People see objects in space as external and stationary (allocentric) [Rizzolatti et al., 1997] [Velmans, 1993]. Cerebellum and forebrain anticipate, coordinate, and compensate for movements.
Frontal-lobe topographic maps can represent egocentric space [Olson et al., 1999], with vertical, right-left, and front-back directions. Coordinate-origin egocenter is in head center, on a line passing through nosebridge. Space points have directions and distances from egocenter. All points make vector space.
As body, head, or eyes move, egocentric space moves, spatial axes move, and point coordinates and geometric figures transform linearly to new coordinate values [Shepard and Metzler, 1971]. Transformations are translation, rotation, reflection, inversion, and scaling (zooming). Motor processing uses tensor transform functions to describe changes from former to current output-vector field [Pellionisz and Llinás, 1982]. To maintain stationary allocentric space, so point coordinates do not change when body moves, visual processing must cancel egocentric spatial-axis coordinate transformations {coordinate transformation and allocentric space}. Visual processing inverts motor-system tensors to transform egocentric coordinate systems in opposite directions from body movements [Pouget and Sejnowski, 1997]. Topographic maps can describe tensors that transform from egocentric to allocentric space. Topographic maps can represent allocentric space.
example
Translating and rotating make spatial axes change direction. After movement, new axes relate to old axes by coordinate transformations. For example, two-dimensional vector (0,1) can translate on y-axis to make vector (0,0), rotate both axes to make vector (1,0), or reflect y-axis to make vector (0,-1). Coordinate transformations do not change dimension number.
stationary space
Perception typically maintains an absolute spatial reference frame. Stationary space allows optimum feature tracking during object and/or body motions. Moving reference frames make all motions three-dimensional, but stationary space makes many movements one-dimensional or two-dimensional.
Gravity exerts vertical force on feet and body. Nervous system analyzes this distributed information and defines vertical axis in space {gravity and vertical direction}.
Foot motions stop at ground. Touch and kinesthetic receptors repeatedly record this information. Nervous system analyzes this distributed information and defines a horizontal plane in space {ground and mental space}. Ground nearest to eye has sight-line perpendicular to ground. Farther-away ground points have sight-lines at smaller angles. All objects are on or vertically above ground.
Vision observes moving and stationary points in space with varying brightnesses and colors. Nervous system analyzes this information to detect perceptual invariants. For space, invariant points are stationary reference points. Invariant lines are stationary coordinate axes {invariants and coordinate axes}: vertical, horizontal right-left, and horizontal near-far. Because invariants stay constant over many situations, invariants can be grounds for meaning.
Nervous system correlates body motions and touch and kinesthetic receptors to extract reference points and three-dimensional space {motions and touches}. Repeated body movements define perception metrics. Such ratios build standard length, angle, time, and mass units that model physical-space lengths, angles, times, and masses. As body, head, and eyes move, they trace geometric structures and motions.
tracking
During body movements, neuron activations follow trajectories across topographic maps. Brain can track moving stimuli. Brain can study before and after effects by tracking stimuli.
stimuli and motions
Stimuli can trigger attention and orientation, and so body moves or turns toward or away. Different stimulus intensities cause different moving or turning rates.
distance
Because distance equals rate times time, motion provides information about distances. Brain can track locations over time. Brain can use interpolation and extrapolation.
horizontal directions and motions
Moving toward or away from stimuli maximizes visual flow and light-intensity gradient, and establishes forward-backward direction. Moving perpendicular to sight-line to stimuli minimizes visual flow and light-intensity gradient, and establishes left-right direction.
vertical direction and motion
Body raising and lowering can indicate vertical direction.
Vision topographic maps have orientation macrocolumns, which align and link orientations to detect line directions and establish all spatial directions {orientation columns and direction} [Blasdel, 1992].
As body moves in a straight line, visual flow and light-intensity gradient establish one forward point (pole). Eye to forward point defines the forward-backward spatial dimension {pole and dimension}.
Body and body parts rotate around balance or equilibrium points {rotation centers and mental space}. Kinesthetic receptors send information to brain, which defines those reference points and builds three-dimensional space.
Topographic-map series can store matrices and so represent tensors {tensors and mental space}. Motor processing uses tensor transform functions to describe changes from former to current output-vector field [Pellionisz and Llinás, 1982]. Tensors can linearly transform coordinates from one coordinate system to another. Output vectors are linear input-vector and spatial-axis-vector functions. Motor-system topographic maps send vector-field output-vector spatial pattern to motor neurons. Muscles move body, head, and eye to specific space locations, or for specific distances or times. Current output-vector field differs from preceding output-vector field by a coordinate transformation.
Topographic-map-neuron types have regular horizontal, vertical, and diagonal spacings, at different small, medium, and large distances. Neuron grids make a spatial network of nodes and links. Neuron grids allow measuring distances and angles and using coordinates. Topographic-map neuron grids have up/down, left/right, and near/far axes {topographic maps and coordinate axes}. Topographic-map spatial axes intersect to establish a coordinate origin and make a coordinate system, so points, lines, and regions have spatial coordinates.
Sensory topographic maps can have lattices of superficial pyramidal cells, whose non-myelinated non-branched axons travel horizontally 0.4 to 0.9 millimeters to synapse in clusters on next superficial pyramidal cells. The skipping pattern aids macrocolumn neuron-excitation synchronization [Calvin, 1995].
Topographic maps have neurons specific for space locations {topographic maps and distances}. Locations involve space direction and distance. If 100 neurons are for radial distance one unit, to have same visual acuity 400 neurons must be for radial distance two units. To have less acuity, 100 neurons can be for radial distance two units.
Vestibular-system saccule, utricle, and semicircular canals detect gravity, body accelerations, and head rotations. From that information, nervous system establishes vertical direction and two horizontal directions {vestibular system and direction}.
Animal eyes are right and left, not above and below, and establish a horizontal plane that visual brain regions maintain {vision and direction}. Vision processing can detect vertical lines and determine height and angle above horizontal plane. Body has right and left as well as front and back, and visual brain regions maintain right, left, front, and back in the horizontal plane.
1-Consciousness-Speculations-Space-Biology
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Date Modified: 2022.0225