I seldom ask this as I usually work at the level of abstractions. But could you please give some examples of topological relationships that are difficult to express computationally? I am not sure I follow exactly what you have in mind.
Thanks. - samantha On 06/16/2015 06:09 PM, J. Andrew Rogers wrote: > >> On Jun 16, 2015, at 3:26 PM, Dean Pomerleau <[email protected] >> <mailto:[email protected]>> wrote: >> In short, growing evidence supporting the importance of cortical >> oscillations in neural processing suggests that this sort of >> analog/digital feedback loop might be critical to how the brain >> works, and that such interactions might be very hard (possible >> intractably hard) to model accurately (i.e. emulation vs. merely >> crude simulation) on a digital computer, in a similar way to how >> protein folding is intractable to model on a digital computer. > > > The tractability challenges of computational dynamics for brain-like > models is related to why we can’t analyze the dynamics of *any* > non-trivial physical world system. It is not coincidence that all “big > data” computation focuses solely on relationships in the electronic > world and not the physical world. > > Interestingly, computer scientists rarely notice that these software > systems do not exist until you point it out. And when you do point it > out they are at a loss to explain why. It is only “obvious” in hindsight. > > > Virtually all existing computer science is based on the manipulation > of graph-like data models and primitives. The problem is that some > systems, notably physical world systems, have relationships that are > fundamentally topological in nature. Graphs are a special, strict > subset of more general topological computing representations; it is > not possible to construct a scalable topological computational model > on top of graph primitives. > > There is no computer science literature for computing on topological > data models. To the extent algorithms and data structures exist to > handle basic topological data models (e.g. R-trees), they exhibit > pathological scalability because they are shoehorned into traditional > graph models. If you want to compute on topological models at scale, > you need to build a completely new computer science stack, from the > most elementary primitives on up. And it needs to have an efficient > implementation on conventional silicon. > > > If you can directly manipulate topologies as computational constructs, > instead of graphs only, many types of computational dynamic suddenly > become *much* more tractable. In practice, the use of inappropriate > algorithms and data structures to represent topological relationships > are responsible for most intractability related to expressions of > physical world system dynamics on a computer. It just never crosses > the mind of most computer scientists working on such things and it is > never discussed in computer science curricula. > > > *AGI* | Archives <https://www.listbox.com/member/archive/303/=now> > <https://www.listbox.com/member/archive/rss/303/2997756-fc0b9b09> | > Modify > <https://www.listbox.com/member/?&;> > Your Subscription [Powered by Listbox] <http://www.listbox.com> > ------------------------------------------- AGI Archives: https://www.listbox.com/member/archive/303/=now RSS Feed: https://www.listbox.com/member/archive/rss/303/21088071-f452e424 Modify Your Subscription: https://www.listbox.com/member/?member_id=21088071&id_secret=21088071-58d57657 Powered by Listbox: http://www.listbox.com
