine the “where” in that imagery of the visual field that will provide the feed-forward visual guidance needed for terrestrial locomotion, but in a slightly different fashion than the “where” provided by the optokinetic process. The “where” developed by the vergence imaging process would provide depth in the apparent imagery, along with its retinotopic locality, operating in a manner analogous to modern 3-D phased array radars.
In addition, this parametric range sensation would not only provide the needed signaling to implement an egocentric motoric command loop, but scaling this next rung in the ladder of dimensionality would be the critical element that Nature would need to begin building the assemblies that will divine cognition from perception imagery.
Now, the bottom-up engineer must not confuse the “depth” resolution described here, as being solely a neural calculation of the apparent divergence angle as the binocular eyes focus on imagery of varying distances from the organism. The divergence angle of the eyes at the point of focusing is merely a by-product of the actual vergence vision mechanism. To explain the vergence imaging process, let us construct an “imaginary laboratory” to use as an example of the primordial vergence imaging process. (And as a note, we will find that the lens machinery developed in the primordial optics does not participate in, or provide any distance accommodation signals in this example).
In this hypothetical laboratory setup, imagine a set of two primordial eyes, eyes whose ganglionic terminations connect to an optic tectum assembly with the circuitry described (in the last discussion) that can resolve the vergence state abstraction process, and which we can “monitor” in our laboratory setup. These eyes are set apart by a particular distance which we shall call the displacement line, and now imagine another line which bisects and is perpendicular to the displacement line between the two eyes. This perpendicular line projects out into the visual field of the eyes, and now imagine three solid spheres of an indistinct but opaque composition arranged on that perpendicular projection line, spaced equi-distantly on the projection line within the visual field, each sphere of the same size and about the same diameter as the imaginary “eyes” in our visualization.
Now, let us engage this optical machinery in our “lab”, and to begin, we will command the eyes to a divergence angle that corresponds to the closest distance, the most “cross-eyed” position that the two eyes can manage. And let us say that this initial convergence point (the point on the perpendicular projection line where the individual gaze lines of the two eyes intersect) is halfway between the displacement line of the eyes and the closest sphere. At all stages of our “experiment”, we are capable of monitoring what the optic tectum “sees”, and at this stage the bottom-up engineer might be surprised that the vergence imaging circuitry in the optic tectum does not “see” anything in its visual field.
The vergence imaging circuitry does not “see” the three spheres at this stage because, analogous to how military 3-D phased array radars operate, the vergence imaging assemblies in this vision system will not “see” anything until there is a phase correlation between coincident imagery being signaled from both eyes. And even though the ganglion cells of the left eye are signaling three spheres in the right hemisphere of that eye, and the ganglion cells of the right eye are signaling three spheres in the left hemisphere of that eye, the phase correlation neurons of the vergence imaging assemblies in the optic tectum will not “see” anything because the entirety of that ganglionic signaling is in separate retinotopic locations, and does not generate a phase coincidence state.
Now, let’s command our laboratory eyes to adjust their divergence to project a gaze intersection farther out on the perpendicular projection line, to a point which corresponds to the center placement of the closest sphere. At this point, the vergence imaging system will “see” just the one sphere, because only the signaling from that object will result in a phase coincidence state. Like an electronic signal filter rejecting frequencies outside of its pass band, the vergence imaging system will not “see” the other two spheres at this point, providing Nature with another neural systematic capable of mechanically discriminating separate objects apart from their background. Perhaps it is while watching a cat jump up onto a shelf that is twice the stature height of the cat for the first time, that one is convinced that the vergence imaging mechanism must operate as so.
This new form of discrimination between the contrast boundaries being signaled by ganglion cells of the vertebrate eyes is also a new form of temporal invariance, which could perfectly complement the topologic semantic of spatial invariance expressed in the optokinetic imaging process. Nature will find a unified vision system combining the semantics of spatial invariance with temporal invariance very useful, but these two vision systems will have to remain separate neural assemblies physiologically within the optic tectum of our primordial tetrapods, with each separate vision “channel” developing their distinct neural maps, until after the development of another very important neural structure that Nature must fully develop in order to implement the egocentric motor command system that terrestrial locomotion demands.
