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Names have scope in CS
Posted:
Oct 6, 2017 4:53 PM



One difference between conventional math notation and runnable, coded math notation is the latter is more explicit about scope.
"Let x = 200" but where and for how long? The name x will be something else on the next page.
In runnable math notation we might assign a name within a function knowing we're strictly within the local "namespace" and not creating side effects more globally. The name "x" has a particular role inside this function only.
Some may complain this is all conceptual overhead and detracts from learning core math. However the issue of the same names having different meanings depending "how used" in a language game, is one we must come to grips with in the humanities.
Sometimes a false hubris leads us into think a "math word" such as "squaring" is automatically global because math is "a universal language." Claims about the universality of math terms are themselves more political than mathematical. Contending empires push their favorite squiggles.
Computer languages have more humility baked into them. We know any given language is one of many. None claim to be "universal".
Sure, following widely shared habits and expectations provides a convenience to others. APL (a computer language) didn't do that. Wolfram Language tries harder to mirror comventional typography.
Board games, games in general, remind us to think in terms of language games i.e. scope. Meaning emerges in context. "Scope" and "context" have similar meaning.
CS will likely prove a useful counterweight for those suffering from a false sense of universality around any one particular notation.
Calculus provides a good example in that Newton's notation for "fluxions" has no widespread following in contemporary K12 treatments.
Kirby



