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Indeed. That set of instructions "exists" in some abstract way as logic, of course, and when we're talking about actually running that set of instructions, e.g. OpenAI servers running ChatGPT, we mean that those hunks of metal and plastic we call "servers," are physically different from other hunks of metal and plastic that are running some different pieces of software, in the sense that the atoms that make up the storage drives and electrons that flow through the atoms that make up the circuitry are different based on differences in the software. The software instantiates itself in the hardware; otherwise, the software can't be said to "exist" in a meaningful way beyond just an abstract concept.
The same logical axioms are hardware independent though. And we can write it on a board, or examine it on GitHub. On the other hand different compilers and different compiler options will produce different output even for the same chipsets, and totally different output for different chips. And when running, the OS, will run the software differently - how the OS or the system API (which all but the simplest of programs need to interact with it) work differs even in minor versions. Which is why updates to an OS can break a once well behaved app. It’s clear that the software running on the hardware is not really one thing, while the abstract software is another. Both exist and the same terminology is used for both - but only the latter is really “pure”. To my mind any software algorithm really exists in the abstract, not in the actuality.
I agree with all of this, though the last part about what a "software algorithm" really is seems more a matter of philosophical worldview than anything else. I think it's important to note that in each and every one of these cases, including the software being written on a board, saved on GitHub, or even just existing purely in someone's head because they've never written it down, the "software" we're talking about exists in physical reality, whether that be markings on a board, the arrangement of atoms on the storage drives on GitHub's servers, or in the patterns of how someone's neurons fire and are connected.
One could hold the worldview that all software already exists, and programmers are merely "discovering" them by writing the code, in a Library of Babel sort of way - all books already exist, writers are merely "discovering" them when they put words on paper, or all paintings already exist, painters are merely "discovering" them when they put brush strokes on canvas - but I'd wager that's a highly atypical way of viewing the existence of software. Most people would agree that Mark Zuckerburg and his team didn't "discover" Facebook, but rather "created" it, even if it was "created" the moment they thought of it before even thinking of what language to program it in.
I suppose you could counter the Library of Babel argument by saying that what we have created is simply something that can exist in a "possibility space," and what makes creation special is that it is the hard work of mapping out the possibility space. Otherwise, as with human attempts to create Xes of Babel, most of what you might get is useless, random noise.
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