The advantage of learning , knowing and applying various analytical methods across the sciences partly lies in getting a leg up on how close (or how far) we generally land from the truth regarding problem solutions in the absence of such methods. Intuition becomes a much more valuable tool once we learn when it is likely to be wrong ( and you’d better not be using intuition to do that ! ). If your experience in life includes events that exceed the normal bounds of cognition (traumas of war and violence at one end of the spectrum and their noetic counterparts at the other- OBE’s, NDE’s, time anomalies , macro psi) then it’s likely your sense of self , emotions and intellect are already finding limits with respect to making sense of the world at large. Derivation and integration are found everywhere in physics and mathematics because nature built them in and the least of us perform these functions at higher level than machines will ever likely achieve (AI arguments notwithstanding). But our cognitive machinery often fails to *consciously* integrate these extremal kinds of experiences in useful ways and we wind up burying them or are even broken by them. Popular press tends more to triumphant storytelling but returning to a war torn world and a body that won’t do what you tell it to is as jarring as birth itself…
Since that last post the war in Ukraine has widened and we’ve had a violent litany of mass murder and mayhem here at home – including the meta atrocity of Uvalde , Texas. These are not random events. The general public doesn’t have the horsepower to integrate any of this at high level. The result is further destabilization. If you’ve found your way here and any of the above makes sense then very likely you’ve not lost touch with the bits of you that know over the long haul everything will be okay. It’s the short haul that’s vexing now.