Gabriel Kron was an important research electrical engineer known for applying differential geometry and algebraic topology to the study of electrical system. Towards the end of his career he published a number of unusual, even by his standards, papers on concepts with names like polyhedral networks, self organizing automata, wave automata, multidimensional space filters and crystal computer, which I think are more or less synonymous. I have obtained a few of these papers and did not understand them at all. If they were not written be Kron, I would be suspicious of them.

I have not been able to find any significant secondary literature on these ideas. The few citations I have tracked down only mention them tangentially, but I have also found no refutations of these papers and no suggestions that Kron had gone off the rails. The papers were published in respectable journals.

I am looking for an understandable exposition or refutation of these ideas, or pointers to such. Also pointers to follow on research by others, possibly using different terminology.

I am not looking for explanations of Kron's other ideas like diakoptics and tensor analysis of networks.

Some of the relevant papers are:

  • G. Kron, Multi-dimensional space filters. Matrix and Tensor Quarterly, 9, 40 - 43 (1958).
  • G. Kron, Basic concepts of multi-dimensional space filters. AIEE Transactions, 78, 554 - 561 (1959).
  • G. Kron, Self-organizing, dynamo-type automata. Matrix and Tensor Quarterly, 11, 42 - 52 (1960).
  • G. Kron, Power-system type self-organizing automata. RAAG Memoirs, III, 392 - 417 (1962).
  • G. Kron, Multi-dimensional curve-fitting with self-organizing automata. Journal of Mathematical Analysis and Applications, 5, 46 - 49 (1962).

I have mainly looked at the last one and material at the end of

  • Diakoptics; the piecewise solution of large-scale systems. MacDonald, London, 1963. 166 pp.
  • $\begingroup$ +1, interesting, if you some let me know too $\endgroup$ – Nikos M. Aug 18 '14 at 17:00
  • $\begingroup$ Without access to these papers, but based on his biography nothing indicates that he has gone "off the rails". Having said that, I think there is a bit of a cult going on around Kron very similar to that surrounding Tesla. His "Tensors for circuits" text is certainly the result of hard work, rewriting known results in a language unfamiliar to the electrical engineer, but it does not seem to contain particularly novel ideas from the viewpoint of a physicist or mathematician. I reserve a harsher or more lenient judgment for later, just in case I can find other papers. $\endgroup$ – CuriousOne Aug 18 '14 at 20:06
  • $\begingroup$ @CuriousOne I have a lot of respect for Kron's work. I think his work on non-Riemannian/quasi-holonomic systems may have been new even to physicists at the time. That is why I would like to figure out what he was getting at with these papers. $\endgroup$ – Daniel Mahler Aug 18 '14 at 22:00
  • $\begingroup$ @DanielMahler: I have only found his collection of papers on circuits, so far, which is probably not quite as inspired as some of the other titles promise. It does show, that he has an independent way of thinking about things, though. It's also actually quite down to earth, which I perceive as a good thing. Judging by what little I know, taking a look at the rest of his work is certainly worth it. $\endgroup$ – CuriousOne Aug 19 '14 at 1:40

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