In what follows we consider the affairs of a single layer of our LWS.
Introductory remarks
We are attempting to define the organisation of LWS data, that is to say the contents of consciousness, in terms of the values of the cells of its layers. We want the data content to be visible in that way. We call that part of the data the explicit data.
But it is quite possible that it will prove more convenient to express some of that data content in the activation processes to be defined on LWS. Or put another way, we have implicit data content in the activation processes defined by our compiler on the explicit data. The compiler might know everything, but it might be neither easy nor necessary to write all of that data in a rather static way to the LWS.
We hope that this will be the exception rather than the rule. We are going to make as much data explicit as possible. Notwithstanding, the hypothesis is that the explicit data, the implicit data and the activation processes in which these last are embedded amount to consciousness.
We are using rules to define the things in our LWS world, rules which we hope are consistent but which are probably not complete. And whether they are or not, the compiler may work in mysterious ways, not applying the rules in a mathematically rigorous way at all, if indeed it uses them in a recognisable way at all. All that is necessary is that it works with the same things that come with, that arise from the rules. Furthermore, it just does the best it can in the time available and it will, from time to time, make mistakes.
Our rules will include dealing with the boundaries of our LWS world, the boundaries of our layers. It is not clear that the brain will work with boundaries in the same way – but we are punting on it needing to do something vaguely equivalent. So long as it works in surfaces rather than in volumes – and we believe that the brain does work in surfaces (and with at least some of the images on those surfaces being recognisable) rather than in volumes, in sheets of neurons rather than spheres of neurons – there is going to need to be some trickery to move from an infinite three or four dimensional real world to a finite two and a bit dimensional brain world.
In the same spirit, we have rules dealing with corners in connected sequences of cells in the square arrays of same which are the layers of LWS. Again, the brain may well do things differently.
Foundations
At reference 1 we talked of rules. Here we attempt a complete set of definitions and rules about what goes on within a layer, in short in the numbered clauses which follow. Goings on between layers will be considered in a paper to follow.
The organisation of a layer into parts and layer objects is largely determined by its high value cells, with some support from the low value cells. But important information is carried by the texture of the interiors of those parts, information which we do not address in this paper.
In illustrating the clauses which follow, we use a red surround for the layer, a surround which marks the boundary of the layer for the purposes of illustration, but is not, itself, part of the layer. In the sense of the order of reference 1, the surround can be thought of as being in front of everything else.
By convention, we use green for background, pink for foreground, blue for high value cells and yellow for low value cells.
Note that we show the surround as a rectangle, although layers are, in fact, square. And that we do not use the otherwise suitable word ‘frame’ as it is used in another sense at reference 2.
In the course of defining layer objects and parts in the clauses which follow, we introduce the important concepts of adjacent, connected, region, bracket and boundary.
- A layer is a large square array of cells, millions of them altogether. Cells take non-negative integer values. There is a low value, probably zero, and a high value, probably twenty or less.
- Two distinct cells are adjacent if either they are on the same column and adjacent rows or they are on the same row and adjacent columns. That is to say that they are touch horizontally or vertically – with diagonally not counting.
- A set of cells S connects the cells A and B if A and B both belong to S and if one can move from A to B by taking a series of horizontal or vertical, one cell steps without leaving S. That is to say, successive pairs on such a walk are adjacent. Connection is trivially symmetric, and clearly transitive in that if A and B are connected and B and C are connected, then A and C are connected. We say that a set S is connected if any two members are connected.
- A regional cell is a cell which takes neither the low value or the high value, but something in-between.
- A region is a maximal connected set of regional cells, bounded by some combination of high value cells, low value cells and the boundary of the layer. Such a set may include both small and large holes. A small hole may be no more than an isolated, high value cell – with such cells probably having a role in the texture mentioned above and which are discussed in the second half of reference 1.
- A region is the interior of a part of a layer object, including here the special objects the foreground and background, dealt with below.
- A region, and in consequence a part, without any holes, is called simple.
- We use brackets to define the relations between neighbouring parts.
- A bracket is a connected sequence of cells, often just three cells, often either a simple horizontal or vertical line, with the following properties. The first cell is in one region and the last cell is in another. The middle part of the sequence is either all blue, high value cells, in which case the bracket is symmetric and is called a blue bracket, or one or more yellow, low value cells is followed by one or more blue, high value cells, in which case the bracket is not symmetric and is called a yellow bracket.
- Parts which can be connected by a short, straight blue bracket are called adjacent. We might go as far as to say exactly three, the minimum value.
- Two distinct parts which are not part of either the background or the foreground, belong to the same layer object if their interiors, their regions, can be connected by a blue bracket.
- If the interiors of two distinct parts which are not part of either the background or the foreground, are connected by a yellow bracket, then the layer objects holding the two parts are distinct and the layer object at the yellow end of the bracket is said to be behind the layer object at the blue end. This defines a partial order on our layer objects.
- In this, we suppose that any two layer objects cannot be connected by both blue and yellow brackets and that we do not have it that one layer object is both behind and in front of another layer object. That said, sometimes the senses or the compiler will make mistakes, with the resultant subjective experience being confusing.
- A layer object is a maximal collection of adjacent parts. A layer object is deemed to be the union of its constituent regions plus its boundary.
