Seeing triangles in dots

Figure 1

In developing their theory of Boolean maps at reference 1, Huang and Pashler talk of what happens when we are asked to focus on the white, red and yellow spots in Figure 1 (part of their Figure 5), with the proposition being that when we focus on the three spots concerned, we will probably be aware of their making a triangle and will probably be aware of little else, at least so long as our attention is indeed on those three spots collectively. Another part of the proposition is that the three spots collectively do have position but do not have colour, although had they all been the same colour, they would have had.

We consider here what might happen here in the world of LWS-N, most recently figuring at reference 2. With our concern not being whether the Huang and Pashler proposition is true or not – with its success with us seeming to depend on the size of the picture and with the occasion – but rather with what LWS-N would do with such a triangle in the event that it was. Or to be more accurate, what the LWS-N compiler would do with it. We think that the answer is in three layers, as follows.

Figure 2

Figure 2 is the triangle part of the content of consciousness, in its own layer. A four part layer object (in blue), with the interior of the triangle not having a texture net (in green) and so not being activated, while the vertices with their interiors and the perimeter of the triangle are.

Figure 3

A slightly different way of doing the triangle is shown in Figure 3 above, a seven part layer object. Here, the sides of the triangle have been promoted to parts of the layer object in their own right, with their own texture nets, just one of which has been sketched in. Not much idea yet as to how one might choose between Figure 2 and Figure 3. Perhaps just two different ways of experiencing the triangle, with the compiler going for one or the other according to circumstances.

Note that in neither Figure 2 nor Figure 3 is there any colour. There are texture nets to give substance and activation, but substance without colour. Perhaps texture nets without any regularities, so activation without anything more, without any internal structure.

Figure 4

While Figure 4 is a simplified version of the original coloured spots, with the spots of interest duplicated and marked with a red node, a colour which would not be expressed on the ground, in LWS-N, and is just used here as a prop. One might add a further texture net to colour in the background.

We have not troubled to vary the texture nets (in green) that we do have to express the colours of the various spots, but that is how it would be done. Something regular and uniform, perhaps some kind of repetitive tiling, something different for each colour.

All these spots being on their own layer, simplifies – perhaps eliminates – unhelpful interaction between the triangle and the spots not on the triangle.

Figure 5

 There might be a third layer to carry the information that the figure 2 is a triangle, linked by a column object to that triangle to ensure concurrent activation. Perhaps Figure 5, a six part layer object, expresses a six letter word meaning triangle. The jury still being out on exactly how this is going to be done. Maybe this layer object would express the sound of the word in question rather than its written form. Maybe the code for motor actions needed to sound the word, silently or otherwise.

The compiler could adjust the relative level of activation of these three layers according to person and circumstance.

Some preliminary thoughts about texture nets

We have already suggested that a random texture net, without any significant regularity or repetition might be used to signify presence and position without anything else.

Even a net which is random in detail can vary in space, both as regards density of nodes and activation. Such nets might well code for something.

Otherwise, the first idea is that regularity and repetition are used to signify things like colour, tone (in music), smell and so on.

Figure 6

Maybe the sort of thing we have in Figure 6 would do for colour – bearing in mind that this picture of repetitive tilings was thrown up by Bing and the colours therein have nothing to do with our texture nets – nor do colours have any place in a texture net, where there are no colours in the ordinary sense of the word. But we do have fourteen distinct tilings, which serve to show off some of the things that can be done. The idea being that activation of the fourteen corresponding texture nets would yield fourteen distinct subjective experiences.

A caveat being the fact that in Figure 6 we have some improper vertices, that is to say one line meeting another line somewhere other than at a corner. So all four tilings on the bottom row do this. A wrinkle that needs to be ironed out.

The idea also being that the right sort of texture net, through its activation (which has been put together by the compiler) is colour. It is not a label saying ‘colour’, it is not a pointer to such a label, it expresses colour, it represents colour in itself.

However, we suspect that colour will be actually be expressed by very simple texture nets, rather simpler than those of Figure 6, because colour can vary a great deal in space and we need to be able to give colour to quite small patches of space. This is less true of music and even less true of smells. So if we close our eyes, a smell might be allowed to occupy quite a large proportion of the space available in LWS-N.

Figure 7

Figure 7 shows a simple triangular net, spanning the space it occupies in a regular way. In this case, equilateral triangles, all of the same size and with just two orientations, up or down.

Figure 8

Here we have sketched a mixture of squares and right triangles, each triangle being a quarter of a square. Four orientations for triangles, just the one orientation for squares. We do not require the squares and triangles to be exact and we suppose that an approximation in space will suffice, with the subjective experience degrading with the approximation.

There are all kinds of other possibilities here, with the number of possibilities rapidly increasing as we allow more complicated mixtures.

A worry here is that while this geometry is expressive, is plausible as a vehicle for the subjective experience, it is not very neural. Neurons might have positions on our bit of cortical sheet, but is it plausible that their synaptic connections will aggregate up in this nice neat way into triangles and squares? Even if we pay more attention to the graph than to the position of the nodes in space?

