Well, since I spent a little time in the military, first, I will also toss my GPS, dig out my magnetic compass or use the North Star or the sun to figure out directions and then, based on terrain features, the knowledge that water runs downhill, decide if I need to cross that crevasse.  

If I do, algebra is not going to guide my steps or determine the fallen tree's strength.  

How is algebra going to help you 'determine if trusting that fallen tree' is the 'right choice'?  I'm willing to learn a new solution to that task.