PereGaea
Laslo Godel
LISTS
The vast majority of PereGaea's inert objects are unlikely, as I said earlier, to possess convenient visual `handles' that will allow them to be Identified. Those of PereGaea's self-reproducing species that eliminate them from their surfaces will thereby improve their chances of survival. The ability to perceive objects made up of Universals would clearly become a vital counterweapon.
To show you how it might evolve, let's jump ahead a little and assume that the Dynism, even at this early stage in its evolution, has made the transition from PereGaea's Ocean to its Land. We'll also assume that located somewhere on this Land is a `rockpile' like this. As you can see, it is only slightly more Earthlike in its appearance than the segment of Ocean we saw earlier. If to some extent it looks a little `cartoonlike', that is because I have drawn it so as to reflect the eight tones and Retinal Box sizes the Dynism's visual system is limited to.
At this stage in its visual evolution, the only objects the Dynism is likely to be able to Identify in the Rockpile are the seven-pointed `flower' down near the bottom, and perhaps a few individual leaves from the Tree. Even the `simplest' objects such as the Rock in the foreground and the Boulders would be completely beyond it.
To perceive such objects, the Dynism will need to acquire a few more additions to its Visual Processor that will enable it to convert the Rockpile into stimulus `borders' as well as tones. But before we can see how these new additions work, we must first look at the most fundamental of our drawing conventions.
This allows a line of finite thickness to represent the indefinitely thin border separating a tonal stimulus either from other stimuli, or from the indefinitely large `stimulus' we describe as `background'. I too am obliged to follow this convention.
Now, if we draw two simple stimuli touching at a common point, this point as you can see resides at the center of a four-arm junction formed by the Borders of the two tonal stimuli with respect to each other, and to their mutual background.
If we then cause one stimulus to overlap the other, the junction turns into an arc Border with two T-shaped Junctions at each end. This introduces a crucial `axiom' upon which the evolution of the new Dynism's visual system wholly depends: a Border must either end in a Junction, or loop back onto itself to enclose a Tone. In other words, the arms of any Junction must eventually link either back to themselves, or to those of others via Borders.
In these two Tone drawings, the Tones may seem to `smooth' into each other with no borders at all. But this new Dynism's eye must also turn continuous tones into discreet ones - again we'll assume eight - in order to operate. The line drawings show where its eye will place the Borders that result. Even the arbitrarily square borders I've put round both drawings will I hope reinforce the point that all tones must end in a border at some point in space.
In many ways Junctions and Borders could be thought of as the inverse of Tones in that, instead of extending through visual space, they occupy the minimum possible. We will refer to all such borders and junctions collectively as `Lineals' to distinguish them from Tones.
To extract its Lineals, the Dynism scans its visual field to extract and matches its Input Patterns exactly as before. .
However, its retinal cells must now either become sensitive to borders as well as tones, or split into two, with each alternate cell specializing in one function. The details of how this genetic accident might occur and its precise outcome need not concern us here The revised Visual Processor will extract its Lineal Patterns according to the following four rules:RULE 1: A Lineal must pass through two of a cell's subcells for the entire cell to register it.
RULE 2:A Lineal must pass through at least eight cells before a pattern can be extracted.
RULE 3: A Lineal must pass through at least two of the four center cells of an array.
RULE 4: All cells registering a Lineal must join either at their vertices or their sides.
One might suppose that 9 x 9 patterns would be more appropriate in this role rather than 8 x 8 since it would allow Lineals to be centered in them. But since the Dynism will almost certainly have evolved higher-resolution patterns by now this is less important. We will continue to use 8 x 8 patterns since they will enable us to see more clearly how Lineal Patterns are extracted and matched. One problem quickly becomes apparent: How does the Dynism's eye cope with borders that coincide with those between the cells of its Retina? Two possible solutions are that a scanning box moves half a cell at at a time horizontally or vertically, or that its eye jiggles slightly but very rapidly, much as those of many terrestrial species do, even our own.
