Re: Re: nature -> "human brain" -> "language terms" ==>> knowledge ?
JS,
Here is something 'vague' for you in the context of Brain function and Mathematics; understanding what is 'behind' Mathematics.
A common tool used is the cartesian coordinate system of X, Y, and Z dimensions. These are supposed to be 'independent' of each other - they are not. The act of putting down the X axis as a FIXED, if "infinite", axis is the act of setting a root context. To then assert the Y axis is to assert Y operating WITHIN the context of X (it moves 'along' that access and so operates WITHIN it). To then assert the Z axis is to do so WITHIN the context set by the previous dimensions. All of this EXPRESSION reflects internal dynamics.
As such, your mind has moved from the general to the particular and in doing so has move from the vague to the crisp re mapping reality. In that movement the method 'hides' its roots - in recursion where each dimension is a dichotomy of +/- (or 0/infinity) so the cartesian coordinate system is an example of deriving meaning from recursion of dichotomies translated into a geometric form. (or more so the recursion of 1 dichotomy, the X number line).
In fact, each 'row' in the recursion of the abstract 0/1 dichotomy is associatable with a geometric representation, with the first full 'form' to come out of that process is the tetrahedron (2^2 realm of four qualities - their development reflects basic growth dynamics where maximising their 'uniqueness' (differentiating) but retaining their overall form within the whole (integrating) is best represented in a tetrahedron form (in our senses our sense of TASTE maps to this form - but ANY four-quality representation will do so).
Thus the Platonic 'ideals' are more so patterns derived from mindless growth dynamics operating within a space of differentiating/integrating (push away/pull in, pull along/push along).
We can then move to the derivation of TYPES of numbers from basic differentiating/integrating qualities (as covered before, in summary:
Sense of Blending (whole) - whole numbers (diff = primes, int = composites)
Sense of Bounding (part) - rational numbers
Sense of Bonding (invarience) - irrational numbers
Sense of Binding (varience) - imaginary numbers
IOW we map these onto the dimensions of X, Y, Z etc etc and in so doing note the association given previously re chemistry and the different types of bonds and their association with blending, bonding, bounding, and binding. IOW we can see how one format (Mathematics) can represent another (Chemistry) - or perhaps you want to focus on Gravity, weak force, strong force, electromagnetic force? Again, with these as fundamentals so we can map one to another to derive meaning with Mathematics giving us a 'useful' set of representations.
Given the core sense of wholes, parts, static relationships (share space), dynamic relationships (share time) that come out of differentiating/integrating, we are dealing with CORE elements of reality as universals that then get customised due to local context.
Chris.
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