Basics
As before, we italicise words which have a special meaning the first time that they are used.
We still have our base data structure of a small number, say around 10, of layers defined on a large square array, some thousands of points in each direction. Following Excel, we call an individual point a cell, a cell which takes a small non-negative integer value, say less than 20.
We consider the set R of rectangles on a layer. We exclude the trivial rectangles, made up of just one cell, on the grounds that they are apt to be confused with noise. But some of our rectangles will have one row and several columns, and some will have several rows and one column. While most will have several rows and several columns.
A rectangle has a perimeter. In the case of small rectangles, the perimeter is the rectangle, but large rectangles have an interior. The value of the interior is the sum of the constituent values, the average is the nearest integer of the average value and the product is the product of the non-zero values. We will make some use of the same three functions on the values of the cells of the perimeters.
Patterns
We have a relation P defined on the set R, where P(r) is true if and only if r is a pattern. Amongst others, this relation has the property that if c is a cell there is at most one rectangle r containing c such that P(r) is true. We use the device of having this relation because we suspect that patterns are not well defined by the rules which follow and we have to allow some compilation process to make a choice, to build the relation P which can support subsequent processing.
If a and b are members of R, we say that a is adjacent to b if and only if a and b have no cells in common but they do have perimeter cells which are next to each other. Next to each other in the sense that the cell a=(x,y) is next to (x+1,y) and to (x,y+1) but not to the diagonal cell (x+1,y+1), and certainly not to cells even further away. This relation is symmetric in that if a is adjacent to b, then b is adjacent to a, but it is neither reflexive nor transitive. A rectangle is not adjacent to itself (reflexive), and it does not follow from the facts that rectangle X is adjacent to Y and that Y is adjacent to Z, that X is adjacent to Z (transitive). It might or might not be.
If a is a member of R then we say that a has a pattern if there is a member b of R such that a is adjacent to b; a is the same size, shape and orientation as b; and, takes the same values as b in its perimeter. This device allows us to put structure on our layer without needing external definition. And it is fairly unlikely that repetition of this sort will arise from noise.
If the rectangle a has a pattern, then the layer object A on a is defined by starting with a and adding adjacent rectangles with the same pattern. Collectively the rectangles of a layer object are known as its elements. Layer objects may include holes. See illustration 1 below.
Note that while the perimeters of al the elements of a layer object are the same, the interiors need not be. The interiors may contain plenty of signal, over and above that carried by the choice of pattern and the arrangement of the elements of the object in space.
Any one cell can only participate in one pattern and so the layer objects on any one layer are disjoint.
But, by extension, we say that two layer objects are adjacent if there is at least one element of one which is adjacent to an element of the other.
The failure of definition alluded to above can be illustrated by the extreme example of every cell on a layer takes the same value. On the rules given above, one could put patterns all over the place. See illustration 3 below.
The onesize of A is the number of cells in A and is always greater than or equal to 4, usually more.
The twosize of A is the number of its elements and is always greater than or equal to 2.
It may turn out that a pattern functions, in some sense, like a common noun, such as colour, ear or bridge. All the layer objects built on any given pattern would then have something in common, if not a common noun. Alternatively, patterns might local, just a device to delineate layer objects without, in themselves, carrying any more information. Dynamic allocation of pattern to object to suit the needs of the moment. That said, it would probably be helpful if all the objects of any one sort in any one frame of consciousness were defined using the same pattern and we suppose this, at least, to be the case in what follows.
Linking objects on the same layer
Where one layer object is adjacent to another, those two objects are deemed to be parts of some larger whole. Note that, by definition, two such objects cannot be defined on the same pattern – although we do not exclude pattern A then pattern B then pattern A. Such an object might turn out to be useful for something. So we might have a body made up of arms, legs, trunk and head. Perhaps four patterns – or six if we distinguish right and left. Part of the idea here is that activation can easily slide from one part to another.
