Thanks for your comments. At first I didn't agree with your distinction and thought "artificial means deliberately made by humans; natural is everything else." But after thinking about it, my distinction of "upward/downward" information could be interpreted as a geometrical difference. Here's how I see it now:
As I have said many times, I think that there is only and exactly one entity in reality capable of knowing and of exercising free will (along with many other primary or secondary capabilities). I think this entity is limited in what it can "think" by what we call logic. For example, it may not at once be consistent and inconsistent. I think Dr. Dick has analytically discovered exactly what these limitations are, namely, consistency implies (i.e. demands, requires, or forces) behavior (of whatever is consistent) to obey the laws of Quantum Mechanics, which implies behavior according to most of the rest of the laws of physics.
In other words, if God creates a consistent world, it must obey the familiar laws of physics.
Now, how might God go about creating a consistent, i.e. physical, universe?
Newton suggested one way: set the pieces in place, establish the initial conditions (wind it up), and let it go. This, doesn't allow for tampering later or else it would blow consistency.
Wolfram is currently suggesting something similar: set the pieces in place, devise an algorithm that will determine the evolution of those pieces, energize the algorithm and let it crank out the natural history of the universe. Here again, there is no tampering later on.
My view extends Wolfram's slightly -- in a way that is more consistent with the web sites that let you play with simple automata. In the web sites, you are allowed to stop the action and change a few bits if you like, and then let it go from there.
I think God has this automaton going but that He can tweak some things from time to time, here and there. To maintain consistency however, that tweaking must remain below the uncertainty threshold of QM. In other words, I think God has the ability to use free will to deliberately choose the outcome of (what we call) "random" quantum events. This is Einstein's hidden variable.
So, in my terminology, downward information is the information used by the automaton algorithm to compute the next state of evolution of the universe. Upward information is whatever God gleans, or can glean, from the universe. Upward information is coded and contains information that can be known.
To sum up (after having rambled longer than I should have), I think you could consider the results of an automaton to be regular, or predictable, or systematic -- like the arrangement of molecules in a crystal -- thus "geometric". And I think you could consider the information produced by a free will to be apparently random -- thus not "geometric".
I may have stretched a few fabrics here, Mike, in order to agree with you, but I guess that just shows the extent to which you have stimulated the discussion. Thanks for your thoughts.