The Mathematical Groundplan in Thinking
There is a saying that the spot under the candleholder is the darkest place in the house. This applies to medical science struggling to comprehend the process at work in thinking. Its product, thought, is always a step ahead of that which thinks. This is nature's circularity, the seed that, before the flower, is again produced in the result.
In more modern times the brain has been likened to a black box, a sealed component in an electronic circuit. We know what goes in and we know what comes out, but not what happens in between. The task before us is to take the lid off the mystery by proposing a mechanism, that operating within the brain suitably fits the facts, bringing light to the agent of light, where ‘light’ refers to our understanding.
We will never reach completion, but a catching up time has arrived. As William Harvey put on the mat for blood circulation, it goes round and round. Nervous energy also goes round and round, and with it, ‘mathematica’, as it exists in the brain's foundation before it was ever inscribed on paper also goes round and round. Circularity is the keyword.
Thinking, Aristotle said, is the highest function, and it reaches its highest form when, as in philosophy, it takes the highest activity, namely its own, as its object. This is pure circularity. Thinking about thinking sheds light on the nature of light, dispelling darkness. The advance we now see in all supporting fields demands that medical science come forward and resolve this issue, the generation of thought within the brain and body that creates it.
A tremendous amount is already known of the brain’s topology and function. A simple outline of the mechanism that gives cohesion to the organ system present in thought itself is however missing. Does thought have its own skeletal system, and if so, what form does it take? We might baulk at the very idea. Spelling and grammar bid us otherwise, but we need to deck it out in terms of a mathematically based neural environment. The abundance and complexity of available knowledge continues to grow exponentially; an ocean of knowledge that invites us to proceed beyond its shoreline and breakers.
In general consensus the brain’s function is mathematically based. Two sides are well defined. First is its monitoring and management of the body's homeostasis; second its control over the organism's interaction with its environment. We can, in these terms, define the brain’s function and purpose. Our sensibility is the feed to the black box. Within the box it generates our feelings and sense of a surrounding world. Broadly speaking, the division is into mind and world, where ‘world’, as in appearance is held within the grip of the mind.
Pursuing the mind/ world distinction within mathematics itself, and borrowing from Grecian terminology, we can call the mathematical impress within the mind, as the essence of subjectivity, mathematica. Its shadow, cast as the world of appearance, is then our common garden mathematics. What then is mathematica?
In rough, mathematica is mathematics in its formative bed, where the latter is not the thinking mind but its metabolic depths, wherein and wherefrom mathematical discipline arises. Thinking also springs from this bed, and then more superficially gives us, or gives rise to that which we call (the discipline of) mathematics. Mathematica is the extreme inside. Mathematics is the extreme outside, and between is the world that takes shape in sense, of sea sky tables and chairs.
The transition from sense to appearance-mediated response is automatic. Given the sensibility of the eye ear touch etc., we do not have to think to be aware. Awareness is first. Thinking follows. The transition from the raw stuff of sense to appreciated form is given by the sealed-in unconscious. The latter takes two forms: the body as the product of infinitely ancestral experience, and the mind as the product of babyhood imprinting. Here the deep unconscious opens onto the subconscious and this onto the conscious.
The neural activity that gives us a thing-filled objective world in appearance only requires that we be awake. We may wonder what tomorrow's weather will be like, and that side belongs to thought, but we do not have to think to be aware of the things around us; “this is a pen,” “this is a picture,” “this is a field,” and “ this is a house.” The two levels here are that which is freely given, for which we have but to be conscious, and that which we add in the process of thinking, which involves interest, assessment and calculation. Penetrate this thinking to its depth and we come to the more diffuse bed of mathematical relationship.
The levels are (a), a subconscious on unconscious appreciation, the imprint level in response; (b), organized thinking, and (c), beneath this, mathematica, whose depth is that of genetically controlled metabolism.
With this our project comes more clearly before us, the distinction between unconscious appreciation and conscious thought, and in the background a mathematical foundation. Mathematics is self-tracking logic. No speculative element enters into its structure. If, besides explicate mathematics, we see that it also has an implicate in-mind side, then we are on our way to learning how the mind “works.”
Stephen W. Taylor MbChB © 2004 November 10