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How to cite:
Łukaszyk, S.; Bieniawski, W. Assembly Theory of Binary Messages (How to Assemble a Black Hole and Use it to Assemble New Binary Information?). Preprints2024, 2024011113. https://doi.org/10.20944/preprints202401.1113.v8
Łukaszyk, S.; Bieniawski, W. Assembly Theory of Binary Messages (How to Assemble a Black Hole and Use it to Assemble New Binary Information?). Preprints 2024, 2024011113. https://doi.org/10.20944/preprints202401.1113.v8
Łukaszyk, S.; Bieniawski, W. Assembly Theory of Binary Messages (How to Assemble a Black Hole and Use it to Assemble New Binary Information?). Preprints2024, 2024011113. https://doi.org/10.20944/preprints202401.1113.v8
APA Style
Łukaszyk, S., & Bieniawski, W. (2024). Assembly Theory of Binary Messages (How to Assemble a Black Hole and Use it to Assemble New Binary Information?). Preprints. https://doi.org/10.20944/preprints202401.1113.v8
Chicago/Turabian Style
Łukaszyk, S. and Wawrzyniec Bieniawski. 2024 "Assembly Theory of Binary Messages (How to Assemble a Black Hole and Use it to Assemble New Binary Information?)" Preprints. https://doi.org/10.20944/preprints202401.1113.v8
Abstract
Using assembly theory, we investigate the assembly pathways of binary strings of length N formed by joining bits present in the assembly pool and the strings that entered the pool as a result of previous joining operations. We show that the string assembly index is bounded from below by the shortest addition chain for N, and we conjecture about the form of the upper bound. We define the degree of causation for the minimum assembly index and show that for certain N it features regularities that can be used to determine a shortest addition chain. We show that a string with the smallest assembly index for N can be assembled by a binary program of length equal to this index if the length of this string is expressible as a product of Fibonacci numbers. We conjecture that there is no binary program that has a length shorter than the length of the string having the largest assembly index for N that could assemble this string. The results confirm that four Planck areas provide a minimum information capacity that corresponds to a minimum thermodynamic (Bekenstein-Hawking) entropy. Knowing that the problem of determining the assembly index is at least NP-complete, we conjecture that this problem is NP-complete, while the problem of creating the string so that it would have a predetermined largest assembly index is NP-hard. The proof of this conjecture would imply P ≠ NP, since every computable problem and every computable solution can be encoded as a finite binary string. Once the new information is assembled by a dissipative structure or by a human, it is subject to the 2nd law of thermodynamics, and nature seeks to optimize its assembly pathway.
Keywords
assembly theory; emergent dimensionality; black holes; shortest addition chains; P versus NP problem; quantum orthogonalization interval theorems; mathematical physics; binputation
Subject
Physical Sciences, Mathematical Physics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
