Literacy is a skill separate from knowing any particular language. Literacy is the meta-ability of understanding that you can read language from, and write lang

Literacy is a skill separate from knowing any particular language. Literacy is the meta-ability of understanding that you can read language from, and write language to, a visual storage medium. It's a kind of forced development of a new acceleration area of your brain for efficiently transforming visual-field symbols into subvocalization sequences, and vice-versa. If you learn one spoken language, and then you become literate, and then you learn another spoken language, and the two languages share a script, then you now know how to read and write in two languages. I would expect numeracy to be the same: a numerate agent would be one that understands that amounts and relationships can be modelled by numbers. That numbers are abstract concepts that exist separately from the symbols used to represent numbers. That there are an infinite number of them, but without identity, and without canonical representation (2 "is" 5 - 3). That you therefore must assign properties not to individual numbers, but to the sets of numbers that obey certain rules — and so you must recognize what rules a number obeys when you see it. And so forth. If I teach you to do an "increment" operation, or a "less than" comparison, in Arabic numerals; and then I teach you how to represent numbers in Roman or Chinese numerals; then you should now be able to do an increment operation or a less-than comparison using those numerals. Likewise for e.g. base 10 vs base 2 numbers. Your understanding of numbers should not depend on the symbols themselves, but should instead be an understanding embedded in something more like an abstract, non-quantized visual field, where numbers can be above or below or between other numbers in an abstract visual sense; intervals can overlap other intervals in an abstract visual sense; etc. (I would expect a hypothetical "fully" numerate system to be able to "imagine" any algebraic structure described to it, to see the properties it has, and to use that structure to "do math". I shouldn't have to teach arithmetic to the agent all over again just because it's now e.g. modular arithmetic. It should be able to derive — and perform! — all the operations of "modular arithmetic", just because it 1. knows regular arithmetic, and then 2. hears a description of a modular ring.)