Bateson on Numbers, Quantity and Pattern

I was looking in Bateson's Mind and Nature for something other than that which eventually caught my attention (I was looking for what he said about calibration and feedback - more about that later). But the book opened on page 49 with the heading "Number is different from quantity". Since I have been thinking a lot about counting and probability recently, this resonated very strongly - Bateson's position with regard to probability is unclear, but his focus on counting here is important and relevant to the way we look at information and data today. Big data, for example, is fundamentally a counting exercise, not a quantifying one. Bateson says:

"Numbers are the product of counting. Quantities are the product of measurement."

So here we are going to get a distinction between counting and measurement...

"This means that numbers can conceivably be accurate because there is a discontinuity between each integer and the next. Between two and three, there is a jump. In the case of quantity, there is no such jump; and because jump is missing in the world of quantity, it is impossible for any quantity to be exact. You can have exactly three tomatoes. You can never have exactly three gallons of water. Always quantity is approximate."

Given the fact that I was looking for his ideas about calibration, this distinction between measurement as an approximation (a calibration?) and counting I found insightful.

"Even when number and quantity are clearly discriminated, there is another concept that must be recognized and distinguished from both number and quantity. For this other concept, there is, I think, no English word, so we have to be content with remembering that there is subset of patterns whose members are commonly called "numbers". Not all numbers are the products of counting. Indeed, it is the smaller, and therefore commoner, numbers that are often not counted but recognised as patterns at a single glance. Cardplayers do not stop to count the pips in the eight of spades and can even recognize the characteristic patterning of pips up to 'ten'. 

In other words, number is of the world of pattern, gestalt and digital computation; quantity is the world of analogic and probabilistic computation."

He then goes on to talk about Otto Koehler's experiments with jackwdaws which appear to count pieces of meat placed in cups. Bateson argues that the jackdaws "count"; I'm not sure (how could we be sure??!) - but there appear to be similarities between the manifest behaviour of the bird and human behaviour in counting.

He then goes on to say that "Quantity does not determine pattern". This one is particularly important for Big Data enthusiasts.

"It is impossible, in principle, to explain any pattern by invoking a single quantity. But note that a ratio between two quantities is already the beginning of pattern. In others words, quantity and pattern are of different logical type and do not readily fit together in the same thinking. 

What appears to be a genesis of pattern by quantity arises where the pattern was latent before the quantity had impact on the system. The familiar case is that of tension which will break a chain at the weakest link. under change of quantity, tension, a latent difference is made manifest or, as the photographers would say, developed. The development of a photographic negative is precisely the making manifest of latent differences laid down in the photographic emulsion by previous differential exposure to light. 

Imagine an island with two mountains on it. A quantitative change, a rise, in the level of the ocean may convert this single island into two islands. This will happen at the point where the level of the ocean rises higher than the saddle between the two mountains. Again, the qualitative pattern was latent before the quantity had impact on it; and when the pattern changed, the change was sudden and discontinuous.

There is a strong tendency in explanatory prose to invoke quantities of tension, energy, and whatnot to explain the genesis of pattern. I believe that such explanations are inappropriate or wrong. From the point of view of any agent who imposes a quantitative change, any change of pattern which may occur will be unpredictable or divergent. "

Pattern is closely tied up with the idea of constraint. In the example of the mountains, quantity might be thought of as an index of change which reveals latent patterning. "More water" is a kind of construct based on the similarity between "a bit of water" and "a lot of water". In reality the difference between "a bit" and "a lot" is revealed through the constraints of nature that it encounters.

There are some similarities between this thinking and the talk about the "tendencies" and "causal powers" of things in Critical Realism. I've always found the Critical Realist approach confused on this (or found myself easily confused by it). In a few paragraphs, Bateson cuts through the urge to make declarations about the nature of a mind-independent reality without losing sight of scientific integrity.