Maps

Our working hypothesis is that UCS, in building visual images in the layers of LWS – see, for example, references 1 and 5 – adds value to the raw images from the eyes. Value in the form of structuring the images into layer objects, their parts and accessories and value in the form of supplementary, non-visual information on other layers. Value which is ultimately derived from its memory, its prior knowledge of the world and its appearance.

Our primary interest is how the brain does this, without props or help from the outside, without paper and pencil, or even a stick in the sand. However, we do do this sort of thing outside. We draw diagrams from life, to bring some order to what otherwise might have little meaning: think, for example, of looking down a microscope at some miscellaneous slice of tissue and then looking at an expert’s annotated & labelled drawing, taken from that same slice of tissue.

While cartographers draw maps of the world and this note is mainly about making such maps, in this case large scale maps, of the order of an inch to the mile, say 1:50,000. And about the various codes and conventions which the cartographers deploy to make them readily comprehensible – user-friendly, to use a phrase that computer people were fond of when we were in the world of work.

The point of all this being that what the cartographers do with maps is comparable, certainly in some ways, to what the UCS does with the LWS. Or in more natural language, how the brain makes what we see out of the light, the electro-magnetic signal, that arrives at our eyes.

Some background

A map is a picture or diagram of a piece of the globe, seen from quite a long way up. In what follows, we suppose that we are looking at a small enough piece of the globe, of the earth, that we can consider it as being flat and that we are looking down at it vertically. The sides of things do not come into the account. We suppose that movables, in particular people, other animals and motor vehicles are also left out of the account – which is not the case in certain mapping applications, for example, satellite surveillance.

Now the Ordnance Survey, when originally mapping the British Isles – including then the whole of Ireland – did it on paper and did it at various scales. There were various series of maps. So one had plans at six inches to the mile, maps at two and a half inches and maps at one inch. In all these cases the British Isles had been tiled up into sheets, sheets which generally butted up to each other, rather than overlapped. In the case of the successors to the one inch maps, the 1:50,000 Landranger maps, there are just about two hundred sheets covering Great Britain. And then there were maps at various smaller scales, organised to cover a quarter of the country in one sheet, one half of the country or something like that.

Each sort of map used its own set of conventions for marking out the physical geography of the land and the various doings of man on that land. For showing the roads, sometimes only a small fraction of those that there were on the ground. For distinguishing urban from rural areas, high ground from low ground and field from forest. Perhaps for marking telephone boxes, police stations and public houses. Often, there was also a lightly printed geographical grid, the grid lines, from which we could compute location, perhaps latitude and longitude, should that not be clear from the remainder, from the named features on the map. These grid lines have been retained on Figure 4 below.

Moving maps from sheets of expensively printed, good quality paper to the computer, series and sheets more or less vanish from view. They are replaced by other features. First, one can pan about, one can pan from Epsom to Leatherhead, or to the Seychelles. Panning is not of present interest. Second, one can zoom in and out; and third, one has a number of different views. The two basic views are aerial (a picture or photograph) and road (a diagram), but there are variations on these themes, some of which add the complication of point of view, with the various digital map providers all coming up with slightly different schemes. They need to be different, one from another. They need their house style.

In the case of aerial, zoom is a bit like what happens when one drives up to a house along a very long drive. The house starts out very small, only occupying a very small part of the field of vision, and steadily grows, grows until one’s nose is touching the front door and one is peering through the letter box. During this process, the detail of the house is steadily elaborated. First one distinguishes chimneys, roof and walls. Then doors and windows. Then the panes of the windows. Then the handle of the front door and the paint flaking off at the bottom of the front door. Then the boot scraper to the side of the door. Then the wasp sitting on the door handle. This all seems to be happening in a more or less smooth and continuous way, but this is something of an illusion.

In the case of road, the illusion of continuity falls away, as the compilers of the maps use different conventions at different scales, just as the compilers of the various series of Ordnance Survey maps did. So, as one zooms in, different classes of road suddenly pop into view. They might change colour. The shape of a house, as viewed from above, suddenly change from some conventional, more or less rectangular shape, to a true plan of the house, taking in its individuality. More and more features - telephone boxes, police stations and public houses – find their way onto the map.

