One of the first mistakes we make with numbers is to combine the cardinal and the ordinal,
Counting sequentially occurs after or contiguous with ordering. that is to say that we deliberately subconsciously or intuitively order objects, actions etc first in order to count second. Thus functionally we decide on first second third etc even before we name them "first", "second", "third" etc and then we give the object a cardinal ,descriptive name, an adjective "one", "two"…..
Thus the ordinal names are descriptive of actions and thus are adverbial.
There is only situational commonality between the two conceptions. that we use the same mark to remind us of two different aspects of a situation does not make those aspects the same, but it does make them analogous.
Analogy has to do with relationships and the main treatment of these sort of relationships that i know of is Hamilton's However Hamilton defers to a prior art which i think he does so mistakenly.
Hamilton for me fully establishes the ordinal action from a motion field and thus founds the ordinal action from which we derive the ordinal names in a recursive reference frame, and the cardinal names in a definitive reference frame, We therefore have at least two distinct namespaces which i may relate to set definitions accordingly. One represents action and dynamism the other passivity and static equilibrium and both are aspects of my interaction with a situation,or a spaciometric situation including spatial intensity as well as visual form.
In this regard, the cardinal names take on an additional tensor reference while he ordinal take on a translational reference.
As you can see the basis of so called numbers is in fact dynamic space and can be codified within the trigonometric relationships, as discussed in a previous post. In this regard the marks now, not the referents which are many and varied, but the numerals themselves take on an additional information referent in terms of encoding data within the situation they refer to. But they are lso capable of being used to record any codified information using their relationships to hold what we like to cal "status " information.
The concept of number consequently becomes troublesome and i therefore like to distinguish this approach as cipherism, leaving numeral and number to a specific meaning currently related to counting and quantifying.
The set of ordinal actions is the set of recursive actions. This is strange because we derive it from smooth flow. But from this we may understand that our interaction with reality is far from smooth, but rather recursive like a continuous convoluted spiral: a convolution. And the best guess is that the motion field is a rotatuinal convoluted field because even if it were not we would not be able to distinguish it at a certain level Fractal consistency is the motive for my guess.
A number is just a word, an adjective… at best an adjectival phrase. As such it is no more significant than any other adjective; or alternatively it indicates that we can develop algebras and arithmetics for other adjectives. When you make that conceptual connection you enter the world of Quantum Chromo Dynamics