Quantum-like Visual Recognition in Mental Degree 2.3
(the external everyday mind)
A sketch of a proposal, v2
Ian Thompson. June 26, 2020
Developed from “Perception in the Mental Degree 2.3”
Introduction
Here we describe the operation principles of vision in a mental degree 2.3 in ways that correspond as much as possible to those of the quantum-physics degree 3.3. The correspondences will result in both similarities and differences which need to be explained.
|
2.3: External Mind |
2.3.1 Concepts of objects and actions |
2.3.2 Thinking of possible objects |
2.3.3 Sensorimotor mind: specific seeing and acting |
|
3.3: Quantum Physics |
3.3.1 Hamiltonian: |
3.3.2 Quantum wave function |
3.3.3 Actual selections Measurements etc. |
The basic idea here is that there are wavefunctions in the mind. These however are not physical wavefunctions giving probabilities for the different outcomes of quantum propensities, but they are epistemic wavefunctions giving degrees of belief of specific visual contents. They thus give knowledge probabilities in the same manner as Bayesian inference methods. We will see some differences from Bayesian methods once we allow some non-commuting operators (a well-known feature of ‘Generalized Quantum Theory’ (Basieva, 2016)).
This wavefunction or field in the mind is thus not in the brain or a property of neural events. It is in fact a form of some mental propensity such as the love or desire for seeing. Forms of such a love or desire form their own discrete degree that is distinct from the brain, but the forms are still closely coupled to brain activity by the principles of influx and selection. The mind produces influx into the brain that sustains and creates neural activities there, and the specific resulting neural events (with further inputs from the body and its senses) selects further mental propensities from the initially available alternatives. The fields in the mind are not in physical space but are in their own space for possible actions.
I am going assume a specific mechanism for how the senses create the first sensory field by means of inputs via the visual cortex in the brain. It is described in Appendix A. My main focus now is how, given this ‘sensory sheet’, animals (from insects to humans) are able to recognize objects in 3D space and their actions and possible actions (affordances).
It is the process of recognizing that we need to understand. The ability to recognize an object still functions if the object is moved around, or rotated, some of many possible transformations such as
Geometric: translate, rotate, dilate, accelerate, spin,
(but not up-down reflections)
Illumination: light intensity, light color, shadowing, occlusions.
Self-generated: eye saccades, moving head, blinking, rotating body,
walking, etc.
Computer vision programs have managed to produce some of these functions, and that might suggest that neural systems in the brain might also succeed. However, the simple invariance of object recognition with respect to rotations, inflations and translations requires convolutional integrals that are not available to neural networks without much more interconnection than is in the brain. The speed of animal object recognition is also a puzzle, given the millisecond time scales of neural propagations (compared to nanoseconds for computers). This article proposes to see whether an explicitly mental scheme could accomplish object recognition on the needed time scale and linked with a plausible complexity of the neural systems in the brain. To guide our theorizing, we look for a scheme using principles corresponding to quantum mechanics with wave-functions, operators (continuous, and projections), superpositions, and probabilities. Such a quantum dynamics has been called Generalized Quantum Theory by Atmanspacher (2006), Filk (2011) and others, though I am treating it not just as a model, but realistically as existing in some mental space.
Mathematical notation and interpretation
The
basic idea of using quantum mechanics as a basis for describing seeing and
beliefs in a mind, is to use a ‘wave function’ or ‘state’ 
to describe the degree of some belief. More
specifically, wave functions are always a function of some coordinates as 
, such that the degree of believing that the
configuration 
is true or is existing, is 
. That is the square modulus of the wave
function, which allows that values of itself may be real positive, real positive or
negative, or complex-valued. In quantum physics 
gives a probability of some events, but here
gives a degree of belief. The number and nature of the coordinates 
need not be fixed, so they will depend on the
complexity of whatever the belief is about. The total degree of belief may be
an integral over all the coordinates of the degree of belief 
. If the space 
of coordinates is mutually exclusive and
complete, then holding a belief about the true configuration should satisfy the
normalization condition
for
corresponds to certainty. An integral of 
corresponds to ignorance, from 
everywhere: a lack of belief altogether about
what is true in the space 
Another kind of belief, slightly above
ignorance, is that all places in are equally likely. This would correspond to
small but constant values everywhere in , such that the integral was still unity rather
than 0.
Sketch of a Method
We
begin by taking the wave function 
to describe the epistemic state of a mind at any
specific time. If there is no previous knowledge of its visual surroundings,
then it starts, when the eyes are opened, to have the value 
, where 
is the knowledge contained in the two-degree ‘sensory
sheet’ that is produced by mental interaction with the visual cortex as
described in Appendix A. The beliefs conveyed by this sensory sheet have
coordinates 
, where 
is the color index R,G or B, the angle 
is the horizontal pan angle 
for humans), and 
is the vertical angle 
. In this method we assume this 
is given and try to determine how 3D objects are
recognized using that information.
