Position on Mathematics
Mathematics does not exist on its own. It does not haunt the vacuum of space. It does not manifest as public objects or substances. It has no will or motivation.
Mathematics is two distinctly different (opposite) things:
1) A private experience of imagined sensory symbol-figures which accompany a motive of quantitative reasoning.
2) A collection of public objects interacting in a logical, causal way, without any private representations, as a consequence of the shapes of multiple rigid bodies.
The problem with functionalist expectations is that they seduce us into a shell game so that when we look at math ‘out there’ (2), we smuggle in the meaning from ‘in here’ (1), and when we look at meaning in here (1) we mis-attribute it to the blind enactment of material bodies.
We assume that the world outside of our minds runs on math not because it actually does, but because our awareness of the public arena is a grossly reduced, indirect logical construction. The universe without, like the universe within, runs on qualitative sensory-motor experiences.
Turning the functionalist expectations around then, we find that the activity of the brain is not the source of human experience, but rather the effect of many kinds of experience on many levels (physical, chemical, biological). These experiences are not generated by information or mathematics, but rather information is an analysis of experiences by someone who knows almost nothing about them first hand.
We are used to thinking of ‘data’ in terms of digital vs analog. Consider however that both of these categories are a-signifying formats. I would like to propose a principle by which subjective, signifying experience is introduced – a qualitative instrumentality of being.
Think of the number line – abstract, linear, literal. A conception of pure quantitative non-awareness. It’s a semantic artifact from which all qualitative content has been stripped. It’s like a Supremetist work of art, really.
The act of measurement itself is to invert qualitative experience – to collapse it into value coordinates on a numberline, allowing us to treat it as a hypothetical object, aka, a figure.
Ordinal position applies to the literal, outward facing specifications of rank. This is where the universe gets the ideas for front and back (anterior and posterior) and interior exterior. As in Chess, rank refers to the relative power of the piece – the order of their significance to the game.
Ordinal disposition applies to the figurative, inward facing qualities associated with rank. This is where the universe gets the ideas for best and worst (superior and inferior). Feeling like a King or Queen, being treated like royalty, having access to first choice in dividing the spoils, etc. Ordinal disposition is about the experiential privilege of rank while ordinal position is about the mechanics associated with delivering or deriving that privilege.
by contrast, Cardinal position I am saying refers to the relative size of a real public phenomenon. The range here is along an axis from the micro to the mega, and can refer to increasing scopes and scale or increasing quantitative complexity. This is about structures nested within structures, separated by spaces of varying size. Rather than in/out, front/back, or high/low-superior/inferior, cardinal position is about spatial-topological extension – long/short, large/small.
Cardinal disposition rounds out the four as an evaluation based on rarity. Like the pawns in chess, their generic abundance relative to the two unique pieces and the three duplicated pieces indicates their disposable rank. This is different from ordinal disposition in that superiority/inferiority derives not from order in a sequence, but from degree of commonality. Where cardinal position is about space and geometry, cardinal disposition is about feelings derived from time and algebra; frequency. How often. Sooner/later. Cheap/dear. Ordinary/exotic. The magic here is in pattern recognition. ‘Three in a row’ is an example of how low caste occurrences can ascend to uncommon value.
The terms for the columns and rows in chess, rank and file, are useful here. The rank can be seen as the vertical axis of qualitative position and disposition, while the single-file of pawns exemplifies the horizontal axis of quantitative position and disposition. Poker hands are a good metaphor to see this as well. Pairs, three and four of a kind, flushes display cardinal significance, straights, high cards, and Royal flushes display ordinal significance. The other hands, full house, straight flush, demonstrate an appreciation of the cardinal disposition of combined cardinal and ordinal values.
Degree of figurativeness in qualia equates to privacy of qualia.
1. Subjects necessarily have access to more qualia which applies to their autobiographical experience than qualia which refers to external, publicly accessible experience.
2. It is proposed that the more strictly personal a quale is, the greater the set of interconnected psychological associations that exists for the individual and the richer and more imaginative those associations can be.
3. Mathematically, the more personal an experience is to us, the more ways we can shift its meaning, making qualitative floridity and associative fluidity directly proportional to privacy.