Sourdough starter into the mash tun?

One of my goals for the year is to not suck at baking anymore. I've had mixed success. I've been reading up on making sourdough bread and starters. it looks like you throw about half of the starter away. Instead of throwing half of it away, I was wondering if anyone has tried to save it all up and throw it in the mash tun when they make a sour beer. I figured I'll be making a Berliner Weisse here in a month or two. I'd expect this would hasten the souring process over just tossing in a handful of grains, (as I usually do).

Thoughts?

 

Well, I usually mash for an hour and then add enough cool water to bring the tun down to about 110F. I toss in a few cups of uncrushed wheat malt. That would have lacto and yeast on it, so it's a bit of a dice roll on what goes in there. I'll admit there was a drain pour among my Berliners. I deliberately fermented in the mash tun. Bad move. As for getting just a little fermentation from wild yeast and lacto from the grains, they come out great. I prefer to boil for 5 min just to sanitize everything.

Hmm. Now I'm thinking the sourdough starter should go into the sacc rest.