This piece will explore self-reference and the geometry of forms. The diagram below represents physical arising and flows from left to right: Geodesic Array (pure form) > State Specific Deformation (crystal) > Vibrational Animation > Reduction (perception). This approach models physical systems with a top-down geometry for which the last step is observation (reduction).
The fourfold emanation model shows how [domain adapted arrays of] simple geometries can give rise to what have been dubbed ‘qualia’: particular sense impressions (EG: the mind’s perception of the physical mushroom, or “mushroom qualia”). Geometric primitives (1) are adapted to model particular mechanical arrays (crystal) in state-specific configurations/deformations. The system is then modelled as vibrating relative to the surface of the crystal (3). This animated form corresponds to the state of minimised internal pressure of the waveform identity prior to observation. In an isolated system, the quantum state transition of reduction (4) [to a lower pressure state] occurs if the interaction of two waveforms accesses a region with less internal pressure than either of the initial 2 waveforms. EG: The eye absorbs light because rods and cones minimise the vibrational pressure of the ambient light.
The evolution of a system is generally characterised by punctuated state transitions followed by (statistically) minimal deviations from waveform identity.
Next, a corresponding mathematical framework will be explored.
The first column lists the degree of self-reference. The second column lists the 5 primary geometric surfaces (note: 3 & 4 are hollow). The third column is the well-known Von Neumann construction of the Natural numbers. The fourth column consists of the union of the 3 topological knot identities of smallest crossing number and the Möbius strip [as the identity of degree of self-reference = 2 (otherwise the sequence wouldn’t instantiate binary dualism: a metaphysical necessity)]. Note that asides from the Von Neumann ordinals, the utility of primitive constructs does not extend past (4).
At right is a diagram denoting the maps between columns. Note that the encirclement operator (GA) is repeatedly applied in order to build the Von Neumann ordinals. Here, the degree of self-reference may be made arbitrarily high, but at the cost of full dimensional penetration: the VN ordinals cannot progress past the circle identity, of dimensionality 2 (out of a total possible 3+1).
This framework makes explicit formal distinctions between particular types of self-reference enable a deeper understanding that eventually mitigates erroneous assumptions. Since the geometries make minimal assumptions, the technology is measurement error/fault-resistant (fewer assumptions = fewer things to be wrong about). Finally, neither infinity nor parallel lines are defined here (each are problematic to establish as legitimate primitives).
These frameworks primarily derive their value from their capacity to coherently integrate meaningful physical information into pre-physical identities. The impersonal ideas also reduce subjective bias while still employing intuitive concepts. The approach does not fix a single equation, but rather equips the practitioner with sufficient tools to optimise waveform approximation itself.
Important Concepts:
1. Ongoing vibration of geometric surfaces and knots.
2. The infinities of calculus are only approximation tools. [The cosmological infinity is uniquely defined, I.E.: Only the universe is infinite, primarily because it is without bounds, and secondarily because infinitely much matter seems to comprise it].
3. The conflation of the circle and the empty set on the basis of [what I perceive as] their functional indistinguishability.
o = { }
The empty set isn’t nothing, it has a non-trivial identity because it instantiates a boundary. The boundary’s tension can be understood to suspend the Natural numbers in equilibrium.
Scientific experiment can thus be understood as the privileging of a particular perspective [that of the measurement device]. It follows that the most accurate measurement minimises the work done on the system under observation (SOU) by the measurement device (MD). It also follows that the relevant information transferred from the SOU to the MD ought to be complete (rendering all necessary properties knowable).
Since all measurement is interferential (causes changes to the system under observation), it follows that the least destructive of all measurements bearing the relevant information over the relevant time interval is the optimised measurement.
Afterthought
None of the 3 self-referential systems is superior to the others: each is optimised for particular applications. Used together, a richer image can begin to form, but a local increase in resolution always lowers resolution elsewhere: a fundamentally dualistic process. The capacity to distinguish true and false thus necessitates the resolving power of dualism. By the least action principle, fundamental reality accords with non-dualism and so the dualism of truth-bearing identities is distinct from, and necessarily yields to, the non-dualism of reality: the source of truth.
The Church of Entropy 