Also, judgement alone might not be enough. Judgement can take you to "something is off", but not necessarily further. I mix music as a hobby and it takes a good amount of practice to step up from recognizing the presence of a problem to actually know where and how to fix it. If you don't know where you should look, you just aimlessly try various things, and it is not unusual to make the problem worse.
Eventually you learn to properly recognize the problems, not just their presence, but their actual nature and implications. But this takes practice.
It is also interesting to consider, that if all transcendental numbers exist physically, then it basically means that there is an experiment that yields the Nth digit of such a number (for any N assuming unlimited physical resources to realize the experiment). If such experiment does NOT exist though, then there cannot be any relevance physically of that Nth digit (otherwise the "relevance" would materialize as an observable physical effect - an experiment!). This is something Turing machines cannot do for uncomputable numbers, like Chaitin's Omega, etc. We can yield the Nth digit of _many_ transcendental numbers (PI, e, trig functions, etc), but not all of them. It is so interesting that physics, machines and the existence of all the real numbers are so intertwined!
Of course one can also ponder, even if a mathematical object is "un-physical", can it be still useful? Like negative frequencies in fourier analysis, non-real solutions to differential equations, etc. Under what conditions can "un-physical" numbers be still useful? How does this relate to physical observation?
And just for the fun of it: when you execute unit tests, you are actually performing physical experiments, trying to falsify your "theory" (program) :D
> The set of all possible mapping from all possible finite strings to booleans is definitely not countable.
Just to add another perspective to this, this is one of the places where classical and constructive mathematics diverge. Do those functions that are not expressible by algorithms (algorithms are countable) even exist? Of course you can define them into existence, but what does that mean?
Another food for thought is to consider if the limits imposed on computation by the Turing machine is a law of physics? Is this an actual physical limit? If so, what does that mean about the functions not expressible by algorithms? What is so exciting about programs/algorithms that they are both a well-defined mathematical object suitable for formal analysis, but they are actually machines as well, fully realizable physically and their properties physically falsifiable.
Before anyone starting to nit-pick, I just put this comment here as a conversation starter, not a precise thought-train: this is a deep rabbit whole that I think is worth to explore for everyone interested in the computational world. I am pretty sure other commenters can add more accurate details!
I am a Scala developer but I agree with your points. The only thing that just simply drives me mad in Rust is mandatory semicolons. Once you are used to be able to omit them then it gets really annoying to go back using them.
"For the most part Pub/Sub delivers each message once, and in the order in which it was published. However, once-only and in-order delivery are not guaranteed: it may happen that a message is delivered more than once, and out of order."
(edit: added translation of unit)