Supplementary

Since posting at reference 1, I have had occasion to sit in front of a brick wall for a few minutes. Not the actual bit of wall snapped left, but a bit of the same building, the former Assembly Rooms from Epsom’s days as a spa town, around the back, and I was able to try our hand at counting courses of bricks.

My bit of wall was in better condition than the top half of that illustrated, more like the bottom half. Around 25 courses were visible through the window, from where I was sitting.

Much easier to count, as one might expect, when the pointing was in good condition, with smart, clean lines, with good contrast.

There was a tendency to count in threes. The eye seemed to be able to get hold of three bricks at a time in a reasonably reliable way.

The bricks were close enough for there to be binocular effects, unlike Vauxhall Tower, which too far away for that sort of thing to be relevant.

When moving the eyes from course to courser without counting, I was conscious of something going on in the mouth department, rather as if there was some counting going on in the unconscious and it was quite close to being articulated out loud.

There was also a tendency to mark the beat of the counting by nodding the head slightly, rather as if one was listening to a piece of music. The sort of thing that can irritate in a concert hall, when you are sitting behind it.

Moving the eye down the rows of bricks in a stepped and controlled way, but not doing anything else, was easy enough. Doing it at a steady pace helped. Counting, but not doing anything else, was even easier. Doing both at the same time was another matter, but again, doing both at a steady and synchronised pace helped. I associated to the business of blending two long strands of RNA (?) together to make a double helix of DNA.

Another wheeze that helped a great deal was following the herring bone of the alternating position of the long bricks, as indicated in Figure 2 above, enlarged and adapted from the lower half of Figure 1. A rhythm generating wheeze not available at the tower.

Tiles on walls or floors is much the same as bricks in walls. But there is a clear size effect, with doing big things a lot easier than doing small things. Where big and small are probably about angular dimensions rather than linear, absolute lengths. So I find that with these two snaps, the counting of which is not that far removed from doing it in real life, the counting is lot harder with the first than it is with the second. Maybe the fovea can be contained within a large brick of the second, but spans several bricks of the first, so in this case fixation is not good enough. Or maybe there are limited resources, and if too big a proportion is put into sorting out the bricks, or whatever, there is not enough left for counting and task management.

Supplementary digression

In English it is OK to count up to around a hundred in this way, after which even saying the numbers silently starts to be too intrusive, too time consuming. French being somewhat different, being more into twenties than English, so OK only up to around seventy. Latin is written rather oddly, but I forget how it sounds. When one hits a limit of this sort, one might want to mark the periods by dropping a marble into an urn, or some other device of that sort, not requiring ocular attention.

While for slow counting, one might do away with counting altogether and just drop marbles into the urn, doing the actual count in slow-time, after the real-time business of scanning the windows, bricks or whatever. I have yet to try this to see how it goes.

In other cases, in particular where one wants to classify as well as count, five bar gates, as illustrated above, can sometimes be helpful, although they do require attention to be shifted briefly from whatever it is that is being counted to the bit of paper on which one is making the gates.

While for fast and irregular counting, perhaps passengers piling off a jumbo jet, a clicker is good. Pressing a clicker does not take too many brain cycles away from marking each successive person crossing one’s imaginary line, such imaginary lines being the modus operandi of the better sort of survey operative everywhere. With a modern clicker not just counting, but able to record a timed sequence of clicks, which would take us off into a quite different world.

Conclusion

There is a motor and rhythm element to successful counting, the successful binding of the tracking of the courses of the bricks with the eyes to the counting with the mouth. When things are going well, maybe one is binding together the two synchronised but almost autonomous streams, rather than alternating between them, with this last making much heavier demands on scarce working memory. Separately synchronising two more or less independent streams of activity to the beat is much more economical – both in real-time and in learning-time – than synchronising them to each other. And I dare say the beat would be visible in the brain waves you look at with an EEG machine, if only one knew where to look.

Perhaps if I practise, I will find myself doing these counts unconsciously, as I have already noticed (at reference 3) when climbing stairs at tube stations.

All of which accords with other stories that I have read about the binding together of different strands of information about one and the same thing needing the support of consciousness. Maybe not a causal relation, but at least another behavioural correlate.

I also associate to stories about the importance of music when a body of men is using a capstan to raise the anchor of a man-of-war of old or when a body of men is marching. Presumably some of this is about synchronisation and some of this is about raising the spirits of possibly tired men generally.

Reference

Reference 1: https://psmv3.blogspot.com/2018/09/shopping-lists.html.

Reference 2: http://epsomandewellhistoryexplorer.org.uk/EpsomSpa.html.

Reference 3: https://psmv3.blogspot.com/2018/02/on-counting-variations.html.