Quoeto uses the LMR grammar system but extends it through 3-d space like the helical grammar of CliYuGa. However Quoeto introduces more axis that have a semantic association. For the λ root of Quoeto (as a language) you will define R for noun, L for verbs and M for the subject – given a typical causal expression. R, L and M are denoted as cirles, they are spheres however. Between R and L the active / passive relation is defined and at the surface of the L (verb-) sphere the adverbs are defined.
The relations between the particles of LMR will span the Intentionality field from R to L and the causality field from L to M. Finally the plane between an assumed future M and the next state of the world R(2) will span the predictor field.
The precision of a statement or a complex prediction about the future state of reality R2 can be used to formalize certainty or expectations. It can also integrate error functions, data streams or expectation intervalls and as such trivially integrate probability to language.
The base – Q of quoeto is pictured here. In its language – version quoeto breaks the recursion before the fourth iteration is engaged. It shortcuts the statement at this recusion layer with a (complex) function of M and R, depicted at the bottom right corner. Te expression starts at λR and the break of the iteration is taking place at the Mϕ by ϕ(M)ϕ.
You can see that L has no trace of its iteration (no λ notion etc) and stays the ‘same’. L is the interactive and dynamic layer between the primarily factual (R) and the primarily theoretic (M) layers. L undergoes a context sensitive evolution and it grows in complexity and precision with local iteration depths (context intensity). It is bound by the final break of the iteration from ϕ(M)λ to a simplex λR(λ). The green projections show that ϕ(M)ϕ is hence a duplex of the two particle-objects. For the 4-dimensionality, the triplex of L is generated.
The previous structure of the grammar extends to R for space complexity, L for time complexity and M represents the program complexity. As M is the irregular / symmetry break field of the grammar it projects to the algortihmic complexity which is the duplex of L and the program complexity: the algorithmic complexity. This translates to how complex algorithms will become when in observed interaction, the dynamic field that is arising will ultimately break the duplex as it approximates a triplex – we define this triplex as the computation boundary and can hence solve the Halting problem for specified environments. The relation between abstraction and computation boundary is introduced as metaphoric – if we are getting too abstract it will become increasingly difficult to stay on track (realign a metaphor to actual particles). If a computation is so dense that it requires more steps then possible by any quantum or spintronics hardware it is a local computation boundary. The global computation boundary is associated to black hole entropy. The latter is the boundary after which information cannot be recovered as such.
Beware: this is not ‘textbook quoeto physics’, it is just an outline how complex geometric systems and submath can be arranged into a 4D grammar system like quoeto.
Intentionality plane and the causal plane from the language mode are compressed into a momentum field which now contains a frame of reference – the duplex of the two planes generates an inertial system that is bound in its explicity by the shannon compression barrier. The semantic actuality is hence replaced by bit-compressibility. The predictor field is complexified as it starts earlier and can now contain modes or transpositions of hyperheuristics.