The Information Requirements of Complex Biological and Economic Systems with Algorithmic Information Theory

The Information Requirements of Complex Biological and Economic Systems with Algorithmic Information Theory

S. DEVINE 

Victoria Management School, Victoria University of Wellington, Wellington, New Zealand

Page: 
367-376
|
DOI: 
https://doi.org/10.2495/DNE-V12-N3-367-376
Received: 
N/A
| |
Accepted: 
N/A
| | Citation

OPEN ACCESS

Abstract: 

This article interprets the natural laws creating and maintaining a complex system, such as an ­ecology or an economy, distant from equilibrium, as computations on a real world Universal Tur-ing Machine (UTM). As a laboratory, UTM can simulate the real world UTM, from the perspective of algorithmic information theory, the number of bits in the shortest, appropriately coded binary algorithm that specifies a real world system on a laboratory UTM defines its algorithmic entropy and its information content. As only algorithmic entropy differences matter, and differences are UTM-independent, ­differences measured on the laboratory UTM align with entropy changes in the real world. The ­system’s distance from equilibrium in bits defines its order. Computations require energy. Landauer’s principle identifies the minimum energy per bit (or the real world equivalent) to drive the computation that creates and sustains a real world system in a homeostatic state distant from equi-librium. This high-grade energy carries the computational instructions that do work on the system, ejecting disorder as heat and waste. While replication algorithms drive the emergence of complex ecological systems (doi:10.1016/j.biosystems.2015.11.008), in economic systems, individual agent behaviour can be captured by computer algorithms akin to the perspective of an adaptive system paradigm. Rather than specifying detailed behavioural routines for an economy, a narrative is used to identify the information drivers that create an ordered far-from-equilibrium economic system. The narrative shows that, somewhat like the interdependence of species in a vibrant ecology, agents trade, utilise technology, and amalgamate to form more complex structures creating order and driving the economy further from equilibrium. An ordered economy is a better economy. Order-creating invest-ments (infrastructure, machines etc.) enhance economic performance, in contrast to non-ordering investments that extract wealth from ­others, adding nothing.

Keywords: 

Algorithmic Information Theory, economic complexity and economic order, emergence, energy and economic sustainability, non-equilibrium economics.

  References

[1] Li, M. & Vitanyi, P.M.B., An Introduction to Kolmogorov Complexity and its Applica-tions, 3rd edn., Springer-Verlag: New York, 2008. https://doi.org/10.1007/978-0-387-49820-1

[2] Devine, S.D., Understanding how replication processes can maintain systems away from equilibrium using algorithmic information theory. Biosystems, 140, pp. 8–22, 2016. https://doi.org/10.1016/j.biosystems.2015.11.008

[3] Chaitin, G., A theory of program size formally identical to information theory. Journal of the ACM, 22, pp. 329–340, 1975. https://doi.org/10.1145/321892.321894

[4] Solomonoff, R.J., A formal theory of inductive inference; part 1 and part 2. Information and Control, 7, pp. 1–22, 224–254, 1964.

[5] Kolmogorov, K., Three approaches to the quantitative definition of information. Prob-lems of Information Transmission, 1, pp. 1–7, 1965.

[6] Chaitin, G., On the length of programs for computing finite binary sequences. Journal of the ACM, 13, pp. 547–569, 1966. https://doi.org/10.1145/321356.321363

[7] Zurek, W.H., Algorithmic randomness and physical entropy. Physical Review A, 40(8), pp. 4731–4751, 1989. https://doi.org/10.1103/PhysRevA.40.4731

[8] Bennett, C.H., Thermodynamics of computation- a review. International Journal of Theoretical Physics, 21(12), pp. 905–940, 1982. https://doi.org/10.1007/BF02084158

[9] Conway, J., Game of life. Wikepedia, 2016.

[10] Landauer, R., Irreversibility and heat generation in the computing process. IBM Journal of Research and Development, 5, pp. 183–191, 1961. https://doi.org/10.1147/rd.53.0183

[11] Bennett, C.H., Logical reversibility of computation. IBM Journal of Research and Development, 17, pp. 525–532, 1973. https://doi.org/10.1147/rd.176.0525

[12] Bennett, C.H., Logical depth and physical complexity. The Universal Turing Machine-a Half-Century Survey, ed. R. Herken, Oxford University Press: Oxford, pp. 227–257, 1988.

[13] Zurek, W.H., Thermodynamics of of computation, algorithmic complexity and the information metric. Nature, 341, pp. 119–124, 1989. https://doi.org/10.1038/341119a0

[14] Leff, H.S. & Rex, A.F., Maxwell’s Demon: Entropy, Information, computing. Princeton University Press: Princeton, 1990. https://doi.org/10.1887/0750307595

[15] Berut, A., Arakelyan, A., Petrosyan, S., Ciliberto, A., Dillenschneider, R. & Lutz, E., Experimental verification of Landauers principle linking information and thermody-namics. Nature, 483, pp. 187–190, 2012. https://doi.org/10.1038/nature10872

[16] Jun, Y., Gavrilov, M. & Bechhoefer, J., High-precision test of Lan-dauer’s principle in a feedback trap. Physical Review Letters, 113, p. 190601, 2014. https://doi.org/10.1103/PhysRevLett.113.190601

[17] Hong, J., Lambson, B., Dhuey, S. & Bokor, J., Experimental test of Landauer’s principle in single-bit operations on nanomagnetic memory bits. Science Advances, 2(3), 2016. https://doi.org/10.1126/sciadv.1501492

[18] Devine, S.D., The insights of algorithmic entropy. Entropy, 11(1), pp. 85–110, 2009. https://doi.org/10.3390/e11010085

[19] Szathmary, E. & Maynard Smith, J., From replicators to reproducers: the first major transitions leading to life. Journal of Theoretical Biology, 187, pp. 555–571, 1997. https://doi.org/10.1006/jtbi.1996.0389

[20] Nelson, R.R. & Winter, S.G., An Evolutionary Theory of Economic Change. Belknap: Cambridge, MA, 1982.

[21] Arthur, W.B., Holland, J.B., Le Baron, B., Palmer, R. & Tayler, P. (eds), Asset Pricing Under Endogenous Expectations in an Artificial Stock Market, volume XXVII of The Economy as an Evolving System II. SFI Studies in the Sciences of Complexity. Addison-Wesley: Reading [MA], 1997.

[22] Schneider, E.D. & Kay, J.J., Life as a manifestation of the second law of thermodynam-cis. Mathematical and Computer Modelling, 16(6–8), pp. 25–48, 1994. https://doi.org/10.1016/0895-7177(94)90188-0