Here’s an exercise in separating fundamentals from conventions: if we held a technical summit with all of the galaxy’s advanced alien civilizations, what would we find we had in common, and what would we find inscrutable?
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Now we compare programming languages. We’d find some low level constructs have developed very differently. Maybe they’d have balanced tertiary numbers instead of twos-complement and u-law fractional numbers instead of floating point. Our bitwise ops may have no analog.
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So, let’s ask: what parts of programming would we have in common? We’d share the mathematical integers, and data structures analogous to Cartesian products (structs) and sums (unions), and functions with side effects, and pure functions as a special case.
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We’d have transactions as a way of running concurrent operations atomically. We’d have most of Knuth’s algorithms in common (maybe they’d have some major breakthroughs we lack!)
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The goal of a high level programming language is to be something that we and these alien civilizations could agree on as universal and principled, and free of quirks and arbitrarity.
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We already have several axiomatic systems, most notably ZF vs ZFC (as the axiom of choice is/has been controversial). It would be interesting to discover what axioms other intelligent species came up with.
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I could never understand why some people would reject AC. It's equivalent to "Cartesian product of a collection of non-empty sets is non-empty". They must have a very weird intuitive concept of was a set is, if it does not satisfy this axiom.
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Could this be because we define valid math as the thing we can agree on?
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I am really not sure that math will be shared. Math happen because our brain has to categorise stuff and there is no reason to believe that their form of thinking would be the same. At best there would be some form of our math that would cover their way of thinking.
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for example let’s imagine they think with a form of graph that include an idea of transition between nodes. Then some part of Graph theory would be there but the rest would be radically different (like geometry) and other wouldn’t exist (arithmetic)
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I don't think maths would be shared, its a language too and it surely must depend on physiology
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