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This is a *facinating* question! Think about it though: we're kind of trapped by our conception of how computers should work. In fact however, entirely analog systems that use no symbology whatsoever are possible. <aside>For the technical, they would not be Turing Machines, or even Finite State Machines, in fact the best analogue to point to is an oil refinery with completely continuous/non-discrete processes!</aside> You could deal with all those "datapoints" with continuous mechanisms that involved no conventional symbology whatsoever!
Buffy
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It makes sense to me that if you posit the lifeform as a malleable templater. That is the lifeform can become on demand or create on demand your "boundaryless datum stream artifact producer"(oil refinery analog) using its stored experience or memory, then a non-discrete manufactory is not only possible but would be far more efficient than the incremental symbol transmission system we use to bend metal.
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Now on the other hand, symbology can be a very broad term, and as a result, verbal communication alone could be a sole mechanism for communication and be *recorded* but not *written*. Is that symbology? If so, then dolphins definitely already use it and they are closer to us than we imagine....
Buffy
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That requires the receiver to have eidetic memory and simply retransmit it down the time line? That fits in very well with the above as a tool using scheme.
I'm starting to think that maybe a crystalline fractionation and growth approach might lead to something like you describe. But it would be so slow and cold by what we would normally expect of life......
Damocles