"Well you have at least described a few things that it isn't. I see your point on arrow heads. Are they all made only by chipping? What about bone? Is it possible they were sharpening bone and the lines cross because they switched from the left hand to the right hand? If it is a numbering system...what number is it? How do you prove that those triangles were used as a counting system? How do you know that someone wasn't trying to groove scales on a rock that looked like a fish? It is interesting...I just don't understand how archaelogists say things with such certainty some times."
I can't fully answer your question. I'm not an archaeologist. But tally stones are pretty common items, archaeology speaking. I assume that they've been related to some form of tallying or counting based on other information.
I don't normally just automatically reject something just because I don't have all the information myself. If a journal article refers to an object by its use, then I assume they have reason to do so.
If I waited until I researched everything that interests me somewhat, I'd have to drop a lot of things from my life. So, I generally work with what the specialists in an field have to say. If they're wrong, then I'll find some other explanation at another time.
What I don't do is assume the information is incorrect, based on nothing but my very limited personal knowledge. I do know about some toolmaking items, since I have a small collection of my own. Beyond that, I pay attention to the experts.
I didn't assume anything. All I did was ask a simple question about the process that archaeologists use to verify the statements that they make. Is it a theory? Are there similar stones being used by indigenous people today? There is a difference between asking someone to describe how they came to a conclusion and just outright dismissing something. Since you said yourself that you are no expert in archaeology perhaps we should leave the question for someone that is. The question was intended to help me understand how much of archaeology is based on science and what part is pure hypothesis.