Functional Crossings

Fred is a Mechanics lecturer at Delft Technical University. He is also an avid sea kayaker. Fred invited me as a guest to a "Functionals Workshop" for his students. One of the two examples he used was the mathematical approach of crossing a river with current. The other was a mechanics example of a string connected between two points. Both examples heavily relied on integration and differentiation and culminating into the same 'functionals' theory.

Integration and differentiation went way over my head when I was in school, losing most of my hair in the process. My maths only got partially 'repaired' as part of my IT studies in College. My one year in Econometrics there was a real nightmare though, fortunately not mandatory and it did not stand in the way of my IT-carreer. Integration, differentiation and Pythagoras, forever lost on me I thought, until today.

So in short, I was already glad that I could barely follow the 'magic' involved in transposing one formula into another. Lots of aha moments of remembering that I actually have been tought the basics all those years ago. Stored in dark crevasses of my mind. The river crossing 'metaphor' helped. As for the string I could only think of 'resonating bridges'. Highly complex things made 'calculable' by... maths...

So the shortest time to cross a river with current (not minding where you end up) is in a straight line [correction] on a straight course perpendicular to the river (omega is zero). Easy, but formally mathematically explained, not so, but very much simplified and useful.

Friday a recap and the shortest time for a crossing with variations in current but ending up at a specific point. Forget about the tidal vectors in the sea kayak navigation books. This will be 'hardcore' maths. Simplified 'formulated' math problems will find it's way off the paper and into the real world, be it in vectors or a real crossing.

I am looking forward to my next crossing to the Skerries with Fred in May. There might actually be a fourth way of doing this crossing. I am learning.