Embedding words in numbers: chartering new territory

If you are an engineer and you want to predict what happens if you heat a slab of steel, you use a computer program to solve the heat parabolic partial differential equation. It took hundreds of years to understand that we can represent our physical world with numerical variables that obey differential equations.

In the 17^th century Gottfried Leibnitz dreamed of automating human thinking. At the turn of twentieth century the work of Giuseppe Peano, Gottlob Frege, and, above all, A. M. Whitehead and Bertrand Russell lead to the first system of mathematical logic that automated logic thinking. However, “embedding” logic in numbers, in 1931 Kurt Godel proved that any formal system of logic is essentially incomplete.

Automating ordinary language had to wait the development of very powerful computers. It is only in the last two decades that Generative Artificial Intelligence has created systems that can mimic the human ability to use ordinary language.

The key to this surprising capability is the embedding of words in numerical vectors. After embedding words, neural networks, that are numerical algorithms, perform cognitive operations. This is unchartered territory, a truly interdisciplinary effort that includes computational linguistics, theory of complexity, linguistics, mathematics, logic, and philosophy.