Here we talk about how a unit of that data, a layer object, might be coded up to represent something which is mainly red – with things like the uniform patch of red top left in the illustration being relatively unusual in the natural world in which we evolved.
We have a division of labour here between the various layer objects making up our data structure and the various elements making up an individual layer object. Here we look at what might be done within an individual layer object, an object defined by a collection of contiguous soft centred patterns, the elements of our object.
The sizes, shapes and perimeters of all the elements of our layer object are identical, by definition. While the interiors, or soft centres, will usually vary.
We suppose that our layer object has extent rather than length, is space like rather than line like. But we want to allow a bit of structure within that extent. We want to allow variation of colour and we want to allow lines to highlight transition from one part of the object to another. This might, for example, help us represent all or part of the folded red cloth, middle left in the illustration. Or we might, of course, just settle for patches of slightly different colour, with any lines being implicit rather than explicit. But the present thought is that explicit will help the activation process trace out and make conscious the structure before us.
We suggest below one way of using soft centres to do this, to define colours and lines, one way among many, with the target being the sort of red pictures illustrated. We note in passing that we are probably some way off, some years off, knowing how the brain actually does this. And we wonder in passing whether it would help to look at the machinery which some cephalopods – octopuses, squids, cuttlefish and such like – use to change the colour of their skin, machinery which can take input from their two eyes, very much like our own, process it, and pump it back out to the skin as camouflage. Although judging from a quick google, that does not seem to be the way that flexible fashion is going, where the technology seems to be common or garden LED arrays mounted on a flexible substrate. But, for cephalopods, see reference 2.
Our soft centre is a small rectangular array of integers, from low value to high value, perhaps 0 to 10, or [0,10], where this last notation means 0, 10 and all the integers between. Although, as will be seen in what follows, there may be advantage in the upper bound, the high value, being a prime number, say 7 or 11. Small rectangle in the sense of not usually more than, say, ten columns or ten rows. And remembering that the perimeter will take two of each from each element of the layer object. We call the individual elements of such an array its cells.
We suppose that any colour can be represented, at least after a fashion, by a soft centre of any size, although (for the moment anyway) the soft centres of any one layer object will all be the same size. But more size, then more information, more detail.
We further suppose that the colour of an element as a whole is not changed by permuting the values of its cells, which two suppositions taken together suggest that subjective colours are a function of the values of the cells taken together, rather than separately. As far as colour is concerned, it is their statistical properties which count, not their geometrical properties.
And given that we use just a small number of integer bins for the values of the cells, we think that there should not be that much noise, although our arrangements will need to allow for some.
And lastly, we suppose that the representation of colour in our element is self contained. It and its associated activation process have to amount to the experience of seeing red, without reference to anything else in our data structure, and certainly not to anything else outside. However, if this particular experience of seeing red was to do with or was associated with, for example, some fire engine, then that fire engine would need to be included in our data structure, inclusion which would be likely to include other properties and emotional colour. But for present purposes we suppose that our seeing of red does not come with baggage of that sort. We suppose that we can be conscious of seeing red without it coming with baggage of that sort. We suppose that a baby experiences red before it attaches red to other stuff in its world.
We imagine that it is this property of being self contained which accounts for the brain’s profligate use of bits and bytes, compared with a computer, where the data is not self contained at all, is meaningless in the absence of all the other data and information which is needed to give it context and meaning. Location 512,673 might well contain an integer of four bytes, but that is of no help at all unless you are told what that location is all about – and that telling might amount to a lot more than four bytes.
All that given, we then take the nearest integer of the average value over the interior of an element. In the case that this is high value, the element is declared to be a marker. Such a marker might mark part of a line between two patches of different colour, a bend in such a line, a junction or a crossing of two or more such lines. Contiguous markers build up into a network of lines, not necessarily connected.
In the case that this is low value, we have nothing. Null.
Otherwise the element is declared to be a colour. The present notion is that colour is coded by powers of 2, 3, 5, for red, green, and blue respectively, with it being quite possible that we need to do something more for black and white. And given that high value is some prime number bigger than 5, there is no confusion there. We take the product of the values of the cells in our rectangle, with the combined power of 2 divided by the maximum possible giving the red value in the range [0,1], that of three the green value and that of five the blue value. All along the lines of the RGB values that can be used for colours in MS Office. Any other small primes – we are not allowing big values – are spare and could be used to code other stuff, other stuff appropriate to extents in the way that colour is.
And large elements will be able to capture finer distinctions than small elements. Suppose, for example that our cells can take integer values in the range [0,7], so the maximum value for the power of 2 at a cell is 2. If we have an interior with two rows and two columns, the maximum possible value of the power of 2 for an element as a whole is 8. So we will be able to code for red on a scale of [0,8]. While if we have a three by three interior we will be able to code for red on a scale of [0,18], giving us more than twice as many shades. In this way, it can be seen that large elements will give greater discrimination between colours than small elements.
The product of the values of the interior cells of an element – with the uniqueness of prime decomposition - seems less destructive of detailed information than addition of values.
There is a lack of symmetry here in that, in this context, 2, 3 and 5 are significantly different. Maybe in some obscure way reflecting the distribution of the numbers of colour cones on the retina, approximately and respectively 20:10:1. With the finer detail afforded by the small 2 being reflected by the greater number of corresponding cones. But a plus is that it is an example of the sort of thing that might become a bit of evidence that we all see the colour red in the same way. If red is always based on 2, then the coding and the activation will be the same for everybody. My red is the same as your red.
We still have to work the much larger number of rods into our story.
Remembering in this that we have compilation, which could be used to tidy things up a bit. Remove what appears to be noise from the interior of soft centred patterns.
Conclusions
We have suggested one way in which patches of colours might be coded in our consciousness generating patch of cortex, modelled as a layered data structure associated with compiled activation processes.
The next step is to have a go with this in Excel, where there is enough cell colouring machinery to try some of all this out.
References
Reference 1: http://psmv3.blogspot.co.uk/2017/03/seeing-red-rectangles.html.
Reference 2: Other Minds: The Octopus and the Evolution of Intelligent Life - Godfrey-Smith, Peter – 2017.
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