As the examples below suggest, there is a huge range of possible Junctions and Borders, which would appear to make it necessary for the Dynism to evolve a near-infinite range of Lineal Templates. But if you look closely, Sample 2 is Sample 1 rotated 90 degrees to the left. Also, nearest matching, which operates similarly to that for Tone Patterns, can be used with Junctions that have more than three arms, so that only a few of these need be stored.
Inevitably any rule-based system will have anomalies. For instance, a near-full circle arc like that of Sample 8 will need to break Rule 3, but the Visual Processor matches its pattern as if its center was in the same position as all the others.
Looking at the samples below, a straight line may be picked up by several boxes, since the Processor can have no simple way of determining where its `ends' are. The same applies to Junctions since it can have no simple way of determining where their `centers' are. Sample 10 for instance is actually Sample 1 offset to the upper left. Also, unlike Tone Patterns, `resizing', let alone `reproportioning' Lineal Patterns would serve no useful purpose..
The more complex curve of Sample 11 would be represented in the Object RAM by two smaller Arc patterns and a short Straight.. Sample 12 might be extracted as a Junction by the Box containing it, but its curved arms might cause it to be matched as two arcs joined by an Angle extracted by the Box the next size down.
The Templates the Dynism stores for Lineals then are not only used for Identifying them, but for selecting which of the multiple patterns that may be recorded for each are retained and which discarded. For instance, Junction Templates are all centered, so if a Pattern goes not match in this respect, it can be deleted from the Object Ram. Arcs are the only curves stored, as we've just seen, more complex curves must be assembled from them. `Multiple' straight lines like those of Sample 9 will tend to be placed in the same Location, so those placed there by smaller boxes can be discarded.
Rotations like those of Samples 1 and 2 however must be processed in a different way. The Dynism may store
several rotational versions of each of its templates, but we will assume instead that its Processor acquires several more Virtual Boxes, set out in two `layers' like this:
The first layer, consisting of four boxes, successively rotates an Input Image by 90 degrees. Behind each such box, in the second layer, are three boxes which further rotate the image by one-quarter of 90 degrees, one half, and three-quarters of ninety degrees, possibly via an intermediary 16 x 16 box. In this way they can all be matched simultaneously to the one template at a single rotation that need now evolve in the ROM, This also allows the matching process to become simpler and faster, indeed similar such pre-rotation' mechanisms may evolve for tone patterns.
Like Tone Templates, each Lineal Template has its own Number Flag attached to it. Once a Lineal Pattern is successfully matched, its corresponding Template Number is passed to the Object Buffer in a position determined by its lower left center square.
Now, each of the tonal stimuli the Dynism responds to, as we saw earlier, is defined by its borders. You could think of it as being made up of a `list' of Lineals which proceed around it in a fixed order, or rather the Numbers that represent them. This sequence, via their Locations in the RAM, is in effect what `joins' them all together. Here we see a `leaf' from the Rockpile Flower both as a tone stimulus and as a sequence of Lineals
Each of the Dynism's Tone Templates now also acquires such a Lineal List, a `List Template'. When a tonal stimulus cannot be Identified, perhaps because it is shadowed or partly obscured by another, the Processor constructs a Lineal List from its raw Input Pattern, that is, before it is shrunk or stretched or rotated. It then searches the ROM for the List Template with the largest number of Lineals that matches it both in kind and in sequence. Again a minimum of three or more is required to reduce the risk of a mismatch.
More advanced Dynisms convert their List Templates into Lineal Maps similar to Object Maps, which they can then use in the same way to Identify a stimulus; indeed you could think of the submechanism which does this as deriving from the Object Identifier. This may then allow the Dynism to Identify stimuli - or objects - that have been visually divided by others. Perhaps the main value of List matching at this stage is that, if a stimulus is part of a minimum set needed to identify an Object, the object it belongs to can itself now be Identified. But the value of Lineal Maps soon goes far beyond this. We will now go on and see how the Dynism uses them to Identify `generic' objects like rocks and boulders, for which no ROM Object Maps are possible.
