[metricspaces]

clearly related to measure (in the abstract sense) and harmonics of natural numbers. what has fascinated me for years has been the sense that we need to rebuild number up using complex numbers and harmonic measures. what we get are still numbers but no longer this monotonic sequence which is a ‘lazy’ or ‘simple minded’ way of ordering N. when ordered by harmonic measures of primes, N itself has structure (beyond a simple incrementing list) but the order is strictly limited to measures provided (rational) with the prime roots of the measure. (an example is the ‘primorial’ harmonic measure of {2, 3, 5} - think rings).

in these harmonic measures, ‘gaps’ between various levels naturally would arise from simple (x) op. For non-relative prime members, the mapping n x n is all over the place but for relative prime members, n x n always results in another relative prime in the ring, so, naturally those ‘lines’ are ‘stable’ and ‘in phase’ so ‘manifested’.

in other words, there is stuff in the R realm — in between ‘quanta’ — but we’re not allowed, capable, ever, of seeing or measureing it.[edit: as in they ‘exist’ in the same realm that (sqrt -1) i exists in — an unseen realm we call ‘imaginary’..]