That next important structure is the Cerebellum, (the “Little Cerebrum”), and because of its intimate interface with the new vision system of vergence imaging, the two will evolve hand-in-hand.
The muscle groups which attend to joints in the articulated structure of Tetrapodal organisms have a kinesthetic “map”, whose dimensions are not delineated by spatial attributes as in the visual system, but by definitions of force, tension and contraction. And much like the visual system which implemented a “semantic” to maintain topologic coherence as various transformations were performed across maps in the optic tectum, the terrestrial motoric complex must implement a kinesthetic “semantic” to perform transformations across motor group maps, but with one important difference. The kinesthetic semantic implemented for motor control includes a temporal dimension, which is not a defined abstraction, but is produced mechanically by proprioceptive feedback. This temporal dimension is required because motor control must be divided into individual motor sequences (the bottom-up engineer can finally indulge hierarchical thinking here), which must be serialized creating a motor space.
And as long as the motoric complex can maintain a closed loop between the intentions of motor sequences and their serializing feedback controls, as in the stimulus-bound basal ganglia, then animal movements can remain phylogenetically straight-forward.
But in the environmentally treacherous world of terrestrial locomotion, each step requires a control input that cannot be supplied by somatosensory feedback. Movement of each limb must take into account an infinity of obstacles to programmed motor control.
All of the components of the stimulus-bound motor control system can still be retained, but the closed loop of somesthetic feedback must be opened up, to include the merger of the vergence visual maps with the kinesthetic motor space, a merger which will introduce the terrestrial organism to the Society of Sentient Creatures by creating a new component in the sequencing of motor control: the preparation of motor actions.
In a stimulus-bound motoric complex, the sequence of motor actions begins with initiation, the commencement of motor intentions that have been phylogenetically developed and are triggered by some sensate condition, and subsequently released by the basal ganglia. But the feedback which maintains the sequential flow is after the fact, maintaining motoric actions already initiated.
However, in the world of terrestrial locomotion, every step presents unique obstacles, and this variety makes it impossible for the genome to phylogenetically prepare motoric initiation programs for release by the basal structures. The preparation for each step by the tetrapod must occur in real time in a larger control loop than the stimulus-bound model, which allows for conditional parametric input to be injected into the motor sequencing prior to initiation of motoric actions. This control loop, which anticipates needed control vectoring prior to any system action is called a feed-forward control system, and the cerebellum was fashioned by Nature to perform this very capacity.
Which means that the overall task of the cerebellum is multifold. In order to create this larger feed-forward control loop, the cerebellum must merge the visual space of the vergence imaging process with the kinesthetic space of the motor system, two spaces whose dimensional metrics have very little commonality.
In an early treatment of the integrative nature of the cerebellum, Patricia S. Churchland took a very expansive perspective in her exceptional book, Neurophilosophy: Toward a unified science of the Mind/Brain. Bringing the discourse above the fray of a neuroscience trying to explain behavior as a hyper-connected mass of neurons, she engaged the idea of unifying our conceptualizations of mind and brain with an approach that was telling in many ways, and most appropriate to this discussion, in her generalization of the cerebellum. With an insightful characterization of the cerebellum as a machine specializing in tensor transformations, (an axiomatic system in which a vector state in an arbitrary space can be transformed into a vector state in a space having altogether different frames of reference), and an intuitive understanding that another requirement of the cerebellum is somewhat akin to a cultural translator, (in that different tensor matrices are required as various maps and spaces are transformed into different maps and spaces), Patricia Churchland demonstrated that the ease with which these tensor transformations neatly step around variations in the frames of references between spaces is the very embodiment of invariance.
The proprioceptive motor system, the vergence imaging system, the vestibular system, the somatosensory and auditory systems, all of the varied organic inputs to this cerebellar “United Nations”, whose cultural differences are all equalized through the cerebellums’ invocation of the unique invariants of each space, can now contribute to a singular goal which rises above the immediate frames of reference for each separate system, that of terrestrial locomotion.
