False dichotomy. Mathematics is also a human language. Code and mathematics are more similar in many respects than code and Spanish. but they all share common features of being cultural, mutable, consensus-based, imperfect, and historically embedded.
Wittgenstein's philosophy of mathematics might be interesting to you. His description of calculation as a linguistic process should settle the issue if you buy it.
ok, sure. So you are saying that the OPs statement "code is more easily learned as a child because language is more easily learned as a child" is a pointless narrowing of the idea that "code is more easily learned as a child because all cultural, mutable, consensus based concepts are more easily learned as a child"?
I believe they're roughly synonymous, yes. The processes of aging and aculturation both involve an ossification of our ideas and concepts that make learning new ones comparatively difficult. Vinod Khosla has talked extensively about how he has to fight these processes in himself to bring a 'beginners mind' to bear on new startup ideas. The median effort required to do this is lower in younger people.
By the way, older people who share the characteristics of being only lightly acculturated (i.e. eccentric) share the relevant characteristics with children and may be able to learn things like languages with childlike speed. Hence, I believe, PG's observation that startup founders of any age tend to be weird, quirky, or poorly socialized in various ways.
I don't think your last sentence is a at all true.
all cultural, mutable, consensus based concepts are more easily learned as a child
There are many "hobbies" that have a cultural component. It helps to learn these earlier, because it removes cognitive overhead during later studies. But its simply not true that children are better at learning everything. They are hard-wired for language tho. Plenty of other things they are un/der developed for.
Wittgenstein's philosophy of mathematics might be interesting to you. His description of calculation as a linguistic process should settle the issue if you buy it.
Edit: just found this related item on HN, a math prof examining the nature of a proof: http://profkeithdevlin.org/2014/11/24/what-is-a-proof-really...