In short, if √2 were rational, we could construct an isosceles right triangle with integer sides. Given one such triangle, it is possible to construct another that is smaller. Repeating the construction, we could construct arbitrarily small integer triangles. But this is impossible since there is a lower limit on how small a triangle can be and still have integer sides.

The second implication of fixing everything two ways is that eventually, all the common and simple problems are solved, and what you’re left with is very weird uncommon problems. That’s fine, because there are far fewer of them, and you’re saving a fortune not doing any rote tech support, but the downside is that there’s no rote tech support left: only serious debugging and problem solving. You can’t just teach new support people ten common solutions: you have to teach them to debug.