Since a tensor is a generalized function for transforming vectors into other vectors, this core functionality is central to every cerebellar architecture, but an additional task of the cerebellum is the learning of novel motor programs without the time consuming process of generational experimentation required for genetic memory, and part of that learning is the identification of the specific tensor matrix parameters which accomplish the translation from a given map or space to another, a task which is governed by the frames of reference involved.
The immediate task of the cerebellum, (to orchestrate the many kinesthetic dynamics requiring that forces be applied in particular directions matched by velocity profiles over a range of movement displacements and speeds, the joint and limb trajectories that are formed and controlled from visual target information and ballistic movements and perturbations vectored by proprioceptive and somatosensory inputs), is accomplished by the specific neuroarchitecture of its morphology, which, due to a limited number of neuron specializations, has been the most studied neural organization in central nervous systems. Much like a hundred-piece orchestra, with specialized horn, wind, string and percussion sections, the medial, lateral and visuo-tactic motor systems of the primordial tetrapod must be integrated into an overall concert. In tetrapodal locomotion, the forelimbs provide stabilization and steering, while the hind limbs propel the body forward. As the alternating hind limbs apply differential torque to the dorsal vertebral column, there is a tendency for the animal to turn which must be counter-acted by the forelimbs. And terrestrial locomotion requires a continual redistribution of weight.
This immediate task of motor activity is joined with a somewhat more expansive imperative for the cerebellum to learn survival-promoting motoric programs on a significantly shorter time scale than the generational process that the genome has utilized for stimulus-bound motor programs developed for the basal ganglia.
The neurologic basis for learning by the cerebellum, from a behavioral perspective, is accomplished solely through the process of constructive repetition. This is the reason why the adolescents of many mammalian species engage in “play” on their path to maturity. (The neurophysiological basis for this learning will be outlined in a later discussion). The cerebellum functionally accomplishes this with a two-phased approach.
The first phase of cerebellar operation is the interpretation of motoric intentions, and is essentially a parallel to serial conversion process, where the cerebellum is presented with a wide parallel “word” representing the end state of a motor intention, and the cerebellum converts this parallel representation into a serial sequence of actions, with each individual action sequence representing both the direct motor commands for its execution, and by simultaneous feedback back into the cerebellum for comparison with the initial parallel command, it represents an “intermediate end state”. By serial execution of intermediate motor actions, each one triggered by the end state fed back from the preceding intermediate action, the original overall motor intention is performed through sequential decimation.
Each one of the intermediate motor sequences is actually a program developed by the repetitive execution of what was a primary motor intention that has been learned by the organism previously. The pianist first trains the fingers to strike individual keys, then once learned, the individual finger “programs” can be grouped together as a primary motor command to strike a multi-note chord.
The second phase of cerebellar operation revolves around the very processes that the neural assembly uses to accomplish tensor space translation. The degree of flexibility in cerebellar performance is a direct result of the number and variety of different modal maps and spaces that it can translate between. The auditory, visual, and somatosensory systems all project multiple maps of their prospective sensory signaling, in addition to the motoric intentions of the emotive and metabolic complexes, as part of the wide parallel “command” channel presented to the cerebellum. In humans, it is estimated that there are approximately 19 million fibers projecting to each lateral lobe of the cerebellum, so with each fiber carrying individual serial information, this parallel “command word” is wide enough to represent an astronomical permutation of command states with their motor intentions and the requisite map and space representations. The motoric complex of our primordial organism has come a long way from the primitive “steer left”, “steer right” and “steer forward” helm commands of its primal ancestors. And yet, even with an engine order telegraph having 38 million order positions, with an astronomical number of command permutations, the architecture of the cerebellum is remarkably orderly.
And this dialog could devote large numbers of discussions to this neurologic magic in the cerebellum, but the Organon Sutra must focus on the abstract nature of its activity, because the bottom-up engineer will come to understand that any artificially intelligent agent must also embody these very same abstract functionalities that Nature engineered into the cerebellum hundreds of millions of years ago.