Where two layer objects A and B are defined on the same pattern in the same layer, they are said to be layer peers. Two examples of the same sort of thing in roughly the same time and space.
Straying outside our single layer, A and B are global peers or just peers if they are layer objects defined on the same pattern, without regard as to which layer.
Linking objects on different layers
In what follows we mainly consider objects on adjacent layers. But most of it does extend further.
Suppose that A is a layer object on one layer and B is an object on the other, defined on the same pattern and sharing at least one cell position with A. Then A and B are in some sense the same object, with the two layers providing different views of it, different views which might be active at more or less the same time. It is quite possible for objects on more than two layers to be linked in this way.
Slightly more complicated is the case that A is in two parts, a big A1 and a little A2. Then B on another layer might link to A2, with B perhaps providing non-visual information about A1 – with the point being that B does not have to be defined on the same pattern as the big part A1 of A.
We call the result of extending a layer object to any other parts there may be and to other layers an extended object.
Different again is the case that A is a layer object on one layer and B is an object on the other, defined on different patterns and sharing at least one cell position. Then A and B are not the same object but they do share time and space.
In the hopefully unusual case that A and B are defined on the same pattern, occupy much the same position but are different objects, we simply make sure there is a spare layer between them which will stop any link being made by default.
From the point of view of visual field of the conscious host, at least one anything like ourselves, there will be a point of view and one of these objects will be in front of the other. So, noting that the layers are ordered by their frequency band, we have a natural order of the layers from high to low. Our convention here is that high layer objects may occlude low layer objects. Note also that we will deal with the question of the modality of layer objects in posts to come. In particular, which layer objects, subject to consideration of occlusion, get into the visual field.
Two and a half dimensions
We have started our definition of objects within a single two dimensional layer, with the layer being the strong organisational feature in our world.
An alternative would have been to treat our data structure more like an ordinary three dimensional array and allow adjacency in three rather than two dimensions, with our basic objects being blobs in three dimensions rather than in two dimensions. We have chosen not to do this, believing our world to be essentially two dimensional, with a few third dimension add-ins. One relevant feature of this third dimension being that it is a very small dimension, with just 10 or so cells, unlike the thousands of cells of the other two.
A minus point for layers is that they are a limited resource, limiting, for example, the depth of occlusion and data hierarchies.
A small plus point for the alternative would have been that an object could exist as a single pattern, a single element on a layer, not allowed by the rules we have set out above.
Special patterns
We have two special categories of pattern. In the first, the perimeter is all low values and we have the low pattern, used to describe a background. In the second, the perimeter is all high values and we have the high pattern, used to describe edges and pain.
Other patterns are in between and might be ordered either by their total value or their average value, both vaguely intensity or salience.
In any one layer, some of the cells will be space, not occupied by patterns at all. The only information available is the value of the cells. Almost the void.
While some of the layer will be background, occupied by objects defined on low patterns. This gives us a bit more structure, a bit more signal.
Large layer objects defined on high patterns with high valued interiors will be pain.
Both edges and pain will be further described in posts to come.
Illustration 1
In the illustrations that follow, click to enlarge as necessary.
The illustration shows the contents of a single layer.
All the rectangles have interiors, albeit a lot of these interiors being just a single cell.
It uses three patterns: the blue, five by five; the brown, three by three; and, the yellow, also three by three. Elements of these patterns are arranged into 11 layer objects, 2 of which are, for example, built on the blue pattern, and the larger of which is made up of 25 elements. Layer objects may contain holes, or more picturesquely, lakes and fiords.
As noted above, where one layer object is adjacent to another, meets another on a edge rather than at a point, those two objects are deemed to be part of some larger whole. The top three yellow objects are adjacent to the large blue object, and so make a larger whole in this sense.
While the top two brown objects are not adjacent to the large blue object and so not part of it; rather, they are independent objects in their own right.
Nor is the yellow object, second left, around row 130, adjacent to the large blue object.
