I'd only ever seen numerical simulations of it, but consulting the ever-handy Wikipedia, it looks like the percolation threshold is given by the inverse of the average node degree for Erdos-Renyi random graphs. (http://en.wikipedia.org/wiki/Random_graph). Mind you, Wikipedia does seem to be contradictory on this - the http://en.wikipedia.org/wiki/Erdős–Rényi_model gives ln n/n for the percolation threshold.
Presumably, the two pages are talking about different concepts of percolation threshold, but I would need to drill down into it further... Note that on 2D tilings, the percolation threshold seems somewhere between 0.5 and 0.8 (http://en.wikipedia.org/wiki/Percolation_threshold). But for brains, neither network model is appropriate, so one would need to look at how percolation thresholds go for small world networks, about which Wikipedia doesn't have much to say. Cheers On Tue, Oct 22, 2013 at 11:21:21AM -0500, Jason Resch wrote: > Russell, > > Out of curiosity, is that link density of ~62% derived from 1 - (e^-1) ? > > The concept seems related, as it is also the proportion of hash values that > can be reached by hashing all possible hash values (for a good hash > function with a uniform distribution). > > Jason > > On Mon, Oct 21, 2013 at 4:17 PM, Russell Standish > <li...@hpcoders.com.au>wrote: > > > On Mon, Oct 21, 2013 at 05:01:50PM +0200, Bruno Marchal wrote: > > > > > > >Nevertheless, > > > >you do think there must be some strong indicators why a continuous > > > >(well at least local changes only) conscious path exists between all > > > >conscious states. What is that? > > > > > > By what I called (with a wrong terming) agnosologic path: where each > > > time you lost a mental feature, you lost also the mental reference > > > to it, so you "don't see any difference". > > > > > > This involves amnesia, and I don't use that in UDA or AUDA. But I > > > can also "think" and "discuss" like most participant in the list, on > > > the larger domain than my thesis ! > > > > > > > Ah - I probably missed what you were trying to say earlier. To follow > > on from your "agnosologia", I would hesitate to guess that > > consciousness somehow involves feedback loops. To make another > > analogy, if I take a network, if sufficiently dense, it will have > > cycles (loops), where if you follow the links from a given vertex, you > > will end up back where you start from. > > > > If you start removing links, the number of cycles drops, until > > eventually no cycles are left. That will most likely occur around the > > percolation threshold of the network, which is about 62% link density > > (62% of possible links are actually present) IIRC. > > > > ISTM one loses consciousness (loss of all feedback loops) well before > > losing sufficient memories (the links) to be able to merge into another > > person. This is essentially the reason fading qualia-style arguments > > don't impress me. > > > > Of course this is not a proof. For that, I suspect we need a better > > theory of consciousness. But I'm seeing your analogy, and raising one :). > > > > > > -- > > > > > > ---------------------------------------------------------------------------- > > Prof Russell Standish Phone 0425 253119 (mobile) > > Principal, High Performance Coders > > Visiting Professor of Mathematics hpco...@hpcoders.com.au > > University of New South Wales http://www.hpcoders.com.au > > > > ---------------------------------------------------------------------------- > > > > -- > > You received this message because you are subscribed to the Google Groups > > "Everything List" group. > > To unsubscribe from this group and stop receiving emails from it, send an > > email to everything-list+unsubscr...@googlegroups.com. > > To post to this group, send email to everything-list@googlegroups.com. > > Visit this group at http://groups.google.com/group/everything-list. > > For more options, visit https://groups.google.com/groups/opt_out. > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to everything-list+unsubscr...@googlegroups.com. > To post to this group, send email to everything-list@googlegroups.com. > Visit this group at http://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/groups/opt_out. -- ---------------------------------------------------------------------------- Prof Russell Standish Phone 0425 253119 (mobile) Principal, High Performance Coders Visiting Professor of Mathematics hpco...@hpcoders.com.au University of New South Wales http://www.hpcoders.com.au ---------------------------------------------------------------------------- -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.
