Philosophy of Slopes

[conway]

If I can cast my eyes out of virtually any window. And have them land upon a vertical slope.

And if I can ask any mountain climber if a vertical slope exist, and they unanimously say yes.

And if I can ask any engineer if a vertical slope exist, and they unanimously say yes.

Then why can mathematics not define a vertical slope?

Maybe....just maybe....there is a flaw in the current mathematical construct?