Hi Ivan, On Mon, Jul 12, 2021 at 6:00 AM Ivan V. <[email protected]> wrote:
> > Thank you for asking, and my thoughts are pretty obvious. As I understand, > URE and PLN are all about proofs, so my thoughts may go in that direction. > Suppose we have a natural deduction proof composition: > > > > > > > * --- --- --- --- --- --- --- --- --- I J K > L M N P Q R ----------------- > ----------------- ----------------- A B > C----------------------------------------------------------- > X* > > You can already see the tree-like composition, but as it may span over a > very wide and tall area, it may be required to represent it within an > on-demand scaling system. This example <http://ocog.atspace.cc/> roughly > shows what I have imagined for proof representation. In the example you can > play with ovals, dragging them around and in or out the central area, > zooming proof parts of the current interest. Notice how it is possible to > represent and navigate nearly infinite length proofs, assuming enough > memory space. > Re: navigating trees: if you don't already know this, then I suggest that you really, really should study hyperbolic rotations aka mobius transformations on the poincare disk. They implement your example. I recall seeing a demo of this at SIGGRAPH two or three decades ago. As you pan around on the hyperbolic disk, different parts of the graph get magnified at the center. And, like an MC Escher print, the rest of the graph remains compressed at the edges. For scale-free networks, this doesn't work. And from what I can tell, learning really does result in something close to scale-free networks. What this means in practice is that there's one vertex with a million edges coming off of it. There are two, with half-a-million each. Four, with a quarter-million each, and so on. So almost all vertexes have just a handful of edges connected to them, but as you move around, from vertex to vertex, you bump into these monsters. And you can't really draw them: try drawing a vertex with a thousand edges on your 2Kx2K monitor: most of those edges will be less than one pixel from each-other. It'll be just a big blob. It's important to "eat your own dog-food", as they say, or "smoke your own dope": use your own code to solve actual, real-world problems. This very quickly highlights where all that beautiful theory doesn't quite work out in practice. --linas -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/opencog/CAHrUA34HBqa02JkW9-EVR5OrpSkOWEMGjZBOCPM2vKKpJR2%2B0A%40mail.gmail.com.
