Yeah, I know symbolic dynamics pretty well. I think I wrote most of the wikipedia article on "subshifts of finite type" and the rainbow of related topics - the product topology, the cylinder sets, e.g. most of "measure-preserving dynamical system" There's a vast network of related topics, and they're all interesting.
--linas On Mon, Jun 19, 2017 at 9:56 PM, Ben Goertzel <[email protected]> wrote: > On Tue, Jun 20, 2017 at 5:59 AM, Linas Vepstas <[email protected]> > wrote: > >> , and see how your grammar+semantic approach will be effective (adding > >> somehow a non-linear embedding in the phase space as I already discussed > >> with Ben) > > > > > > Ben has not yet relayed this to me. > > > > -- Linas > > Yeah, it seemed you were already pretty busy! > > The short summary is: For any complex dynamical system, if one embeds > the system's states in a K-dimensional space appropriately, and then > divides the relevant region of that K-dimensional space into discrete > cells... then each trajectory of that system becomes a series of > "words" in a certain language (where each of the discrete cells > corresponds to a word)... I guess you are probably familiar with > this technique, which is "symbolic dynamics" > > One can then characterize a dynamical system, in various ways, via the > inferred grammar of this "symbolic-dynamical language" ... > > I did work on this a couple decades ago using various Markovian > grammar inference tools I hacked myself... > > Enzo at Cisco, as it turns out, had been thinking about applying > similar methods to characterize the complex dynamics of some Cisco > networks... > > So we have been discussing this as an interesting application of the > OpenCog-based grammar inference tools we're now developing ... > > There's plenty more, but that's the high-level summary... > > (Part of the "plenty more" is that there may be a use of deep (or > shallow, depending on the case) neural networks to help with the > initial stage where one embeds the complex system's states in a > K-dimensional space. In a different context, word2vec and adagram are > examples of the power of modern NNs for dimensional embedding.) > > -- Ben > > > -- > Ben Goertzel, PhD > http://goertzel.org > > "I am God! I am nothing, I'm play, I am freedom, I am life. I am the > boundary, I am the peak." -- Alexander Scriabin > > -- > You received this message because you are subscribed to the Google Groups > "opencog" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To post to this group, send email to [email protected]. > Visit this group at https://groups.google.com/group/opencog. > To view this discussion on the web visit https://groups.google.com/d/ > msgid/opencog/CACYTDBeYGVPZJo3OeV3sajuPgaosg9nbBiurttsVU%3Dz23pSg7w% > 40mail.gmail.com. > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "opencog" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To post to this group, send email to [email protected]. Visit this group at https://groups.google.com/group/opencog. To view this discussion on the web visit https://groups.google.com/d/msgid/opencog/CAHrUA36NbnLXzEFJEr33uN%2BPNswLG26w7%3D3FsZJSzp%3DaSmG2yA%40mail.gmail.com. For more options, visit https://groups.google.com/d/optout.
