Not to get all semiotic about it, but |x| notation is a pair of vertical lines. I'm sure that someone has written a calculator program where two 0x7D characters bracketing a symbol means absolute value, but if I've ever seen it, I can't recall.
Although 0x7D is overly specific, since if a sibling comment is correct (I have no reason to think otherwise), | for bitwise OR originates in PL/1, where it would have been encoded in EBCDIC, which codes it as 0x4F.
I'm not really disagreeing with you, the |abs| notation is quite a bit older than computers, just musing on what should count as the first use of "|". I'm inclined to say that it should go to the first use of an encoding of "|", not to the similarly-appearing pen and paper notation, and definitely not the first use of ASCII "|" aka 0x7D in a programming language. But I don't think there's a right answer here, it's a matter of taste.
Because one could argue back to the Roman numeral I, if one were determined to do so: when written sans serif, it's just a vertical line, after all. Somehow, abs notation and "first use of an encoded vertical bar" both seem reasonable, while the Roman numeral and specifically-ASCII don't, but I doubt I can unpack that intuition in any detail.
The language APL\360 of IBM (August 1968) and the other APL dialects that have followed it have used a single "|" as a monadic prefix operator that computes the absolute value and also as a dyadic infix operator that computes the remainder of the division (but with the operand order reversed in comparison with the language C, which is usually much more convenient, especially in APL, where this order avoids the need for parentheses in most cases).
Although 0x7D is overly specific, since if a sibling comment is correct (I have no reason to think otherwise), | for bitwise OR originates in PL/1, where it would have been encoded in EBCDIC, which codes it as 0x4F.
I'm not really disagreeing with you, the |abs| notation is quite a bit older than computers, just musing on what should count as the first use of "|". I'm inclined to say that it should go to the first use of an encoding of "|", not to the similarly-appearing pen and paper notation, and definitely not the first use of ASCII "|" aka 0x7D in a programming language. But I don't think there's a right answer here, it's a matter of taste.
Because one could argue back to the Roman numeral I, if one were determined to do so: when written sans serif, it's just a vertical line, after all. Somehow, abs notation and "first use of an encoded vertical bar" both seem reasonable, while the Roman numeral and specifically-ASCII don't, but I doubt I can unpack that intuition in any detail.