{"id":454147,"date":"2025-04-01T16:39:30","date_gmt":"2025-04-01T16:39:30","guid":{"rendered":"http:\/\/savepearlharbor.com\/?p=454147"},"modified":"-0001-11-30T00:00:00","modified_gmt":"-0001-11-29T21:00:00","slug":"","status":"publish","type":"post","link":"https:\/\/savepearlharbor.com\/?p=454147","title":{"rendered":"The Links Theory 0.0.2<\/span>"},"content":{"rendered":"
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Note: The article was published at the 1st of April, but the translation is in the progress (some parts are still in Russian). I hope for your understanding. This note will be removed once it is ready. Save it to bookmarks to read later, please.<\/em><\/strong><\/p>\n

Last April 1st, as you might have guessed, we were joking. It\u2019s time to fix that, and now everything is \"100\\%\" serious.<\/p>\n

TL;DR (too long; didn’t read)<\/h4>\n

This article contains many letters, but it can be represented using just 4 symbols from set theory<\/a>:<\/p>\n

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\"L<\/p>\n<\/blockquote>\n

Everything else follows from them.<\/p>\n

Overview<\/h2>\n

This article is primarily aimed at programmers and mathematicians, yet we\u2019ve designed it to be accessible to anyone interested in the ideas it presents. We believe that the concepts discussed here can serve as inspiration across a wide range of scientific disciplines.<\/p>\n

Our goal was to create a self-contained text that guides you through each topic in a clear, logical order. Throughout the article, you\u2019ll find links to Wikipedia<\/a> for those who wish to explore specific terms or concepts in more depth \u2014 but these are entirely optional. The text is intended to be easily understood when read from start to finish.<\/p>\n

Every symbol and formula is explained individually, with concise definitions provided where needed. We\u2019ve also included images to help illustrate key ideas. If you come across anything that isn\u2019t clear, please let us know so we can improve it.<\/p>\n

Comparison of theories<\/h2>\n

To quickly dive in, we begin by comparing the mathematical foundations of the two most popular data models<\/a> with that of the associative model of data<\/a>.<\/p>\n

In the course of our research, we discovered that traditional theories were sometimes overly complex or redundant, while at other times they imposed too many artificial constraints. <\/p>\n

This overall lack of flexibility, adaptability, and universality motivated us to search for a simpler yet all-encompassing informational theory and a data storage model that future artificial intelligence could easily understand and effectively utilize. Along the way, we drew inspiration from the workings of our own associative memory and associative thought processes.<\/p>\n

Relational Algebra<\/h3>\n

Relational algebra<\/a> and the relational model<\/a> are based on the concepts of relations<\/a> and n-tuples<\/a>.<\/p>\n

A relation<\/a> is defined as a set<\/a> of n-tuples<\/a>:<\/p>\n

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\"\\mathbf{R [1]<\/a><\/p>\n<\/blockquote>\n

\"\u0420\u0438\u0441.<\/p>\n
Figure 1.<\/strong>\u00a0A table is described by a relation<\/a>\"\\mathbf{R}\", which is represented as a set<\/a> of rows<\/a> \"\\mathbf{r}\", belonging to a Cartesian product<\/a> \"\\mathbf{S_1.<\/figcaption><\/div>\n<\/figure>\n

Where:<\/strong><\/p>\n