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Vladimir,
One of the points I keep making is that perception is inherently subjective. Clarity and distinction require some form of framing from the larger context. Such as with a camera, having to set the aperture, lens, filter, speed, position, direction, etc. Math is abstraction. A generalized view blends details. I went into this a little in the essay, but it goes to the subjective nature of information. It's not as though things do not happen, but that any information about them is incomplete. Consider something as simple as two billard balls hitting each other. How can it be really understood outside of the larger context, how is it perceived from the position of the balls themselves, as opposed to someone watching them. While the reality seems quite objective and clearcut, there is no fully objective view, because even in so simple of a situation, the potential information could go to infinity, as every atom and molecule of the balls, the surface, humidity, etc. plays some part.
So it is a subject that itself could go to infinity.
If I was to suggest some basic necessity for information, it would be that there first has to be some distinction, both within what is being observed and between the observer and the observed. Then there has to be some form of connection in order for these distinctions to be relatable. The connections would have to be more dynamic and the distinctions more static, otherwise any information would be disturbed/lost before it is registered. Light makes a good form of connection, while mass makes good distinctions. Part of the "explaining water to fish" problem.
Obviously this is a broad category, from fleeting thoughts to thousand year old structures. and beyond.
Yet at the stage of the absolute, there is no distinction and so no information, unless viewed from a non-absolute state and then the relationship is not an absolute. Toward infinity, all information blends into white noise. So it is in these relativistic configurations between the extremes.