Computational Intelligence and Consciousness

Eduardo César Garrido Merchán

In recent years there have been many advances in artificial intelligence, especially in the field of automatic generation of texts and images that sometimes compete successfully with human productions. In light of this, the media, and even some scientists, have rung the bells announcing that we are on the verge of creating conscious artificial intelligence, which would compete with human beings as our equal. But others believe that this goal, if it were possible (which is not clear), is much further away than some think.

In an article signed by Eduardo César Garrido Merchán and Sara Lumbreras and published in the journal philosophies with the title Can Computational Intelligence Model Phenomenal Consciousness, the authors review Bertrand Russell's analogy, which asserts that consciousness and intelligence are closely correlated. In other words, any entity that possesses consciousness will also possess a high level of intelligence, and vice versa. In a way, this analogy is similar to the Turing Test, which is much better known.

The limits of mathematics

Kurt Gödel

In the last decades of the nineteenth century, Friedrich Ludwig Gottlob Frege, a professor in the university of Vienna, undertook an ambitious goal: formalizing the arithmetic in a set of axioms and deduction rules, in such a way that every true theorem would be deductible from the axioms by a finite number of applications of the deduction rules. The result was a monumental book, Grundgesetze der Arithmetike (1893-1903), which introduced, among other things, a basic formalization of set theory and a cumbersome notation, quickly replaced by Peano’s, which we are using now.

Unfortunately for Frege, when the second volume of his book was about to be published, he received a letter from Bertrand Russell, proving that his formulation of set theory entails an inconsistency. In Frege’s set theory, some sets are not member of themselves (as the set of all integers, which is not an integer), while other sets are members of themselves (as the set of all infinite sets, which is an infinite set). Russell then defined this set: the set of all sets that are not members of themselves. It is easy to see that this set leads to a paradox: if it is a member of itself, it cannot be a member of itself, and vice versa. Russell’s paradox wreaked havoc with Frege’s work, who had to add a hasty appendix to his book and then abandoned his research on the fundamentals of mathematics.

The limits of quantum computing

Alan Turing

In an interview in a major Spanish newspaper (La Vanguardia) published on July 27, 2019, David Pérez García, a researcher in quantum physics, says this: We are just in the beginning of some technologies that we still don’t know how far they will go. He is right, because the future is hardly predictable, but when it comes to quantum computing we tend to think that these computers, if they are viable, will let us solve problems quite different from those that can be addressed by the traditional computers to which we are used. In this context, however, mathematics can help us distinguish between what can be done, and what is completely impossible.

Although quantum computing is a fairly modern concept, its theoretical foundation was established by Alan Turing during the 1930s. Let us review a little of what he showed, for in this way we can correct a few optimistic ideas spread by the media, often driven by experts who approach the issue from very different points of view, compared to Turing.