After generalizing the Archimedean property of real numbers in such a way as to make it adaptable to non-numeric structures, we demonstrate that the real numbers cannot be used to accurately measure non-Archimedean structures. We argue that, since an agent with Artificial General Intelligence (AGI) should have no problem engaging in tasks that inherently involve non-Archimedean rewards, and since traditional reinforcement learning rewards are real numbers, therefore traditional reinforcement learning probably will not lead to AGI. We indicate two possible ways (...) traditional reinforcement learning could be altered to remove this roadblock. (shrink)

Can an agent's intelligence level be negative? We extend the Legg-Hutter agent-environment framework to include punishments and argue for an affirmative answer to that question. We show that if the background encodings and Universal Turing Machine (UTM) admit certain Kolmogorov complexity symmetries, then the resulting Legg-Hutter intelligence measure is symmetric about the origin. In particular, this implies reward-ignoring agents have Legg-Hutter intelligence 0 according to such UTMs.

In their paper 'Reward is enough', Silver et al conjecture that the creation of sufficiently good reinforcement learning (RL) agents is a path to artificial general intelligence (AGI). We consider one aspect of intelligence Silver et al did not consider in their paper, namely, that aspect of intelligence involved in designing RL agents. If that is within human reach, then it should also be within AGI's reach. This raises the question: is there an RL environment which incentivises RL agents to (...) design RL agents? (shrink)

We consider an extended notion of reinforcement learning in which the environment can simulate the agent and base its outputs on the agent's hypothetical behavior. Since good performance usually requires paying attention to whatever things the environment's outputs are based on, we argue that for an agent to achieve on-average good performance across many such extended environments, it is necessary for the agent to self-reflect. Thus, an agent's self-reflection ability can be numerically estimated by running the agent through a battery (...) of extended environments. We are simultaneously releasing an open-source library of extended environments to serve as proof-of-concept of this technique. As the library is first-of-kind, we have avoided the difficult problem of optimizing it. Instead we have chosen environments with interesting properties. Some seem paradoxical, some lead to interesting thought experiments, some are even suggestive of how self-reflection might have evolved in nature. We give examples and introduce a simple transformation which experimentally seems to increase self-reflection. (shrink)

We describe in our own words a visual phenomenon first described by Gallagher and Tsuchiya in 2020. The key to the phenomenon (as we describe it) is to direct one’s left eye at the image of one's left eye, while simultaneously directing one's right eye at the image of one's right eye. We suggest that one would naturally arrive at this phenomenon if one took a sufficiently literal reading of certain words of Socrates preserved in Plato's Alcibiades. We speculate that (...) perhaps Socrates was aware of the visual phenomenon in question. (shrink)

Internodons are a formalization of Hennig's concept of species. We present an alternative construction of internodons imposing a tree structure on the genealogical network. We prove that the segments (trivial unary trees) from this tree structure are precisely the internodons. We obtain the following spin-offs. First, the generated tree turns out to be an organismal tree of life. Second, this organismal tree is homeomorphic to the phylogenetic Hennigian species tree of life, implying the discovery of a multi-level tree of life: (...) this phylogenetic tree can be obtained by zooming out from the organismal tree, or conversely, the organismal tree of life can be generated by expanding the phylogenetic nodes into unary trees. Finally, the definition of the organismal tree allows an efficient algorithmic transformation of a given genealogical network into its corresponding phylogenetic species tree of life. The latter will be presented in a separate paper. (shrink)