[srean]

I am (mostly) with you except for this bit...

> the number pi arose out of certain constraints and characteristics of the physical world we live in

Pi arose from the notion of a circle, which is an abstractions and axioms. Pi would still be pi in a completely different world under the same axioms and abstractions.

I qualified my statement with 'mostly' because a circular motion can indeed be defined by a differential equation, or in other words by a rule that dictates the 'next' value based on current value (and recent changes). So learning an approximation of a circle is very much in the realms of a sequence learner and it may learn about pi (and made to store the information to retrieve/recognize it later). However learning pi directly from the sequence of digits of pi, which is what you were talking about, that does seem difficult.