I made a small infinity test <http://ocog.atspace.cc/infinite/> too. Each parent virtually has an infinite number of children. Rolling ovals around, zooming ovals in, zooming ovals out, ... Surely it's not exactly perfect, but I could live with it.
pon, 12. srp 2021. u 17:48 Linas Vepstas <[email protected]> napisao je: > 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 > <https://groups.google.com/d/msgid/opencog/CAHrUA34HBqa02JkW9-EVR5OrpSkOWEMGjZBOCPM2vKKpJR2%2B0A%40mail.gmail.com?utm_medium=email&utm_source=footer> > . > -- 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/CAB5%3Dj6UgLR5xMP9WeE%2BWOkqBynGTr%2BNQTwsmUq9JrSuU1Sh1ZA%40mail.gmail.com.
