"Sequences"














Fujii, Hokusai: theculturetrip.com

Multi-dimensional Sequences

  With respect to language in general, the grammar for a language is
  the set of rules that operate on the elements in a sentence.  With
  respect to a programming language, this grammar has been sort of
  formalised in Lisp with the use of S-expressions inside the lambda
  calculus.

  However, there is no simple grammar or re-writing ruleset for a
  multi-dimensional sequence, MDS.  In a effort to define a simple
  grammar for MDS's we're attempting to use re-writing rules for
  a simple sequences inside of loops.  Loops, of course, contain
  the iteration or recursive constructs inside a computer program.

  The analogy of comparing loops to geometric polytopes is in the
  possibility that using loops on rewriting sequences will reduce
  dimensionality and increase order.  Another advantage, maybe a
  necessity, in using loops, is the setting of initial conditions
  and adjusting dynamic mutable variables and functions when
  propagating the computations.

  The picture below is an illustration of this.
  
  
  The formalism for this method of analysis is contained in the notion
  of rewriting systems.  The Church-Turing Lambda Calculus also
  contains the notion of rewriting rules.  Finite state machines
  used in production systems are fundamentally the dynamic elements
  of rewriting rulesets.

  The construction of a self-aware kind of machine, I think, depends
  innately on a feed back system built inside of the recursive loop.
  This is the idea in 3Lisp, and the recursive tower of
  Brian Smith. [1, 2]
 



  
  [1]  Reflection and Sentantics in Lisp, Brian Cantwell Smith, 1984.

  [2]  The Mystery of the Tower Revealed, Mitchell Wand and Daniel
       Friedman, 1988.
  



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Articles

Zen Gardens -
Breaty to a Machine
2019-12-29

Structure of the Machine -
Dimensionality Reduction
Using Prefix Trees
2019-12-31

Multi-dimensional Sequences
2020-1-2

Temporal Sequences
2020-1-4