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Dimensional Complexity and Algorithmic Efficiency

DOI: 10.4236/ijmnta.2022.111001, PP. 1-10

Keywords: Symbolic Intelligence, Dimensional Complexity, Algorithmic Efficiency, Notational Unification, Turing Complete Machine, Unified Theory

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Abstract:

This paper uses the concept of algorithmic efficiency to present a unified theory of intelligence. Intelligence is defined informally, formally, and computationally. We introduce the concept of dimensional complexity in algorithmic efficiency and deduce that an optimally efficient algorithm has zero time complexity, zero space complexity, and an infinite dimensional complexity. This algorithm is used to generate the number line.

References

[1]  Hosch, W.L. (2022) Incompleteness Theorem. Encyclopedia Britannica.
[2]  Panu, R. (2013) Gödel’s Incompleteness Theorems. Stanford Encyclopedia of Philosophy.
[3]  Church, A. (1936) An Unsolvable Problem of Elementary Number Theory. American Journal of Mathematics, 58, 345-363.
https://doi.org/10.2307/2371045
[4]  Turing, A.M. (1937) On Computable Numbers, with an Application to the Entscheidungs Problem. Proceedings of the London Mathematical Society, 42, 230-265.
https://doi.org/10.1112/plms/s2-42.1.230
[5]  Kushner, B.A. (2006) The Constructive Mathematics of A. A. Markov. The American Mathematical Monthly, 113, 559-566.
https://doi.org/10.1080/00029890.2006.11920338
[6]  Markov, A.A. (1960) The Theory of Algorithms. American Mathematical Society Translations, Series 2, 15, 1-14.
https://doi.org/10.1090/trans2/015/01
[7]  Kuo, W. and Zuo, M.J. (2003) Optimal Reliability Modeling: Principles and Applications. John Wiley & Sons, Hoboken, 62.
[8]  Juliette, K. (2020) Kurt Gödel. Stanford Encyclopedia of Philosophy.
https://plato.stanford.edu/entries/goedel
[9]  Davis, M. (2006) The Incompleteness Theorem. Notices of the AMS, 53, 414.
[10]  Panu, R. (2020) Gödel’s Incompleteness Theorems. Stanford Encyclopedia of Philosophy.
[11]  Cook, S.A. (2007) An Overview of Computational Complexity. ACM Turing Award Lectures. Association for Computing Machinery, New York.
https://doi.org/10.1145/1283920.1283938
[12]  McCann, L. (2009) Analysis of Discrete Structures. University of Arizona CSc 345, 1-2.
[13]  Ellefsen, B. (2020) Calculating Big-O(x3).
https://math.stackexchange.com/q/2126104
[14]  Knuth, D.E. (1976) Big Omicron and Big Omega and Big Theta. SIGACT News, 8, 18-24.
https://doi.org/10.1145/1008328.1008329
[15]  Vitányi, P. and Meertens, L. (1985) Big Omega versus the Wild Functions. ACM SIGACT News, 16, 56-59.
https://doi.org/10.1145/382242.382835
[16]  Seehorn, A. (2021) The History of Equality Symbols in Math. sciencing.com.
[17]  Cajori, F. (1928) A History of Mathematical Notations: Vol. 1—Notations in Elementary Mathematics. The Open Court Company, London, 297-298.
[18]  Krantz, S.G. (2016) A Primer of Mathematical Writing.

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