- We define the boundary of a layer object iteratively. First we take all the high value cells which are adjacent to a regional cell of one of its constituent parts, but excluding high value cells in holes in the regions. Second, we add any further high value cells which can be reached from those we already have, making a maximal set. We require this set to be complete, for the corners to be filled in. Third we add any low value cells which are adjacent to a regional cell of one of its constituent parts, and again excluding low value cells in holes in the regions. Fourth, we add any further low value cells which can be reached from those low value cells we already have, making a maximal set. We require this set to be complete and we call it the boundary of the layer object.
- The boundaries of distinct layer objects are disjoint.
- While the boundary of a part cannot be not well defined in this way, as much of the boundary is apt to be shared with other parts. We do not have it that a layer object is the union of its disjoint parts.
- In terms of our rectangular array of cells, the boundary cells are the cells of the first and last rows and the first and last columns. Otherwise the top and bottom rows and the leftmost and rightmost columns
- Exceptionally, any region which contains boundary cells from the top row of the layer is a part of the special layer object called the background, special in the sense that it may be made up of what might otherwise be thought of several layer objects.
- A region which does not contain boundary cells from the top row but which does contains boundary cells from the bottom row of the layer is part of the special layer object called the foreground, special in the same sense.
- Any other region which contains boundary cells is part of the background.
- The foreground and the background are behind all the other layer objects. The foreground is deemed to be in front of the background.
- Some layers will not have backgrounds and some layers will not have foregrounds. Some will have neither.
- A non-trivial layer is thus mainly made up of layer objects, foreground and background. There will be some left over cells, not part of any of the foregoing. Some of them will be functional, some not.
- Non-trivial is not altogether fair. A layer made up entirely of background may still have interesting texture. Such a layer might be what we first see when we open our eyes after waking, what we see before we start parsing the layer into parts and layer objects.
One important consequence of all this is that if we spread out from an interior cell of a layer object, we know when we have reached its boundary. Simple, local properties will be enough, and there is no need to look at the big picture. So to that extent, a good fit with how the activation of neurons might spread out over a layer object.
Illustrations
We now illustrate the workings of these rules with snips from Excel. Snips with only a small number of cells – compared with the number on a real layer – but hopefully enough for illustrative purposes.
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| Figure 1 |
In the top middle of the snip above, we show two pairs of adjacent blue cells. Below that a pair of blue cells which are not adjacent, and below that a group of green cells none of which are adjacent to each other.
On the left, we show a connected brown region, a region with a small hole.
On the right, we show a grey path connecting two green cells, superimposed on a copy of that same brown region.
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| Figure 2 |
Here we show on the left a maximal brown region, bordered by a stretch of blue above and a stretch of yellow below. Not strictly necessary, but we fill in the corners of the borders, for example cells 28J and 28U. While the brown region on the right is not maximal because the cells in the holes are regional cells.
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| Figure 3 |
Here we show a single layer object with four parts: brown, green, pink and grey. The layer object is deemed to include those four interiors, plus the blue boundaries. internal and external, plus the yellow boundary. Yellow boundaries are mostly external.
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| Figure 4 |
Here the brown object now includes a hole, a hole which in this case is occupied by a fourth part for the layer object as a whole.
At one time we thought of making a special use of containing relations of this sort – brown containing green – and we may well do again.
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| Figure 5 |
Here the brown part has swallowed up most of the pink part in order to make room for a larger hole. However, in this case the hole is a purple, a one part layer object in its own right, isolated from the brown part by its yellow fringe. A fringe giving rise to yellow brackets.
This purple object is behind the object of which the brown region is part.
Sometimes, we will want to link this purple part with something else, perhaps the background.
Perhaps one can see the background through the hole in the brown region. Such linking will be accomplished with column objects, to be brought back to life in a paper to come.
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| Figure 6 |
Here we show three layer objects, bottom left with one part, below that top left with two parts. And this last above that right, also with one part.
We show three brackets. A yellow bracket left, a blue bracket top middle and another yellow bracket right. Notice that a blue bracket will often have just three cells, while a yellow bracket must have at least four.
It may be that the amount of yellow reflects, in some way, how far one object is behind another.
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| Figure 7 |
Here we have changed things a little, and now show just two objects, both above and below each other, which is not allowed, although it is not that difficult to devise improbable things which might lend themselves to this sort of treatment. Nevertheless, the subjective experience might well be confused.
The bottom left part and the right hand part are parts of the same layer object by virtue of the blue bracket shown in dashed dark, across a slightly artificial bridge connecting the two halves, but a bridge which is within the rules nonetheless.
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| Figure 8 |
Here, we start with a two part layer object left and go through the process of defining its boundary. First, in the middle, we have all the high value cells which are adjacent to an interior cell. Second, on the right, we add in all the high value cells which can be reached from the ones that we already have. As required, the resultant set is complete, the corners have all been filled in.
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| Figure 9 |
Third we add in the low value cells which are adjacent to an interior cell. Fourth we add in any further low value calls which can be reached from those we already have. Again, as required, the result is complete. We show the completed boundary in dark grey on the right. Corners all filled in, as required.
We allow curious growths, both interior and exterior. These may turn out to have some function. We had, for example, thought of using such shapes as layer object identifiers or qualifiers.
Conclusions
We have set down some rules for layers and illustrated quite a lot of them. In episode two, we will turn to what happens when things meet the surround. So far, everything has been well inside the layer surround.
Abbreviations
LWS – local workspace. The proposed vehicle for consciousness. Named for contrast with the GWS – the global workspace – of Baars and his colleagues.
References
Reference 1: http://psmv3.blogspot.co.uk/2017/06/on-elements.html.
Reference 2: http://psmv3.blogspot.co.uk/2017/06/on-scenes.html.
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