I took a week off and stayed in a quiet place on a small lake in the alps. Hiking, reading, thinking, ... At one evening in the twilight time, I made this picture with my iPhone. Dark, reflecting water, reed, and the vague view of hills and mountains (BTW, in reality it was a fantastic tuning).
But I did not see the water birds in the reed, and especially the quick-diving grebes hunting small trouts, chevalier, .. and not the pikes hunting small perches, .. All I could see in a sunny moment, was hidden in the dark? No, I saw the grebes when they came to the surface, a silhouette.
What if this was my only view? And I remembered Umberto Eco: "It is important what we know, but much more important is, what we do not know".
How about mathematical software? Is a black-box principle enough? Input/Output? No, a good mathematical software needs black-box and white-box principles well designed. Symbolic and numerical computation integrated. Like Mathematica.