5.1 Computability of Quantum Consciousness

The following proof of computability of quantum consciousness is done by Mr. Tang in 2016.  What we would like to find out is whether this theorem can be done by machine.  Also, if this is done, whether the proof can be expanded to more generalized condition, and whether the laid-out plan to prove computability of quantum intelligence and quantum creativity can also be done by AI, possibly with the assistance of LLM.

5.1.1      Maguire’s Postulate

Maguire [1] postulates the following: 

Maguire’s Postulate: Consciousness is classical data compression.

Or consciousness is integrated data compression where the term “integrated” is originated from Tononi [2] and defined by Maguire [3] below.  Whether this Postulate is reasonable is still under debate, but we shall enrich the Postulate in this Chapter. This is originated from the Occam’s Razor Principle: entities should not multiplied beyond necessity, attributed to William of Ockham in the 13th Century.  The principle promotes simplicity.  It is generally believed that the more you compress data of some investigated phenomena, the better you can learn, generalize and predict unknown future.  However, to further substantiate this idea, the classical Kolmogorov complexity C, or the length of shortest description of the data working for a classical Turing machine, should be used with the concept of edit distance.

5.1.2      Edit Distance

References

[1] P. Maguire and R. Maguire, "Consciousness is Data Compression," Department of Computer Science, NUI Maynooth, Co.Kildare, Ireland, 2010.

[2] G. TONONI, "Consciousness as Integrated Information: a Provisional Manifesto," Biol. Bull., vol. 215, p. 216–242, 2008. 

[3] P. Maguire, R. Maguire, P. Moser and V. Griffith, "Is Consciousness Computable? Quantifying Integrated Information Using Algorithmic Information Theory," Department of Computer Science, NUI, Maynooth, Ireland, 2014.

[4] P. M. B. Vitányi, "Quantum Kolmogorov Complexity Based on Classical Description," IEEE TRANSACTIONS ON INFORMATION THEORY, vol. 47, no. 6, pp. 2464-2479, 2001. 

[5] J. H. Reif and S. Chakraborty, "Efficient and Exact Quantum Compression," aDepartment of Computer Science, Duke University, Durham, NC, 2007.