As the closed feedback loop of stimulus-bound movements opens up to include the feed-forward guidance of vergence imagery, the end states of locomotive action which comprised the entirety of stimulus-bound motor intentions must now be translated from initial state vector trajectories which may include any number of intermediate state translation steps to finally coincide with that final end state.
It is the function of the cerebellum to choose the proper form of mapping translation at each step. Although the simultaneous task in the sequential decimation of the overall motoric intention command into intermediate steps is just as important, intermediates would not be possible if the cerebellum could not perform the proper translations at each step.
And these translations are accomplished in the cerebellum through the neurologic equivalent of tensor functions. A tensic space representation embodies the metrical relations between distinct possible positions within it, since the characteristic property of tensors is that they satisfy the principle of invariance under certain coordinate transformations.
Einstein was heavily dependent on tensor transformations in expressing his mathematical theories of relativity, because formulating the fundamental laws of physics in a tensor form ensures that they are “form-invariant”, and therefore they are objectively representing the physical reality and do not depend on an observers coordinate system.
Similarly, having the same form in different coordinate systems allows the cerebellum to seamlessly meld together the seeming disparate frames of reference between visual, haptic, and proprioceptive mapping inputs.
A tensor function translates positions (and more importantly, the 4-dimensional momentum vectors of a position) from one tensic space to another tensic space, even if, and especially if, the two spaces have differing frames of reference.
The cerebellum learns these tensor translations by establishing a parametric definition which curves the dimensional geometry of one space relative to another. This parametric “warping” is adjusted through repetition, which is why repetition is the learning modus of the cerebellum, and the essence of this parametric geometry adjustment, which is itself a linear expression, is a nonlinear relation of tensor spaces themselves.
Within a tensic space, (which when defined mathematically, is at minimum a metric, 7-dimensional definition), Euclidean distance can be defined in one of two bases. Euclidean distance can be defined implicitly, relative to the metrics of the dimensions of that space, or Euclidean distance can be defined (in tensic spaces) explicitly, relative to the points of possible existence within that space. The difference between the two bases is that the implicit definition reduces to the simple 3-dimensional distance of Euclidean space, whereas the explicit definition carries the 4-dimensional momentum component of tensic points along with it. The nonlinearity that the cerebellum exploits are translations with explicit vectors from one space to either explicit or implicit vectors in another space. The implementation of explicit definitions, with their momentum vectors, allows the cerebellum to “time-stamp” intermediate motor states and parameterize the motor space, giving the cerebellum a mechanism to sequentialize overall motor activity.
The translation of tensic spaces brings the conversation back to the vergence imaging process which began the discussion. Although much of the research on the cerebellum focuses on its functional role in directing motor activity, its true operation should be considered from the standpoint of the egocentric perspective it provides to visual input. Instead of just accepting signaling from the visual space to affect calculations in its motor space, it creates a seamless, visuo-motor space that is inclusive of the two. But to do this also requires some additional information than just the image maps developed in the optic tectum by the vergence image process.
To develop a true egocentric motoric system, the cerebellum must have a 3-D visualization for 360 degrees around the ego-center. And since even the most evolved vision systems can provide no more than about 140 degrees of vergence imagery, providing full-space sensation must be accomplished mechanically.
It is the binocular vergence that provides the mechanical support for the immediate 3-D vergence field, and conjugate eye movements not only provide a mechanism to optically track moving objects in an animals’ field of view, but to also mechanically extend the 3-D vergence field out to an additional degree of vertical as well as horizontal coverage. And finally, excursions of the head, in conjunction with neck displacements, provide the egocentric system with not only a full 3-D horizon, but something also just as significant.
The mechanical gaze angle of the eyes relative to the ego-center in the parallel “command word” sent to the cerebellum as a primary motor command acts as a form of memory for the cerebellar learning process, providing a temporal continuity with which to string together the instantaneous signaling from the immediate optical vergence process, in addition to providing a code for the 360 degree spatial location. This memory is an essential component in the cerebellums’ process of sequential decimation, providing an overall time continuity for the individual motor steps to follow. Perhaps this is why a persons’ gaze lowers when they are following a learned process that is not well practiced (such as, for many people, talking!).
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