Rules: supplemental

Composite objects and sequences

We have made rules about layer objects and their parts, which gives us two layers of structure. See references 2 and 3. Here we supplement those rules by adding a third layer to give us composite objects and sequences.

With activation first flowing across the part, then the layer object, then the composite object. In which the layer objects making up a composite object are not bound together as tightly as the parts of a layer object, while the parts of a layer object are not bound together as tightly as the cells of a part.

Or looking ahead, activation flowing across the parts of the sequence, from beginning to end.

Note that while the parts of layer objects in the illustrations that follow are generally shown as being something close to rectangles, there is nothing in the rules which says they should not be some other shape. In the case of visual layer objects, for example, the shape of parts will depend on how the brain has broken down the raw image on the retina, on how the brain has parsed it. We expect that parts of this sort will need relatively more blue cells for their definition than is the case here. More fiddling about.

Figure 1

In this snip we have three layer objects, say left on the top, middle in the middle and right at the bottom, with, other things being equal, activation flowing from top to bottom. In this we make use of the order on touching layer objects introduced at reference 1. We retain the convention that the high value cells are coloured blue and the low value cells, which both contribute to the definition of the layer objects and define the order on them, are coloured yellow.

The left hand object is made up of four parts (A, B, C and D), the middle and right hand objects of three each, (E, F and G) and (H, I and J). Note that this labelling with upper case letters was for convenience and has nothing to do with the data, the meaning carried by those parts.

We construe this structure as having order at the top level, at the level of the objects and as not having order at the level of the parts. Each object is just a small unordered collection of parts.

We then restrict the structure so that each of its constituent layer objects, apart from the bottom object, comes before exactly one other object. And that each of its constituent objects, apart from the top object, comes after exactly one other object. We have a chain of objects, not a network. Neither the background nor the foreground are allowed to participate.

We call a maximal structure of this sort, involving at least two layer objects, a composite object.

Noting the possibility that we might in the future find a use for the network variety, a maximal collection of layer objects linked together by order. But we do not need this for the sequences which follow.

Figure 2

We now introduce layer objects which can be considered as a sequence of parts. In the snip above of a layer object with seven simple parts, we have shown the sequence running across the page, possibly with an assumption of from left to right, but that need not be the case and such sequences can run in any direction – although it is true that horizontal and vertical are easier, as that best fits the organisation of our layers into an array of cells. In the same sort of way as I believe humans are generally best at vertical lines.

We believe that such sequences could be defined in a rigorous way, in which one rule might be that an intermediate part has exactly two neighbours and a terminal part exactly one.  Another might be that a sequence has exactly two terminal parts. inter alia, ensuring that a sequence does not come back to its beginning.

But this sequence of parts does not have a beginning or an end. There is nothing in the data to say which of the two terminal parts is the beginning and which is the end.

Figure 3

Here we combine the two devices to give us two layers of ordered structure. Three objects, with, from left to right, two , three and two parts. A slightly stronger structure than that with which we started. One in which, furthermore, the beginning is already defined, in this case the left most part. No need to do anything extra. A structure which we call a sequence.

A sequence must involve at least two layer objects.

In papers to follow we will use such sequences to link column objects together and to hold something very like simple natural language – in which the idea is that each layer object of the sequence corresponds to a phrase, with a sentence typically being made up of a number of phrases, all tied together with a verb. Something which we might write as something like:

(subject=cow verb=run across=field with=calf(her)).

Very like too, at least in its use of the equals sign, the sort of unnatural language used to write the pages you see on the internet, with the snip that follows being drawn from at random.

Figure 4

Conclusions

We have used the rules set out in reference 2 to build two new structures, the composite object and the sequence.

References

Reference 1: http://psmv3.blogspot.co.uk/2017/06/on-elements.html.

Reference 2: http://psmv3.blogspot.co.uk/2017/07/rules-episode-one.html.

Reference 3: http://psmv3.blogspot.co.uk/2017/07/rules-episode-two.html.

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