What is a presymbolic computational system? Shannon entropy deals with alphabets in much the same capacity as Turing machines read symbols on a tape. Fundamentally it is about differentiating between states. I don't see how you can get a meaningful definition of information before starting with the notion of discrete states. Even fuzzy logic needs a semantic of states.

Presymbolic computation is the motivation for the first restricted Boltzmann machine, Paul Smolensky’s “Harmonium”. It’s a great paper.

https://apps.dtic.mil/sti/citations/ADA620727

Presymbolic computation appears to me to be an invented term. Any theoretical or actual system can be framed in computational terms when analysed, but the properties provided through the use of symbols will still exist in a system, whether or not that analysis has been performed. The paper you cite appears to me to lean in the direction of cybernetics and control theory, that would naturally be able to translate into terms aligned to information theory. The same rules will apply to any physical system, no matter how complicated you believe it to be.

Not sure what you mean by “invented term.”

in any case, there seems to be a difference in describing a system with symbols and computational systems that use symbols for information processing. Some information processing seems possible in systems that don’t use symbols.

Any computational system uses symbols, whether or not a person has analysed the system and defined those symbols; information is symbols.

You are suggesting that information was not existing before symbols?

Where and when information exists so do symbols, in the abstract sense. It’s not symbols as representation of meaning but symbols as mediating meaning.

That’s a strong claim that is not common. Humans are generally considered to be the only animals capable of symbolic thought [1]. Information flows in far simpler systems than symbolic systems.

[1] https://www.nytimes.com/2014/12/07/magazine/hunting-for-the-...

No, the interesting thing about Shannon entropy is that it is totally independent of how information is represented (as symbols, alphabets, numbers, structured objects, whatever).

It is based on the symbol set exchanged, so how is it independent?

Information is a function only of the probabilities, not of the symbols.

Shannon entropy works for anything you can assign an alphabet of symbols to. It doesn't need the thing itself to be symbolic, just the description of the thing.

That seems like a strong claim. Any proof?

Sure. https://people.math.harvard.edu/~ctm/home/text/others/shanno...

Particularly part 4, The Continuous Channel. No discrete symbols there!

Maybe I’m not reading it properly, but in part 5, where he deals with transmission of continuous signals he doesn’t use his entropy formulation. He uses a distance metric, showing the difference between the sent signal and the received.