Gödel's seminal work directly contradicted one of the great minds of mathematics and limited the field forever Kurt Gödel, the man who ruined mathematics, was one of the most important thinkers of the 20th century. He was born in 1906, smack-bang in the middle of the greatest crisis that maths has ever known. Just a few decades later, he would help resolve this turmoil, but in doing so doom mathematicians to a smaller world than the one that came before. Mathematics, as an intellectual framework, is incredibly powerful. The entire point is taking one set of logical ideas and using them to build another, making maths the closest thing we have to a cognitive perpetual-motion machine - there is always a new mathematical idea lurking across the horizon, and we just need to assemble the steps to get there.

Mathematicians say they proved reality is real. Researchers say it's impossible to use algorithmic computation to generate everything in our universe. Breakthroughs, discoveries, and DIY tips sent every weekday. Despite how it may feel some days, we probably aren't stuck in a computer simulation . An international team of mathematicians says that they have once-and-for-all determined that our reality is, in fact, .

This paper provides a definitive, unifying framework for the Symbol Grounding Problem (SGP) by reformulating it within Algorithmic Information Theory (AIT). We demonstrate that the grounding of meaning is a process fundamentally constrained by information-theoretic limits, thereby unifying the Gödelian (self-reference) and No Free Lunch (statistical) perspectives. We model a symbolic system as a universal Turing machine and define grounding as an act of information compression. The argument proceeds in four stages. First, we prove that a purely symbolic system cannot ground almost all possible "worlds" (data strings), as they are algorithmically random and thus incompressible. Second, we show that any statically grounded system, specialized for compressing a specific world, is inherently incomplete because an adversarial, incompressible world relative to the system can always be constructed. Third, the "grounding act" of adapting to a new world is proven to be non-inferable, as it requires the input of new information (a shorter program) that cannot be deduced from the system's existing code. Finally, we use Chaitin's Incompleteness Theorem to prove that any algorithmic learning process is itself a finite system that cannot comprehend or model worlds whose complexity provably exceeds its own. This establishes that meaning is the open-ended process of a system perpetually attempting to overcome its own information-theoretic limitations.

It is often argued that the underlying reason for this aversion to thinking is to reduce the associated fitness costs [15, 108]. Indeed, such costs to thinking are not difficult to find. In particular, it turns out that brains are extraordinarily expensive metabolically on a per-unit-mass basis, far more than almost all other organs (the heart and liver being the sole exceptions -- see [29, 108, 79, 16]). Consistent with this, it is not just that the software comprising our minds that seems tailored to reduce metabolic costs; the hardware supporting that software -- the physical architecture of our brains -- also seems tailored to reduce metabolic costs. We do not have a good understanding of exactly how our hardware is used to provide the ability of humans to engage in activities requiring high levels of abstract intelligence.

It is a robot researcher with good communication skills; you can ask it to answer questions about various areas of knowledge and it will write short documents in various formats and in excellent English. Or write bad poetry, incomprehensible jokes, and obey a command like "Write Tetris in C." What comes out looks like it could be, too. Coders love that sort of thing, and have been stuffing Stack Overflow's dev query boards with generated snippets. Just one problem – the quality of the code is bad. So bad, Stack Overflow has screamed "STOP!" and is mulling general guidelines to stop it happening again.

There is an increasing interest in applying recent advances in AI to automated reasoning, as it may provide useful heuristics in reasoning over formalisms in first-order, second-order, or even meta-logics. To facilitate this research, we present MATR, a new framework for automated theorem proving explicitly designed to easily adapt to unusual logics or integrate new reasoning processes. MATR is formalism-agnostic, highly modular, and programmer-friendly. We explain the high-level design of MATR as well as some details of its implementation. To demonstrate MATR's utility, we then describe a formalized metalogic suitable for proofs of Gödel's Incompleteness Theorems, and report on our progress using our metalogic in MATR to semi-autonomously generate proofs of both the First and Second Incompleteness Theorems.

I present the proof of Goedel's First Incompleteness theorem in an intuitive manner, while covering all technically challenging steps. I present generalizations of Goedel's fixed point lemma to two-sentence and multi-sentence versions, which allow proof of incompleteness through circular versions of the liar's paradox. I discuss the relation of Goedel's First and Second Incompletneness theorems to Goedel's Completeness theorems, and conclude with remarks on implications of these results for mathematics, computation, theory of mind and AI.

Playing human games such as chess and Go has long been considered to be a major benchmark of human capabilities. Computer programs have become robust chess players and, since the late 1990s, have been able to beat even the best human chess champions; though, for a long time, computers were unable to beat expert Go players -- the game of Go has proven to be especially difficult for computers. However, in 2016, a new program called AlphaGo finally won a victory over a human Go champion, only to be beaten by its subsequent versions (AlphaGo Zero and AlphaZero). AlphaZero proceeded to beat the best computers and humans in chess, shogi and Go, including all its predecessors from the Alpha family [1]. Core to AlphaZero's success is its use of a deep neural network, trained through reinforcement learning, as a powerful heuristic to guide a tree search algorithm (specifically Monte Carlo Tree Search). The recent successes of machine learning are good reason to consider the limitations of learning algorithms and, in a broader sense, the limitations of AI. In the context of a particular competition (or'game'), a natural question to ask is whether an absolute winner AI might exist -- one that, given sufficient resources, will always achieve the best possible outcome.

I recently started a new newsletter focus on AI education. TheSequence is a no-BS( meaning no hype, no news etc) AI-focused newsletter that takes 5 minutes to read. The goal is to keep you up to date with machine learning projects, research papers and concepts. I was recently having a debate about strong vs. weak AI with one of my favorite new thinkers in this market and it reminded me of something that I wrote over a year ago. So I decided to dust it off and restructure those thoughts in a new article.

I recently started a new newsletter focus on AI education. TheSequence is a no-BS( meaning no hype, no news etc) AI-focused newsletter that takes 5 minutes to read. The goal is to keep you up to date with machine learning projects, research papers and concepts. I was recently having a debate about strong vs. weak AI with one of my favorite new thinkers in this market and it reminded me of something that I wrote over a year ago. So I decided to dust it off and restructure those thoughts in a new article.