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> If you knew somehow that some symbol corresponds to 20, then you’d know they didn’t use base 20 because base b doesn’t have a single symbol for b.
Well, this is plainly false.
Looks like translating a positional numbering system from ancient cultures than ruling out or not if they had the concept of zero. It may be a single use symbol, here is nothing, instead of being part of bigger amounts. Numbering systems doesn't have to be positional (nor go too far).
Gosh I love Wittgenstein for this.
I highly recommend suffering through both early and late Wittgenstein (only wrote 2 books and essentially invented one of the 3 branches of philosophy).
Expect to only understand 10% of what he says, but that is normal.
Separately, pragmatism by William James is an easy 4 hour read and you can have 2/3 of the branches of meta philosophy.
Zero has two roles: as a positional placeholder and as a cardinal value (nothingness or net-zero). This only addresses the former.
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Afaict, most ancient civization have conception of "nothingness" or "emptiness". The dispute is often whether they consider it as a number or not
We have both. Zero and Null are different data types.
What I wonder is: why has nobody noticed that code editors lack a concept of 0?
When you're writing code, you can express any concept except that of an unfilled hole. We've rearranged every part of the coding process in a twisted-up way, all for the lack of a way to express lack.
If you want to be more clear about what I mean, look to tools which can express holes like https://scratch.mit.edu and https://hazel.org. They give the feeling of letting things snap together like lego bricks. Indeed, lego bricks themselves function because of the negative space (the holes) in them!
Like Madlibs?
This could be interesting but too vague for me to understand what you mean. Could it be explained more clearly, or link some blog entry?
How about an `extern` variable in C?
A million variations exist. I'm looking for a programming-language-agnostic concept. The closest you'll find are templating languages like Handlebars
Delimited continuations? Though I'm not totally clear what you're asking for. Semantics or syntax?