The director Denis Villeneuve and cinematographer Greig Fraser in their Dune: Part Two movie made a curious decision to film the scenes on the surface of the Giedi Prime planet in the infrared spectrum. It turned out to have interesting aesthetics and there are some interesting related physics to discuss and speculate about how realistic the look of it is.
S.B. Pshenichnikov
The article outlines a new mathematical apparatus for verbal calculations in NLP (natural language processing). Words are embedded not in a real vector space, but in an algebra of extremely sparse matrix units. Calculations become evidence-based and transparent. The example shows forks in calculations that go unnoticed when using traditional approaches, and the result may be unexpected.
The use of IT in Natural Language Processing (NLP) requires standardization of texts, for example, tokenization or lemmatization.
After this, you can try to use mathematics, since it is the highest form of standardization and turns the objects under study into ideal ones, for example, data tables into matrices of elements. Only in the language of matrices can one search for general patterns in data (numbers and texts).
If text is turned into numbers, then in NLP these are first natural numbers for numbering words, which are then embedded into real vectors is irreversible ed in a real vector space.
Perhaps we should not rush to do this but come up with a new type of numbers that is more suitable for NLP than numbers for studying physical phenomena. These are matrix hyperbinary numbers. Hyperbinary numbers are one of the types of hypercomplex numbers.
Hyperbinary numbers have their own arithmetic, and if you get used to it, it will seem more familiar and simpler than Pythagorean arithmetic.
In Decision Support Systems (DSS), the texts are value judgments and a numbered verbal rating scale. Next (as in NLP), the numbers are turned into vectors of real numbers and used as sets of weighted arithmetic average coefficients.
I always pay attention to assessing the complexity of programming in a particular language. Programming is indeed not an easy task and this is perceived as a fact and usually does not require any confirmation.
But the concept of “complexity” is akin to the term “heap”. For some, five coconuts is not so much, but for someone who ate one and “didn’t want any more,” this means that even one coconut will be too much for him.
The same goes for the complexity of programs. It seems that the constant increase in the complexity of programs is obvious to everyone and is observed in all areas of application of IT technologies, and programming languages themselves become more and more complex as they develop, but assessing “complexity” using numerical metrics is a problem. obviously a thankless task, but also “You can’t manage what you can’t measure...”
Typically, talk of “complexity” only implies value judgments without any numerical evaluation. And since I am personally interested in the issue of the complexity of programming languages, I decided to calculate the complexity of implementing the gcc compiler on some conditional “parrots”. What if we could see some patterns of difficulty changing over time?
Practically all programming languages are built either on the principle of similarity (to make like this one, only with its own blackjack) or to realize some new concept (modularity, purity of functional calculations, etc.). Or both at the same time.
But in any case, the creator of a new programming language doesn't take his ideas randomly out of thin air. They are still based on his previous experience, obsession with the new concept and other initial settings and constraints.
Is there a minimal set of lexemes, operators, or syntactic constructs that can be used to construct an arbitrary grammar for a modern general-purpose programming language?