I find the unreasonable effectiveness of formal systems to be this: just as the shaman crosses into the "spirit world" and uses their experience there to predict happenings in our world, we can turn statements about bridges and dynamic loads in our world into formal statements, arrangements of symbols, and manipulate them mindlessly according to a formal system, yet the resulting safety margins do indeed predict happenings in our world.
(A city once gave an engineering school the contract to demolish an old bridge. The date was agreed upon, but that afternoon the city had to sent representatives out at lunchtime to insist that even though it hadn't been formally specified in the contract, their intent —and the neighbour's expectations— had always been that the bridge would be blown up all at once, not that little bits be blown off all morning to see how much structure could be removed before collapse...)
I find the unreasonable effectiveness of formal systems to be this: just as the shaman crosses into the "spirit world" and uses their experience there to predict happenings in our world, we can turn statements about bridges and dynamic loads in our world into formal statements, arrangements of symbols, and manipulate them mindlessly according to a formal system, yet the resulting safety margins do indeed predict happenings in our world.
(A city once gave an engineering school the contract to demolish an old bridge. The date was agreed upon, but that afternoon the city had to sent representatives out at lunchtime to insist that even though it hadn't been formally specified in the contract, their intent —and the neighbour's expectations— had always been that the bridge would be blown up all at once, not that little bits be blown off all morning to see how much structure could be removed before collapse...)