You're pretending the string points to some number to pretend it is a number.
It is a string.
Nothing else.
All it's features cannot be captured in any other representation of it.
I got news for you: Your string doesn’t exist either. No more than the number it refers to, and arguably less.
For all your realist grandstanding, by treating the string as a thing, an entity, you’re using a couple dozen symbolic equivalence relations.
“The string” was born as a pattern of electric and chemical signals (1) in your frontal cortex, and probably other areas of the brain like the motor cortex (when we silently vocalise words, our motor cortex is constantly preparing mock instructions to the speech organs).
When you decided to type it, you transformed (2) it into a series of funny shapes according to a man-made mapping you had memorised in primary school, and identified the keys on your keyboard where someone had marked those shapes.
Your keyboard then sent a pattern of electric pulses (3) to your CPU, according to a set of man-made rules someone had programmed it with. The CPU transformed that series into a different series of electric pulses (4) according to yet another lookup table, to save it as a spatial pattern of 0s and 1s (5) in memory. Your graphics driver transformed that into yet another series of electric pulses (6), which caused a spatial pattern of dark and light pixels (7) on your screen. This pattern caused a sequence of electric signals in your visual nerve (8), which you translated back to some mental representation of the digits (9).
When you decided that you had indeed typed what you wanted to type and pressed the send button, your computer compiled the representation in (5) into yet another sequence of 0s and 1s or electric pulses (10) to send to the server. The server transcoded it back into something it could store on disk, possibly in the same format your computer used internally, but just as likely in yet another (11). And when I requested the page, it was transformed back into (10), and with my different graphics driver, different screen, different brain and different native language, we’re up to at least 15-16 different physical manifestations of “the string” before either of us has read it out loud, which would add yet another series of manifestations (movement patterns of the tongue and jaws, air pressure modulations, auditory nerve excitement patterns…).
You accept all of these equivalencies as valid – some of them arbitrarily defined by a human, some the accidental product of evolutionary history – and even accept that the string 0.999… is “defined to mean” another string, equally a collection of two dozen physically unrelated things only held together by the symbolic relations humans defined to hold between them.
But when I want to talk about the number it refers to you cry foul. You pretend you only want to talk about real things.
That’s just inconsistent cherry-picking. The string is no more real, no less a figment of human imagination, than the number, and arguably less of the former and more of the latter.
