I think belts are a measure of where you are, although many instructors do it differently.
So, yes, I fully believe progress can be measured.
For example, I've heard Leo Vieira say that you get you blue, when you start doing Jiu Jitsu, and applying technique (rather than just wrestling and spazzing out, like most beginners who don't have a clue about what they are supposed to be doing).
You get your purple when you're no longer confused (as in, no more "oh, shit, what do I do from here again?"), but you know your way around the mat very well. And you get your brown when you are a stud at your game, and have very accurate answers from anywhere -- you're 'vocabulary' is sound. Finally, you get your black when you have the maturity to wear one.
Another BB once told me, he gives his blacks when a student's body just does 'Jiu Jitsu' naturally without thinking (paraphrase).
However, my point was that this is a relationship between you and your instructor, and no one else. Too many people are caught up in the, 'where you got your belt' argument. Or the 'what does my belt mean in the broader community?' argument. My opinion is that when you start stressing over what your belts means to others, you've lost an important character trait.
It is important to have rankings that aren't laughed at, of course. But, it is beyond sensible to start that whole, 'a brown at your school is like a blue at mine' argument.
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