Wolpert’s Theorem about Mutual Unpredictability and the Impossibility of Subuniverses to Predict with Highest Resolution of Causality-Control are Rediscoveries of Concepts from Theory of Universe and Mind – Entangled with Unnecessary Mathematical Notation and Unsatisfiable Premises
https://www.researchgate.net/publication/403842042_Wolpert's_Theorem_about_Mutual_Unpredictability_and_the_Impossibility_of_Subuniverses_to_Predict_with_Highest_Resolution_of_Causality-Control_are_Rediscoveries_of_Concepts_from_Theory_of_Universe_and
In a discussion from 8.2025 on AGI List, a part of which I archived at SIGI-2025 as a paper, titled "Power overrides intelligence", Matt Mahoney mentioned some "Wolpert's law" of which I didn't know at the time. Later that year I discovered it without searching for it from other publications, and I found out that in fact this is a fork of my own "Arnaudov's laws" (principles), published and explained 4-5 years before the first paper of Wolpert (2007-2008) and up to 16 years before a consequent paper from 2018*. There is a match even on "Liar's paradox" - it is addressed in my work as well, however I "scaled" it to even more absurd form, ridiculed it and explained why it was nonsense and it didn't prove what the "cheaters" intended. It is related to the concept in TUM "resolution of causality-control and perception"; comparison of representation with different and incompatible RCCP. "What's the color of the rainbow?" (one color) These are ill-posed problems, presented as well-posed by "cheaters". In this circumstances, any higher-resolution answer is correct, as the lower-resolution causality-control doesn't have capacity to distinguish the answers.
The original "law" from TUM also reflects the hierarchical structure of the predictions and CCUs, which work as and are created by hierarchical universal simulators of virtual universes, i.e. predictors and causers, which are multi-resolution, multi-range, multi-scale, multi-domain, multi-precision, ... multi- ... Wolpert has a corresponding concept "a general-purpose prediction device, capable of correctly predicting different aspects of the universe’s future", however his "devices", at least so long as I interpreted the paper, are flat and they predict/not predict, true/false", "A/not A" - 1-bit nonsense in the real Universe, as explained in TUM.
This paper is a chapter from the book "Reflections on Everything", or "Listove", the second-largest volume from "The Prophets of the Thinking Machines: AGI & Transhumanism: History, Theory and Pioneers; Past, Present and Future", SIGI-2025, 10.2025.
Abstract
This work presents a critical and comparative analysis of the theoretical limits of prediction, inference, and control in physical systems, focusing on the framework introduced by David H. Wolpert and its relationship to the Theory of Universe and Mind (TUM). Wolpert’s theorems establish that no inference device embedded within a universe can achieve complete and error-free prediction, observation, or control of other devices, and that mutual perfect predictability between independent agents is impossible. These results are often interpreted as formal limits on knowledge, extending earlier ideas such as the impossibility of Laplace’s demon.
The present paper argues that these conclusions correspond to principles previously articulated within TUM, where the universe is modeled as a hierarchical computational structure composed of interacting causality-control units (CCUs). In this framework, predictive and causal capacities are determined by the resolution of causality-control and perception (RCCP), with higher-level subsystems operating on compressed representations of lower-level dynamics. As a consequence, all subsystems exhibit bounded predictive power, limited memory, and partial control, while only the universe as a whole achieves maximal resolution and completeness.
The analysis further examines the assumptions underlying formal inference models, particularly the treatment of devices as independent entities. It is argued that, in physically realized systems, all subsystems are inherently correlated due to shared origin, continuous interaction, and embedding within a common dynamical structure. This challenges the applicability of certain formal premises and suggests that observed limits on prediction arise from structural and hierarchical constraints rather than solely from logical or computational restrictions.
Additionally, the paper critiques the use of highly abstract logical formulations – such as binary query models and paradox-based arguments – as insufficient for capturing the multi-scale, continuous, and physically grounded nature of real-world systems. Instead, it advocates for models that incorporate hierarchical organization, varying resolutions, and the interplay between compression and prediction.
The conclusion is that while formal results on the limits of inference are valid and significant, they can be more comprehensively interpreted within a broader framework that accounts for the hierarchical and embedded nature of cognition and physical processes.
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This work is a chapter from the book “Reflections on Everything”, or “Listove” (Листове по всичко), which is an appendix and the second-biggest volume from the hyperbook “The Prophets of The Thinking Machines: Artificial General Intelligence and Transhumanism: History, Theory and Pioneers; Past, Present and Future”, T.Arnaudov, 2025-1.2026 – all published at the yearlong virtual conference “Self-Improving General Intelligence/Thinking Machines” 2025, organized by The Sacred Computer: Thinking Machines, Creativity and Human Development, a virtual multi- and interdisciplinary AGI and Transhumanism research and development laboratory, created in 2000. The first classic works of Theory of Universe and Mind were published between 2001 and 2004. Core ideas from the theory were presented in a lecture at Technical University of Sofia in September 2009 and in the world’s first university course in AGI at the University of Plovdiv “Paisii Hilendarski”, Bulgaria in 2010 and 2011.
The Sacred Computer: Thinking Machines, Creativity and Human Development: 2000-2026
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* See references to my work in the paper and in the referred books
* Physical limits of inference, David H. Wolpert, MS 269-1, NASA Ames Research Center, Moffett Field, CA 94035, USA, https://arxiv.org/pdf/0708.1362 [Submitted on 10 Aug 2007 (v1), last revised 23 Oct 2008 (this version, v2)]
* Theories of Knowledge and Theories of Everything, D.Wolpert, February 2018
10 days ago