A digression on pixels

Suppose we have built up an aerial picture of the whole of Surrey, expressed as a square array of pixels, say one million pixels high by one million pixels wide – that is to say roughly ten times as many pixels as there are neurons in the human brain – but a comparison which is fraught with all kinds of interesting difficulties of its own.

Suppose our viewing screen is another square array of pixels, one thousand pixels high by one thousand pixels wide.

If we view the whole of Surrey, one viewing pixel needs to summarise a million source pixels, and it is easy enough to specify some bit of mathematics to do that, although the result is apt to be a bit of a blur, not terribly informative.

If, on the other hand, we view a very small part of Surrey, we might have a square of one hundred viewing pixels to cover just one source pixel. With the usual drill being that each of the hundred pixels is a copy of the source pixel, giving a rather chunky – or perhaps clunky – look to the picture on the screen.

Usually we do something in between, with one viewing pixel covering a number of source pixels, and we get something reasonably informative. But there can be some odd artefacts, with the mapping between one lot of pixels and another, say between ten by ten blocks of pixels and seven by seven blocks of pixels, sometimes giving rise to odd visual effects. The mapping process sometimes breaks down a bit at the edges.

Figure 1

Something of roughly the same sort is illustrated above, showing how we struggle to represent a thin straight, but sloping line, on a rectangular array of pixels, or in this case, a rectangular array of cells on an Excel worksheet. Note the regularly alternating displacement of the stack of short horizontal bars of blue cells. Made rather bigger and seen from a suitable distance, such an array might look quite like our conception of what a straight line should look like.

And we suppose that the brain which, while numerically large, is also finite, must do something of the same sort. We think it unlikely that it expresses a thin line in the form ‘y = Ax + B’ – which might be close to the case in a technical drawing package on a computer.

Some foreground

The maps that we use in what follows come from Microsoft (reference 2) and the Ordnance Survey (reference 3), all captured by ALT plus print screen. We dare say that rather different points could be made by looking at Google (reference 4) but we leave that to another occasion – or to the reader.

All the maps which follow are of roughly the same area, around 8km wide by 4km deep, centred on Oxshott Heath and Esher Common, a mainly affluent, near suburban area just outside Greater London, which last just gets into the frame, top right.

Figure 2

An aerial view, from satellite or aeroplane, which is more or less untouched by human hand. The A3 is clearly visible running across the middle of the frame, and it is easy enough to distinguish large buildings, built up areas, open ground (pale), and woodland (dark). But more than that can get quite difficult, difficult to the point where some people make a good living out of interpreting aerial photographs.

Figure 3

Here we have much the same area in what bing calls aerial view, in which the raw aerial photograph has been touched up to make the road system more visible. Plus they have added the names of the bigger roads, the names of places and the names of some of the bigger attractions, like golf courses and Chessington World of Adventures.

Figure 4

Now we move onto maps proper, where, rather than annotating a photograph, we have a diagram, but a diagram which is geographically accurate, rather than something like the famous London Underground map which pays scant regard to geography. Geographical truth was sacrificed for ready comprehension of the underground system, a map which more or less completely displaced the original version, which paid much more regard to geography, but which was, in consequence, rather untidy.

In the example which follows at Figure 5, we have what we think is the underground network as it was in 1908, superimposed on a lightly drawn map of the same part of London. But even here there has been some tidying up of the locations of the stations. Being geographically accurate at that level of detail was not a practical proposition.

While Ordnance Survey have come up with the best compromise between being geographically accurate and being informative in other ways that I know of – although I believe there are vaguely similar maps of the US, of France and no doubt of other places – with us having had the considerable advantages of being both rich and, geographically speaking, small. A compromise which started with the various series of one inch maps and carried on with their successors, the Landranger maps – although it remains to be seen how long they will survive commercial imperatives in a time of rapid change.

