I say you moved on from being a beginner when:
Your beer turns out like it should on a regular basis
You stop worrying about every little thing and still make good beer
When your brew day becomes easy even though your doing the exact same thing you used to sweat over
Theres always things to learn and changing information...that doesn't mean your a beginner
You beat me to it, for the most part.
Started brewing Dec 2016. I now have 30 batches in, 27 of them all-grain. I can brew repeatable beers. I understand that the brewing process is resiliant to small errors. Brew day is much easier.
I'm helping a buddy get started in brewing. He brewed his first "independent" brew Sunday, though I had to go over and help him through much of it. He's asking question after question--and I know the answers! He's the beginner...I don't think I'm in that category any longer.
I have about 14 books on brewing, avidly read and participate in HBT, built a keezer, built a stir-plate, keg my beer, use oxygen in my wort, use a fermentation chamber, do starters, test my PH and can adjust water. I sold my kettle, chiller, and burner to my beginner buddy, and upgraded to a Spike kettle, a Jaded Hydra chiller, and a Hellfire burner. I can brew beer that i believe you'd like to drink, assuming you'd like the styles I brew.
I would say I'm no longer a beginner. I wouldn't say I'm advanced, there's still a lot to learn and until I master Water I won't consider myself anything other than...
...a brewing Journeyman.
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But as several have said, just because I'm not a beginner doesn't mean I stopped learning. I follow a mantra of continuous quality improvement, striving to do something better every time I brew.
I've gotten to the point where, when I buy a new book, I'm not learning as much. That's a sign. I'm still learning, trying different processes, and I'll continue to do that. I love drinking my beer, but I love playing with the process and learning more and more about it, just as much.
A brewing Journeyman. That's me.