I want to return to what seems to me the high-school-naive idea of how an AGI's 
or any body of knowledge can and/or does grow - i.e. linearly, mathematically 
and logically.

Correct me, but I haven't seen any awareness in AI of the huge difficulties 
that result from the problem of : how do you test acquired knowledge?

Such difficulties are fundamental to all current philosophical and sociological 
treatments of the growth of knowledge - and arguably they apply to the growth 
of personal as well as formal, organized knowledge. Consider this blurb for an 
example of the real complexity of knowledge's growth::

"Thagard analyzes the development and acceptance of scientific ideas. At the 
heart of the book is a case study of the recent dramatic shift in medical 
understanding of peptic ulcers, most of which are now believed to be caused by 
infection by the bacterium Helicobacter pylori. When this explanation was first 
proposed in 1983, it was greeted with intense skepticism by most medical 
experts, but it became widely accepted over the next decade. Thagard discusses 
the psychological processes of discovery and acceptance, the physical processes 
involving instruments and experiments, and the social processes of 
collaboration, communication, and consensus that brought about this 
transformation in medical knowledge.

How Scientists Explain Disease challenges both traditional philosophy of 
science, which has viewed science as largely a matter of logic, and 
contemporary science studies that view science as largely a matter of power. 
Drawing on theories of distributed computing and artificial intelligence, Paul 
Thagard develops new models that make sense of scientific change as a complex 
system of cognitive, social, and physical interactions."

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agi
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