Yes, Marina - I'm - we're - so late !!!!! Partly because being new to this whole 'thing' I just couldn't believe that we could discuss our entries with one another - I was literally in a state of denial. Well better late than never !!
You queried my position on the geometry of space - well, my short answer is no - I do not believe that space possesses any properties including geometrical curving or warping in response to gravity. I have come to believe that light gets curved or lensed around large bodies for the same reason it bends in water. Einstein did not know of 'heliopauses' or 'magnetospheres' but which phenomena are more than capable of bending any light transitting them.
So 'my' geometric objects exist only on solid bodies.
Among several points I liked about your essay was where you discussed 'mediums' & I haven't noticed anyone else doing so. Mediums play a very pivotal role in my schema.
I found it useful to recognise several different grades or levels of information (as the full set of geometrical objects present in our universe). Medium bourn information being of the second grade or 'order' as I call them. We ourselves as you noted have access to the world of information exclusively via some one or another medium, which means that all our information is 'second hand' - & of course as we all know much of the information has been transferred from medium, to medium to medium many, many times.
But, according to my view, there are things that have access to information directly, literally face-to-face, specifically all of the inanimate objects here in our universe. I call these 'first order' information-users, and one of the things it is worth noting about these face-to-face informivores is that they read with near infinite accuracy as the information they encounter is 'first hand' - is raw, original, complete & pristine.
Ours in some high contrast has been copied & recopied so often it is a wonder it has any informational value left within it. Which is why 'we see through a glass darkly'.
Never mind, nature has made up for this inadequacy as it has provided most if not quite all of its 'higher order' informivores with an ever increasing number & variety of senses of differing sensory modes - & there are many more than just the classic five !!
So while the rocks & stones beneath our feet & the atoms & molecules in the air get their information first hand - right from off of the surfaces of their fellow interactees - & once having got it, read it with near infinite accuracy they are only able to deal with one unit of information at any one sitting.
There are other levels of information in 'my' scheme &, guess what ! they tend to parallel your own 8 step break down of the 'participation' process. But a particularly important distinction (of not a few !!) between our two viewpoints is that I am convinced that our brains are 'thinking machines' & not just computers, & that like all good thinking machines they operate analogue-ly not digitally.
So yes ! My own investigations have led me to conclude that 'information' is NOT digits - no kind nor amount of them (including any that can be extracted from quantum phenomena!), nor how algorithmically-well they may be massaged & shunted through any device that uses them.
Unequivocally they - digits - make for wonderful COUNTING & CALCULATING assistants, witness our own now many & various, most excellent, counting, calculating devices BUT according to my investigations real thinking is an entirely different phenomenon from mere counting, calculating & computing.
For which phenomenon - real thinking - real information is required.
My own investigations led me to discover what I have come to believe real information is & as it so transpires it turns out to be an especially innocuous - not to omit almost entirely overlooked & massively understudied - phenomenon, none other than the sum total of geometrical objects otherwise quite really & quite properly present here in our universe. Not digits.
One grade (the secondary one) of geometrical-cum-informational objects lavishly present here in our cosmos, is comprised of all the countless trillions & trillions of left-over bump-marks still remaining on all previously impacted solid objects here in our universe - that is to say, all of the left-over dents, scratches, scars, vibrations & residues (just the shapes of residues - not their content!) (really) existing here in the universe.
Examples of some real geometrical objects of this secondary class in their native state are all of the craters on the Moon. Note that these craters are - in & of themselves - just shapes - just geometrical objects. And the reason they are, also one & at the same time, informational objects too, can be seen by the fact that each 'tells a story' - each advertises (literally) some items of information on its back - each relates a tale of not only what created it but when, where & how fast & from what angle the impacting object descended onto the Moon's surface. Again, each literally carries some information on its back.
(Note : Not a digit in sight !!)
How we actually think - rather than just count, calculate & compute - with these strictly non-digital entities, specifically these geometrical-cum-informational objects, in precisely the way we do, please see my essay.
I did not make the distinction between computing with digits & real thinking with real information, sufficiently strongly in my essay.
This contest is such a wonderful 'sharing' - Wow - & open to amateurs like myself - Wow. How great is that !!! Thank you Foundational Questions Institute!!! What a great pleasure it has been to participate. What a joy to read, share & discuss with other entrants !!!
Margriet O'Regan