We show that in Kabbalah, the esoteric teaching of Judaism, there were developed ideas of unconventional automata in which operations over characters of the Hebrew alphabet can simulate all real processes producing appropriate strings in accordance with some algorithms. These ideas may be used now in a syllogistic extension of Lindenmayer systems (L-systems), where we deal also with strings in the Kabbalistic-Leibnizean meaning. This extension is illustrated by the behavior of Physarum polycephalum plasmodia which can implement, first, the Aristotelian syllogistic and, second, a Talmudic syllogistic by qal wa-homer.
[1] A. Adamatzky, V. Erokhin, M. Grube, Th. Schubert, and A. Schumann, “Physarum Chip Project: Growing Computers From Slime Mould,” International Journal of Unconventional Computing, 8(4), 2012, pp. 319–323.
[2] A. Adamatzky, “Physarum machine: implementation of a Kolmogorov-Uspensky machine on a biological substrate,” Parallel Processing Letters, vol. 17, no. 04, 2007, pp. 455–467.
[3] A. Adamatzky, Physarum Machines: Computers from Slime Mould (World Scientific Series on Nonlinear Science, Series A). World Scientific Publishing Company, 2010.
[4] A. Lindenmayer, “Mathematical models for cellular interaction in development. parts I and II,” Journal of Theoretical Biology, 18, 1968, pp. 280–299; 300–315.
[5] J. Łukasiewicz, Aristotle’s Syllogistic From the Standpoint of Modern Formal Logic. Oxford Clarendon Press, 2nd edition, 1957.
[6] Y. Matveyev, “Symbolic computation and digital philosophy in early Ashkenazic Kabbalah,” [in:] Schumann, A. (ed.), Judaic Logic. Gorgias Press, 2010, 245–256.
[7] K. Niklas, Computer Simulated Plant Evolution. Scientific American, 1985.
[8] A. Schumann and A. Adamatzky, “Logical Modelling of Physarum Polycephalum,” Analele Universitatii Din Timisoara, seria Matemtica-Informatica 48 (3), 2010, pp. 175–190.
[9] A. Schumann and A. Adamatzky, “Physarum Spatial Logic,” New Mathematics and Natural Computation 7 (3), 2011, pp. 483–498.
[10] A. Schumann and L. Akimova, “Simulating of Schistosomatidae (Trematoda: Digenea) Behaviour by Physarum Spatial Logic,” Annals of Computer Science and Information Systems, Volume 1. Proceedings of the 2013 Federated Conference on Computer Science and Information Systems. IEEE Xplore, 2013, pp. 225–230.
[11] A. Schumann, “On Two Squares of Opposition: the Leśniewski’s Style Formalization of Synthetic Propositions,” Acta Analytica 28, 2013, pp. 71–93.
[12] A. Schumann and K. Pancerz, “Towards an Object–Oriented Programming Language for Physarum Polycephalum Computing,” in M. Szczuka, L. Czaja, M. Kacprzak (eds.), Proceedings of the Workshop on Concurrency, Specification and Programming (CS&P’2013), Warsaw, Poland, September 25–27, 2013, pp. 389–397.
[13] A. Schumann, “Two Squares of Opposition: for Analytic and Synthetic Propositions,” Bulletin of the Section of Logic 40 (3/4), 2011, pp. 165–178.
[14] P. Prusinkiewicz and A. Lindenmayer, The Algorithmic Beauty of Plants. Springer-Verlag, 1990.
[15] Yisrael Ury, Charting the Sea of Talmud: A Visual Method for Understanding the Talmud. 2012.
[16] J. J. M. M. Rutten, “Universal coalgebra: a theory of systems,” Theor. Comput. Sci., 249 (1), 2000, pp. 3–80.