# The Archimedean trap: Why traditional reinforcement learning will probably not yield AGI

arXiv: https://arxiv.org/abs/2002.10221 · HTML: https://mlsanity.com/paper/2002.10221/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2020.

## Built on by (most cited first, 6 of 6)

- [A Survey on Reinforcement Learning Methods in Character Animation](https://mlsanity.com/paper/2203.04735/) (2022)
- [Computable Artificial General Intelligence](https://mlsanity.com/paper/2205.10513/) (2022)
- [On the Computation of Meaning, Language Models and Incomprehensible Horrors](https://mlsanity.com/paper/2304.12686/) (2023)
- [Measuring Intelligence and Growth Rate: Variations on Hibbard's Intelligence Measure](https://mlsanity.com/paper/2101.12047/) (2021)
- [Reward-Punishment Symmetric Universal Intelligence](https://mlsanity.com/paper/2110.02450/) (2021)
- [Representation and Invariance in Reinforcement Learning](https://mlsanity.com/paper/2112.07752/) (2021)

## Abstract (arXiv)

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.