Our task, therefore, is to find a fast and plausible method for finding patterns in the sensory sheet that can be recognized as ‘objects’ such 2D shapes, 3D objects, or as 4D (3D+time) processes and affordances. There are an enormously large number of such objects, and for each object there are a great many various translation, dilation and rotation (etc) operations by means of which every recognizable object may appear in the visual field. Some of those operations are necessary just for the eye, head and bodily movements that humans themselves initiate, but do not initially change the location of objects in the room that have been recognized. And objects seem to be recognized once they (or something similar) has appeared in past experience, even if the prior expectation of such objects are very small or practically zero. The reliability of the method does have to be 100%, as witnessed by ambiguities, misunderstandings, and known visual paradoxes. It is often capable of being distracted, as witnessed by ‘gorilla in the room’ experiments.
In
physical quantum mechanics, the final mechanism of observations is the random
selection of quantum alternatives 
. . The result 
of such selections comes back into the
mathematics as a projection operator 
, so that the initial wave function is changed as
for constant 
which is the degree of overlap between 
and . The constant 
has the value needed to normalize the new to unity. We here expect something similar in
mental quantum mechanics, whereby the mental state is also changed by a projection operation when
something like a is observed in the sensory sheet . Indeed such seems plausible, since is now purely and that should be the result of seeing the
object 
. However it must be more complicated than this.
For multiple objects can be seen, and that would not be permitted by the above
projection operation if the different have no overlaps with each other: 
. We rather believe that seeing successive
objects increments our visual knowledge, not just changing it always to
the most recent object seen. Furthermore, each new object seen has its own set
of dimensions for rotation and translation: the whole mind is not rotated when
imagining a new orientation of an object.
I
therefore suggest a new kind of ‘projection operator’ appropriate for mental
recognitions. When an object is recognized, this new operator adds a new
component (with its new dimensions) to the main mental state . To do this we need a quantum formalism allowing
for changing numbers of objects. The ‘creation operators’ 
of field theory are what we need. Using them, we
can theorize that when a new object is recognized during a visual fixation, the
epistemic state 
of the mind is incremented as
This
is, therefore, to define new projection operators like 
.
Such
a ‘fixation equation’ is however still not quite right for vision. By the above
equation, the projection operator 
for producing knowledge state only functions when that knowledge is already
present (to some non-zero extent) in the initial state of . That is because it only has an effect if the
overlap 
. But it is not the final knowledge which is in initially, only the appearances of objects from
the sensory sheet . It is those appearances which should be sought
in the initial . And the appearance of an object depends on bodily translations, rotations, etc.
Let
us define, therefore, for each object its appearance 
, given a specific translation vector 
and a rotation vector 
. (By using 4-dimensional vectors, time shifts
can be included in , and with quaternions scale changes can be
included in .) The recognition operator should now be
something like 
. This could in the fixation equation as
The
recognition now correctly depends on the similarity of visual appearances
according to the overlap integral 
for the visual sheet component . However, we have not yet explained what
particular translations or rotations enter into this equation. Recognition seems to
occur for any translation or rotation (within some limits). How? Let us
try to make an operator with a superposition of all possible rotations
and translations, such as
This can be rewritten so that projection operator appears in the first part of the second term:
This
operator effectively broadcasts the knowledge 
of object to all possible translations and rotations (restricted
by the limits of the two integrals, not yet specified). Then, whenever in a
fixation one translation and rotation of the object produces an appearance that
matches some part of the visual field, then the above ‘composite projection
operator’ is enacted to produce new knowledge of the object in the sensory
mind.
(more details to come).
Appendix A: Producing the Sensory Field
A scheme for how the visual field 
in the sensory or corporeal mind could arise from a scheme
of influx.
This scheme requires
1. that whenever any influx occurs, the upper source degree gains some awareness of how successful that influx was in achieving the desire that produced the influx.
2. So: the sensory mind starts of as a combination of all colors red, green, blue (RGB), as in white light from which all can be produced by modifications.
3. the sensory mind generates influx into the visual system (e.g. visual cortex) for each of the 3 colors: R, G and B.
4. the visual cortex accepts that influx according to its input from the color-sensitive cones in the retina. If red is being viewed, then influx of the R-kind is more successful, and so on.
5. So the sensory spiritual gets a lot of information about what combinations of R-influx, G-influx, and B-influx are successful, everywhere in the visual field to which attention is directed.
6.
From that information of various
'success rates', the sensory spiritual generates in itself a mental image of
the visual field as a function 
,
where 
is
the color index R,G or B, the angle 
is
the horizontal pan angle 
for
humans), and 
is
the vertical angle 
.