So the second idea is that rather than using geometry, as in the foregoing, we use statistics. So we might, for example, regard the density of nodes as a key variable. Or the average number of links per node. Or the average length of links. These all being variables which do not depend on the net being planar and which might vary in a modest way across the extent of a texture net. And with a bit of imagination one can come up with lots of such variables, some more plausible than others.

The third idea is that rather than just having one sort of node and one sort of link, we allow a small number of each, perhaps three sorts of node and three sorts of link; a sort of alphabet. Combinations then give us lots of possibilities.

The fourth, and so far last, idea is topology. So far we have a planar texture net suspended in a part, in a hole in a planar shape net. We might go further and allow texture nets to have more complicated shapes, but restricting them to the representation of smoothly curving two dimensional sheets in three dimensional space. All the nodes would be in the plane of our bit of cortical sheet, but the graph would suggest three dimensions, would embed nicely into three dimensions. We do not pursue these possibilities here.

So geometry, statistics, alphabet and topology – so far. Four ways of jointly exploiting the position (geometry) and connections (graph) of our neurons to give some body, some life to our shape nets. Some of which is not that different from the soft centred patterns of the now obsolete LWS-W; not surprising as we address the same problem of how to inject some content and meaning into fairly simple data structure. See references 5 and 6.

Modality

We see texture nets as a general purpose device for the expression of all the senses, all the stimuli coming into the brain – noting that reference 4 argues that that is all there is. Anything which gets coded up in the brain takes the form of stuff coming in from one or other of the senses.

So we need to sort out how we are to distinguish the various modalities, what it is that distinguishes the various modalities – sight, sound and so on – bearing in mind that there are some people – synaesthetics - who get fairly muddled up in this department. The distinguishing features, whatever they might be, need to be able to break down.

A first step might to be to identify some candidates for such distinguishing.

Conclusions

We have offered some suggestions as to how LWS-N might code up Huang and Pashler’s triangle and digressed onto the business of texture nets more generally, albeit in a very preliminary way.

We will be talking more about texture nets in due course.

References

Reference 1: A Boolean map theory of visual attention - Huang, L., & Pashler, H. – 2007. Abstract: a theory is presented that attempts to answer two questions. What visual contents can an observer consciously access at one moment? Answer: only one feature value (e.g., green) per dimension, but those feature values can be associated (as a group) with multiple spatially precise locations (comprising a single labelled Boolean map). How can an observer voluntarily select what to access? Answer: in one of two ways: (a) by selecting one feature value in one dimension (e.g., selecting the colour red) or (b) by iteratively combining the output of (a) with a pre-existing Boolean map via the Boolean operations of intersection and union. Boolean map theory offers a unified interpretation of a wide variety of visual attention phenomena usually treated in separate literatures. In so doing, it also illuminates the neglected phenomena of attention to structure.

Reference 2: https://psmv3.blogspot.com/2018/05/a-modest-change-to-layer-objects-of-lws.html.

Reference 3: http://psmv3.blogspot.com/2017/07/binding.html. Includes some discussion of column objects, albeit in the context of LWS-W rather than LWS-N.

Reference 4: The Mind Is Flat: The Illusion of Mental Depth and the Improvised Mind - Nick Chater – 2018. To which I owe reference 1 and the whole triangle story.

Reference 5: https://psmv3.blogspot.com/2017/03/soft-centred-patterns.html.

Reference 6: https://psmv3.blogspot.com/2017/04/shapes-not-numbers.html.

Group search key: srd.

Carex

Finding a fine bed of carex pendula behind the pond at Stamford Green yesterday morning, it was a good opportunity to start training Felicity in its wonders. We will make a connoisseur of her yet.

Frames

From time to time I comment on the artistic device of allowing part of the picture to stray out of its frame, most recently at reference 1. A device which can go so far as having the picture including a frame in paint, inside and in addition to the frame in wood which holds the picture as a whole, and having people or things in the picture crossing the frame in paint.

This morning I noticed a new variation, of which Cortana could only manage the pale imitation left, in which the shadows thrown from the net curtains onto the chimney breast opposite blended in an intriguing way with the reflections of the buildings on the river on the view of Delft hanging thereon.

Cortana could not cope with all the variations in this scene, which she has rather exaggerated, when compared with the subjective experience, with the rather subtle blend of the shadows with the reflections more or less lost.

PS: note the trusty pill box on the mantlepiece. I am hoping that I might get something more tasteful - arty even - for my birthday; tasteful while equally practical.

Reference 1: https://psmv3.blogspot.com/2018/07/arts-crafts-2.html.

Reference 2: View of Delft - Vermeer - 1660.

Odd light

Cortana captured something of the rather odd, mid afternoon light as I came down past the Festival Hall.

Mixed buildings

Heading down from the Strand, I was struck by the fine of mixture of buildings and styles. A proper city, all mixed up - with the City proper in danger of becoming a rather homogenous mixture of rather ugly, try-hard, show-off modern. Will it age down to the comfortable mix we have here?

Cheese hunt

After a pause for the hot weather, time to buy cheese again, so off to London. Good day for it; sunny but not hot.

