Assembly Theory Reduced to Shannon Entropy and Rendered Redundant by Naive Statistical Algorithms
<|reference_start|>Assembly Theory Reduced to Shannon Entropy and Rendered Redundant by Naive Statistical Algorithms: In this paper we give answer to an argument trying to show the divergence of Assembly Theory from LZ compression. We formally proved that any implementation of the concept of `copy number' underlying Assembly Theory (AT) and its assembly index (Ai) is equivalent to Shannon Entropy and not fundamentally or methodologically different from algorithms like ZIP and PNG via an LZ compressing grammar. Here we show that the weak empirical correlation between Ai and LZW, which the authors offered as a defence against the previously proven result that the assembly index calculation method is an LZ scheme, is based on an incomplete and misleading experiment. When the experiment is completed and conducted properly, the asymptotic convergence to LZ compression and Shannon Entropy is evident and aligned with the mathematical proof previously offered. Therefore, this completes both the theoretical and empirical demonstrations that any variation of the copy-number concept underlying AT, which resorts to counting the number of object repetitions `to arrive at a measure for life', is equivalent to statistical compression and Shannon Entropy. We demonstrate that the authors' `we-are-better-because-we-are-worse' defence argument against compression does not withstand basic scrutiny, and that their primary empirical results separating organic from inorganic compounds have not only been previously reported -- sans claims to unify physics and biology -- but are also driven solely by molecular length, not by any special feature of life captured by their assembly index. Finally, we show that Ai is a special case of our Block Decomposition Method introduced almost a decade earlier.<|reference_end|>
@article{ozelim2024assembly,
    title={Assembly Theory Reduced to Shannon Entropy and Rendered Redundant by
  Naive Statistical Algorithms},
    author={Luan Ozelim, Abicumaran Uthamacumaran, Felipe S. Abrah~ao, Santiago
  Hern'andez-Orozco, Narsis A. Kiani, Jesper Tegn'er, Hector Zenil},
    journal={arXiv preprint arXiv:2408.15108},
    year={2024},
    archivePrefix={arXiv},
    eprint={2408.15108},
    primaryClass={cs.IT cs.CC math.IT}
}