Algebra and language (writing) are two different learning tools. When they are combined, we can expect new methods of machine understanding to emerge. To determine the meaning (to understand) is to calculate how the part relates to the whole. Modern search algorithms already perform the task of meaning recognition, and Google’s tensor processors perform matrix multiplications (convolutions) necessary in an algebraic approach. At the same time, semantic analysis mainly uses statistical methods. Using statistics in algebra, for instance, when looking for signs of numbers divisibility, would simply be strange. Algebraic apparatus is also useful for interpreting the calculations results when recognizing the meaning of a text.
The previous work from ref [1] describes the method of transforming a sign sequence into algebra through an example of a linguistic text. Two other examples of algebraic structuring of texts of a different nature are given to illustrate the method.
The mathematical model of signed sequences with repetitions (texts) is a multiset. The multiset was defined by D. Knuth in 1969 and later studied in detail by A. B. Petrovsky [1]. The universal property of a multiset is the existence of identical elements. The limiting case of a multiset with unit multiplicities of elements is a set. A set with unit multiplicities corresponding to a multiset is called its generating set or domain. A set with zero multiplicity is an empty set.
In [1,2,3] texts (sign sequences with repetitions) were transformed (coordinated) into algebraic systems using matrix units as word images. Coordinatization is a necessary condition of algebraization of any subject area. Function (arrow) (7) in [1]) is a matrix coordinatization of text. One can perform algebraic operations with words and fragments of matrix texts as with integers, but taking into account the noncommutativity of multiplication of words as matrices. Structurization of texts is reduced to the calculation of ideals and categories of texts in matrix form.
The published material is in the Appendix of my book [1]
Modern civilization finds itself at a crossroads in which to choose the meaning of life. Because of the development of technology, the majority of the world's population may be "superfluous" - not in demand in the production of values. There is another option, where each person is a supreme value, an absolute individual and can be indispensably useful in the technology of the collective mind.
In the eighties of the last century, the task of creating a scientific field of "collective intelligence" was set. Collective intelligence is defined as the ability of the collective to find solutions to problems more effectively than each participant individually. The right collective mind must be...