Two large bill boards - maybe eight feet by twelve feet - have appeared on Station Approach, attached to what I take to be a Network Rail wall. I wondered about the regulation of such matters; presumably one is not free to erect such things without asking someone's permission.

While maybe half the young box plants in the beds a bit further on have died, the entire plants being a very pale shade of yellow. Was it the drought or is some selective bug at work - there being quite a lot of talk in the gardening pages about box bugs at the moment? Or at least so BH tells me. It is also true that there is something wrong with some of the well established box bushes at the bottom of our garden, bushes which see little direct sunlight. And that there are plenty of well established box bushes on Box Hill, a hill made  mainly of chalk and so not very wet at all. More research needed.

Pulled a Bullingdon at Waterloo 2 to make it to Drury Lane in 9 minutes and 12 seconds.

Strolled through to Neal's Yard Dairy to find that they had taken on a Francophone counter hand to chat up all the French tourists; to convince them that there was good cheese to be had from this side of the channel. Sadly, during the course of my visit, he managed a good deal of chat but did not pull any sales. Maybe the French have to warm slowly to the idea of this good cheese. I took Lincolnshire Poacher for regular consumption and half a Gubbeen for irregular consumption - quite good but I thought it could have done with a couple of days longer than I gave it. BH happy enough with it as it was.

Onto the Crown, where the barmaid with tattoos remains missing, but I was able to observe the ebb and flow of holiday makers around Seven Dials. Some of them quite fetchingly turned out.

Onto to Terroirs, more or less empty this Friday lunchtime. The verdict was that it was a locals place rather than a tourist place and the locals were all on holiday. Also, for a change, we had an English waitress - who worked quite hard on her food and wine flannel. Both turned out well, with my eatable being something new to me called an onglet - a beefy version of pork belly but not at all fatty - and a touch of Slovenian, something different from the stuff bought towards the end of reference 1. Wound up with a drop of their excellent Calvados. Bread as good as ever. Chocolate tart a bit hard and sweet for me, but we got it down.

I could not place the accent of the waitress, which I thought south London but which turned out to be Reading and Oxford. I associated to the Maigret story that I was reading at the time in which Maigret was able to establish a rapport with the beautiful girl friend of a posh villain by guessing that she came from the Sainte Reparate area of Nice, then rather dodgy. A female of the people, just as Maigret was a male of the people. Also to a young lady we once knew who had a regional accent, possibly from Kings Lynn, and was rather uncomfortable about it, despite the fact that I found it rather attractive. Perhaps the game plan of such ladies was to blend with us speakers of proper English, this being before the current policy which rules that you don't get a job on the BBC unless you can sport a regional accent.

Called in Gordon's on the way back to Waterloo, to find the place fairly full of holiday makers, eating rather than drinking, and the facilities up some very steep stairs. Probably best to practise a bit before the light goes and before one has taken on too much freight. I thought it best not to take a peek at their wine list. But I must do so before too long, it already being many years since I took a drop there.

Just about managed to work the self service machine in Smiths, but managed to exit with a handful of their unusual plastic bags, which I was presumably supposed to pay for.

Also managed to chatter to various unsuspecting passengers in the train. But if they minded, it did not show.

PS: according to Wikipedia: a hanger steak, also known as butcher's steak, is a cut of beef steak prized for its flavour. Derived from the diaphragm of a steer or heifer, it typically weighs about 450 to 675 grams ... This cut is taken from the plate, which is the lower belly of the animal. In the past it was sometimes known as butcher's steak, because butchers would often keep it for themselves rather than offer it for sale ... The hanger steak is usually the most tender cut on an animal ... The hanger steak has historically been more popular in Europe. In Britain it is referred to as skirt, which is not to be confused with the American skirt steak. In French it is known as the onglet, in Italian ...

Reference 1: https://psmv3.blogspot.com/2018/07/wine-shipper.html.

Depression

Three depressing news items over breakfast.

First, the police found it necessary to strip search a young woman who would not talk to them - by removal of her clothes by scissors, no less. Why could she not simply have been put into a cell for a while?

Second, the people organising our health care have been directed to cut the queues (no doubt caused by their inefficiency) by contracting some of the work out to the private sector (where things are done so much better). The people who issue these directives are not dim in the ordinary sense of the word, so why does it not occur to them that the reason that there are queues is because there is not enough money in the system and that paying contractors a great deal of money to the work instead is hardly the way to make what money there is go further.

Third, there still seems to be no progress in the investigation of the shooting of someone (who appears to have been a career criminal) on the M62 near Huddersfield, getting on for two years ago now. When are we going to be reassured that vigilante justice is not on the loose? The continuing silence is not encouraging, depressing even.

PS: some days later: email inquiry elicited prompt reply. The trial scheduled for the spring is now scheduled for the autumn - with this trial being one of the things blocking public progress with this investigation.

Reference 1: https://psmv3.blogspot.com/search?q=huddersfield.

Reference 2: https://policeconduct.gov.uk/news/update-ipcc-investigation-following-fatal-shooting-yassar-yaqub.