It is quite possible that some of the small objects are representatives of extended objects. They are small and not very informative in this view, but might be quite different in another.
But as far as this layer is concerned, there is just one extended object, made up of the large blue object and the top three yellow objects.
Illustration 2
In the illustration above we plot the number of elements, as a percentage of the total, by layer, of a number of rather extravagantly extended objects, one extended object to each plot. For these purposes we have supposed there to be ten layers.
Except that A is a layer object which has not been extended and F is invalid as it has become disconnected. B exists on two adjacent layers, the first layer being a little larger than the second. C through E start to stretch things out, ending up with the invalid F.
Illustration 3
Here we have imposed some of the patterns from illustration 1 onto a field of sevens. The patterns break none of our rules, but they are not, nevertheless really there.
And a reminder that the task we have set ourselves is to conjure meaning out of the void. Our data structure needs to be interesting of itself, to be self contained and we should not need to go any elsewhere else in order to create that interest. Indeed, we are not able to go elsewhere, there is nowhere else to go. See reference 1 and, more particularly, reference 2.
We associate to the way in which can impose structure onto things like floor coverings involving lots of random dots of various sizes and colour, or like clouds. As far as the first is concerned, it is often pairings of dots which are like eyes which appear first, testimony to the interest us far-seeing vertebrates have to take in each other if we are to survive and prosper.
Illustrations 4 and 5
Here we have a blue object on top of a black lined yellow object behind, on the layer below. We suppose that the patterns on which both objects are defined, the elements of both objects are the cells of the Excel worksheet from which the illustration has been taken.
One option would be to extend the yellow part of the black lined object to the upper layer, thus having the visible parts of the yellow object on the same layer as the blue object, which would simplify activation of the visible part of the scene.
One problem is that in order to do this at all, the visible yellow needs to amount to proper patterns. It would not do if the isolated pair of yellow elements middle right was actually a singleton: singletons are not the stuff of layer objects, although we could probably relax the rules on that point, given that there is a proper object underneath.
Another, more serious problem is that in order to do this neatly, all the objects need to be defined on the same rectangular grid, so that yellow elements are either entirely visible or entirely invisible.
Otherwise we get the problems illustrated below, where the patterns on which the three objects – the green, the blue and the yellow – are defined are not neatly aligned. This is not necessarily fatal if the elements, the outlined rectangles, are small relative to the objects they are defining, but certainly messier than we would have liked.
Other issues
We might decide to restrict our world of rectangles to small, square rectangles, all defined on the same grid. Substantially reducing the number of possibilities in this way has both advantages – for example in dealing with illustration 5 – and disadvantages.
We want to treat several objects as a collective. So we see all the members of the darts team and we are conscious of both some or all of the members and the team as a whole.
This object is member of that category. We might have a number of objects in the visual field and we are conscious of them all being in some category. Perhaps they are all defined using the eskimo pattern, with data about eskimos in general being stored in some object which is not visualised, does not make it to the visual field.
This object describes that object in a non-sensory way.
This object describes that object in a sensory but non-visual way.
Spatial distortions of the visual field in layers. We refer here to the distortions in the various brain mappings of the visual – and other sensory fields.
Thinking of the large amount of noise in amongst the electrical activity of the brain, it might be appropriate to allow soft pattern matching, where while we retain the insistence that two instances of a pattern must have the same shape, we might be more flexible about matching the values.
Thinking of our organisation of the world of consciousness into frames, takes and scenes (see reference 3), there might be a role for a function like ‘pop the top layer’ to move our data structure from one take to the next.
Conclusions
We have made a fresh start to the business of seeing red, hopefully putting it on a slightly firmer foundation.
References
Reference 1: http://psmv3.blogspot.co.uk/2017/03/seeing-red-rectangles.html.
Reference 2: http://psmv3.blogspot.co.uk/2017/02/restatement-of-hypothesis.html.
Reference 3: http://psmv3.blogspot.co.uk/2016/08/describing-consciousness.html.
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