On Mon, Jul 12, 2021, 10:59 AM Ivan V. <[email protected]
<mailto:[email protected]>> wrote:
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] <mailto:[email protected]>>
napisao je:
Hi Ivan,
On Mon, Jul 12, 2021 at 6:00 AM Ivan V.
<[email protected] <mailto:[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]
<mailto:[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]
<mailto:[email protected]>.
To view this discussion on the web visit
https://groups.google.com/d/msgid/opencog/CAB5%3Dj6UgLR5xMP9WeE%2BWOkqBynGTr%2BNQTwsmUq9JrSuU1Sh1ZA%40mail.gmail.com
<https://groups.google.com/d/msgid/opencog/CAB5%3Dj6UgLR5xMP9WeE%2BWOkqBynGTr%2BNQTwsmUq9JrSuU1Sh1ZA%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]
<mailto:[email protected]>.
To view this discussion on the web visit
https://groups.google.com/d/msgid/opencog/CACYTDBeOoqMRD20KFDYPGG1YfRqT0qW4wehOGtTKSqTb%3D6L2Jw%40mail.gmail.com
<https://groups.google.com/d/msgid/opencog/CACYTDBeOoqMRD20KFDYPGG1YfRqT0qW4wehOGtTKSqTb%3D6L2Jw%40mail.gmail.com?utm_medium=email&utm_source=footer>.
