Pi is computable. What is computable, can be represented in finite information (the algorithm used to compute the number). Almost all real numbers are not computable.
Now tie this with computability theory. Almost all real numbers are uncomputable. It's obvious that they don't "exist" in any sense if by "exist" we mean "computable". Now consider that entropy, is information, is the measure of randomness, or uncomputability, is time. What is uncomputable, coming into existence, is the passage of time.
So Airbnb has tried to unsuccessfully pivot to a payments infra company for several years now. Notable acquisitions for this effort include acqui-hiring ChangeTip, a bitcoin micropayments platform, and Tilt, a social payments platform. But Square and CashApp are way ahead of the curve. I suspect there's internal political problems.
but it's not uncommon for jr. devs to believe every piece of code deserves the most efficient runtime. Runtime speed causing projects to fail is very uncommon. What does add an incredible amount of work time is combing through a codebase looking for micro optimizations. I've never once seen a jr. dev who claimed to care about efficiency start by writing benchmarks over large parts of the system and using that to find real bottlenecks. No, they always comb through the code trying to impress the sr. dev. with their algorithmic knowledge.
> Runtime speed causing projects to fail is very uncommon.
That's true. What is common, however, is bad runtime performance losing you users and bleeding your money. Not doing dumb things (like using a list where a vector would do), and taking a moment every now and then to go over your product with a profiler and fix the biggest bottlenecks early, can save you a ton of money in cloud bills (it might even turn out that your product actually doesn't need to horizontally scale at all, giving you further reduction-of-complexity benefits). Or you might end up delivering features that were impossible to do with bad performance (see e.g. https://news.ycombinator.com/item?id=22712103).
Y'all are gonna call me a crackpot, but consider P, PSPACE and IP. PSPACE is (probably) much more powerful than P. Also PSPACE=IP (interactive proofs). Learn interactively. Treat your compiler as the prover, you as the verifier. Don't try to understand everything by simply reading the manual -- that's only utilizing P, not PSPACE.
