This is an important point, but one I feel the article acknowledges well.
There are many impossibility problems that can be solved by relaxing some constraints (like wait-free) or by accepting some unsolvability (we don’t worry too hard about our programs halting in practice, and we generally trust compressed sensing results because the probability of failure is provably delta, say), or just by changing some desiderata.
Great examples include arrows impossibility theorem or the no good clustering result, each of which have solutions if the assumptions that operationalize our intuition are changed slightly.
There are many impossibility problems that can be solved by relaxing some constraints (like wait-free) or by accepting some unsolvability (we don’t worry too hard about our programs halting in practice, and we generally trust compressed sensing results because the probability of failure is provably delta, say), or just by changing some desiderata.
Great examples include arrows impossibility theorem or the no good clustering result, each of which have solutions if the assumptions that operationalize our intuition are changed slightly.