Update on a + b = c
Karl Javorszky · Qeios · 2024
This numeric model organizes the collection of sentences _a+b=c_ for _a, b ≤ 16_. The update involves speaking also about such states of the world which are not the case. The etalon collection of 136 pairs of _(a, b)_ is placed in a habitat that is subject to periodic changes. We sort, resort, and order the logical primitives according to their diverse aspects. For sorting, we use the concept known as permutations. For grouping, we make use of the cyclic properties of permutations. We find an upper limit for the number of group relations that are concurrently possible on an assembly to be _n? = exp(ln(partition(n))²)_. The relations _n! / n?_ are fundamental. The work is an instruction manual on how to build the databases out of which the results are read out. The pairs of natural numbers organize themselves into paths within self-made geometries. The basic patterns that simple logical elements show when being reordered are archaic building material for logic. The terms of place and material become data in a data depositionary that is an element. Above this mother matrix of facts (which element is where when) there is a matrix of order, relations, and predictions. The accounting image of the inventory and the factual state of the inventory are two slightly deviating sets of data, which maintain a common currency of predictability resp. degree of certainty. The mutual expectations - predictions are an inbuilt feature of the symbols set and picture the rationally explainable world within the Eddington delineation. Its rules can be learnt by means of the data set we suggest the reader builds on their own computer.