I am halfway good painter and graphic designer, but nobody is able to read when I write by hand

And I still suck at playing
A bit more serious now:
if you're good at painting or drawing, it just means (like Deathblade Eric said) that you have
a good eye-brain-hand coordniation, but that doesn't mean that you're going to play well.
My brother for example tried to learn bass a few years ago for months and he just didn't get it.
But he is an awesome (and I mean really awesome) artist, draws very realistic paintings and builds sculputres
that are so realistic that a few of them are presented in museums of natural science.
My old guitar player on the other side was one of the most gifted musicians I've ever met,
plays 6 instruments (sax,drums, bass, guitar, keys and cello) but if he starts to draw something
serious, it just looks like a 4 year old put his thumb into paint and tried something out
