Our next IPI Lecture will be on Saturday, 25th of May at 16.00 London time.
Title: Assembly Theory of Bitstrings
Abstract: Bit is the smallest amount and the quantum of information. We used assembly theory to investigate the assembly pathways of binary strings of length N formed by joining bits present in the assembly pool and the bitstrings that entered the pool as a result of previous joining operations. The bitstring assembly index (the smaller amount of steps required to assembly a bitstring of length N) is bounded from below by the shortest addition chain for N. We conjecture about the form of the upper bound. We define the degree of causation for the minimum assembly index that happened to reveal regularities for certain N that can be used to determine the length of the shortest addition chain for N. We explored the idea of assembling bitstrings by other bitstrings (binputation) and it turned that a bitstring 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 bitstring is expressible as a product of Fibonacci numbers. 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 in fact NP-complete, while the problem of creating the bitstring 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 bitstring. The lower bound on the bitstring assembly index implies a creative path and an optimization path of the evolution of information, where only the latter is available to Turing machines (artificial intelligence). Furthermore, the upper bound hints at the role of dissipative structures and collective, in particular human, intelligence in this evolution.
Author: Dr. Szymon Łukaszyk
BIO: Szymon Łukaszyk received his M.Eng. degree in the applications of
genetic algorithms in mechanics in 1996 and a D.Eng. degree on the
Łukaszyk-Karmowski metric and its practical applications in 2004 at the Cracow
University of Technology. After completing postgraduate Law on Industrial
Property studies at Jagiellonian University, he heads his own patent attorneys’
office. His research interests include emergent dimensionality, entropic
gravity, assembly theory, quantum mathematics, and mathematical physics.
25th of May at 16.00 London time. Online ZOOM lecture - link will be emailed to the IPI members.