By way of example, one of the compromises, one of the ways in which these maps are made legible is in the width of the roads, with roads of any particular class shown at a more or less uniform width, but a width which does not respect the scale of the map. Roads are generally shown as being much fatter than they really are – but at least you can see them, which is not always the case in Figure 2 and which can be very difficult in wooded areas. Furthermore, the various bumps and wriggles have been smoothed out. I think cartographers call all this generalisation and you can read more about it at reference 7 – a reference which also includes layer talk of a sort which is also to be found at reference 5.

We get various features added to the map, sometimes in the form of icons, sometimes in the form of text, but without any attempt to represent appearance, beyond location; we have moved right away from photograph to diagram. We even get the odd public house, including, for example ‘The Bear’, noticed at reference 6, here bottom middle, just below Oxshott and denoted ‘PH’. Rather more attention is paid to churches, reflecting the interest in such in the nineteenth century – still useful now as landmarks – and we recall being told that the Northern Irish version of Ordnance Survey distinguishes eleven different sorts of church – by denomination rather than by architecture – while we only go so far as to distinguish spire from tower from neither.

Another tricky area is the placement of this text on the map, text which adds important value to the map, but which is apt to obscure whatever is underneath, a problem which LWS avoids by keeping text and image on different layers. Both can be active at once, without one obscuring or occluding the other, although one layer is likely to be dominant and people vary in the extent which they can have two or more layers active at the same time. A different sort of compromise than that of the Landranger map, where the product that you get, that you see, is all on the one layer, all on the one image.

The use of colour is rather more straightforward, with a fairly small palette being used to mark out land types – for example marsh or moor – and the various uses to which the land in question is being put. So a pink is used for buildings, in the present examples mainly suburban housing. Land type and use by colour is often supplemented by little icons, so, in Figure 4, small tree icons are used to distinguish broad-leaved from narrow-leaved woodland.

Our hypothesis that LWS, in so far as visual images are concerned, lies somewhere between Figure 3 and Figure 4. More of a manufacture, a construct than Figure 3 but less of a diagram than Figure 4.

Figure 5

The old tube map, mentioned above.

Figure 6

Just to round out the story, Figure 6 is the Ordnance Survey map cut down to the free, basic version. A bit palid at this scale, but it becomes more informative, more like a street map when you zoom in.

Figure 7

The bing road map is similarly impoverished compared with Landranger. But it also will come into its own at larger scales, in more built up areas, for example the centre of London, where it is marginally better than Ordnance Survey in that it offers a bit more annotation, marking, for example, quite a lot of eateries. Do they have to pay to appear?

But a fast moving area. Ordnance Survey online did not offer until recently, at least as far as we were aware, street maps. And another of their newish offerings is Aerial 3D, not yet perfect but better than anything else of the sort that I have seen. Better than bing’s Bird’s eye, at least for mountains.

Figure 8

Just to round things off completely, we show part of an old Ordnance Survey map covering roughly the same area, with thanks to the National Library of Scotland. No colour and fewer icons, but plenty of interest in woods, field boundaries and acreages. Don’t know what has happened to the A3, which as the main road from the Old Admiralty building in Whitehall to the naval base at Portsmouth, must have existed at the time.

Conclusions

Mapping provides an interesting parallel to what the UCS does with visual images.

From the consumer’s point of view, at least the consumer privileged with a bird’s eye view of the world, it does a lot of the grunt work, rendering a complex world down to a comprehensible, two dimensional image. An invaluable aid to both comprehension and communication.

But also providing some insight into the sort of thing that LWS is trying to achieve with its layers, layer objects and properties.

PS: digressing, we wonder what a buzzard might see with its bird’s eye view. Guessing, we suppose both more and less: it might be able to see and know a mouse from 200m up, but it does not know a railway or a police station when it sees one.

References

Reference 1: http://psmv3.blogspot.co.uk/2017/08/occlusion.html.

Reference 2: https://www.bing.com/maps/.

Reference 3: https://www.ordnancesurvey.co.uk/shop/os-maps-online.html.

Reference 4: https://www.google.co.uk/maps.

Reference 5: http://psmv3.blogspot.co.uk/2017/04/a-ship-of-line.html.

Reference 6: http://psmv3.blogspot.co.uk/2017/07/bears.html.

Reference 7: https://www.ordnancesurvey.co.uk/support/understanding-gis/generalisation.html.